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References

Published online by Cambridge University Press:  18 September 2020

Richard M. Martin
Affiliation:
University of Illinois, Urbana-Champaign
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Electronic Structure
Basic Theory and Practical Methods
, pp. 704 - 755
Publisher: Cambridge University Press
Print publication year: 2020

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References

[1] Martin, R. M., Reining, L., and Ceperley, D. M., Interacting Electrons: Theory and Computational Approaches, Cambridge University Press, Cambridge, UK, 2016.Google Scholar
[2] Lorentz, H. A., Theory of Electrons, reprint of volume of lectures given at Columbia University in 1906, Dover, New York, 1952.Google Scholar
[3] Zeeman, P., “The effect of magnetisation on the nature of light emitted by a substance,” translated by Arthur Stanton from the Proceedings of the Physical Society of Berlin, Nature 55:347, 1897.Google Scholar
[4] Thomson, J. J., “Cathode rays,” Phil. Mag., Series 5 44:310312, 1897.Google Scholar
[5] Thomson, J. J., “Cathode rays,” The Electrician: A Weekly Illustrated Journal of Electrical Engineering, Industry and Science 39, 1897.Google Scholar
[6] Rutherford, E., “The scattering of α and β particles by matter and the structure of the atom,Phil. Mag., Series 6 21:669688, 1911.CrossRefGoogle Scholar
[7] Bohr, N., “On the constitution of atoms and molecules,” Phil. Mag., Series 6 26:125, 1913.Google Scholar
[8] Jammer, M., The Conceptual Development of Quantum Mechanics, McGraw-Hill, New York, 1966.Google Scholar
[9] Sources of Quantum Mechanics, edited by van de Waerden, B. L., North Holland, Amsterdam, 1967.Google Scholar
[10] Messiah, A., Quantum Mechanics, vol. I, Wiley, New York, 1964.Google Scholar
[11] Hoddeson, L. and Baym, G., “The development of the quantum-mechanical electron theory of metals: 1900–1928,” Proc. Roy. Soc. A 371:8, 1987.Google Scholar
[12] Hoddeson, L. and Baym, G., “The development of the quantum-mechanical electron theory of metals: 1928–1933,” Rev. Mod. Phys. 59:287, 1987.CrossRefGoogle Scholar
[13] Hoddeson, L., Braun, E., Teichmann, J., and Weart, S., Out of the Crystal Maze, chapters for the history of solid state physics, Oxford University Press, New York, Oxford, 1992.Google Scholar
[14] Stern, O., “Ein Weg zur experimentellen Prüfung der Richtungsquantelung im Magnetfeld” [Experiment to test the applicability of the quantum theory to the magnetic field], Z. Physik 7:249253, 1921.CrossRefGoogle Scholar
[15] Gerlach, W. and Stern, O., “Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld (Experimental test of the applicability of the quantum theory to the magnetic field),” Z. Physik 9:349352, 1922.CrossRefGoogle Scholar
[16] Compton, A. H., “Possible magnetic polarity of free electrons: Estimate of the field strength of the electron,” Z. Phys. 35:618625, 1926.Google Scholar
[17] Goudschmidt, S. A. and Uhlenbeck, G. H., “Die Kopplungsmöglichkeiten der Quantenvek-toren im Atom,” Z. Phys. 35:618625, 1926.Google Scholar
[18] Pauli, W., “Uber den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplex Struktur der Spektren,” Z. Phys. 31:765, 1925.Google Scholar
[19] Stoner, E. C., “The distribution of electrons among atomic levels,” Phil. Mag. 48:719, 1924.CrossRefGoogle Scholar
[20] Fermi, E., “Zur Quantelung des Idealen Einatomigen Gases,” Z. Phys. 36:902, 1926.CrossRefGoogle Scholar
[21] Bose, S. N., “Plancks Gesetz und Lichtquanten-hypothese,” Z. Phys. 26:178, 1924.CrossRefGoogle Scholar
[22] Einstein, A., “Quantheorie des Idealen Einatomigen Gases,” Sber. preuss Akad. Wiss. p. 261, 1924.Google Scholar
[23] Heisenberg, W., “Mehrkorperproblem und Resonanz in der Quantenmechanik,” Z. Phys. 38:411, 1926.CrossRefGoogle Scholar
[24] Dirac, P. A. M., “On the theory of quantum mechanics,” Proc. R. Soc. A 112:661, 1926.Google Scholar
[25] Slater, J. C., “The theory of complex spectra,” Phys. Rev. 34:1293, 1929.Google Scholar
[26] Dirac, P. A. M., “The quantum theory of the electron,” Proc. R. Soc. A 117:610624, 1928.Google Scholar
[27] Dirac, P. A. M., “The quantum theory of the electron. Part II,” Proc. R. Soc. A 118:351361, 1928.Google Scholar
[28] Lewis, G. N., “The atom and the molecule,” J. Am. Chem. Soc. 38:762786, 1916.Google Scholar
[29] Heitler, W. and London, F., “Wechselwirkung neutraler Atome und homopolare Bindung nach der Quantenmechanik,” Z. Phys. 44:455, 1927.Google Scholar
[30] Pauli, W., “Uber Gasentartung und Paramagnetismus,” Z. Phys. 41:91, 1927.Google Scholar
[31] Sommerfeld, A., “Zur Elektronen Theorie der Metalle auf Grund der Fermischen Statistik,” Z. Phys. 47:43, 1928.Google Scholar
[32] Drude, P., “Bestimmung optischer Konstanten der Metalle,” Wied. Ann. 39:481554, 1897.Google Scholar
[33] Drude, P., Lehrbuch der Optik (Textbook on Optics), S. Hirzel, Leipzig, 1906.Google Scholar
[34] Bethe, H., “Theorie der Beugung von Elektronen in Kristallen,” Ann. Phys. (Leipzig) 87:55, 1928.Google Scholar
[35] Bloch, F., “Uber die Quantenmechanik der Elektronen in Kristallgittern,” Z. Phys. 52:555, 1928.Google Scholar
[36] Peierls, R. E., “Zur Theorie der galvanomagnetischen Effekte,” Z. Phys. 53:255, 1929.Google Scholar
[37] Peierls, R. E., “Zur Theorie der electrischen und thermischen Leitfähigkeit von Metallen,” Ann. Phys. (Leipzig) 4:121, 1930.Google Scholar
[38] Wilson, A. H., “The theory of electronic semiconductors,” Proc. R. Soc. A 133:458, 1931.Google Scholar
[39] Wilson, A. H., “The theory of electronic semiconductors – II,” Proc. R. Soc. A 134:277, 1931.Google Scholar
[40] Seitz, F., The Modern Theory of Solids, McGraw-Hill Book Company, New York, 1940, reprinted in paperback by Dover Press, New York, 1987.Google Scholar
[41] Kimball, G. E., “The electronic structure of diamond,” J. Chem. Phys. 3:560, 1935.Google Scholar
[42] Shockley, W., “On the surface states associated with a periodic potential,” Phys. Rev. 56: 317323, 1939.Google Scholar
[43] Shockley, W., “Energy band structure of sodium cloride,” Phys. Rev. 50:754759, 1937.Google Scholar
[44] Pines, D., The Many Body Problem, Advanced Book Classics, originally published in 1961, Addison-Wesley, Reading, MA, 1997.Google Scholar
[45] Abrikosov, A. A., Gorkov, L. P., and Dzyaloshinski, I. E., Methods of Quantum Field Theory in Statistical Physics, Prentice-Hall, Englewood Cliffs, NJ, 1963.Google Scholar
[46] Luttinger, J. M. and Ward, J. C., “Ground-state energy of a many-fermion system. II,” Phys. Rev. 118:14171427, 1960.Google Scholar
[47] Luttinger, J. M., “Fermi surface and some simple equilibrium properties of a system of interacting fermions,” Phys. Rev. 119:11531163, 1960.Google Scholar
[48] Slater, J. C., Solid-State and Molecular Theory: A Scientific Biography, John Wiley & Sons, New York, 1975.Google Scholar
[49] Hartree, D. R., The Calculation of Atomic Structures, John Wiley & Sons, New York, 1957.Google Scholar
[50] Hartree, D. R., “The wave mechanics of an atom with non-Coulombic central field: Parts I, II, III,” Proc. Cambridge Phil. Soc. 24:89,111,426, 1928.Google Scholar
[51] Hylleraas, E., “Neue Berectnumg der Energie des Heeliums im Grundzustande, sowie tiefsten Terms von Ortho-Helium,” Z. Phys. 54:347, 1929.Google Scholar
[52] Hylleraas, E. A., “Uber den Grundterm der Zweielektronenprobleme von H− , He, Li+ , Be+ usw,” Z. Phys. 65:209, 1930.CrossRefGoogle Scholar
[53] Fock, V., “Naherungsmethode zur Losung des quanten-mechanischen Mehrkorperprobleme,” Z. Phys. 61:126, 1930.CrossRefGoogle Scholar
[54] Wigner, E. P. and Seitz, F., “On the constitution of metallic sodium,” Phys. Rev. 43:804, 1933.Google Scholar
[55] Sommerfeld, A. and Bethe, H., “Elektronentheorie der Metalle,” Handbuch der Physik 24/2:333, 1933.Google Scholar
[56] Slater, J. C., “The electronic structure of metals,” Rev. Mod. Phys. 6:209280, 1934.Google Scholar
[57] Wigner, E. P. and Seitz, F., “On the constitution of metallic sodium II,” Phys. Rev. 46:509, 1934.Google Scholar
[58] Slater, J. C., “Electronic energy bands in metals,” Phys. Rev. 45:794801, 1934.Google Scholar
[59] Herman, F. and Callaway, J., “Electronic structure of the germanium crystal,” Phys. Rev. 89:518519, 1953.Google Scholar
[60] Krutter, H. M., “Energy bands in copper,” Phys. Rev. 48:664, 1935.CrossRefGoogle Scholar
[61] Slater, J. C., “Wave function in a periodic potential,” Phys. Rev. 51:846851, 1937.Google Scholar
[62] Slater, J. C., “An augmented plane wave method for the periodic potential problem,” Phys. Rev. 92:603608, 1953.Google Scholar
[63] Saffren, M. M. and Slater, J. C., “An augmented plane wave method for the periodic potential problem II,” Phys. Rev. 92:1126, 1953.Google Scholar
[64] Herring, W. C., “A new method for calculating wave functions in crystals,” Phys. Rev. 57:1169, 1940.CrossRefGoogle Scholar
[65] Fermi, E., “Displacement by pressure of the high lines of the spectral series,” Nuovo Cimento 11:157, 1934.Google Scholar
[66] Hellmann, H., “A new approximation method in the problem of many electrons,” J. Chem. Phys. 3:61, 1935.CrossRefGoogle Scholar
[67] Hellmann, H., “Metallic binding according to the combined approximation procedure,” J. Chem. Phys. 4:324, 1936.Google Scholar
[68] Herman, F., “Theoretical investigation of the electronic energy band structure of solids,” Rev. Mod. Phys. 30:102, 1958.Google Scholar
[69] Herman, F., “Elephants and mahouts – Early days in semiconductor physics,” Phys. Today June, 1984:56, 1984.Google Scholar
[70] Heisenberg, W., “The theory of ferromagnetism,” Z. Phys. 49:619636, 1928.Google Scholar
[71] Dirac, P. A. M., “Quantum mechanics of many-electron systems,” Proc. R. Soc. A 123: 714733, 1929.Google Scholar
[72] Bohr, N., Studier over Metallernes Elektrontheori (thesis), 1911.Google Scholar
[73] van Leeuwen, H. J., Vraagstukken uit de Electrontheorie van het Magnetisme (thesis), 1911.Google Scholar
[74] van Leeuwen, H. J., “Problemes de la Theorie Electronique du Magnetisme,” J. Phys. Radium 6:361, 1921.Google Scholar
[75] Pauling, L., The Nature of the Chemical Bond, 3rd ed., Cornell University Press, Ithaca, NY, 1960.Google Scholar
[76] Wigner, E. P., “On the interaction of electrons in metals,” Phys. Rev. 46:10021011, 1934.Google Scholar
[77] Mott, N. F. and Peierls, R., “Discussion of the paper by De Boer and Verwey,” Proc. Phys. Soc. A 49:72, 1937.Google Scholar
[78] Mott, N. F., “The basis of the theory of electron metals, with special reference to the transition metals,” Proc. Phys. Soc. A 62:416, 1949.Google Scholar
[79] Mott, N. F., Metal–Insulator Transitions, Taylor & Francis, London/Philadelphia, 1990.Google Scholar
[80] de Boer, J. H. and Verwey, E. J. W, “Semi-conductors with partially and with completely filled 3d-lattice bands,” Proc. Phys. Soc. 49:59–71, 1937.Google Scholar
[81] Anderson, P. W., “More is different: Broken symmetry and the nature of the heirachical styructure of science,” Science 177:393396, 1972.Google Scholar
[82] More Is Different: Fifty Years of Condensed Matter Physics, edited by Ong, N.-P. and Bhatt, R., Princeton University Press, Princeton, NJ, 2001.Google Scholar
[83] Hohenberg, P. and Kohn, W., “Inhomogeneous electron gas,” Phys. Rev. 136:B864–871, 1964.Google Scholar
[84] Kohn, W. and Sham, L. J., “Self-consistent equations including exchange and correlation effects,” Phys. Rev. 140:A1133–A1138, 1965.Google Scholar
[85] Car, R. and Parrinello, M., “Unified approach for molecular dynamics and density functional theory,” Phys. Rev. Lett. 55:24712474, 1985.Google Scholar
[86] Kane, C. L. and Mele, E. J., “Z2 topological order and the quantum spin Hall effect,” Physical Review Letters 95:146802, 2005.Google Scholar
[87] Kane, C. L. and Mele, E. J., “Quantum spin Hall effect in graphene,” Physical Review Letters 95:226801, 2005.Google Scholar
[88] Andrei Bernevig, B. and Zhang, S.-C., “Quantum spin Hall effect,” Phys. Rev. Lett. 96:106802, 2006.Google Scholar
[89] Thouless, D. J., Kohmoto, M., Nightingale, M. P., and den Nijs, M., “Quantized Hall conductance in a two-dimensional periodic potential,” Phys. Rev. Lett. 49:405408, 1982.Google Scholar
[90] Born, M. and Oppenheimer, J. R., “Zur Quantentheorie der Molekeln,” Ann. Physik 84:457, 1927.Google Scholar
[91] Born, M. and Huang, K., Dynamical Theory of Crystal Lattices, Oxford University Press, Oxford, 1954.Google Scholar
[92] Rowlinson, J. S., “Legacy of van der Waals,” Nature 244:414417, 1973.Google Scholar
[93] van der Waals, J. D., Nobel Lectures in Physics, Elsevier, Amsterdam, 1964, pp. 254265.Google Scholar
[94] Wang, S. C., “The problem of the normal hydrogen molecule in the new quantum mechanics,” Phys. Rev. 31:579586, 1928.Google Scholar
[95] Slater, J. C. and Kirkwood, J. G., “The van der Waals forces in gases,” Phys. Rev. 37:682697, 1931.Google Scholar
[96] Eisenschitz, R. and London, F., “Uber das Verhaltnis der van der Waalsschen Krafte zu den homopolaren Bindungskraften,” Z. Phys. 60:491527, 1930.Google Scholar
[97] London, F., “Zur Theorie und Systematik der Molekularkrafte,” Z. Phys. A 63:245279, 1930.Google Scholar
[98] Chaikin, P. M. and Lubensky, T. C., Principles of Condensed Matter Physics, Cambridge University Press, Cambridge, UK, 1995.Google Scholar
[99] Zuo, J. M., Blaha, P., and Schwarz, K., “The theoretical charge density of silicon: Experimental testing of exchange and correlation potentials,” J. Phys. Condens. Matter. 9:75417561, 1997.CrossRefGoogle Scholar
[100] Lu, Z. W., Zunger, A., and Deutsch, M., “Electronic charge distribution in crystalline diamond, silicon, and germanium,” Phys. Rev. B 47:93859410, 1993.Google Scholar
[101] Yin, M. T. and Cohen, M. L., “Theory of static structural properties, crystal stability, and phase transformations: Application to Si and Ge,” Phys. Rev. B 26:56685687, 1982.Google Scholar
[102] Nielsen, O. H. and Martin, R. M., “Stresses in semiconductors: Ab initio calculations on Si, Ge, and GaAs,” Phys. Rev. B 32(6):37923805, 1985.Google Scholar
[103] Moruzzi, V. L., Williams, A. R., and Janak, J. F., “Local density theory of metallic cohesion,” Phys. Rev. B 15:28542857, 1977.Google Scholar
[104] Moruzzi, V. L., Janak, J. F., and Williams, A. R., Calculated Electronic Properties of Metals, Pergamon Press, New York, 1978.Google Scholar
[105] Murnaghan, F. D., “The compressibility of media under extreme pressures,” Proc. Nat. Acad. Sci. USA 50:244247, 1944.Google Scholar
[106] Howland, L. P., “Band structure and cohesive energy of potassium chloride,” Phys. Rev. 109:1927, 1958.CrossRefGoogle Scholar
[107] DeCicco, P. D., “Self-consistent energy bands and cohesive energy of potassium chloride,” Phys. Rev. 153:931, 1967.Google Scholar
[108] Rudge, W. E., “Variation of lattice constant in augmented-plane-wave energy-band calculation for lithium,” Phys. Rev. 181:1033, 1969.Google Scholar
[109] Ross, M. and Johnson, K. W., “Augmented-plane-wave calculation of the total energy, bulk modulus, and band structure of compressed aluminum,” Phys. Rev. B 2:4709, 1970.CrossRefGoogle Scholar
[110] Snow, E. C., “Total energy as a function of lattice parameter for copper via the self-consistent augmented-plane-wave method,” Phys. Rev. B 8:5391, 1973.Google Scholar
[111] Janak, J. F., Moruzzi, V. L., and Williams, A. R., “Ground-state thermomechanical proerties of some cubic elements in the local-density formalism,” Phys. Rev. B 12:12571261, 1975.Google Scholar
[112] Zhang, G.-X., Reilly, A. M., Tkatchenko, A., and Scheffler, M., “Performance of various density-functional approximations for cohesive properties of 64 bulk solids,” New J. Phys. 20:063020, 2018.Google Scholar
[113] Blum, V., Gehrke, R., Hanke, F., Havu, P., Havu, V., Ren, X., Reuter, K., and Scheffler, M., “Ab initio molecular simulations with numeric atom-centered orbitals,” Comput. Phys. Commun. 180:21752196, 2009.Google Scholar
[114] Isaacs, E. B. and Wolverton, C., “Performance of the strongly constrained and appropriately normed density functional for solid-state materials,” Phys. Rev. Materials 2:063801, 2018.Google Scholar
[115] Marsman, M, Paier, J, Stroppa, A, and Kresse, G, “Hybrid functionals applied to extended systems,” J. Phys. Condens. Matter 20:064201, 2008.Google Scholar
[116] Fu, Y. and Singh, D. J., “Applicability of the strongly constrained and appropriately normed density functional to transition-metal magnetism,” Phys. Rev. Lett. 121:207201, 2018.Google Scholar
[117] Mao, H.-K., Chen, X.-J., Ding, Y., Li, B., and Wang, L., “Solids, liquids, and gases under high pressure,” Rev. Mod. Phys. 90:015007, 2018.Google Scholar
[118] Biswas, R., Martin, R. M., Needs, R. J., and Nielsen, O. H., “Complex tetrahedral structures of silicon and carbon under pressure,” Phys. Rev. B 30(6):32103213, 1984.Google Scholar
[119] Yin, M. T., “Si-III (BC-8) crystal phase of Si and C: Structural properties, phase stabilities, and phase transitions,” Phys. Rev. B 30:17731776, 1984.Google Scholar
[120] Ackland, G. J., “High-pressure phases of group IV and III–V semiconductores,” Rep. Prog. Phys. 64:483516, 2001.Google Scholar
[121] Mujica, A., Rubio, A., Munoz, A., and Needs, R. J., “High-pressure phases of group IVa, IIIa–Va and IIb–VIa compounds,” Rev. Mod. Phys. 75:863912, 2003.Google Scholar
[122] Kasper, J. S. and Jr. Wentorf, R. H., “The crystal structures of new forms of silicon and germanium,” Acta Cryst. 17:752, 1964.Google Scholar
[123] Needs, R. J. and Mujica, A., “Theoretical description of high-pressure phases of semiconductors,” High Press. Res. 22:421, 2002.Google Scholar
[124] Olijnyk, H., Sikka, S. K., and Holzapfel, W. B., “Structural phase transitions in Si and Ge under pressures up to 50 GPa,” Phys. Lett. 103A:137, 1984.Google Scholar
[125] Hu, J. Z. and Spain, I. L., “Phases of silicon at high pressure,” Solid State Commun. 51:263, 1984.Google Scholar
[126] McMahan, A. K., “Interstitial-sphere linear muffin-tin orbital structural calculations for C and Si,” Phys. Rev. B 30:58355841, 1984.Google Scholar
[127] Xiao, B., Sun, J., Ruzsinszky, A., Feng, J., Haunschild, R., Scuseria, G. E., and Perdew, J. P., “Testing density functionals for structural phase transitions of solids under pressure: Si, SiO2, and Zr,” Phys. Rev. B 88:184103, 2013.Google Scholar
[128] Shahi, C., Sun, J., and Perdew, J. P., “Accurate critical pressures for structural phase transitions of group IV, III–V, and II–VI compounds from the SCAN density functional,” Phys. Rev. B 97:094111, 2018.Google Scholar
[129] Sengupta, N., Bates, J. E., and Ruzsinszky, A., “From semilocal density functionals to random phase approximation renormalized perturbation theory: A methodological assessment of structural phase transitions,” Phys. Rev. B 97:235136, 2018.Google Scholar
[130] Pickard, C. J. and Needs, R. J., “Ab initio random structure searching,” J. Phys. Condens. Matter 23:053201, 2011.Google Scholar
[131] Needs, R. J. and Pickard, C. J., “Perspective: Role of structure prediction in materials discovery and design,” APL Materials 4:053210, 2016.Google Scholar
[132] Wolpert, D. H. and Macready, W. G., “No free lunch theorems for optimization,” IEEE Trans. Evol. Comput. 1:6782, 1997.Google Scholar
[133] Kirkpatrick, S., Gelatt, C. D., and Vecchi, M. P., “Optimization by simulated annealing,” Science 220:671680, 1983.Google Scholar
[134] Yang, X.-S., in Nature-Inspired Optimization Algorithms, edited by Yang, X.-S., Elsevier, Oxford, 2014, pp. 99–110.Google Scholar
[135] Kennedy, J. and Eberhart, R. C., in Proceedings of the IEEE International Conference on Neural Networks, Piscataway, NJ, 1995, edited by X.-S. Yang, Available at IEEE Xplore Digital Library, ieeexplore.ieee.org.Google Scholar
[136] Back, T., Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithm, Oxford University Press, Oxford, U.K., 1990.Google Scholar
[137] Lyakhov, A. O., Oganov, A. R., Stokes, H. T., and Zhu, Q., “New developments in evolutionary structure prediction algorithm USPEX,” Comput. Phys. Commun. 184:11721182, 2013.Google Scholar
[138] Oganov, A. R. and Glass, C. W., “Crystal structure prediction using ab initio evolutionary techniques: Principles and applications,” J. Chem. Phys. 124:244704, 2006.Google Scholar
[139] Mailhiot, C. L. H. Yang, , and McMahan, A. K., “Polymeric nitrogen,” Phys. Rev. B 46:14419– 14435, 1992.Google Scholar
[140] Eremets, M. I., Gavriliuk, A. G., Trojan, I. A., Dzivenko, D. A., and Boehler, R., “Single-bonded cubic form of nitrogen,” Nat. Mater. 3:558563, 2004.Google Scholar
[141] Eremets, M. I., Gavriliuk, A. G., Serebryanaya, N. R., Trojan, I. A., Dzivenko, D. A., Boehler, R., Mao, H. K., and Hemley, R. J., “Structural transformation of molecular nitrogen to a single-bonded atomic state at high pressures,” J. Chem. Phys. 121:1129611300, 2004.Google Scholar
[142] Benchafia, E. M., Yao, Z., Yuan, G., Tsengmin Chou, H. Piao, X. Wang, , and Iqbal, Z., “Cubic gauche polymeric nitrogen under ambient conditions,” Nat. Commun. 8:930, 2017.Google Scholar
[143] Pickard, C. J. and Needs, R. J., “High-pressure phases of nitrogen,” Phys. Rev. Lett. 102:125702, 2009.Google Scholar
[144] McMahon, J. M., Morales, M. A., Pierleoni, C., and Ceperley, D. M., “The properties of hydrogen and helium under extreme conditions,” Rev. Mod. Phys. 84:16071653, 2012.Google Scholar
[145] Ashcroft, N. W., “Hydrogen dominant metallic alloys: High temperature superconductors?,” Phys. Rev. Lett. 92:187002, 2004.Google Scholar
[146] Duan, D., Liu, Y., Tian, F., Li, D., Huang, X., Zhao, Z., Yu, H., Liu, B., Tian, W., and Cui, T., “Pressure-induced metallization of dense (H2 S)2 H2 with high-Tc superconductivity,” Sci. Rep. 4:6968, 2014.Google Scholar
[147] Li, Y., Hao, J., Liu, H., Li, Y., and Ma, Y., “The metallization and superconductivity of dense hydrogen sulfide,” J. Chem. Phys. 140:174712, 2014.Google Scholar
[148] Drozdov, A. P., Eremets, M. I., Troyan, I. A., Ksenofontov, V., and Shylin, S. I., “Conventional superconductivity at 203 Kelvin at high pressures in the sulfur hydride system,” Nature 525:73, 2015.Google Scholar
[149] Einaga, M., Sakata, M., Ishikawa, T., Shimizu, K., Eremets, M. I., Drozdov, A. P., Troyan, I. A., Hirao, N., and Ohishi, Y., “Crystal structure of the superconducting phase of sulfur hydride,” Nat. Phys. 12:835, 2016.Google Scholar
[150] Bernstein, N., Stephen Hellberg, C., Johannes, M. D., Mazin, I. I., and Mehl, M. J., “What superconducts in sulfur hydrides under pressure and why,” Phys. Rev. B 91:060511, 2015.CrossRefGoogle Scholar
[151] Papaconstantopoulos, D. A., Klein, B. M., Mehl, M. J., and Pickett, W. E., “Cubic H3 S around 200 GPa: An atomic hydrogen superconductor stabilized by sulfur,” Phys. Rev. B 91:184511, 2015.Google Scholar
[152] Duan, D., Huang, X., Tian, F., Li, D., Yu, H., Liu, Y., Ma, Y., Liu, B., and Cui, T., “Pressure-induced decomposition of solid hydrogen sulfide,” Phys. Rev. B 91:180502, 2015.CrossRefGoogle Scholar
[153] Benoit, M., Romero, A. H., and Marx, D., “Reassigning hydrogen-bond centering in dense ice,” Phys. Rev. Lett. 89:145501, 2002.Google Scholar
[154] Liu, H., Naumov, I. I., Hoffmann, R., Ashcroft, N. W., and Hemley, R. J., “Potential high-Tc superconducting lanthanum and yttrium hydrides at high pressure,” Proc. Natl. Acad. Sci. U.S.A. 114:69906995, 2017.Google Scholar
[155] Peng, F., Sun, Y., Pickard, C. J., Needs, R. J., Wu, Q., and Ma, Y., “Hydrogen clathrate structures in rare earth hydrides at high pressures: Possible route to room-temperature superconductivity,” Phys. Rev. Lett. 119:107001, 2017.Google Scholar
[156] Somayazulu, M., Ahart, M., Mishra, A. K., Geballe, Z. M., Baldini, M., Meng, Y., Struzhkin, V. V., and Hemley, R. J., “Evidence for superconductivity above 260 K in lanthanum superhydride at megabar pressures,” Phys. Rev. Lett. 122:027001, 2019.Google Scholar
[157] Kübler, J. and Eyert, V., in Electronic and Magnetic Properties of Metals and Ceramics, edited by Buschow, K. H. J., VCH-Verlag, Weinheim, Germany, 1992, p. 1.Google Scholar
[158] Stoner, E. C., “Collective electron ferromagnetism. II. Energy and specific heat,” Proc. Roy. Soc. A 169:339371, 1939.Google Scholar
[159] Herring, C., in Magnetism IV: Exchange Interactions among Itinerant Electrons, edited by Rado, G. and Suhl, H., Academic Press, New York, 1966.Google Scholar
[160] Niu, Q. and Kleinman, L., “Spin-wave dynamics in real crystals,” Phys. Rev. Lett. 80:2205– 2208, 1998.Google Scholar
[161] Gebauer, R. and Baroni, S., “Magnons in real materials from density-functional theory,” Phys. Rev. B 61:R6459–R6462, 2000.Google Scholar
[162] Nielsen, O. H. and Martin, R. M., “Quantum-mechanical theory of stress and force,” Phys. Rev. B 32(6):37803791, 1985.Google Scholar
[163] Nielsen, O. H. and Martin, R. M., “First-principles calculation of stress,” Phys. Rev. Lett. 50(9):697700, 1983.Google Scholar
[164] Nielsen, O. H., “Optical phonons and elasticity of diamond at megabar stresses,” Phys. Rev. B 34:58085819, 1986.Google Scholar
[165] Lattice Dynamics, edited by Wallis, R. F., Pergamon Press, London, 1965.Google Scholar
[166] Dynamical Properties of Solids, vol. 3, edited by Horton, G. K. and Maradudin, A. A., North-Holland, Amsterdam, 1979.Google Scholar
[167] Kunc, K. and Martin, R. M., “Density-functional calculation of static and dynamic properties of GaAs,” Phys. Rev. B 24(4):23112314, 1981.Google Scholar
[168] Ordejon, P., Artacho, E., Cachau, R., Gale, J., Garcia, A., Junquera, J., Kohanoff, J., Machado, M., Sanchez-Portal, D., Soler, J. M., and Weht, R., “Linear scaling DFT calculations with numerical atomic orbitals,” Mat. Res. Soc. Symp. Proc. 677, 2001.Google Scholar
[169] Cohen, R. E. and Krakauer, H., “Electronic-structure studies of the differences in ferroelectric behavior of BaTix O3 and PbTix O3,” Ferroelectrics 136:65, 1992.Google Scholar
[170] Ho, K.-M., Fu, C.-L., and Harmon, B. N., “Vibrational frequencies via total-energy calculations: Applications to transition metals,” Phys. Rev. B 29:15751587, 1984.Google Scholar
[171] Chadi, D. J. and Martin, R. M., “Calculation of lattice dynamical properties from electronic energies: Application to C, Si and Ge,” Solid State Commun. 19(7):643646, 1976.Google Scholar
[172] Wendel, H. and Martin, R. M., “Theory of structural properties of covalent semiconductors,” Phys. Rev. B 19(10):52515264, 1979.Google Scholar
[173] Waghmare, U. V. and Rabe, K. M., “Ab initio statistical mechanics of the ferroelectric phase transition in PbTiO3,” Phys. Rev. B 55:61616173, 1997.Google Scholar
[174] García-Fernández, P., Wojdeł, J. C., Íñiguez, J., and Junquera, J., “Second-principles method for materials simulations including electron and lattice degrees of freedom,” Phys. Rev. B 93:195137, 2016.Google Scholar
[175] King-Smith, R. D. and Vanderbilt, D. H., “Theory of polarization of crystalline solids,” Phys. Rev. B 47:16511654, 1993.Google Scholar
[176] Resta, R., “Macroscopic polarization in crystalline dielectrics: the geometric phase approach,” Rev. Mod. Phys. 66:899915, 1994.Google Scholar
[177] Berry, M. V., “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. A 392:4547, 1984.Google Scholar
[178] De Cicco, P. D. and Johnson, F. A., “The quantum theory of lattice dynamics. IV,” Proc. R. Soc. A 310:111119, 1969.Google Scholar
[179] Sham, L. J., “Electronic contribution to lattice dynamics in insulating crystals,” Phys. Rev. 188:14311439, 1969.Google Scholar
[180] Pick, R., Cohen, M. H., and Martin, R. M., “Microscopic theory of force constants in the adiabatic approximation,” Phys. Rev. B 1:910920, 1970.Google Scholar
[181] Baroni, S., de Gironcoli, S., and Dal Corso, A., “Phonons and related properties of extended systems from density-functional perturbation theory,” Rev. Mod. Phys. 73:515562, 2001.Google Scholar
[182] Giannozzi, P., de Gironcoli, S., Pavoni, P., and Baroni, S., “Ab initio calculation of phonon dispersion in semiconductors,” Phys. Rev. B 43:7231, 1991.Google Scholar
[183] Tsuchiya, T., Tsuchiya, J., Umemoto, K., and Wentzcovitch, R. M., “Phase transition in MgSiO3 perovskite in the earth’s lower mantle,” Earth Planet. Sc. Lett. 224:241248, 2004.Google Scholar
[184] Gillan, M. J., Alfe, D., Brodholt, J., Vocadlo, L., and Price, G. D., “First-principles modelling of earth and planetary materials at high pressures and temperatures,” Rep. Prog. Phys. 69:2365– 2441, 2006.Google Scholar
[185] Wentzcovitch, R. and Stixrude, L., “Theoretical and computational methods in mineral physics: Geophysical applications,” Rev. Mineral Geochem. 71:iii–vi, 2010.Google Scholar
[186] Alfè, D., Kresse, G., and Gillan, M. J., “Structure and dynamics of liquid iron under Earth’s core conditions,” Phys. Rev. B 61:132142, 2000.Google Scholar
[187] Mao, H. K., Wu, Y., Chen, L. C., Shu, J. F., and Jephcoat, A. P., “Static compression of iron to 300 GPa and Fe0.8 Ni0.2 alloy to 260 GPa: Implications for composition of the core,” J. Geophys. Res. B 95:2173721742, 1990.Google Scholar
[188] Alfe, D., “Iron at Earth core conditions from first principles calculations,” Rev. Mineral Geochem. 71:337354, 2010.Google Scholar
[189] Schwegler, E., Galli, G., Gygi, F., and Hood, R. Q., “Dissociation of water under pressure,” Phys. Rev. Lett. 87:265501, 2001.Google Scholar
[190] Pauling, L., “The structure and entropy of ice and of other crystals with some randomness of atomic arrangement,” J. Am. Chem. Soc. 157:2680, 1935.Google Scholar
[191] Jeffery, A., An Introduction to Hydrogen Bonding, Oxford University Press, Oxford, UK, 1997.Google Scholar
[192] Luzar, A. and Chandler, D., “Hydrogen-bond kinetics in liquid water,” Nature 379:5557, 1996.Google Scholar
[193] Pham, T. A., Ogitsu, T., Lau, E Y., and Schwegler, E., “Structure and dynamics of aqueous solutions from PBE-based first-principles molecular dynamics simulations,” J. Chem. Phys. 145:154501, 2016.Google Scholar
[194] Gaiduk, A. P., Gustafson, J., Gygi, F., and Galli, G., “First-principles simulations of liquid water using a dielectric-dependent hybrid functional,” J. Phys. Chem. Lett. 9:30683073, 2018.Google Scholar
[195] Chen, M., Ko, H.-Y., Remsing, R. C., Calegari, Marcos F. Santra, A., B., Sun, Z., Selloni, A., Car, R., Klein, M. L., Perdew, J. P., and Wu, X., “Ab initio theory and modeling of water,” Proc. Natl. Acad. Sci. U.S.A. 114:10846–10851, 2017.Google Scholar
[196] Skinner, L. B., Huang, C., Schlesinger, D., Pettersson, L. G. M., Nilsson, A., and Benmore, C. J., “Benchmark oxygen-oxygen pair-distribution function of ambient water from X-ray diffraction measurements with a wide q-range,” J. Chem. Phys. 138:074506, 2013.Google Scholar
[197] Gillan, M. J., Alfe, D., and Michaelides, A., “Perspective: How good is DFT for water?,” J. Chem. Phys. 144:130901, 2016.Google Scholar
[198] DiStasio, R. A., Santra, B., Li, Z., Wu, X., and Car, R., “The individual and collective effects of exact exchange and dispersion interactions on the ab initio structure of liquid water,” J. Chem. Phys. 141:084502, 2014.Google Scholar
[199] Goncharov, A. F., Struzhkin, V. V., Mao, H.-K., and Hemley, R. J., “Raman spectroscopy of dense H2 O and the transition to symmetric hydrogen bonds,” Phys. Rev. Lett. 83:19982001, 1999.Google Scholar
[200] Lee, C., Vanderbilt, D., Kari Laasonen, R. Car, , and Parrinello, M., “Ab initio studies on high pressure phases of ice,” Phys. Rev. Lett. 69:462–465, 1992.Google Scholar
[201] Boero, M., Parrinello, M., and Terakura, K., “First principles molecular dynamics study of Ziegler–Natta heterogeneous catalysis,” J. Am. Chem. Soc. 120:7462752, 1998.Google Scholar
[202] Boero, M., Parrinello, M., Huffer, S., and Weiss, H., “First principles study of propene polymerization in Ziegler–Natta heterogeneous catalysis,” J. Am. Chem. Soc. 122:501509, 2000.Google Scholar
[203] Penev, E., Kratzer, P., and Scheffler, M., “Effect of the cluster size in modeling the H2 desorption and dissociative adsorption on Si(001),” J. Chem. Phys. 110:39863994, 1999.Google Scholar
[204] Harrison, W. A., “Theory of polar semiconductor surfaces,” J. Vac. Sci. Technol. 16:1492– 1496, 1979.Google Scholar
[205] Martin, R. M., “Atomic reconstruction at polar interfaces of semiconductors,” J. Vac. Sci. Technol. 17(5):978981, 1980.Google Scholar
[206] Wilson, A. A., Thermodynamics and Statistical Mechanics, Cambridge University Press, Cambridge, U.K., 1957.Google Scholar
[207] Wilson, A. A., Fundamentals of Statistical and Thermal Physics, McGraw-Hill, New York, 1965.Google Scholar
[208] Qian, G. X., Martin, R. M., and Chadi, D. J., “First-principles calculations of atomic and electronic structure of the GaAs (110) surface,” Phys. Rev. B 37:1303, 1988.Google Scholar
[209] Garcia, A. and Northrup, J. E., “First-principles study of Zn- and Se-stabilized ZnSe(100) surface reconstructions,” J. Vac. Sci. Technol. B 12:26782683, 1994.Google Scholar
[210] Northrup, J. E. and Froyen, S., “Structure of GaAs(001) surfaces: The role of electrostatic interactions,” Phys. Rev. B 50:2015, 1994.Google Scholar
[211] Franciosi, A. and Van de Walle, C. G., “Heterojunction band offset engineering,” Surf. Sci. Rep. 25:1, 1996.Google Scholar
[212] Van de Walle, C. G. and Martin, R. M., “Theoretical study of band offsets at semiconductor interfaces,” Phys. Rev. B 35:81548165, 1987.Google Scholar
[213] Van de Walle, C. G. and Martin, R. M., “‘Absolute’ deformation potentials: Formulation and ab initio calculations for semiconductors,” Phys. Rev. Lett. 62:20282031, 1989.Google Scholar
[214] Ohtomo, A. and Hwang, H. Y., “A high-mobility electron gas at the LaAlO3/SrTiO3 heteroin-terface,” Nature 427:423, 2004.Google Scholar
[215] Vaziri, S., et al., “Ultrahigh thermal isolation across heterogeneously layered two-dimensional materials,” Sci. Adv. 5, 2019.Google Scholar
[216] Li, T. and Galli, G., “Electronic properties of MoS2 nanoparticles,” J. Phys. Chem. C 111:1619216196, 2007.Google Scholar
[217] Mak, K. F., Lee, C., Hone, J., Shan, J., and Heinz, T. F., “Atomically thin MoS2 : A new direct-gap semiconductor,” Phys. Rev. Lett. 105:136805, 2010.Google Scholar
[218] Ellis, Jason K., Lucero, Melissa J., and Scuseria, G. E., “The indirect to direct band gap transition in multilayered MoS2 as predicted by screened hybrid density functional theory,” Appl. Phys. Lett. 99:261908, 2011.Google Scholar
[219] Geim, A. K. and Grigorieva, I. V., “Perspective: Van der Waals heterostructures,” Nature 499:419, 2013.Google Scholar
[220] Novoselov, f K. S., Mishchenko, A., Carvalho, A., and Castro Neto, A. H., “2D materials and van der Waals heterostructures,” Science 353, 2016.Google Scholar
[221] Knight, W. D., Clemenger, K., de Heer, W. A., Saunders, W. A., Chou, M. Y., and Cohen, M. L., “Electronic shell structure and abundances of sodium clusters,” Phys. Rev. Lett. 52:2141, 1984.Google Scholar
[222] Brack, M., “The physics of simple metal clusters: Self-consistent jellium model and semiclas-sical approaches,” Rev. Mod. Phys. 65:677732, 1993.Google Scholar
[223] Rothlisberger, U., Andreoni, W., and Giannozzi, P., “Thirteen-atom clusters: Equilibrium geometries, structural transformations, and trends in Na, Mg, Al, and Si,” J. Chem. Phys. 92:1248, 1992.Google Scholar
[224] Phillips, J. C., “Electron-correlation energies and the structure of Si13 ,” Phys. Rev. B 47:14132, 1993.Google Scholar
[225] Grossman, J. C. and Mitas, L., “Quantum Monte Carlo determination of elecronic and structural properties of Sin clusters (n ≤ 20),” Phys. Rev. Lett. 74:13231325, 1995.Google Scholar
[226] Grossman, J. C. and Mitas, L., “Family of low-energy elongated Sin (n ≤ 50) clusters,” Phys. Rev. B 52:1673516738, 1995.Google Scholar
[227] Kroto, H. W., Heath, J. R., O’Brien, S. C., Curl, R. F., and Smalley, R. E., “C60 : Buckminster-fullerene,” Nature 318:162, 1985.Google Scholar
[228] Iijima, S., “Helical microtubules of graphitic carbon,” Nature 354:56, 1991.Google Scholar
[229] Novoselov, K. S., Geim, A. K., Morozov, S. V., Jiang, D., Zhang, Y., Dubonos, S. V., Grigorieva, I. V., and Firsov, A. A., “Electric field effect in atomically thin carbon films,” Science 306:666669, 2004.Google Scholar
[230] Kratschmer, W., Lamb, L.D., Fostiropoulos, K., and Huffman, D.R., “Solid C60 : A new form of carbon,” Nature 347:354, 1990.Google Scholar
[231] Haddon, R. C., et al., “Conducting films of C60 and C70 by alkali-metal doping,” Nature 350:320, 1991.Google Scholar
[232] Hamada, N., Sawada, S., and Oshiyama, A., “New one-dimensional conductors: Graphitic microtubules,” Phys. Rev. Lett 68:15791581, 1992.Google Scholar
[233] Saito, R., Fujita, M., Dresselhaus, G., and Dresselhaus, M. S., “Electronic structure of graphene tubules based on C60,” Phys. Rev. B 46:18041811, 1992.Google Scholar
[234] Saito, R., Dresselhaus, G., and Dresselhaus, M. S., Physical Properties of Carbon Nanotubes, Imperial College Press, London, 1998.Google Scholar
[235] Rizzo, D. J., Veber, G., Cao, T., Bronner, C., Chen, T., Zhao, F., Rodriguez, H., Louie, S. G., Crommie, M. F., and Felix Fischer, R., “Topological band engineering of graphene nanoribbons,” Nature 560:204–208, 2018.Google Scholar
[236] Cao, T., Zhao, F., and Louie, S. G., “Topological phases in graphene nanoribbons: Junction states, spin centers, and quantum spin chains,” Phys. Rev. Lett. 119:076401, 2017.Google Scholar
[237] Damascelli, A., Shen, Z.-X., and Hussain, Z., “Angle-resolved photoemission studies of the cuprate superconductors,” Rev. Mod. Phys. 75:473, 2003.Google Scholar
[238] Ibach, H. and Luth, H., Solid State Physics: An Introduction to Theory and Experiment, Springer-Verlag, Berlin, 1991.Google Scholar
[239] Huffner, S., Photoelectron Spectroscopy, 2nd ed., Springer-Verlag, Berlin, 1995.Google Scholar
[240] Imada, M., Fujimori, A., and Tokura, Y., “Metal-insulator transitions,” Rev. Mod. Phys. 70:10391263, 1998.Google Scholar
[241] Hedin, L. and Lundquist, S., in Solid State Physics, vol. 23, edited by Ehenreich, H., Seitz, F., and Turnbull, D., Academic Press, New York, 1969, p. 1.Google Scholar
[242] Garza, A. J. and Scuseria, G. E., “Predicting band gaps with hybrid density functionals,” J. Phys. Chem. Lett. 7:41654170, 2016.Google Scholar
[243] Yang, Z.-H., Peng, H., Sun, J., and Perdew, J. P., “More realistic band gaps from meta-generalized gradient approximations: Only in a generalized Kohn–Sham scheme,” Phys. Rev. B 93:205205, 2016.Google Scholar
[244] Skone, J. H., Govoni, M., and Galli, G., “Self-consistent hybrid functional for condensed systems,” Phys. Rev. B 89:195112, 2014.Google Scholar
[245] Zangwill, A. and Soven, P., “Density-functional approach to local-field effects in finite systems: Photoabsorption in the rare gases,” Phys. Rev. A 21:1561, 1980.Google Scholar
[246] Runge, E. and Gross, E. K. U., “Density-functional theory for time-dependent systems,” Phys. Rev. Lett. 52:9971000, 1984.Google Scholar
[247] Burke, K., Werschnik, J., and Gross, E. K. U., “Time-dependent density functional theory: Past, present, and future,” J. Chem. Phys. 123:062206, 2005.Google Scholar
[248] Time-Dependent Density Functional Theory, Lecture Notes in Physics, vol. 706, edited by Marques, M. A. L., Ullrich, C. A., Nogueira, F., Rubio, A., Burke, K., and Gross, E. K. U., Springer, Berlin, 2006.Google Scholar
[249] Ullrich, C., Time-Dependent Density-Functional Theory: Concepts and Applications, Oxford University Press, Oxford, UK, 2012.Google Scholar
[250] Density-Functional Methods for Excited States (Topics in Current Chemistry), edited by Ferre, N., Filatov, M., and Huix, M.-Rotllant, Springer International, Switzerland, 2016.Google Scholar
[251] Staedele, M., Moukara, M., Majewski, J. A., Vogl, P., and Gorling, A., “Exact exchange Kohn– Sham formalism applied to semiconductors,” Phys. Rev. B 59:1003110043, 1999.Google Scholar
[252] Paier, J., Marsman, M., and Kresse, G., “Dielectric properties and excitons for extended systems from hybrid functionals,” Phys. Rev. B 78:121201, 2008.Google Scholar
[253] Refaely-Abramson, S., Jain, M., Sharifzadeh, S., Neaton, J. B., and Kronik, L., “Solid-state optical absorption from optimally tuned time-dependent range-separated hybrid density functional theory,” Phys. Rev. B 92:081204, 2015.Google Scholar
[254] Bardeen, J., “Theory of the work function. II. The surface double layer,” Phys. Rev. 49:653, 1936.Google Scholar
[255] Chen, Y. L., Chu, J.-H., Analytis, J. G., Liu, Z. K., Igarashi, K., Kuo, H.-H., Qi, X. L., Mo, S. K., Moore, R. G., Lu, D. H., Hashimoto, M., Sasagawa, T., Zhang, S. C., Fisher, I. R., Hussain, Z., and Shen, Z. X., “Massive Dirac fermion on the surface of a magnetically doped topological insulator,” Science 329:659662, 2010.CrossRefGoogle ScholarPubMed
[256] Thouless, D. J., “Quantization of particle transport,” Phys. Rev. B 27:60836087, 1983.Google Scholar
[257] Zhang, H., Liu, C.-X., Qi, X.-L., Dai, X., Fang, Z., and Zhang, S.-C., “Topological insulators in Bi2 Se3, Bi2 Te3, Sb2 Te3 with a single Dirac cone on the surface,” Nat. Phys. 5:438442, 2009.Google Scholar
[258] Ritz, W., “Uber eine neue Methode zur Losung Gewisser Variationsprobleme der mathema-tischen Physik,” Reine Angew. Math. 135:1, 1908.Google Scholar
[259] Strutt, J. W. (Lord Rayleigh), Theory of Sound, Dover Publications, New York, 1945. First published in 1877.Google Scholar
[260] Jones, W. and March, N. H., Theoretical Solid State Physics, vol. 1, John Wiley & Sons, New York, 1976.Google Scholar
[261] Matthews, J. and Walker, R. L., Mathematical Methods of Physics, W. A. Benjamin, Inc., New York, 1964.Google Scholar
[262] Arfken, G. B., Weber, H. J., and Harris, F. E., Mathematical Methods of Physics, 7th ed., Academic Press, Waltham, MA, 2012.Google Scholar
[263] Ehrenfest, P., “Bemurkung über die angenäherte Gültigkeit der klassischen Mechanik inner-halb der Quantenmechanik,” Z. Phys. 45:455, 1927.Google Scholar
[264] Born, M. and Fock, V., “Beweis des Adiabatensatzes,” Z. Phys. 51:165, 1928.Google Scholar
[265] Güttiger, P., “Das Verhalten von Atomen im magnetischen Drefeld,” Z. Phys. 73:169, 1931.Google Scholar
[266] Pauli, W., Handbuch der Physik, Springer, Berlin, 1933. Pages 83–272 relate to force and stress.Google Scholar
[267] Hellmann, H., Einfuhrung in die Quantumchemie, Franz Duetsche, Leipzig, 1937.Google Scholar
[268] Feynman, R. P., “Forces in molecules,” Phys. Rev. 56:340, 1939.Google Scholar
[269] Pulay, P., “Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules. I. Theory,” Mol. Phys. 17:197204, 1969.Google Scholar
[270] Fock, V., “Naherungsmethode zur Losung des quanten-mechanischen Mehrkorperprobleme,” Z. Phys. 63:855, 1930.Google Scholar
[271] Harris, J., “Adiabatic-connection approach to Kohn–Sham theory,” Phys. Rev. A 29:1648, 1984.Google Scholar
[272] Gunnarsson, O. and Lundqvist, B. I., “Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism,” Phys. Rev. B 13:42744298, 1976.Google Scholar
[273] Parr, R. G. and Yang, W., Density-Functional Theory of Atoms and Molecules, Oxford University Press, New York, 1989.Google Scholar
[274] Szabo, A. and Ostlund, N. S., Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory, Dover, Mineola, New York, 1996. Unabridged reprinting of 1989 version.Google Scholar
[275] McWeeny, R. D. and Sutcliffe, B. T., Methods of Molecular Quantum Mechanics, 2nd ed., Academic Press, New York, 1976.Google Scholar
[276] White, C. A., Johnson, B. G., Gill, P. M.W., and Head-Gordon, M., “Linear scaling density functional calculations via the continuous fast multipole method,” Chem. Phys. Letters 253:268278, 1996.Google Scholar
[277] Koopmans, T., “Uber die Zuordnung von Wellenfunktionen und Eigenwerten zu den Einzel-nen Elektronen Eines Atoms,” Physica 1:104113, 1934.Google Scholar
[278] Landau, E. M. and Pitaevskii, L. P., Statistical Physics: Part 1, Pergamon Press, Oxford, U.K., 1980.Google Scholar
[279] MacDonald, J. K. L., “Successive approximations by the Rayleigh–Ritz variation method,” Phys. Rev. 43:830, 1933.Google Scholar
[280] Ashcroft, N. W. and Mermin, N. D., Solid State Physics, W. B. Saunders Company, Philadelphia, PA, 1976.Google Scholar
[281] Heine, V., Group Theory, Pergamon Press, New York, 1960.Google Scholar
[282] Tinkham, M., Group Theory and Quantum Mechanics, McGraw-Hill, New York, 1964.Google Scholar
[283] Lax, M. J., Symmetry Principles in Solid State and Molecular Physics, Wiley, New York, 1974.Google Scholar
[284] Slater, J. C., Symmetry and Energy Bands in Crystals, Dover, New York, 1972. Corrected and reprinted version of 1965 Quantum Theory of Molecules and Solids, vol. 2.Google Scholar
[285] Kittel, C., Introduction to Solid State Physics, John Wiley & Sons, New York, 1996.Google Scholar
[286] Moreno, J. and Soler, J. M., “Optimal meshes for integrals in real- and reciprocal-space unit cells,” Phys. Rev. B 45:1389113898, 1992.Google Scholar
[287] Monkhorst, H. J. and Pack, J. D., “Special points for Brillouin-zone integrations,” Phys. Rev. B 13:51885192, 1976.Google Scholar
[288] MacDonald, A. H., “Comment on special points for Brillouin-zone integrations,” Phys. Rev. B 18:58975899, 1978.Google Scholar
[289] Baldereschi, A., “Mean-value point in the Brillouin zone,” Phys. Rev. B 7:52125215, 1973.Google Scholar
[290] Chadi, D. J. and Cohen, M. L., “Electronic structure of Hg1−x Cdx Te alloys and charge-density calculations using representative k points,” Phys. Rev. B 8:692699, 1973.Google Scholar
[291] Janak, J. F., in Computational Methods in Band Theory, edited by Marcus, P. M., Janak, J. F., and Williams, A. R., Plenum, New York, 1971, pp. 323339.Google Scholar
[292] Blöchl, P. E., Jepsen, O., and Andersen, O. K., “Improved tetrahedron method for Brillouin-zone integrations,” Phys. Rev. B 49:1622316233, 1994.Google Scholar
[293] Gilat, G., “Analysis of methods for calculating spectral properties in solids,” J. Comput. Phys. 10:432–65, 1972.Google Scholar
[294] Gilat, G., “Methods of Brillouin zone integration,” Methods Comput. Phys. 15:317–70, 1976.Google Scholar
[295] MacDonald, A. H., Vosko, S. H., and Coleridge, P. T., “Extensions of the tetrahedron method for evaluating spectral properties of solids,” J. Phys. C: Solid State Phys. 12:29913002, 1979.Google Scholar
[296] Van Hove, L., “The occurrence of singularities in the elastic frequency distribution of a crystal,” Phys. Rev. 89:11891193, 1953.Google Scholar
[297] Pines, D., Elementary Excitations in Solids, Wiley, New York, 1964.Google Scholar
[298] Pines, D. and Nozières, P., The Theory of Quantum Liquids, vol. 1 (Advanced Book Classics), Addison-Wesley Inc., Redwood City, CA, 1989. Originally published in 1966.Google Scholar
[299] Moll, N., Bockstedte, M., Fuchs, M., Pehlke, E., and Scheffler, M., “Application of generalized gradient approximations: The diamond-beta-tin phase transition in Si and Ge,” Phys. Rev. B 52:25502556, 1995.Google Scholar
[300] Marder, M., Condensed Matter Physics, John Wiley & Sons, New York, 2000.Google Scholar
[301] Martin, R. M., “Fermi-surface sum rule and its consequences for periodic Kondo and mixed-valence systems,” Phys. Rev. Lett. 48:362365, 1982.Google Scholar
[302] Goedecker, S., “Decay properties of the finite-temperature density matrix in metals,” Phys. Rev. B 58:35013502, 1998.Google Scholar
[303] Gibbs, J. W., “Fourier series,” Nature (letter to the editor) 59:200, 1898.Google Scholar
[304] Ismail-Beigi, S. and Arias, T. A., “Locality of the density matrix in metals, semiconductors and insulators,” Phys. Rev. Lett. 82:21272130, 1999.Google Scholar
[305] von Barth, U. and Hedin, L., “A local exchange–correlation potential for the spin polarized case: I,” J. Phys. C 5:1629, 1972.Google Scholar
[306] Mahan, G. D., Many-Particle Physics, 3rd ed., Kluwer Academic/Plenum Publishers, New York, 2000.Google Scholar
[307] Wigner, E. P., “Effects of the electron interaction on the energy levels of electrons in metals,” Trans. Faraday Soc. 34:678, 1938.Google Scholar
[308] Gell-Mann, M. and Brueckner, K. A., “Correlation energy of an electron gas at high-density,” Phys. Rev. 106:364, 1957.Google Scholar
[309] Carr, W. J. and Maradudin, A.A., “Ground state energy of a high-density electron gas,” Phys. Rev. 133:371, 1964.Google Scholar
[310] Carr, W. J., “Energy, specific heat, and magnetic properties of the low-density electron gas,” Phys. Rev. 122:1437, 1961.Google Scholar
[311] Ceperley, D. M. and Alder, B. J., “Ground state of the electron gas by a stochastic method,” Phys. Rev. Lett. 45:566569, 1980.Google Scholar
[312] Vosko, S., Wilk, L., and Nusair, M., “Accurate spin-dependent electron liquid correlation energies for local spin density calculations: A critical analysis,” Can. J. Phys. 58:1200, 1983.Google Scholar
[313] Perdew, J. P. and Zunger, A., “Self-interaction correction to density-functional approximations for many-electron systems,” Phys Rev. B 23:5048, 1981.Google Scholar
[314] Holm, B., “Total energies from GW calculations,” Phys. Rev. Lett. 83:788791, 1999.Google Scholar
[315] Ortiz, G. and Ballone, P., “Correlation energy, structure factor, radial distribution function and momentum distribution of the spin-polarized uniform electron gas,” Phys. Rev. B 50:1391– 1405, 1994.Google Scholar
[316] Kwon, Y., Ceperley, D. M., and Martin, R. M., “Effects of backflow correlation in the three-dimensional electron gas: Quantum Monte Carlo study,” Phys. Rev. B 58:68006806, 1998.Google Scholar
[317] Maggio, E. and Kresse, G., “Correlation energy for the homogeneous electron gas: Exact bethe-salpeter solution and an approximate evaluation,” Phys. Rev. B 93:235113, 2016.Google Scholar
[318] Gori-Giorgi, P., Sacchetti, F., and Bachelet, G. B., “Analytic structure factors and pair correlation functions for the unpolarized electron gas,” Phys. Rev. B 61:73537363, 2000.Google Scholar
[319] Ortiz, G., Harris, M., and Ballone, P., “Correlation energy, structure factor, radial density distribution function, and momentum distribution of the spin-polarized electron gas,” Phys. Rev. Lett. 82:53175320, 1999.Google Scholar
[320] Slater, J. C., “Cohesion in monovalent metals,” Phys. Rev. 35:509, 1930.Google Scholar
[321] Aulbur, W. G., Jonsson, L., and Wilkins, J. W., “Quasiparticle calculations in solids,” Solid State Physics 54:1218, 2000.Google Scholar
[322] Lyo, I.-W. and Plummer, E. W., “Quasiparticle band structure of Na and simple metals,” Phys. Rev. Lett. 60:15581561, 1988.Google Scholar
[323] Jensen, E. and Plummer, E. W., “Experimental band structure of Na,” Phys. Rev. Lett. 55:1912, 1985.Google Scholar
[324] Lindhard, J., “On the properties of a gas of charged particles,” Kgl. Danske Videnskab. Selskab, Mat.-fys. Medd. 28:1–57, 1954.Google Scholar
[325] Pines, D. and Nozières, P., The Theory of Quantum Liquids, vol. 1 (Advanced Book Classics), Westview Press, Boulder, CO, 1999. Originally published W. A. Benjamin, New York, 1966.Google Scholar
[326] David Mermin, N., “Thermal properties of the inhomogeneous electron gas,” Phys. Rev. 137:A1441–1443, 1965.Google Scholar
[327] Thomas, L. H., “The calculation of atomic fields,” Proc. Cambridge Phil. Roy. Soc. 23:542– 548, 1927.Google Scholar
[328] Fermi, E., “Un metodo statistico per la determinazione di alcune priorieta dell’atome,” Rend. Accad. Naz. Lincei 6:602607, 1927.Google Scholar
[329] Dirac, P. A. M., “Note on exchange phenomena in the Thomas–Fermi atom,” Proc. Cambridge Phil. Roy. Soc. 26:376385, 1930.Google Scholar
[330] von Weizsacker, C. F., “Zur Theorie der Kernmassen,” Z. Phys. 96:431, 1935.Google Scholar
[331] Teller, E., “On the stability of molecules in the Thomas–Fermi theory,” Rev. Mod. Phys. 34:627631, 1962.Google Scholar
[332] Kohn, W., in Highlights in Condensed Matter Theory, edited by Bassani, F., Fumi, F., and M. Tosi, P., North Holland, Amsterdam, 1985, p. 1.Google Scholar
[333] Levy, M., “Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the n-representability problem,” Proc. Natl. Acad. Sci. U.S.A. 76:6062, 1979.Google Scholar
[334] Levy, M., “Electron densities in search of hamiltonians,” Phys. Rev. A 26:1200, 1982.Google Scholar
[335] Levy, M. and Perdew, J. P., in Density Functional Methods in Physics, edited by Dreizler, R. M. and da Providencia, J., Plenum, New York, 1985, p. 11.Google Scholar
[336] Lieb, E., in Physics as Natural Philosophy, edited by Shimony, A. and Feshbach, H., MIT Press, Cambridge, 1982, p. 111.Google Scholar
[337] Lieb, E., “Density functionals for Coulomb systems,” Int. J. Quant. Chem. 24:243, 1983.Google Scholar
[338] Lieb, E., in Density Functional Methods in Physics, edited by Dreizler, R. M. and da Providencia, J., Plenum, New York, 1985, p. 31.Google Scholar
[339] Gilbert, T. L., “Hohenberg-Kohn theorem for nonlocal external potentials,” Phys. Rev. B 12:2111, 1975.Google Scholar
[340] Gunnarsson, O., Lundqvist, B. I., and Wilkins, J. W., “Contribution to the cohesive energy of simple metals: Spin-dependent effect,” Phys. Rev. B 10:13191327, 1974.Google Scholar
[341] Jones, R. O. and Gunnarsson, O., “The density functional formalism, its applications and prospects,” Rev. Mod. Phys. 61:689746, 1989.Google Scholar
[342] Vignale, G. and Rasolt, M., “Current- and spin-density-functional theory for inhomogeneous electronic systems in strong magnetic fields,” Phys. Rev. B 37:1068510696, 1988.Google Scholar
[343] Vignale, G. and Kohn, W., “Current-dependent exchange–correlation potential for dynamical linear response theory,” Phys. Rev. Lett. 77:20372040, 1996.Google Scholar
[344] Capelle, K. and Gross, E. K. U., “Spin-density functionals from current-density functional theory and vice versa: A road towards new approximations,” Phys. Rev. Lett. 78:18721875, 1997.Google Scholar
[345] van Leeuwen, R., “Causality and symmetry in time-dependent density-functional theory,” Phys. Rev. Lett. 80:12801283, 1998.Google Scholar
[346] Perdew, J. P., Parr, R. G., Levy, M., and Jr. Balduz, J. L., “Density-functional theory for fractional particle number: Derivative discontinuities of the energy,” Phys. Rev. Lett. 49:1691–1694, 1982.Google Scholar
[347] Maitra, N. T., Souza, I., and Burke, K., “Current-density functional theory of the response of solids,” Phys. Rev. B 68:045109, 2003.Google Scholar
[348] Wannier, G., “Dynamics of band electrons in electric and magnetic fields,” Rev. Mod. Phys. 34:645, 1962.Google Scholar
[349] Nenciu, G., “Dynamics of band electrons in electric and magnetic fields: Rigorous justification of the effective hamiltonians,” Rev. Mod. Phys. 63:91, 1991.Google Scholar
[350] Gonze, X., Ghosez, Ph., and Godby, R. W., “Density-polarization functional theory of the response of a periodic insulating solid to an electric field,” Phys. Rev. Lett. 74:40354038, 1995.Google Scholar
[351] Martin, R. M. and Ortiz, G., “Functional theory of extended coulomb systems,” Phys. Rev. B 56:11241140, 1997.Google Scholar
[352] Martin, R. M. and Ortiz, G., “Recent developments in the theory of polarization in solids,” Solid State Commun. 102:121126, 1997.Google Scholar
[353] Harriman, J. E., “Orthonormal orbitals for the representation of an arbitrary density,” Phys. Rev. A 24:680682, 1981.Google Scholar
[354] Harrison, W. A., Electronic Structure and the Properties of Solids, Dover, New York, 1989.Google Scholar
[355] Antropov, V. P., Katsnelson, M. I., van Schilfgaarde, M., and Harmon, B. N., “Exchange-coupled spin-fluctuation theory: Application to Fe, Co, and Ni,” Phys. Rev. Lett. 75:729732, 1995.Google Scholar
[356] Uhl, M. and Kübler, J., “Ab initio spin dynamics in magnets,” Phys. Rev. Lett. 77:334337, 1996.Google Scholar
[357] Oda, T., Pasquarello, A., and Car, R., “Fully unconstrained approach to noncollinear magnetism: Application to small fe clusters,” Phys. Rev. Lett. 80:36223625, 1998.Google Scholar
[358] Bylander, D. M., Niu, Q., and Kleinman, L., “Fe magnon dispersion curve calculated with the frozen spin-wave method,” Phys. Rev. B 61:R11875–R11878, 2000.Google Scholar
[359] Harris, J., “Simplified method for calculating the energy of weakly interacting fragments,” Phys. Rev. B 31:17701779, 1985.Google Scholar
[360] Weinert, M., Watson, R. E., and Davenport, J. W., “Total-energy differences and eigenvalue sums,” Phys. Rev. B 32:21152119, 1985.Google Scholar
[361] Foulkes, W. M. C. and Haydock, R., “Tight-binding models and density-functional theory,” Phys. Rev. B 39:1252012536, 1989.Google Scholar
[362] Sankey, O. F. and Niklewski, D. J., “Ab initio multicenter tight-binding model for molecular dynamics simulations and other applications in covalent systems,” Phys. Rev. B 40:3979– 3995, 1989.Google Scholar
[363] Methfessel, M., “Independent variation of the density and potential in density functional methods,” Phys. Rev. B 52:8074, 1995.Google Scholar
[364] Read, A. J. and Needs, R. J., “Tests of the Harris energy functional,” J. Phys. Condens. Matter 1:7565, 1989.Google Scholar
[365] Zaremba, E., “Extremal properties of the Harris energy functional,” J. Phys. Condens. Matter 2:2479, 1990.Google Scholar
[366] Robertson, I. J. and Farid, B., “Does the Harris energy functional possess a local maximum at the ground-state density?,” Phys. Rev. Lett. 66:32653268, 1991.Google Scholar
[367] Jacobsen, K. W., Norskov, J. K., and Puska, M. J., “Interatomic interactions in the effective-medium theory,” Phys. Rev. B 35:74237442, 1987.Google Scholar
[368] Nicholson, D. M. C., Stocks, G. M., Wang, Y., Shelton, W. A., Szotek, Z., and Temmerman, W. M., “Stationary nature of the density-functional free energy: Application to accelerated multiple-scattering calculations,” Phys. Rev. B 50:1468614689, 1994.Google Scholar
[369] Gillan, M. J., “Calculation of the vacancy formation energy in aluminum,” J. Phys. Condens. Matter 1:689, 1989.Google Scholar
[370] Marzari, N., Vanderbilt, D., and Payne, M. C., “Ensemble density-functional theory for ab initio molecular dynamics of metals and finite-temperature insulators,” Phys. Rev. Lett. 79:1337–1340, 1997.Google Scholar
[371] Dederichs, P. H. and Zeller, R., “Self-consistency iterations in electronic-structure calculations,” Phys. Rev. B 28:5462, 1983.Google Scholar
[372] Pickett, W. E., “Pseudopotential methods in condensed matter applications,” Comput. Phys. Commun. 9:115, 1989.Google Scholar
[373] Ho, K.-M., Ihm, J., and Joannopoulos, J. D., “Dielectric matrix scheme for fast convergence in self-consistent electronic-structure calculations,” Phys. Rev. B 25:42604262, 1982.Google Scholar
[374] Broyden, C. G., “A class of methods for solving nonlinear simulataneous equations,” Math. Comput. 19:577593, 1965.Google Scholar
[375] Bendt, P. and Zunger, A., “New approach for solving the density-functional self-consistent-field problem,” Phys. Rev. B 26:31143137, 1982.Google Scholar
[376] Srivastava, G. P., “Broyden’s method for self-consistent field convergence acceleration,” J. Phys. A 17:L317, 1984.Google Scholar
[377] Singh, D., Krakauer, H., and Wang, C. S., “Accelerating the convergence of self-consistent linearized augmented-plane-wave calculations,” Phys. Rev. B 34:83918393, 1986.Google Scholar
[378] Garza, A. J. and Scuseria, G. E., “Comparison of self-consistent field convergence acceleration techniques,” J. Chem. Phys. 137:054110, 2012.Google Scholar
[379] Nakano, Masahiko, Seino, Junji, and Nakai, Hiromi, “Assessment of self-consistent field convergence in spin-dependent relativistic calculations,” Chem. Phys. Letters 657:65–71, 2016.Google Scholar
[380] Vanderbilt, D. and Louie, S. G., “Total energies of diamond (111) surface reconstructions by a linear combination of atomic orbitals method,” Phys. Rev. B 30:6118, 1984.Google Scholar
[381] Johnson, D. D., “Modified Broyden’s method for accelerating convergence in self-consistent calculations,” Phys. Rev. B 38:1280712813, 1988.Google Scholar
[382] Allen, M. and Tildesley, D., Computer Simulation of Liquids, Oxford University Press, New York, Oxford, 1989.Google Scholar
[383] Parrinello, M. and Rahman, A., “Crystal structure and pair potentials: A molecular-dynamics study,” Phys. Rev. Lett. 45:11961199, 1980.Google Scholar
[384] Souza, I. and Martins, J. L., “Metric tensor as the dynamical variable for variable-cell-shape molecular dynamics,” Phys. Rev. B 55:87338742, 1997.Google Scholar
[385] Payne, M. C., Teter, M. P., Allan, D. C., Arias, T. A., and Joannopoulos, J. D., “Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients,” Rev. Mod. Phys. 64:10451097, 1992.Google Scholar
[386] Gritsenko, O., van Leeuwen, R., and Baerends, E. J., “Analysis of electron interaction and atomic shell structure in terms of local potentials,” J. Chem. Phys. 101:8455, 1994.Google Scholar
[387] Perdew, J. P. and Levy, M., “Physical content of the exact Kohn–Sham orbital energies: Band gaps and derivative discontinuities,” Phys. Rev. Lett. 51:18841887, 1983.Google Scholar
[388] Sham, L. J. and Schlüter, M., “Density-functional theory of the energy gap,” Phys. Rev. Lett. 51:18881891, 1983.Google Scholar
[389] Almbladh, C. and von Barth, U., “Exact results for the charge and spin densities, exchange– correlation potentials, and density-functional eigenvalues,” Phys. Rev. B 31:3231, 1985.Google Scholar
[390] Levy, M., Perdew, J. P., and Sahni, V., “Exact differential equation for the density and ionization energy of a many-particle system,” Phys. Rev. A 12:27452748, 1984.Google Scholar
[391] Gorling, A., “Density-functional theory for excited states,” Phys. Rev. A 54:39123915, 1996.Google Scholar
[392] Janak, J. F., “Proof that ∂e/∂ni = ϵi in density-functional theory,” Phys. Rev. B 18:7165, 1978.Google Scholar
[393] Mearns, D., “Inequivalence of physical and Kohn–Sham Fermi surfaces,” Phys. Rev. B 38:5906, 1988.Google Scholar
[394] Ullrich, C. A., “Time-dependent density-functional theory beyond the adiabatic approximation: Insights from a two-electron model system,” J. Chem. Phys. 125:234108, 2006.Google Scholar
[395] Maitra, N. T., “Perspective: Fundamental aspects of time-dependent density functional theory,” J. Chem. Phys. 144:220901, 2016.Google Scholar
[396] Jansen, H. J. F., “Many-body properties calculated from the Kohn–Sham equations in density-functional theory,” Phys Rev. B 43:12025, 1991.Google Scholar
[397] Oliveira, L. N., Gross, E. K. U., and Kohn, W., “Density-functional theory for superconductors,” Phys. Rev. Lett. 60:24302433, 1988.Google Scholar
[398] Lüders, M., Marques, M. A. L., Lathiotakis, N. N., Floris, A., Profeta, G., Fast, L., Continenza, A., Massidda, S., and Gross, E. K. U., “Ab initio theory of superconductivity. I. Density functional formalism and approximate functionals,” Phys. Rev. B 72:024545, 2005.Google Scholar
[399] Marques, M. A. L., Lüders, M., Lathiotakis, N. N., Profeta, G., Floris, A., Fast, L., Continenza, A., Gross, E. K. U., and Massidda, S., “Ab initio theory of superconductivity. II. Application to elemental metals,” Phys. Rev. B 72:024546, 2005.Google Scholar
[400] Seidl, A., Görling, A., Vogl, P., Majewski, J. A., and Levy, M., “Generalized Kohn–Sham schemes and the band-gap problem,” Phys. Rev. B 53:37643774, 1996.Google Scholar
[401] Levy, M. and Perdew, J. P., “Hellmann-Feynman, virial, and scaling requisites for the exact universal density functionals: Shape of the correlation potential and diamagnetic susceptibility for atoms,” Phys. Rev. A 32:20102021, 1985.Google Scholar
[402] Gunnarsson, O., Jonson, M., and Lundqvist, B. I., “Descriptions of exchange and correlation effects in inhomogeneous electron systems,” Phys. Rev. B 20:3136, 1979.Google Scholar
[403] Kolos, W. and Wolniewicz, L., “Potential-energy curves for the X1 σg+, b 3σu+, and C 1πu states of the hydrogen molecule,” J. Chem. Phys. 43:2429, 1965.Google Scholar
[404] Almbladh, C. O. and Pedroza, A. C., “Density-functional exchange–correlation potentials and orbital eigenvalues for light atoms,” Phys. Rev. A 29:23222330, 1984.Google Scholar
[405] Hood, R. Q., Chou, M. Y., Williamson, A. J., Rajagopal, G., Needs, R. J., and Foulkes, W. M. C., “Exchange and correlation in silicon,” Phys. Rev. B 57:89728982, 1998.Google Scholar
[406] Lejaeghere, K., et al., “Reproducibility in density functional theory calculations of solids,” Science 351, 2016.Google Scholar
[407] Herman, F., Van Dyke, J. P., and Ortenburger, I. P., “Improved statistical exchange approximation for inhomogeneous many-electron systems,” Phys. Rev. Lett. 22:807, 1969.Google Scholar
[408] Svendsen, P. S. and von Barth, U., “Gradient expansion of the exchange energy from second-order density response theory,” Phys. Rev. B 54:1740217413, 1996.Google Scholar
[409] Perdew, J. P. and Burke, K., “Comparison shopping for a gradient-corrected density func-tional,” Int. J. Quant. Chem. 57:309319, 1996.Google Scholar
[410] Becke, A. D., “Density-functional exchange-energy approximation with correct asymptotic behavior,” Phys. Rev. A 38:30983100, 1988.Google Scholar
[411] Perdew, J. P. and Wang, Y., “Accurate and simple analytic representation of the electron-gas correlation energy,” Phys. Rev. B 45:1324413249, 1992.Google Scholar
[412] Perdew, J. P., Burke, K., and Ernzerhof, M., “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77:38653868, 1996.Google Scholar
[413] Koch, W. and Holthausen, M. C., A Chemists’ Guide to Density Funcitonal Thoery, Wiley-VCH, Weinheim, 2001.Google Scholar
[414] Ma, S.-K. and Brueckner, K. A., “Improved statistical exchange approximation for inhomogeneous many-electron systems,” Phys. Rev. 165:1831, 1968.Google Scholar
[415] Mardirossian, N. and Head-Gordon, M., “Thirty years of density functional theory in computational chemistry: An overview and extensive assessment of 200 density functionals,” Mol. Phys. 115:23152372, 2017.Google Scholar
[416] Lee, C., Yang, W., and Parr, R. G., “Development of the Colle–Salvetti correlation-energy formula into a functional of the electron density,” Phys. Rev. B 37:785789, 1988.Google Scholar
[417] Colle, R. and Salvetti, O., “Approximate calculation of the correlation energy for the closed and open shells,” Theo. Chim. Acta 53:5963, 1979.Google Scholar
[418] Krieger, J. B., Chen, Y., Iafrate, G. J., and Savin, A., “Construction of an accurate SIC-corrected correlation energy functional based on an electron gas with a gap,” preprint, 2000.Google Scholar
[419] Rey, J. and Savin, A., “Virtual space level shifting and correlation energies,” Int. J. Quant. Chem. 69:581587, 1998.Google Scholar
[420] Towler, M. D., Zupan, A., and Causa, M., “Density functional theory in periodic systems using local gaussian basis sets,” Comput. Phys. Commun. 98:181205, 1996.Google Scholar
[421] Hamann, D. R., “Generalized gradient theory for silica phase transitions,” Phys. Rev. Lett. 76:660663, 1996.Google Scholar
[422] White, J. A. and Bird, D. M., “Implementation of gradient-corrected exchange-correlation potentials in Car-Parrinello total-energy calculations,” Phys. Rev. B 50:49544957, 1994.Google Scholar
[423] Kim, Y.-H., Lee, I.-H. Nagaraja, S., Leburton, J. P., Hood, R. Q., and Martin, R. M., “Two-dimensional limit of exchange–correlation energy functional approximations,” Phys. Rev. B 61:52025211, 2000.Google Scholar
[424] Zhao, Y. and Truhlar, D. G., “The M06 suite of density functionals for main group thermo-chemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals,” Theor. Chem. Acc. 120:215241, 2008.Google Scholar
[425] Snyder, J. C., Rupp, M., Hansen, K., Müller, K.-R., and Burke, K., “Finding density functionals with machine learning,” Phys. Rev. Lett. 108:253002, 2012.Google Scholar
[426] Becke, Axel D., “Perspective: Fifty years of density-functional theory in chemical physics,J. Chem. Phys. 140:301, 2014.Google Scholar
[427] Kummel, S. and Kronik, L., “Orbital-dependent density functionals: Theory and applications,” Rev. Mod. Phys. 80:360, 2008.Google Scholar
[428] Perdew, J. P. and Schmidt, K., “Jacob’s ladder of density functional approximations for the exchange–correlation energy,” AIP Conf. Proc. 577:120, 2001.Google Scholar
[429] Sham, L. J. and Schlüter, M., “Density functional theory of the band gap,” Phys. Rev. B 32:3883, 1985.Google Scholar
[430] Perdew, J. P., Yang, W., Burke, K., Yang, Z., Eberhard Gross, K. U., Scheffler, M., Scuseria, G. E., Henderson, T. M., Zhang, I. Y., Ruzsinszky, A., Peng, H., Sun, J., Trushin, E., and Görling, A., “Understanding band gaps of solids in generalized Kohn–Sham theory,” Proc. Natl. Acad. Sci. U.S.A. 114:2801–2806, 2017.Google Scholar
[431] Baer, R. and Kronik, L., “Time-dependent generalized Kohn–Sham theory,” Eur. Phys. J. B 91:170, 2018.Google Scholar
[432] Becke, A. D., “A new mixing of Hartree–Fock and local density-functional theories,” J. Chem. Phys. 98:13721377, 1993.Google Scholar
[433] Perdew, J. P., Ernzerhof, M., and Burke, K., “Rationale for mixing exact exchange with density functional approximations,” J. Chem. Phys. 105:99829985, 1996.Google Scholar
[434] Marques, M. A. L., Vidal, J., Oliveira, M. J. T., Reining, L., and Botti, S., “Density-based mixing parameter for hybrid functionals,” Phys. Rev. B 83:035119, 2011.Google Scholar
[435] Heyd, J., Scuseria, G. E., and Ernzerhof, M., “Hybrid functionals based on a screened coulomb potential,” J. Chem. Phys. 118:82078215, 2003.Google Scholar
[436] Heyd, J., Scuseria, G. E., and Ernzerhof, M., “Erratum: Hybrid functionals based on a screened Coulomb potential [J. Chem. Phys. 118, 8207 (2003)],” J. Chem. Phys. 124:219906, 2006.Google Scholar
[437] Krukau, A. V., Vydrov, O. A., Izmaylov, A. F., and Scuseria, G. E., “Influence of the exchange screening parameter on the performance of screened hybrid functionals,” J. Chem. Phys. 125:224106, 2006.Google Scholar
[438] Chen, W., Miceli, G., Rignanese, G.-M., and Pasquarello, A., “Nonempirical dielectric-dependent hybrid functional with range separation for semiconductors and insulators,” Phys. Rev. Materials 2:073803, 2018.Google Scholar
[439] Tkatchenko, A. and Scheffler, M., “Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data,” Phys. Rev. Lett. 102:073005, 2009.Google Scholar
[440] Baer, R., Livshits, E., and Salzner, U., “Tuned range-separated hybrids in density functional theory,” Annu. Rev. Phys. Chem. 61:85109, 2010.Google Scholar
[441] Perdew, J. P., Sun, J., Martin, R. M., and Delley, B., “Semilocal density functionals and constraint satisfaction,” Int. J. Quant. Chem. 116:847851, 2016.Google Scholar
[442] Becke, A. D. and Roussel, M. R., “Exchange holes in inhomogeneous systems: A coordinate-space model,” Phys. Rev. A 39:37613767, 1989.Google Scholar
[443] Tao, J., Perdew, J. P., Staroverov, V. N., and Scuseria, G. E., “Climbing the density functional ladder: Nonempirical meta–generalized gradient approximation designed for molecules and solids,” Phys. Rev. Lett. 91:146401, 2003.Google Scholar
[444] Sun, J., Ruzsinszky, A., and Perdew, J. P., “Strongly constrained and appropriately normed semilocal density functional,” Phys. Rev. Lett. 115:036402, 2015.Google Scholar
[445] Brandenburg, J. G., Bates, J. E., Sun, J., and Perdew, J. P., “Benchmark tests of a strongly constrained semilocal functional with a long-range dispersion correction,” Phys. Rev. B 94:115144, 2016.Google Scholar
[446] Sharp, R. T. and Horton, G. K., “A variational approach to the unipotential many-electron problem,” Phys. Rev. 90:317, 1953.Google Scholar
[447] Casida, M. E., in Recent Developments and Applications of Density Functional Theory, edited by Seminario, J. M., Elsevier, Amsterdam, 1996, p. 391.Google Scholar
[448] Bylander, D. M. and Kleinman, L., “The optimized effective potential for atoms and semiconductors,” Int. J. Mod. Phys. 10:399425, 1996.Google Scholar
[449] Grabo, T., Kreibich, T., Kurth, S., and Gross, E. K. U., in Strong Coulomb Correlations in Electronic Structure: Beyond the Local Density Approximation, edited by Anisimov, V. I., Gordon & Breach, Tokyo, 1998.Google Scholar
[450] Krieger, J. B., Li, Y., and Iafrate, G. J., “Exact relations in the optimized effective potential method employing an arbitrary Exc [{ψ}],” Phys. Lett. A 148:470473, 1990.Google Scholar
[451] Krieger, J. B., Li, Y., and Iafrate, G. J., “Construction and application of an accurate local spin-polarized Kohn–Sham potential with integer discontinuity: Exchange-only theory,” Phys. Rev. A 45:101, 1992.Google Scholar
[452] Krieger, J. B., Li, Y., and Iafrate, G. J., in Density Functional Theory, edited by Gross, E. K. U. and Dreizler, R. M., Plenum Press, New York, 1995, p. 191.Google Scholar
[453] Slater, J. C., “A simplification of the Hartree–Fock method,” Phys. Rev. 81:385390, 1951.Google Scholar
[454] Svane, A. and Gunnarsson, O., “Localization in the self-interaction-corrected density-functional formalism,” Phys Rev. B 37:9919, 1988.Google Scholar
[455] Svane, A. and Gunnarsson, O., “Transition-metal oxides in the self-interaction-corrected density functional formalism,” Phys Rev. Lett. 65:11481151, 1990.Google Scholar
[456] Temmerman, W. M., Szotek, Z., and Winter, H., “Self-interaction corrected electronic structure of La2 CuO4,” Phys Rev. B 47, 1993.Google Scholar
[457] Svane, A., Szotek, Z., Temmerman, W. M., Lægsgaard, J., and Winter, H., “Electronic structure of cerium pnictides under pressure,” J. Phys. Condens. Matter 10:53095325, 1998.Google Scholar
[458] Anisimov, V. I., Zaanen, J., and Andersen, O. K., “Band theory and Mott insulators: Hubbard U instead of Stoner I,” Phys. Rev. B 44:943, 1991.Google Scholar
[459] Anisimov, V. I., Aryasetiawan, F., and Lichtenstein, A. I., “First principles calculations of the electronic structure and spectra of strongly correlated systems: The LDA + U method,” J. Phys. Condens. Matter 9:767808, 1997.Google Scholar
[460] Hubbard, J., “Electron correlations in narrow energy bands. IV. The atomic representation,” Proc. R. Soc. Lond. A 285:542560, 1965.Google Scholar
[461] Baeriswyl, D., Campbell, D. K., Carmelo, J. M. P., and Guinea, F., The Hubbard Model, Plenum Press, New York, 1995.Google Scholar
[462] Dabo, I., Ferretti, A., Poilvert, N., Li, Y., Marzari, N., and Cococcioni, M., “Koopmans’ condition for density-functional theory,” Phys. Rev. B 82:115121, 2010.Google Scholar
[463] Nguyen, N. L., Colonna, N., Ferretti, A., and Marzari, N., “Koopmans-compliant spectral functionals for extended systems,” Phys. Rev. X 8:021051, 2018.Google Scholar
[464] Langreth, D. C. and Perdew, J. P., “Exchange–correlation energy of a metallic surface: Wave-vector analysis,” Phys. Rev. B 15:28842901, 1977.Google Scholar
[465] Ren, X., Rinke, P., Joas, C., and Scheffler, M., “Random-phase approximation and its applications in computational chemistry and materials science,” J. Mater. Sci. 47:74477471, 2012.Google Scholar
[466] DiStasio, R. A Jr., Gobre, V. V., and Tkatchenko, A., “Many-body van der Waals interactions in molecules and condensed matter,” J. Phys. Condens. Matter 26:213202, 2014.Google Scholar
[467] Harl, J., Schimka, L., and Kresse, G., “Assessing the quality of the random phase approximation for lattice constants and atomization energies of solids,” Phys. Rev. B 81:115126, 2010.Google Scholar
[468] Dion, M., Rydberg, H., Schröder, E., Langreth, D. C., and Lundqvist, B. I., “Van der Waals density functional for general geometries,” Phys. Rev. Lett. 92:246401, 2004.Google Scholar
[469] Casimir, H. B. G. and Polder, D., “The influence of retardation on the London–van der Waals forces,” Phys. Rev. 73:360372, 1948.Google Scholar
[470] Grimme, S., Antony, J., Ehrlich, S., and Krieg, H., “A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu,” J. Chem. Phys. 132:154104, 2010.Google Scholar
[471] Brinck, T., Murray, J. S., and Politzer, P., “Polarizability and volume,” J. Chem. Phys. 98:4305– 4306, 1993.Google Scholar
[472] Hirshfeld, F. L., “Bonded-atom fragments for describing molecular charge densities,” Theoret. Chim. Acta 44:129138, 1977.Google Scholar
[473] Román-Pérez, Guillermo and Soler, José M., “Efficient implementation of a van der Waals density functional: Application to double-wall carbon nanotubes,” Phys. Rev. Lett. 103:096102, 2009.Google Scholar
[474] Vydrov, O. A. and Van Voorhis, T., “Improving the accuracy of the nonlocal van der Waals density functional with minimal empiricism,” J. Chem. Phys. 130:104105, 2009.Google Scholar
[475] Vydrov, O. A. and Van Voorhis, T., “Nonlocal van der Waals density functional: The simpler the better,” J. Chem. Phys. 133:244103, 2010.Google Scholar
[476] Becke, A. D. and Johnson, E. R., “A simple effective potential for exchange,” J. Chem. Phys. 124:221101, 2006.Google Scholar
[477] Tran, F. and Blaha, P., “Accurate band gaps of semiconductors and insulators with a semilocal exchange–correlation potential,” Phys. Rev. Lett. 102:226401, 2009.Google Scholar
[478] Waroquiers, D., et al., “Band widths and gaps from the Tran–Blaha functional: Comparison with many-body perturbation theory,” Phys. Rev. B 87:075121, 2013.Google Scholar
[479] Kurth, S., Perdew, J.P., and Blaha, P., “Molecular and solid-state tests of density functional approximations: LSD, GGAs, and meta-GGAs,” Int. J. Quantum Chem. 75:889, 1999.Google Scholar
[480] Jackson, J. D., Classical Electrodynamics, Wiley, New York, 1962.Google Scholar
[481] Herman, F. and Skillman, S., Atomic Structure Calculations, Prentice-Hall, Engelwood Cliffs, NJ, 1963.Google Scholar
[482] Fischer, C. F., The Hartree–Fock Method for Atoms: A Numerical Approach, John Wiley & Sons, New York, 1977.Google Scholar
[483] Slater, J. C., Quantum Theory of Atomic Structure, vol. 1, McGraw-Hill, New York, 1960.Google Scholar
[484] Slater, J. C., Quantum Theory of Atomic Structure, vol. 2, McGraw-Hill, New York, 1960.Google Scholar
[485] Koonin, S. E. and Meredith, D. C., Computational Physics, Addison Wesley, Menlo Park, CA, 1990.Google Scholar
[486] Hybertsen, M. S. and Louie, S. G., “Spin–orbit splitting in semiconductors and insulators from the ab initio pseudopotential,” Phys. Rev. B 34:2920, 1986.Google Scholar
[487] Theurich, G. and Hill, N. A., “Self-consistent treatment of spin–orbit coupling in solids using relativistic fully separable ab initio pseudopotentials,” Phys. Rev. B 64:073106, 1986.Google Scholar
[488] Vukajlovic, F. R., Shirley, E. L., and Martin, R. M., “Single-body methods in 3d transition-metal atoms,” Phys. Rev. B 43:3994, 1991.Google Scholar
[489] Slater, J. C., The Self-Consistent Field Theory for Molecules and Solids: Quantum Theory of Molecules and Solids, vol. 4, McGraw-Hill, New York, 1974.Google Scholar
[490] McMahan, A. K., Martin, R. M., and Satpathy, S., “Calculated effective hamiltonian for La2Cu04 and solution in the Anderson impurity approximation,” Phys. Rev. B 38:6650, 1988.Google Scholar
[491] Herbst, J. F., Lowy, D. N., and Watson, R. E., “Single-electron energies, many-electron effects, and the renormalized-atom scheme as applied to rare-earth metals,” Phys. Rev. B 6:1913– 1924, 1972.Google Scholar
[492] Herbst, J. F., Watson, R. E., and Wilkins, J. W., “Relativistic calculations of 4f excitation energies in the rare-earth metals: Further results,” Phys. Rev. B 17:30893098, 1978.Google Scholar
[493] Andersen, O. K. and Jepsen, O., “Explicit, first-principles tight-binding theory,” Physica 91B:317, 1977.Google Scholar
[494] Straub, G. K. and Harrison, Walter A., “Analytic methods for the calculation of the electronic structure of solids,” Phys. Rev. B 31:7668–7679, 1985.Google Scholar
[495] Andersen, O. K., “Simple approach to the band structure problem,” Solid State Commun. 13:133136, 1973.Google Scholar
[496] Liberman, f, “Virial theorem in self-consistent-field calculations,” Phys. Rev. B 3:2081– 2082, 1971.Google Scholar
[497] Janak, J. F., “Simplification of total-energy and pressure calculations in solids,” Phys. Rev. B 20:39853988, 1974.Google Scholar
[498] Mackintosh, A. R. and Andersen, O. K., in Electrons at the Fermi Surface, edited by Springford, M., Cambridge Press, Cambridge, 1975, p. 149.Google Scholar
[499] Heine, V., in Solid State Physics, edited by Ehenreich, H., Seitz, F., and Turnbull, D., Academic Press, New York, 1980, Vol. 35, p. 1.Google Scholar
[500] Amaldi, E., D’Agostino, O., Fermi, E., Pontecorvo, B., Rasetti, F., and Segre, E., “Artificial radioactivity induced by neutron bombardment – II,” Proc. R. Soc. Lond. A 149:522558, 1935.Google Scholar
[501] Callaway, J., “Electron energy bands in sodium,” Phys. Rev. 112:322, 1958.Google Scholar
[502] Antoncik, E., “A new formulation of the method of nearly free electrons,” Czech. J. Phys. 4:439, 1954.Google Scholar
[503] Antoncik, E., “Approximate formulation of the orthogonalized plane-wave method,” J. Phys. Chem. Solids 10:314, 1959.Google Scholar
[504] Phillips, J. C. and Kleinman, L., “New method for calculating wave functions in crystals and molecules,” Phys. Rev. 116:287, 1959.Google Scholar
[505] Herring, W. C. and Hill, A. G., “The theoretical constitution of metallic beryllium,” Phys. Rev. 58:132, 1940.Google Scholar
[506] Heine, V., in Solid State Physics, edited by Ehrenreich, H., Seitz, F., and Turnbull, D., Academic, New York, 1970, p. 1.Google Scholar
[507] Cohen, M. L. and Heine, V., in Solid State Physics, edited by Ehrenreich, H., Seitz, F., and Turnbull, D., Academic, New York, 1970, p. 37.Google Scholar
[508] Harrison, W. A., Pseudopotentials in the Theory of Metals, Benjamin, New York, 1966.Google Scholar
[509] Blöchl, P. E., “Generalized separable potentials for electronic-structure calculations,” Phys. Rev. B 41:54145416, 1990.Google Scholar
[510] Vanderbilt, D., “Soft self-consistent pseudopotentials in a generalized eigenvalue formalism,” Phys. Rev. B 41:7892, 1990.Google Scholar
[511] Herman, F., “Calculation of the energy band structures of the diamond and germanium crystals by the method of orthogonalized plane waves,” Phys. Rev. 93:1214, 1954.Google Scholar
[512] Woodruff, T. O., “Solution of the Hartree–Fock–Slater equations for silicon crystal by the method of orthogonalized plane waves,” Phys. Rev. 98:1741, 1955.Google Scholar
[513] Herman, F., “Speculations on the energy band structure of Ge–Si alloys,” Phys. Rev. 95:847, 1954.Google Scholar
[514] Bassani, F., “Energy band structure in silicon crystals by the orthogonalized plane-wave method,” Phys. Rev. 263:1741, 1957.Google Scholar
[515] Lax, B., “Experimental investigations of the electronic band structure of solids,” Rev. Mod. Phys. 30:122, 1958.Google Scholar
[516] Cohen, M. H. and Heine, V., “Cancellation of kinetic and potential energy in atoms, molecules, and solids,” Phys. Rev. 122:1821, 1961.Google Scholar
[517] Ashcroft, N. W., “Electron–ion pseudopotentials in metals,” Phys. Lett. 23:4853, 1966.Google Scholar
[518] Abarenkov, I. V. and Heine, V., “The model potential for positive ions,” Phil. Mag. 12:529, 1965.Google Scholar
[519] Animalu, A. O. E., “Non-local dielectric screening in metals,” Phil. Mag. 11:379, 1965.Google Scholar
[520] Animalu, A. O. E. and Heine, V., “The screened model potential for 25 elements,” Phil. Mag. 12:1249, 1965.Google Scholar
[521] Christiansen, P. A., Lee, Y. S., and Pitzer, K. S., “Improved ab initio effective core potentials for molecular calculations,” J. Chem. Phys. 71:44454450, 1979.Google Scholar
[522] Krauss, M. and Stevens, W. J., “Effective potentials in molecular quantum chemistry,” Ann. Rev. Phys. Chem 35:357, 1984.Google Scholar
[523] Hamann, D. R., Schlüter, M., and Chiang, C., “Norm-conserving pseudopotentials,” Phys. Rev. Lett. 43:14941497, 1979.Google Scholar
[524] Topp, W. C. and Hopfield, J. J., “Chemically motivated pseudopotential for sodium,” Phys. Rev. 7:12951303, 1973.Google Scholar
[525] Engel, E., A., Schmid, R. N., Dreizler, R. M., and Chetty, N., “Role of the core-valence interaction for pseudopotential calculations with exact exchange,” Phys. Rev. B 64:125111– 125122, 2001.Google Scholar
[526] Shirley, E. L., Allan, D. C., Martin, R. M., and Joannopoulos, J. D., “Extended norm-conserving pseudopotentials,” Phys. Rev. B 40:3652, 1989.Google Scholar
[527] Lüders, G., “Zum zusammenhang zwischen S-Matrix und Normierungsintegrassen in der Quantenmechanik,” Z. Naturforsch. 10a:581, 1955.Google Scholar
[528] Bachelet, G. B., Hamann, D. R., and Schlüter, M., “Pseudopotentials that work: From H to Pu,” Phys. Rev. B 26:4199, 1982.Google Scholar
[529] Vanderbilt, D., “Optimally smooth norm-conserving pseudopotentials,” Phys. Rev. B 32:8412, 1985.Google Scholar
[530] Kerker, G. P., “Non-singular atomic pseudopotentials for solid state applications,” J. Phys. C 13:L189, 1980.Google Scholar
[531] Troullier, N. and Martins, J. L., “Efficient pseudopotentials for plane-wave calculations,” Phys. Rev. B 43:19932006, 1991.Google Scholar
[532] Rappe, A. M., Rabe, K. M., Kaxiras, E., and Joannopoulos, J. D., “Optimized pseudopotentials,” Phys. Rev. B 41:1227, 1990.Google Scholar
[533] Kresse, G., Hafner, J., and Needs, R. J., “Optimized norm-conserving pseudopotentials,” J. Phys. Condens. Matter 4:7451, 1992.Google Scholar
[534] Louie, S. G., Froyen, S., and Cohen, M. L., “Nonlinear ionic pseudopotentials in spin-density-functional calculations,” Phys. Rev. B 26:17381742, 1982.Google Scholar
[535] Hamann, D. R., “Optimized norm-conserving Vanderbilt pseudopotentials,” Phys. Rev. B 88:085117, 2013.Google Scholar
[536] Goedecker, S. and Maschke, K., “Transferability of pseudopotentials,” Phys. Rev. A 45:8893, 1992.Google Scholar
[537] Teter, M., “Additional condition for transferability in pseudopotentials,” Phys. Rev. B 48:5031– 5041, 1993.Google Scholar
[538] Filippetti, A., Vanderbilt, D., Zhong, W., Cai, Y., and Bachelet, G. B., “Chemical hardness, linear response, and pseudopotential transferability,” Phys. Rev. B 52:1179311804, 1995.Google Scholar
[539] Kleinman, L. and Bylander, D. M., “Efficacious form for model pseudopotentials,” Phys. Rev. Lett. 48:14251428, 1982.Google Scholar
[540] Gonze, X., Stumpf, R., and Scheffler, M., “Analysis of separable potentials,” Phys. Rev. B 44:8503, 1991.Google Scholar
[541] van Setten, M.J., Giantomassi, M., Bousquet, E., Verstraete, M. J., Hamann, D. R., Gonze, X., and Rignanese, G.-M., “The pseudodojo: Training and grading a 85 element optimized norm-conserving pseudopotential table,” Comput. Phys. Commun. 226:3954, 2018.Google Scholar
[542] Blöchl, P. E., “Projector augmented-wave method,” Phys. Rev. B 50:1795317979, 1994.Google Scholar
[543] Holzwarth, N. A. W., Matthews, G. E., Tackett, A. R., and Dunning, R. B., “Comparison of the projector augmented-wave, pseudopotential, and linearized augmented-plane-wave formalisms for density-functional calculations of solids,” Phys. Rev. B 55:20052017, 1997.Google Scholar
[544] Kresse, G. and Joubert, D., “From ultrasoft pseudopotentials to the projector augmented-wave method,” Phys. Rev. B 59:17581775, 1999.Google Scholar
[545] Marsman, M. and Kresse, G., “Relaxed core projector-augmented-wave method,” J. Chem. Phys. 125:104101, 2006.Google Scholar
[546] Blöchl, P. E., “The projector augmented wave method: Algortithm and results,” Conference of the Asian Consortium for Computational Materials Science, Bangalore, India, 2001.Google Scholar
[547] Baroni, S. and Resta, R., “Ab initio calculation of the macroscopic dielectric constant in silicon,” Phys. Rev. B 33:7017, 1986.Google Scholar
[548] Hybertsen, M. S. and Louie, S. G., “Ab initio static dielectric matrices from the density-functional approach. I. Formulation and application to semiconductors and insulators,” Phys. Rev. B 35:5585, 1987.Google Scholar
[549] Slichter, C. P., Principles of Magnetic Resonance, 3rd ed., Springer Verlag, Berlin, 1996.Google Scholar
[550] Mauri, F., Pfrommer, B. G., and Louie, S. G., “Ab initio theory of NMR chemical shifts in solids and liquids,” Phys. Rev. Lett. 77:53005303, 1996.Google Scholar
[551] Gregor, T., Mauri, F., and Car, R., “A comparison of methods for the calculation of NMR chemical shifts,” J. Chem. Phys. 111:18151822, 1999.Google Scholar
[552] Bachelet, G. B., Ceperley, D. M., and Chiocchetti, M. G. B., “Novel pseudo-hamiltonian for quantum Monte Carlo simulations,” Phys. Rev. Lett. 62:20882091, 1989.Google Scholar
[553] Foulkes, M. W. C. and Schlüter, M., “Pseudopotentials with position-dependent electron masses,” Phys. Rev. B 42:1150511529, 1990.Google Scholar
[554] Bosin, A., Fiorentini, V., Lastri, A., and Bachelet, G. B., “Local norm-conserving pseudo-hamiltonians,” Phys. Rev. A 52:236, 1995.Google Scholar
[555] Shirley, E. L. and Martin, R. M., “GW quasiparticle calculations in atoms,” Phys. Rev. B 47:1540415412, 1993.Google Scholar
[556] Shirley, E. L. and Martin, R. M., “Many-body core-valence partitioning,” Phys. Rev. B 47:1541315427, 1993.Google Scholar
[557] Dolg, M., Wedig, U., Stoll, H., and Preuss, H., “Energy-adjusted ab initio pseudopotentials for the first row transition elements,” J. Chem. Phys. 86:866872, 1987.Google Scholar
[558] Segall, B., “Energy bands of aluminum,” Phys. Rev. 124:17971806, 1961.Google Scholar
[559] Heine, V., “The band structure of aluminum III. A self-consistent calculation,” Proc. Roy. Soc. (London) A240:361, 1957.Google Scholar
[560] Heine, V. and Weaire, D., in Solid State Physics, edited by Ehrenreich, H., Seitz, F., and Turnbull, D., Academic, New York, 1970, p. 249.Google Scholar
[561] Cohen, M. L. and Chelikowsky, J. R., Electronic Structure and Optical Properties of Semiconductors, 2nd ed., Springer-Verlag, Berlin, 1988.Google Scholar
[562] Ihm, J., Zunger, A., and Cohen, M. L., “Momentum-space formalism for the total energy of solids,” J. Phys. C 12:4409, 1979.Google Scholar
[563] Chiang, T. C., Knapp, J. A., Aono, M., and Eastman, D. E., “Angle-resolved photoemission, valence-band dispersions e(k), and electron and hole lifetimes for GaAs,” Phys. Rev. B 21:35133522, 1980.Google Scholar
[564] Pandey, K. C. and Phillips, J. C., “Nonlocal pseudopotentials for Ge and GaAs,” Phys. Rev. B 9:15521559, 1974.Google Scholar
[565] Yu, P. Y. and Cardona, M., Fundamentals of Semiconductors: Physics and Materials Properties, Springer-Verlag, Berlin, 1996.Google Scholar
[566] Wang, L. W. and Zunger, A., “Solving Schrödinger’s equation around a desired energy: Application to silicon quantum dots,” J. Chem. Phys. 48:23942397, 1994.Google Scholar
[567] Wang, L. W., Kim, J., and Zunger, A., “Electronic structures of [110]-faceted self-assembled pyramidal InAs/GaAs quantum dots,” Phys. Rev. B 59:56785687, 1999.Google Scholar
[568] Beck, T. L., “Real-space mesh techniques in density-functional theory,” Rev. Mod. Phys. 72:10411080, 2000.Google Scholar
[569] Chelikowsky, J. R., Troullier, N., Saad, Y., and Wu, K., “Finite-difference-pseudopotential method: Electronic structure calculations without a basis,” Phys. Rev. Lett. 72:12401243, 1994.Google Scholar
[570] Chelikowsky, J. R., Troullier, N., and Saad, Y., “Higher-order finite-difference pseudopotential method: An application to diatomic molecules,” Phys. Rev. B 50:1135511364, 1994.Google Scholar
[571] Kronik, L., et al., “PARSEC the pseudopotential algorithm for real-space electronic structure calculations: Recent advances and novel applications to nano-structures,” Phys. Stat. Sol. B 243:10631079, 2006.Google Scholar
[572] Saad, Y., Chelikowsky, J., and Shontz, S., “Numerical methods for electronic structure calculations of materials,” SIAM Review 52:354, 2010.Google Scholar
[573] Ghosh, S. and Suryanarayana, P., “SPARC: Accurate and efficient finite-difference formulation and parallel implementation of density functional theory: Extended systems,” Comput. Phys. Commun. 216:109125, 2017.Google Scholar
[574] Fornberg, B. and Sloan, D., in Acta Numerica 94, edited by Iserles, A., Cambridge Press, Cambridge, 1994, pp. 203267.Google Scholar
[575] Chelikowsky, J. R. Vasiliev, I. and Martin, R. M., “Surface oxidation effects on the optical properties of silicon nanocrystals,” Phys. Rev. B 65:121302, 2002.Google Scholar
[576] Briggs, E. L., Sullivan, D. J., and Bernholc, J., “Real-space multigrid-based approach to large-scale electronic structure calculations,” Phys. Rev. B 54:1436214375, 1996.Google Scholar
[577] Collatz, L., The Numerical Treatment of Differential Equations, 3rd ed., Springer-Verlag, Berlin, 1960.Google Scholar
[578] Schofield, G., Chelikowsky, J. R., and Saad, Y., “A spectrum slicing method for the Kohn Sham problem,” Comput. Phys. Commun. 183:497505, 2012.Google Scholar
[579] Lin, L., Lu, J., Ying, L., and Weinan, E. W., “Adaptive local basis set for Kohn Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation,” Journal of Computational Physics 231:21402154, 2012.Google Scholar
[580] Xu, Q., Suryanarayana, P., and Pask, J. E., “Discrete discontinuous basis projection method for large-scale electronic structure calculations,” J. Chem. Phys. 149:094104, 2018.Google Scholar
[581] Brandt, A., “Multi-level adaptive solutions to boundary-value problems,” Mat. Comp. 31:333– 390, 1977.Google Scholar
[582] Briggs, E. L., Sullivan, D. J., and Bernholc, J., “Large-scale electronic-structure calculations with multigrid acceleration,” Phys. Rev. B 52:R5471–R5474, 1995.Google Scholar
[583] Heiskanen, M., Torsti, T., Puska, M. J., and Nieminen, R. M., “Multigrid method for electronic structure calculations,” Phys. Rev. B 63:245106, 2001.Google Scholar
[584] Bernholc, J., Hodak, M., and Lu, W., “Recent developments and applications of the real-space multigrid method,” J. Phys. Condens. Matter 20:294205, 2008.Google Scholar
[585] Pask, J. E. and Sterne, P. A., “Finite element methods in ab initio electronic structure calculations,” Model. Simul. Mater. Sci. Eng. 13:R71–R96, 2005.Google Scholar
[586] Motamarri, P., Das, S., Rudraraju, S., Ghosh, K., Davydov, D., and Gavini, V., “DFT-FE: A massively parallel adaptive finite-element code for large-scale density functional theory calculations,” Comput. Phys. Commun., 246:106853, 2020.Google Scholar
[587] Ghosh, K., Ma, H., Gavini, V., and Galli, G., “All-electron density functional calculations for electron and nuclear spin interactions in molecules and solids,” Phys. Rev. Mater. 3:043801, 2019.Google Scholar
[588] Mohr, S., Ratcliff, L. E., Boulanger, R., Genovese, L., Caliste, D., Deutsch, T., and Goedecker, S., “Daubechies wavelets for linear scaling density functional theory,” J. Chem. Phys. 140:204110, 2014.Google Scholar
[589] Daubechies, I., Ten Lectures on Wavelets, SIAM, Philadelphia, PA, 1992.Google Scholar
[590] Wei, S. and Chou, M. Y., “Wavelets in self-consistent electronic structure calculations,” Phys. Rev. Lett. 76:26502653, 1996.Google Scholar
[591] Cho, K., Arias, A., Joannopoulos, J. D., and Lam, P. K., “Wavelets in electronic structure calculations,” Phys. Rev. Lett. 71:18081811, 1994.Google Scholar
[592] Mohr, S., Ratcliff, L. E., Genovese, L., Caliste, D., Boulanger, R., Goedecker, S., and Deutsch, T., “Accurate and efficient linear scaling dft calculations with universal applicability,” Phys. Chem. Chem. Phys. 17:3136031370, 2015.Google Scholar
[593] Gygi, F., “Electronic-structure calculations in adaptive coordinates,” Phys. Rev. B 48:11692– 11700, 1993.Google Scholar
[594] Hamann, D. R., “Application of adaptive curvilinear coordinates to the electronic structure of solids,” Phys. Rev. B 51:73377340, 1995.Google Scholar
[595] Gygi, F. and Galli, G., “Real-space adaptive-coordinate electronic-structure calculations,” Phys. Rev. B 52:R2229–R2232, 1995.Google Scholar
[596] Modine, N. A., Zumbach, G., and Kaxiras, E., “Adaptive-coordinate real-space electronic-structure calculations for atoms, molecules, and solids,” Phys. Rev. B 55:1028910301, 1997.Google Scholar
[597] Hamann, D. R., “Comparison of global and local adaptive coordinates for density-functional calculations,” Phys. Rev. B 63:075107, 2001.Google Scholar
[598] Mihaly, L. and Martin, M. C., Solid State Physics: Problems and Solutions, 2nd ed., Wiley-VCH, Berlin, Germany, 2009.Google Scholar
[599] Yin, M. T. and Cohen, M. L., “Theory of ab initio pseudopotential calculations,” Phys. Rev. B 25:74037412, 1982.Google Scholar
[600] Herring, W. C. and Nichols, M. H., “Thermionic emission,” Rev. Mod. Phys. 21:185270, 1949.Google Scholar
[601] Kunc, K. and Martin, R. M., “Atomic structure and properties of polar Ge-GaAs(100) interfaces,” Phys. Rev. B 24(6):34453455, 1981.Google Scholar
[602] Wimmer, E., Krakauer, H., Weinert, M., and Freeman, A. J., “Full-potential self-consistent linearized-augmented-plane-wave method for calculating the electronic structure of molecules and surfaces: O2 molecule,” Phys. Rev. B 24:864875, 1981.Google Scholar
[603] Laasonen, K., Car, R., Lee, C., and Vanderbilt, D., “Implementation of ultrasoft pseudopotentials in ab initio molecular dynamics,” Phys. Rev. B 43:6796, 1991.Google Scholar
[604] Gygi, F. and Baldereschi, A., “Self-consistent Hartree–Fock and screened-exchange calculations in solids: Application to silicon,” Phys. Rev. B 34:44054408, 1986.Google Scholar
[605] Chawla, S. and Voth, G. A., “Exact exchange in ab initio molecular dynamics: An efficient plane-wave based algorithm,” J. Chem. Phys. 108:46974700, 1998.Google Scholar
[606] Sorouri, A., Foulkes, W. M. C., and Hine, N. D. M., “Accurate and efficient method for the treatment of exchange in a plane-wave basis,” J. Chem. Phys. 124:064105, 2006.Google Scholar
[607] Wu, X., Selloni, A., and Car, R., “Order-N implementation of exact exchange in extended insulating systems,” Phys. Rev. B 79:085102, 2009.Google Scholar
[608] Kunc, K. and Martin, R. M., “Ab initio force constants in GaAs: A new approach to calculation of phonons and dielectric properties,” Phys. Rev. Lett. 48(6):406409, 1982.Google Scholar
[609] Yin, M. T. and Cohen, M. L., “Ab initio calculation of the phonon dispersion relation: Application to Si,” Phys. Rev. B 25:43174320, 1982.Google Scholar
[610] Wei, S. and Chou, M. Y., “Ab initio calculation of force constants and full phonon dispersions,” Phys. Rev. Lett. 69:27992802, 1992.Google Scholar
[611] Marzari, N. and Singh, D. J., “Dielectric response of oxides in the wieghted density approximation,” Phys. Rev. B 62:1272412729, 2000.Google Scholar
[612] Meunier, V., Roland, C., Bernholc, J., and Buongiorno Nardelli, M., “Electronic and field emission properties of boron nitride/carbon nanotube superlattices,” Appl. Phys. Lett. 81:46, 2002.Google Scholar
[613] Slater, J. C. and Koster, G. F., “Simplified LCAO method for the periodic potential problem,” Phys. Rev. 94:14981524, 1954.Google Scholar
[614] Jones, H., Mott, N., and Skinner, “A theory of the form of the X-ray emission bands of metals,” Phys. Rev. 45:379, 1934.Google Scholar
[615] Harrison, W. A., Elementary Electronic Structure, World Publishing, Singapore, 1999.Google Scholar
[616] Papaconstantopoulos, D. A., Handbook of Electronic Structure of Elemental Solids, Plenum, New York, 1986.Google Scholar
[617] Stiles, M. D., “Generalized Slater-Koster method for fitting band structures,” Phys. Rev. B 55:41684173, 1997.Google Scholar
[618] Louie, S. G., in Carbon Nanotubes, edited by Dresselhaus, M. S., Dresselhaus, G., and Ph. Avouris, Springer-Verlag, Berlin, 2001, pp. 113145.Google Scholar
[619] Xu, C. H., Wang, C. Z., Chan, C. T., and Ho, K. M., “A transferable tight-binding potential for carbon,” J. Phys. Condens. Matter 4:6047, 1992.Google Scholar
[620] Blase, X., Benedict, L. X., Shirley, E. L., and Louie, S. G., “Are fullerene tubules metallic?,” Phys. Rev. Lett 72:18781881, 1994.Google Scholar
[621] Machon, M., Reich, S., Thomsen, C., Sanchez-Portal, D., and Ordejon, P., “Ab initio calculations of the optical properties of 4-a-diameter single-walled nanotubes,” Phys. Rev. B 66:155410, 2002.Google Scholar
[622] Papaconstantopoulos, D. A., Mehl, M. J., Erwin, J. C., and Pederson, M. R., in Tight-Binding Approach to Computational Materials Science, edited by Turchi, P. E. A., Gonis, A., and Columbo, L., Materials Research Society, Warrendale, PA, 1998.Google Scholar
[623] Rubio, A., Corkill, J. L., and Cohen, M. L., “Theory of graphitic boron nitride nanotubes,” Phys. Rev. B 49:50815084, 1994.Google Scholar
[624] Chopra, N. G., Luyken, R. J., Cherrey, K., Crespi, V. H., Cohen, M. L., Louie, S. G., and Zettl, A., “Boron nitride nanotubes,” Science 269:966, 1995.Google Scholar
[625] Mele, E. J. and Kral, P., “Electric polarization of heteropolar nanotubes as a geometric phase,” Phys. Rev. Lett. 88:056803, 2002.Google Scholar
[626] Hybertsen, M. S., Schlüter, M., and Christensen, N. E., “Calculation of Coulomb interaction parameters for La2 CuO4 using a constrained-density-functional approach,” Phys. Rev. B 39:9028, 1989.Google Scholar
[627] Vogl, P., Hjalmarson, H. P., and Dow, J. D., “A semi-empirical tight-binding theory of the electronic structure of semiconductors,” Europhys. Lett. 44:365, 1983.Google Scholar
[628] Papaconstantopoulos, D. A., Handbook of the Band Structure of Elemental Solids: From Z = 1 to Z = 112, 2nd ed. Springer, New York, 2015.Google Scholar
[629] Shi, L. and Papaconstantopoulos, D. A., “Modifications and extensions to Harrison’s tight-binding theory,” Phys. Rev. B 70:205101, 2004.Google Scholar
[630] Sankey, O. F. and Niklewski, D. J., “Ab initio multicenter tight-binding model for molecular-dynamics simulations and other applications in covalent systems,” Phys. Rev. B 40:3979, 1989.Google Scholar
[631] Cohen, R. E., Mehl, M. J., and Papaconstantopoulos, D. A., “Tight-binding total-energy method for transition and noble metals,” Phys. Rev. B 50:1469414697, 1994.Google Scholar
[632] Porezag, D., Frauenheim, Th., Köhler, Th., Seifert, G., and Kaschner, R., “Construction of tight-binding-like potentials on the basis of density-functional theory: Application to carbon,” Phys. Rev. B 51:1294712957, 1995.Google Scholar
[633] Goodwin, L., Skinner, A. J., and Pettifor, D. G., “Generating transferable tight-binding parameters – Application to silicon,” Europhys. Lett. 9:701, 1989.Google Scholar
[634] Kwon, I., Biswas, R., Wang, C. Z., Ho, K. M., and Soukoulis, C. M., “Transferable tight-binding models for silicon,” Phys. Rev. B 49:7242, 1994.Google Scholar
[635] Lenosky, T. J., Kress, J. D., Kwon, I., Voter, A. F., Edwards, B., Richards, D. F., Yang, S., and Adams, J. B., “Highly optimized tight-binding model of silicon,” Phys. Rev. B 55:15281544, 1997.Google Scholar
[636] Wang, C. Z., Pan, B C, and Ho, K. M., “An environment-dependent tight-binding potential for Si,” J. Phys. Condens. Matter 11:2043–2049, 1999.Google Scholar
[637] Kim, J., Wilkins, J. W., Khan, F. S., and Canning, A., “Extended Si [311] defects,” Phys. Rev. B 55:16186, 1997.Google Scholar
[638] Kim, J., Kirchhoff, F., Wilkins, J. W., and Khan, F. S., “Stability of Si-interstitial defects: From point to extended defects,” Phys. Rev. Lett. 84:503, 2000.Google Scholar
[639] Bernstein, N., Mehl, M. J., Papaconstantopoulos, D. A., Papanicolaou, N. I., Bazant, M. Z., and Kaxiras, E., “Energetic, vibrational, and electronic properties of silicon using a nonorthogonal tight-binding model,” Phys. Rev. B 62:44774487, 2000.Google Scholar
[640] Bacalis, N. C., Papaconstantopoulos, D. A., Mehl, M. J., and Lach-hab, M., “Transferable tight-binding parameters for ferromagnetic and paramagnetic iron,” Physica B 296:125129, 2001.Google Scholar
[641] Jensen, F., An Introduction to Computational Chemistry, John Wiley & Sons, New York, 1998.Google Scholar
[642] Cramer, C. J., Essentials of Computational Chemistry: Theories and Models, Wiley, New York, 2002.Google Scholar
[643] Eschrig, H., Optimized LCAO Methods, Springer, Berlin, 1987.Google Scholar
[644] Orlando, R., Dovesi, R., Roetti, C., and Saunders, V. R., “Ab initio Hartree–Fock calculations for periodic compounds: application to semiconductors,” J. Phys. Condens. Matter 2:7769, 1990.Google Scholar
[645] Saunders, V. R., Dovesi, R., Roetti, C., Causa, M., Harrison, N. M., Orlando, R., and Zicovich-Wilson, C. M., CRYSTAL User’s Manual (University of Torino, Torino). See http://www.theochem.unito.it/, 2003.Google Scholar
[646] Soler, J. M., Artacho, E., Gale, J., Garcia, A., Junquera, J., Ordejon, P., and Sanchez-Portal, D., “The SIESTA method for ab intio order-N materials simulations,” J. Phys. Condens. Matter 14:27452779, 2002.Google Scholar
[647] Boys, S. F., “Electron wave functions I. A general method for calculation for the stationary states of any molecular system,” Proc. R. Soc. Lond. A 200:542, 1950.Google Scholar
[648] Shao, Y. H., White, C. A., and Head-Gordon, M., “Efficient evaluation of the Coulomb force in density-functional theory calculations,” J. Chem. Phys. 114:65726577, 2001.Google Scholar
[649] Perry, J. K., Tahir-Kheli, J., and Goddard, W. A., “Antiferromagnetic band structure of La2 CuO4 : Becke-3-Lee-Yang-Parr calculations,” Phys. Rev. B 63:144510, 2001.Google Scholar
[650] Kudin, K. N., Scuseria, G. E., and Martin, R. L., “Hybrid density-functional theory and the insulating gap of UO2 ,” Phys. Rev. Lett. 89:266402, 2002.Google Scholar
[651] Rohlfing, M., Krüger, P., and Pollmann, J., “Quasiparticle band structures of clean, hydrogen-and sulfur-terminated Ge(001) surfaces,” Phys. Rev. B 54:1375913766, 1996.Google Scholar
[652] Scuseria, G. E., “Linear scaling density functional calculations with gaussian orbitals,” J. Phys. Chem. A 103:47824790, 1999.Google Scholar
[653] Delley, B., “An all-electron numerical method for solving the local density functional for polyatomic molecules,” J. Chem. Phys. 92:508517, 1990.Google Scholar
[654] Koepernik, K. and Eschrig, H., “Full-potential nonorthogonal local-orbital minimum-basis band-structure scheme,” Phys. Rev. B 59:17431757, 2000.Google Scholar
[655] Delley, B., “From molecules to solids with the DMol3 approach,” J. Chem. Phys. 113:7756–7764, 2000.Google Scholar
[656] Junquera, J., Paz, O., Sanchez-Portal, D., and Artacho, E., “Numerical atomic orbitals for linear-scaling calculations,” Phys. Rev. B 64:235111, 2001.Google Scholar
[657] Pederson, M. R. and Jackson, K. A., “Variational mesh for quantum-mechanical simulations,” Phys. Rev. B 41:74537461, 1990.Google Scholar
[658] Becke, A. D., “A multicenter numerical integration scheme for polyatomic molecules,” J. Chem. Phys. 88:25472553, 1988.Google Scholar
[659] Ordejón, P., Artacho, E., and Soler, J. M., “Selfconsistent order-N density-functional calculations for very large systems,” Phys. Rev. B 53:R10441–R10444, 1996.Google Scholar
[660] Baraff, G. A. and Schluter, M., “Self-consistent Green’s-function calculation of the ideal Si vacancy,” Phys. Rev. Lett. 41:892, 1978.Google Scholar
[661] Bernholc, J., Lipari, N. O., and Pantelides, S. T., “Self-consistent method for point defects in semiconductors: Application to the vacancy in silicon,” Phys. Rev. Lett. 41:895, 1978.Google Scholar
[662] Feibelman, P. J., “First-principles total-energy calculation for a single adatom on a crystal,” Phys. Rev. Lett. 54:26272630, 1985.Google Scholar
[663] Feibelman, P. J., “Force and total-energy calculations for a spatially compact adsorbate on an extended, metallic crystal surface,” Phys. Rev. B 35:26262646, 1987.Google Scholar
[664] Louie, S. G., Ho, K.-M., and Cohen, M. L., “Self-consistent mixed-basis approach to the electronic structure of solids,” Phys. Rev. B 19:17741782, 1979.Google Scholar
[665] Li, G. and Chang, Y., “Planar-basis pseudopotential calculations of the Si(001)2 x 1 surface with and without hydrogen passivation,” Phys. Rev. B 48:1203212036, 1993.Google Scholar
[666] Loucks, T., The Augmented Plane Wave Method, Benjamin, New York, 1967.Google Scholar
[667] Dimmock, J. O., in Solid State Physics, vol. 26, edited by Ehenreich, H., Seitz, F., and Turnbull, D., Academic Press, New York, 1971, pp. 104274.Google Scholar
[668] Chodorow, M. I., “Energy band structure of copper,” Phys. Rev. 55:675, 1939.Google Scholar
[669] Burdick, G. A., “Energy band structure of copper,” Phys. Rev. 129:138150, 1963.CrossRefGoogle Scholar
[670] Thiry, P., Chandesris, D., Lecante, J., Guillot, C., Pinchaux, R., and Petroff, Y., “E vs k and inverse lifetime of Cu(110),” Phys. Rev. Lett. 43:8285, 1979.Google Scholar
[671] Mattheiss, L. F., “Energy bands for the iron transition series,” Phys. Rev. 134:A970–A973, 1964.CrossRefGoogle Scholar
[672] Slater, J. C., “Magnetic effects and the Hartree–Fock equation,” Phys. Rev. 82:538541, 1951.Google Scholar
[673] Kübler, J., Theory of Itinerant Electron Magnetism, Oxford University Press, Oxford, 2001.Google Scholar
[674] Heine, V., “s–d interaction in transition metals,” Phys. Rev. 153:673682, 1967.Google Scholar
[675] Connolly, J. W. D., “Energy bands in ferromagnetic nickel,” Phys. Rev. 159:415, 1967.CrossRefGoogle Scholar
[676] Ziman, J., in Solid State Physics, vol. 26, edited by Ehenreich, H., Seitz, F., and Turnbull, D., Academic Press, New York, 1971, pp. 1101.Google Scholar
[677] Korringa, J., “On the calculation of the energy of a Bloch wave in a metal,” Physica 13:392, 1947.Google Scholar
[678] Kohn, W. and Rostocker, N., “Solution of the Schrodinger equation in periodic lattices with an application to metallic lithium,” Phys. Rev. 94:1111, 1954.Google Scholar
[679] Strutt [Lord Rayleigh], J. W., “On the influence of obstacles arranged in rectangular order upon the properties of a medium,” Phil. Mag. Series 5 34:481–502, 1892.Google Scholar
[680] Zeller, R., Dederichs, P. H., Ujfalussy, B., Szunyog, L., and Weinberger, P., “Theory and convergence properties of the screened Korringa–Kohn–Rostoker method,” Phys. Rev. B 52:88078812, 1995.Google Scholar
[681] Huhne, T., Zecha, C., Ebert, H., Dederichs, P. H., and Zeller, R., “Full-potential spin-polarized relativistic Korringa–Kohn–Rostoker method implemented and applied to bcc Fe, fcc Co, and fcc Ni,” Phys. Rev. B 58:10236, 1998.Google Scholar
[682] Butler, W. H., Dederichs, P. H., Gonis, A., and Weaver, R. L., Applications of Multiple Scattering Theory to Material Science, Materials Research Society, Pittsburg, Penn., 1992.Google Scholar
[683] Economou, E.N., Green’s Functions in Quantum Physics, 2nd ed., Springer-Verlag, Berlin, 1992.Google Scholar
[684] Lloyd, P. and Smith, P. V., “Multiple scattering theory in condensed materials,” Adv. Phys. 21:29, 1972.Google Scholar
[685] Gyorffy, B. L., in Applications of Multiple Scattering Theory to Material Science, edited by Butler, W. H., Dederichs, P. H., Gonis, A., and Weaver, R. L., Materials Research Society, Pittsburgh, PA, 1992, pp. 525.Google Scholar
[686] Lloyd, P., “Wave propagation through an assembly of spheres II: The density of single particle eigenstates,” Proc. Phys. Soc, London 90:207–216, 1967.Google Scholar
[687] Müller, S. and Zunger, A., “Structure of ordered and disordered alpha-brass,” Phys. Rev. B 63:094204, 2001.CrossRefGoogle Scholar
[688] Sovesn, P., “Coherent-potential model of substitutional disordered alloys,” Phys. Rev. 156:809– 813, 1967.Google Scholar
[689] Velicky, B., Kirkpatrick, S., and Ehrenreich, H., “Single-site approximations in the electronic theory of simple binary alloys,” Phys. Rev. 175:747766, 1968.Google Scholar
[690] Lax, M., “Multiple scattering of waves,” Rev. Mod. Phys. 23:287310, 1951.Google Scholar
[691] Beeby, J. L., “Electronic structure of alloys,” Phys. Rev. 135:A130, 1964.Google Scholar
[692] Stocks, G. M., Temmerman, W. M., and Gyorffy, B. L., “Complete solution of the Korringa– Kohn–Rostocker coherent-potential-approximation equations: Cu–Ni alloys,” Phys. Rev. Lett. 41:339343, 1978.Google Scholar
[693] Faulkner, J. S. and Stocks, G. M., “Calculating properties with the coherent-potential approximation,” Phys. Rev. B 21:32223244, 1980.Google Scholar
[694] Butler, W. H., “Theory of electronic transport in random alloys: Korringa–Kohn–Rostoker coherent-potential approximation,” Phys. Rev. B 31:3260, 1985.CrossRefGoogle ScholarPubMed
[695] Johnson, D. D., Nicholson, D. M., Pinski, F. J., Gyorffy, B. L., and Stocks, G. M., “Total-energy and pressure calculations for random substitutional alloys,” Phys. Rev. B 41:97019716, 1990.Google Scholar
[696] Tatarchenko, A. F., Stepanyuk, V. S., Hergert, W., Rennert, P., Zeller, R., and Dederichs, P. H., “Total energy and magnetic moments in disordered Fex Cu1−x alloys,” Phys. Rev. B 57:52135219, 1998.Google Scholar
[697] Staunton, J. B., Poulter, J., Ginatempo, B., Bruno, E., and Johnson, D. D., “Incommensurate and commensurate antiferromagnetic spin fluctuations in Cr and Cr alloys from ab initio dynamical spin susceptibility calculations,” Phys. Rev. Lett. 82:33403343, 1999.CrossRefGoogle Scholar
[698] Andersen, O. K., in Computational Methods in Band Theory, edited by Marcus, P. M., Janak, J. F., and Williams, A. R., Plenum, New York, 1971, p. 178.Google Scholar
[699] Skriver, H., The LMTO Method, Springer, New York, 1984.Google Scholar
[700] Andersen, O. K., “Linear methods in band theory,” Phys. Rev. B 12:30603083, 1975.Google Scholar
[701] Andersen, O. K. and Jepsen, O., “Explicit, first-principles tight-binding theory,” Phys. Rev. Lett. 53:25712574, 1984.Google Scholar
[702] Keller, J., “Modified muffin tin potentials for the band structure of semiconductors,” J. Phys. C: Solid State Phys. 13:L85–L87, 1980.Google Scholar
[703] Glötzel, D., Segall, B., and Andersen, O. K., “Self-consistent electronic structure of Si, Ge and diamond LMTO-ASA method,” Solid State Commun. 36:403, 1980.Google Scholar
[704] Wang, Y., Stocks, G. M., Shelton, W. A., Nicholson, D. M. C., Szotec, Z., and Temmerman, W. M., “Order-N multiple scattering approach to electronic structure calculations,” Phys. Rev. Lett. 75:28672870, 1995.Google Scholar
[705] Andersen, O. K., Pawlowska, Z., and Jepsen, O., “Illustration of the LMTO tight-binding representation: Compact orbitals and charge density in Si,” Phys. Rev. B 34:52535269, 1986.Google Scholar
[706] Soler, J. M. and Williams, A. R., “Augmented-plane-wave forces,” Phys. Rev. B 42:97289731, 1990.Google Scholar
[707] Yu, R., Singh, D., and Krakauer, H., “All-electron and pseudopotential force calculations using the linearized-augmented-plane-wave method,” Phys. Rev. B 93:64116422, 1991.Google Scholar
[708] Mishra, S. and Satpathy, S., “Kronig-penny model with the tail-cancellation method,” Am. J. Phys. 69:512513, 2001.Google Scholar
[709] Singh, D. J., Planewaves, Pseudopotentials, and the APW Method, Kluwer Academic Publishers, Boston, 1994, and references therein.Google Scholar
[710] Williams, A. R., Kübler, J., and Jr. Gelatt, C. D., “Cohesive properties of metallic compounds: Augmented-spherical-wave calculations,” Phys. Rev. B 19:6094–6118, 1979.Google Scholar
[711] Koelling, D. D. and Arbman, G. O., “Use of energy derivative of the radial solution in an augmented plane wave method: application to copper,” J. Phys. F: Met. Phys. 5:20412054, 1975.Google Scholar
[712] Krakauer, H., Posternak, M., and Freeman, A. J., “Linearized augmented plane-wave method for the electronic band structure of thin films,” Phys. Rev. B 19:17061719, 1979.Google Scholar
[713] Weinert, M., Wimmer, E., and Freeman, A. J., “Total-energy all-electron density functional method for bulk solids and surfaces,” Phys. Rev. B 26:45714578, 1982.Google Scholar
[714] Mattheiss, L. F. and Hamann, D. R., “Linear augmented-plane-wave calculation of the structural properties of bulk Cr, Mo, and W,” Phys. Rev. B 33:823840, 1986.Google Scholar
[715] Blaha, P., Schwarz, K., Sorantin, P., and Tsrickey, S.B., “Full-potential, linearized augmented plane wave programs for crystalline systems,” Comput. Phys. Commun. 59(2):399, 1990.Google Scholar
[716] Pickett, W. E., “Electronic structure of the high-temperature oxide superconductors,” Rev. Mod. Phys. 61:433, 1989.Google Scholar
[717] Jansen, H. J. F. and Freeman, A. J., “Total-energy full-potential linearized augmented-plane-wave method for bulk solids: Electronic and structural properties of tungsten,” Phys. Rev. B 30:561569, 1984.Google Scholar
[718] Cohen, R. E., Pickett, W. E., and Krakauer, H., “Theoretical determination of strong electron– phonon coupling in YBa2 Cu3 O7,” Phys. Rev. Lett. 64:25752578, 1990.Google Scholar
[719] Krakauer, H., Pickett, W. E., and Cohen, R., “Analysis of electronic structure and charge density of the high-temperature superconductor YBa2 Cu3 O7,” J. Superconductivity 1:111, 1988.Google Scholar
[720] Methfessel, M., “Elastic constants and phonon frequencies of Si calculated by a fast full-potential linear-muffin-tin-orbital method,” Phys. Rev. B 38:1537, 1988.Google Scholar
[721] Methfessel, M., Rodriguez, C. O., and Andersen, O. K., “Fast full-potential calculations with a converged basis of atom-centered linear muffin-tin orbitals: Structural and dynamic properties of silicon,” Phys. Rev. B 40:2009, 1989.Google Scholar
[722] Methfessel, M. and van Schilfgaarde, M., in Electronic Strcuture and Physical Properties of Solids: The Uses of the LMTO Method, edited by Dreysse, H., Springer, Heidelberg, 1999, pp. 114147.Google Scholar
[723] Jepsen, O., Andersen, O. K., and Mackintosh, A. R., “Electronic structure of hcp transition metals,” Phys. Rev. B 12:30843103, 1977.Google Scholar
[724] Fujiwara, T., “Electronic structure calculations for amorphous alloys,” J. Non-crystalline Solids 61-62:1039–48, 1984.Google Scholar
[725] Nowak, H. J., Andersen, O. K., Fujiwara, T., Jepsen, O., and Vargas, P., “Electronic-structure calculations for amorphous solids using the recursion method and linear muffin-tin orbitals: Application to Fe80 B20,” Phys. Rev. B 44:35773598, 1991.Google Scholar
[726] Bose, S. K., Jepsen, O., and Andersen, O. K., “Real-space calculation of the electrical resistivity of liquid 3d transition metals using tight-binding linear muffin-tin orbitals,” Phys. Rev. B 48:42654275, 1993.Google Scholar
[727] Bachelet, G. B. and Christensen, N. E., “Relativistic and core-relaxation effects on the energy bands of gallium arsenide and germanium,” Phys. Rev. B 31:879887, 1985.Google Scholar
[728] Satpathy, S. and Pawlowska, Z., “Construction of bond-centered Wannier functions for silicon bands,” Phys. Stat. Sol. (b) 145:555–565, 1988.Google Scholar
[729] Christensen, N. E., “Dipole effects and band offsets at semiconductor interfaces,” Phys. Rev. B 37:4528, 1988.Google Scholar
[730] Lambrecht, W. R. L., Segall, B., and Andersen, O. K., “Self-consistent dipole theory of heterojunction band offsets,” Phys. Rev. B 41:2813, 1990.Google Scholar
[731] Duthi, J. C. and Pettifor, D. G., “Correlation between d-band occupancy and crystal structure in the rare earths,” Phys. Rev. Lett. 38:564567, 1977.Google Scholar
[732] Haydock, R., in Recursion Method and Its Applications, edited by Pettifor, D. G. and Weaire, D. L., Springer-Verlag, Berlin, 1985.Google Scholar
[733] Friedel, J., “Electronic structure of primary solid solutions in metals,” Adv. Phys. 3:446, 1954.Google Scholar
[734] Andersen, O. K., Saha-Dasgupta, T., Tank, R., Arcangeli, C., Jepsen, O., and Krier, G., in Electronic Structure and Physical Properties of Solids, edited by Dreysse, H., Springer, Berlin, 1998, pp. 384.Google Scholar
[735] Andersen, O. K. and Saha-Dasgupta, T., “Muffin-tin orbitals of arbitrary order,” Phys. Rev. B 62:R16219–R16222, 2000.Google Scholar
[736] Weyrich, K. H., “Full-potential linear muffin-tin-orbital method,” Phys. Rev. B 37:10269– 10282, 1988.Google Scholar
[737] Greengard, L., “Fast algorithms for classical physics,” Science 265:909914, 1994.Google Scholar
[738] Fulde, P., Electron Correlation in Molecules and Solids, 2nd ed., Springer-Verlag, Berlin, 1993.Google Scholar
[739] Bowler, D. R. and Miyazaki, T., “O(N) methods in electronic structure calculations,” Rep. Prog. Phy. 75:036503, 2012.Google Scholar
[740] Gordon, Mark S., Fedorov, Dmitri G., Pruitt, Spencer R., and Slipchenko, Lyudmila V., “Fragmentation methods: A route to accurate calculations on large systems,” Chem. Rev. 112:632–672, 2012.Google Scholar
[741] Cole, D. J. and Nicholas D., M. Hine, , “Applications of large-scale density functional theory in biology,” J. Phys. Condens. Matter 28:393001, 2016.Google Scholar
[742] Kohn, W., “Density functional and density matrix method scaling linearly with the number of atoms,” Phys. Rev. Lett. 76:31683171, 1996.Google Scholar
[743] Aarons, J., Sarwar, M., Thompsett, D., and Skylaris, C.-K., “Perspective: Methods for large-scale density functional calculations on metallic systems,” J. Chem. Phys. 145:220901, 2016.Google Scholar
[744] Baer, R. and Head-Gordon, M., “Sparsity of the density matrix in Kohn–Sham density functional theory and an assessment of linear system-size scaling methods,” Phys. Rev. Lett. 79:39623965, 1997.Google Scholar
[745] Hierse, W. and Stechel, E., “Order-N methods in self-consistent density-functional calculations,” Phys. Rev. B 50:1781117819, 1994.CrossRefGoogle ScholarPubMed
[746] Yang, W. T., “Absolute-energy-minimum principles for linear-scaling electronic-structure calculations,” Phys. Rev. B 56:92949297, 1997.Google Scholar
[747] Ankudinov, A. L., Bouldin, C. E., Rehr, J. J., Sims, J., and Hung, H., “Parallel calculation of electron multiple scattering using Lanczos algorithms,” Phys. Rev. B 65:104107, 2002.Google Scholar
[748] Galli, G. and Parrinello, M., in Computer Simulations in Material Science, edited by Meyer, M. and Pontikis, V., Kluwer, Dordrecht, 1991, pp. 283304.Google Scholar
[749] Goringe, C. M., Bowler, D. R., and Hernandez, E., “Tight-binding modelling of materials,” Rep. Prog. Phys. 60:14471512, 1997.Google Scholar
[750] Pettifor, D. G., “New many-body potential for the bond order,” Phys. Rev. Lett. 63:24802483, 1989.Google Scholar
[751] Aoki, M., “Rapidly convergent bond order expansion for atomistic simulations,” Phys. Rev. Lett. 71:3842, 1993.Google Scholar
[752] Horsfield, A. P., “A comparison of linear scaling tight-binding methods,” Mater. Sci. Eng. 5:199, 1996.Google Scholar
[753] Haydock, R., in Solid State Physics, vol. 35, edited by Ehenreich, H., Seitz, F., and Turnbull, D., Academic Press, New York, 1980, p. 1.Google Scholar
[754] Haydock, R., Heine, V., and Kelly, M. J., “Electronic structure based on the local atomic environment for tight-binding bands: II,” J. Phys. C 8:25912605, 1975.Google Scholar
[755] Drabold, D. A., Ordejon, P., Dong, J. J., and Martin, R. M., “Spectral properties of large fullerenes: from cluster to crystal,” Solid State Commun. 96:833, 1995.Google Scholar
[756] Xu, C. H. and Scuseria, G., “An O(N) tight-binding study of carbon clusters up to C8640 : The geometrical shape of the giant icosahedral fullerenes,” Chem. Phys. Lett. 262:219, 1996.Google Scholar
[757] Drabold, D. A. anf Sankey, O. F., “Maximum entropy approach for linear scaling in the electronic structure problem,” Phys. Rev. Lett. 70:3631–3634, 1993.Google Scholar
[758] Ordejón, P., Drabold, D. A., Martin, R. M., and Itoh, S., “Linear scaling method for phonon calculations from electronic structure,” Phys. Rev. Lett. 75:13241327, 1995.Google Scholar
[759] Yang, W. T., “Direct calculation of electron density in density functional theory,” Phys. Rev. Lett. 66:14381441, 1991.CrossRefGoogle ScholarPubMed
[760] Goedecker, S. and Colombo, L., “Efficient linear scaling algorithm for tight-binding molecular dynamics,” Phys. Rev. Lett. 73:122125, 1994.Google Scholar
[761] Voter, A. F., Kress, J. D., and Silver, R. N., “Linear-scaling tight binding from a truncated-moment approach,” Phys. Rev. B 53:1273312741, 1996.Google Scholar
[762] Silver, R. N. and Roder, H., “Calculation of densities of states and spectral functions by Chebyshev recursion and maximum entropy,” Phys. Rev. E 56:48224829, 1997.Google Scholar
[763] Goedecker, S., “Low complexity algorithms for electronic structure calculations,” J. Comp. Phys. 118, 1995.Google Scholar
[764] Jovanovic, D. and Leburton, J. P., “Self-consistent analysis of single-electron charging effects in quantum-dot nanostructures,” Phys. Rev. B 49:7474, 1994.Google Scholar
[765] Parrinello, A. Alavi, and Frenkel, D., “Ab initio calculation of the sound velocity of dense hydrogen: Implications for models of Jupiter,” Science 269:1252–4, 1995.Google Scholar
[766] Corkill, J. L. and Ho, K. M., “Electronic occupation functions for density-matrix tight-binding methods,” Phys. Rev. B 54:53405345, 1996.Google Scholar
[767] Li, X.-P., Nunes, R. W., and Vanderbilt, D., “Density-matrix electronic-structure method with linear system-size scaling,” Phys. Rev. B 47:1089110894, 1993.Google Scholar
[768] Mauri, F., Galli, G., and Car, R., “Orbital formulation for electronic structure calculation with linear system-size scaling,” Phys. Rev. B 47:99739976, 1993.Google Scholar
[769] Ordejón, P., Drabold, D. A., Grumbach, M. P., and Martin, R. M., “Unconstrained minimization approach for electronic computations that scales linearly with system size,” Phys. Rev. B 48:1464614649, 1993.Google Scholar
[770] Kim, J., Mauri, F., and Galli, G., “Total-energy global optimizations using nonorthogonal localized orbitals,” Phys. Rev. B 52:16401648, 1995.Google Scholar
[771] Nunes, R. W. and Vanderbilt, D., “Generalization of the density-matrix method to a nonorthogonal basis,” Phys. Rev. B 50:1761117614, 1994.Google Scholar
[772] Itoh, S., Ordejón, P., Drabold, D., and Martin, R. M., “Structure and energetics of giant fullerenes: An order-N molecular dynamics study,” Phys. Rev. B 53:21322140, 1996.Google Scholar
[773] Qiu, S. Y., Wang, C. Z., Ho, K. M., and Chan, C. T., “Tight-binding molecular dynamics with linear system-size scaling,” J. Phys. Condens. Matter 6:9153, 1994.Google Scholar
[774] Liu, S., Perez-Jorda, J. M., and Yang, W., “Nonorthogonal localized molecular orbitals in electronic structure theory,” J. Chem. Phys. 112:1634, 2000.Google Scholar
[775] Stechel, E. B., Williams, A. R., and Feibelman, P. J., “N-scaling algorithm for density-functional calculations of metals and insulators,” Phys. Rev. B 49:1008810101, 1994.Google Scholar
[776] Press, W. H. and Teukolsky, S. A., Numerical Recipes, Cambridge University Press, Cambridge, 1992.Google Scholar
[777] Stephan, U. and Drabold, D. A., “Order-N projection method for first-principles computations of electronic quantities and Wannier functions,” Phys. Rev. B 57:63916407, 1998.Google Scholar
[778] Stephan, U., Drabold, D. A., and Martin, R. M., “Improved accuracy and acceleration of variational order-N electronic-structure computations by projection techniques,” Phys. Rev. B 58:1347213481, 1998.Google Scholar
[779] Stephan, U., Martin, R. M., and Drabold, D. A., “Extended-range computation of Wannier-like functions in amorphous semiconductors,” Phys. Rev. B 62:68856888, 2000.Google Scholar
[780] de Pablo, P. J., Moreno-Herrero, F., Colchero, J., Herrero, J. G., Herrero, P., Baro, A. M., Ordejon, P., Soler, J. M., and Artacho, E., “Absence of DC-conductivity in lambda-DNA,” Phys. Rev. Lett. 85:49924995, 2000.Google Scholar
[781] Hernandez, E. and Gillan, M. J., “Self-consistent first-principles technique with linear scaling,” Phys. Rev. B 51:1015710160, 1995.Google Scholar
[782] Fattebert, J.-L. and Bernholc, J., “Towards grid-based O(N) density-functional theory methods: Optimized nonorthogonal orbitals and multigrid acceleration,” Phys. Rev. B 62:1713–1722, 2000.Google Scholar
[783] Haynes, P. D. and Payne, M. C., “Localized spherical-wave basis set for O(N) total energy pseudopotential calculations,” Comput. Phys. Commun. 102:1727, 1997.Google Scholar
[784] Marx, D. and Hutter, J., Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods, Cambridge University Press, Cambridge, UK, 2009.Google Scholar
[785] Payne, M. C., Joannopoulos, J. D., Allan, D. C., Teter, M. P., and Vanderbilt, D. M., “Molecular dynamics and ab initio total energy calculations,” Phys. Rev. Lett. 56:2656, 1986.Google Scholar
[786] Sankey, O. F. and Allen, R. E., “Atomic forces from electronic energies via the Hellmann-Feynman theorem, with application to semiconductor (110) surface relaxation,” Phys. Rev. B 33:71647171, 1986.Google Scholar
[787] Thijssen, J. M., Computational Physics, Cambridge University Press, Cambridge, U.K., 2000.Google Scholar
[788] Ryckaert, J. P., Ciccotti, G., and Berendsen, H. J. C., “Numerical integration of the cartesian equations of motion of a system with constraints: Molecular dynamics of n-alkanes,” J. Comput. Phys. 23:327, 1977.Google Scholar
[789] Car, R. and Parrinello, M., in Simple Molecular Systems at Very High Density, edited by Polian, A., Loubeyre, P., and Boccara, N., Plenum, New York, 1989, p. 455.Google Scholar
[790] Remler, D. K. and Madden, P. A., “Molecular dynamics without effective potentials via the Car-Parrinello approach,” Mol. Phys. 70:921, 1990.Google Scholar
[791] Pastore, G., Smargiassi, E., and Buda, F., “Theory of ab initio molecular-dynamics calculations,” Phys. Rev. A 44:6334, 1991.Google Scholar
[792] Payne, M. C., “Error cancellation in the molecular dynamics method for total energy calculations,” J. Phys. Condens. Matter 1:21992210, 1989.Google Scholar
[793] Car, R., Parrinello, M., and Payne, M., “Comment on ‘error cancellation in the molecular dynamics method for total energy calculations,” J. Phys. Condens. Matter 3:95399543, 1991.Google Scholar
[794] Grumbach, M. P. and Martin, R. M., “Phase diagram of carbon at high pressures and temperatures,” Phys. Rev. B 54:1573015741, 1996.Google Scholar
[795] Tuckerman, M. E. and Parrinello, M., “Integrating the Car-Parrinello equations. I. Basic integration techniques,” J. Chem. Phys. 101:1302, 1994.Google Scholar
[796] Tuckerman, M. E. and Parrinello, M., “Integrating the Car-Parrinello equations. II. Multiple time scale techniques,” J. Chem. Phys. 101:1316, 1994.Google Scholar
[797] Galli, G., Martin, R. M., Car, R., and Parrinello, M., “Ab initio calculation of properties of carbon in the amorphous and liquid states,” Phys. Rev. B 42:7470, 1990.Google Scholar
[798] Elstner, M., Porezag, D., Jungnickel, G., Elsner, J., Haugk, M., Frauenheim, Th., Suhai, S., and Seifert, G., “Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties,” Phys. Rev. B 58:72607268, 1998.Google Scholar
[799] Correa, A. A., Bonev, S. A., and Galli, G., “Carbon under extreme conditions: Phase boundaries and electronic properties from first-principles theory,” Proc. Natl. Acad. Sci. U.S.A. 103:12041208, 2006.Google Scholar
[800] Wang, X., Scandolo, S., and Car, R., “Carbon phase diagram from ab initio molecular dynamics,” Phys. Rev. Lett. 95:185701, 2005.Google Scholar
[801] Eggert, J. H., et al., “Melting temperature of diamond at ultrahigh pressure,” Nat. Phys. 6:40–43, 2010.Google Scholar
[802] Bundy, F. P., Bassettand, W. A., Weathers, M. S., Hemley, R. J., Mao, H. K., and Goncharov, A. F., “The pressure-temperature phase and transformation diagram for carbon; updated through 1994,” Carbon 34:141153, 1996.Google Scholar
[803] Galli, G., Martin, R. M., Car, R., and Parrinello, M., “Melting of diamond at high pressure,” Science 250:1547, 1990.Google Scholar
[804] Mitchell, A. C., Shaner, J. W., and Keller, R. N., “The use of electrical-conductivity experiments to study the phase diagram of carbon,” Physica 139:386, 1986.Google Scholar
[805] Sugino, O. and Car, R., “Ab initio molecular dynamics study of first-order phase transitions: Melting of silicon,” Phys. Rev. Lett. 74:18231826, 1995.Google Scholar
[806] Landau, L. D. and Lifshitz, E. M., Theory of Elasticity, Pergamon Press, Oxford, U.K., 1958.Google Scholar
[807] Nye, J. F., Physical Properties of Crystals, Oxford University Press, Oxford, U.K., 1957.Google Scholar
[808] Wendel, H. and Martin, R. M., “Charge density and structural properties of covalent semiconductors,” Phys. Rev. Lett. 40(14):950953, 1978.Google Scholar
[809] Ho, K.-M., Fu, C.-L., Harmon, B. N., Weber, W., and Hamann, D. R., “Vibrational frequencies and structural properties of transition metals via total-energy calculations,” Phys. Rev. Lett. 49:673676, 1982.Google Scholar
[810] Heine, V. and Samson, J. H., “Magnetic, chemical and structural ordering in transition metals,” J. Phys. F 13:2155, 1983.Google Scholar
[811] Baroni, S., Giannozzi, P., and Testa, A., “Green’s function approach to linear response in solids,” Phys. Rev. Lett. 58:18611864, 1987.Google Scholar
[812] Quong, A. A. and Klein, B. M., “Self-consistent-screening calculation of interatomic force constants and phonon dispersion curves from first principles,” Phys. Rev. B 46:1073410737, 1992.Google Scholar
[813] Gonze, X. and Vigneron, J. P., “Density functional approach to non-linear response coefficients in solids,” Phys. Rev. B 39:13120, 1989.Google Scholar
[814] Savrasov, S. Y. and Savrasov, D. Y., “Linear-response theory and lattice dynamics: A muffin-tin-orbital approach,” Phys. Rev. B 54:1647016486, 1996.Google Scholar
[815] Sternheimer, R. M., “Electronic polarizabilities of ions from the Hartree–Fock wave functions,” Phys. Rev. 96:951, 1954.Google Scholar
[816] Gonze, X., “Perturbation expansion of variational principles at arbitrary order,” Phys. Rev. A 52:10861095, 1995.Google Scholar
[817] Gonze, X., “Adiabatic density-functional perturbation theory,” Phys. Rev. A 52:10961114, 1995.Google Scholar
[818] de Gironcoli, S., “Lattice dynamics of metals from density-functional perturbation theory,” Phys. Rev. B 51:6773, 1995.Google Scholar
[819] Resta, R. and Kunc, K., “Self-consistent theory of electronic states and dielectric response in semiconductors,” Phys. Rev. B 34:71467157, 1986.Google Scholar
[820] Littlewood, P. B., “On the calculation of the macroscopic polarisation induced by an optic phonon,” J. Phys. C 13:4893, 1980.Google Scholar
[821] Resta, R., Posternak, M., and Baldereschi, A., “Towards a quantum theory of polarization in ferroelectrics: The case of KNbO3 ,” Phys. Rev. Lett. 70:10101013, 1993.Google Scholar
[822] Ghosez, Ph., Gonze, X., Lambin, Ph., and Michenaud, J.-P., “Born effective charges of barium titanate: Band-by-band decomposition and sensitivity to structural features,” Phys. Rev. B 51:67656768, 1995.Google Scholar
[823] Zhong, W., King-Smith, R. D., and Vanderbilt, D., “Giant LO–TO splittings in perovskite ferroelectrics,” Phys. Rev. Lett. 72:36183621, 1994.Google Scholar
[824] Allen, P. B. and Mikovic, B., in Solid State Physics, vol. 37, edited by Ehrenreich, H., Seitz, F., and Turnbull, D., Academic, New York, 1982, p. 1.Google Scholar
[825] Rainer, D., Progress in Low Temperature Physics, vol. 10, North-Holland, Amsterdam, 1986, pp. 371424.Google Scholar
[826] Gunnarsson, O. E., “Superconductivity in fullerides,” Rev. Mod. Rev. 69:575606, 1997.Google Scholar
[827] Eliashberg, G. M., “Interactions between electrons and lattice vibrations in a superconductor [translation: Sov. Phys. JETP 11, 696 (1960)],” Zh. Eksp. Teor. Fiz. 38:966, 1960.Google Scholar
[828] Gaspari, G. D. and Gyorffy, B. L., “Electron–phonon interactions, d resonances, and superconductivity in transition metals,” Phys. Rev. Lett. 28:801805, 1972.Google Scholar
[829] Hopfield, J. J., “Angular momentum and transition-metal superconductivity,” Phys. Rev. 186:443451, 1969.Google Scholar
[830] Savrasov, S. Y. and Savrasov, D. Y., “Electron–phonon interactions and related physical properties of metals from linear-response theory,” Phys. Rev. B 54:1648716501, 1996.Google Scholar
[831] Dacorogna, M. M., Cohen, M. L., and Lam, P. K., “Self-consistent calculation of the q dependence of the electron–phonon coupling in aluminum,” Phys. Rev. Lett. 55:837840, 1985.Google Scholar
[832] Cooke, J. F., “Neutron scattering from itinerant-electron ferromagnets,” Phys. Rev. B 7:1108–1116, 1973.Google Scholar
[833] Savrasov, S. Y., “Linear response calculations of spin fluctuations,” Phys. Rev. Lett. 81:2570–2573, 1998.Google Scholar
[834] Ament, L. J. P., van Veenendaal, M., Devereaux, T. P., Hill, J. P., and van den Brink, J., “Resonant inelastic X-ray scattering studies of elementary excitations,” Rev. Mod. Phys. 83:705767, 2011.Google Scholar
[835] Thouless, D. J. and Valatin, J. G., “Time-dependent Hartree–Fock equations and rotational states of nuclei,” Nucl. Phys. 31:211, 1962.Google Scholar
[836] Ando, T., Fowler, A., and Stern, F., “Density-functional calculation of sub-band structure in accumulation and inversion layers,” Phys. Rev. B 13:34683477, 1976.Google Scholar
[837] Ullrich, C. A., Gossmann, U. J., and Gross, E. K. U., “Density-functional approach to atoms in strong laser-pulses,” Ber. Bunsenges. Phys. Chem 99:488497, 1995.Google Scholar
[838] Fundamentals of Time-Dependent Density Functional Theory, Vol. 837 of Lecture Notes in Physics, edited by Marques, M. A., Maitra, N. T., Nogueira, F. M., Gross, E., and Rubio, A., Springer, Berlin, Heidelberg, 2012.Google Scholar
[839] van Leeuwen, R., “Causality and symmetry in time-dependent density-functional theory,” Phys. Rev. Lett. 80:12801283, 1998.Google Scholar
[840] Caro, M., Correa, A. A., Artacho, E., and Caro, A., “Stopping power beyond the adiabatic approximation,” Sci. Rep. 7:2618, 2017.Google Scholar
[841] Onida, G., Reining, L., and Rubio, A., “Electronic excitations: Density-functional versus many-body Green’s-function approaches,” Rev. Mod. Phys. 74:601, 2002.Google Scholar
[842] Walker, B., Saitta, A. M., Gebauer, R., and Baroni, S., “Efficient approach to time-dependent density-functional perturbation theory for optical spectroscopy,” Phys. Rev. Lett. 96:113001, 2006.Google Scholar
[843] Rocca, D., Gebauer, R., Saad, Y., and Baroni, S., “Turbo charging time-dependent density-functional theory with Lanczos chains,” J. Chem. Phys. 128:154105, 2008.Google Scholar
[844] Malcolu, O. B., Gebauer, R., Rocca, D., and Baroni, S., “turboTDDFT: A code for the simulation of molecular spectra using the Liouville–Lanczos approach to time-dependent density-functional perturbation theory,” Comput. Phys. Commun. 182:17441754, 2011.Google Scholar
[845] Flocard, H., Koonin, S., and Weiss, M., “Three-dimensional time-dependent Hartree–Fock calculations: Application to 16O + 16O collisions,” Phys. Rev. C 17:16821699, 1978.Google Scholar
[846] Yabana, K. and Bertsch, G. F., “Time-dependent local-density approximation in real time,” Phys. Rev. B 54:44844487, 1996.Google Scholar
[847] Sugino, O. and Miyamoto, Y., “Density-functional approach to electron dynamics: Stable simulation under a self-consistent field,” Phys. Rev. B 59:25792586, 1999.Google Scholar
[848] Talezer, H. and Kosloff, R., “An accurate and efficient scheme for propagating the time-dependent Schrödinger equation,” J. Chem. Phys. 81:39673971, 1984.Google Scholar
[849] Ullrich, C., Time-Dependent Density-Functional Theory: Concepts and Applications, Oxford University Press, Oxford, U.K., 2012.Google Scholar
[850] Maier, T. M., Bahmann, H., Arbuznikov, A. V., and Kaupp, M., “Validation of local hybrid functionals for TDDFT calculations of electronic excitation energies,” J. Chem. Phys. 144:074106, 2016.Google Scholar
[851] Vasiliev, I., Ogut, S., and Chelikowsky, J. R., “Ab initio excitation spectra and collective electronic response in atoms and clusters,” Phys. Rev. Lett. 82:19191922, 1999.Google Scholar
[852] Yannouleas, C. and Landman, U., “Molecular dynamics in shape space and femtosecond vibrational spectroscopy of metal clusters,” J. Phys. Chem. A 102:25052508, 1998.Google Scholar
[853] Rubio, A., Alonso, J. A., Blase, X., Balbas, L. C., and Louie, S. G., “Ab initio photoabsorption spectra and structures of small semiconductor and metal clusters,” Phys. Rev. Lett. 77:247– 250, 1996.Google Scholar
[854] Yoffe, A. D., “Semiconductor quantum dots and related systems: Electronic, optical, luminescence and related properties of low dimensional systems,” Adv. Phys. 50:1208, 2001.Google Scholar
[855] Belomoin, G., Smith, A, Rao, S., Twesten, R., Therrien, J., Nayfeh, M., Wagner, L., Mitas, L., and Chaieb, S., “Observation of a magic discrete family of ultrabright Si nanoparticles,” Appl. Phys. Lett 80:841–843, 2002.Google Scholar
[856] Tsolakidis, A., Sanchez-Portal, D., and Martin, R. M., “Calculation of the optical response of atomic clusters using time-dependent density functional theory and local orbitals,” Phys. Rev. B 66:235416, 2002.Google Scholar
[857] Bauernschmitt, R., Ahlrichs, R., Hennrich, F. H., and Kappes, M. M., “Experiment versus time dependent density functional theory prediction of fullerene electronic absorption,” J. Am. Chem. Soc. 120:50525059, 1998.Google Scholar
[858] Hanson-Heine, M. W. D., M. W. G., and Besley, N. A., “Assessment of time-dependent density functional theory with the restricted excitation space approximation for excited state calculations of large systems,” Mol. Phys. 116:1452–1459, 2018.Google Scholar
[859] Kronik, L., Stein, R., Refaely-Abramson, S., and Baer, R., “Excitation gaps of finite-sized systems from optimally tuned range-separated hybrid functionals,” J. Chem. Theory Comput. 8:15151531, 2012.Google Scholar
[860] Bertsch, G. F., Iwata, J.-I., Rubio, Angel, and Yabana, K., “Real-space, real-time method for the dielectric function,” Phys. Rev. B 62:7998–8002, 2000.Google Scholar
[861] Krieger, J. B. and Iafrate, G. J., “Time evolution of Bloch electrons in a homogeneous electric field,” Phys. Rev. B 33:54945500, 1986.Google Scholar
[862] van Leeuwen, R., “Key concepts of time-dependent density-functional theory,” Int. J. Mod. Phys. B 15:19692023, 2001.Google Scholar
[863] Marques, M. A. L., Castro, A., and Rubio, A., “Assessment of exchange–correlation functionals for the calculation of dynamical properties of small clusters in time-dependent density functional theory,” J. Chem. Phys. 115:30063014, 2001.Google Scholar
[864] Steslicka, M., “From Tamm to Shockley: An historical comment,” Prog. Surf. Sci. 42:1118, 1993.Google Scholar
[865] Tamm, I., “Ueber eine moegliche Art der Elektronenbindung an Kristalloberflaechen,” Z. Phys. 76:849850, 1932.Google Scholar
[866] De, R. Kronig, L. and Penney, W. G., “Quantum mechanics of electrons in crystal lattices,” Proc. R. Soc. A 130:499513, 1931.Google Scholar
[867] Davisson, C. and Germer, L. H., “Diffraction of electrons by a crystal of nickel,” Phys. Rev. 30:705740, 1927.Google Scholar
[868] LaShell, S., McDougall, B. A., and Jensen, E., “Spin splitting of an Au(111) surface state band observed with angle resolved photoelectron spectroscopy,” Phys. Rev. Lett. 77:34193422, 1996.Google Scholar
[869] Yan, H., Stadtmuller, B., Haag, N., Jakobs, S., Seidel, J., Jungkenn, D., Mathias, S., Cinchetti, M., Aeschlimann, M., and Felser, C., “Topological states on the gold surface,” Nat. Commun. 6:10167, 2015.Google Scholar
[870] Rashba, E. I. and Sheka, V. I., “Symmetry of energy bands in crystals of wurtzite type ii. symmetry of bands with spin–orbit interaction included (English translation: Supplemental Material to the paper by G. Bihlmayer, O. Rader, and R. Winkler, Focus on the Rashba effect, New J. Phys. 17, 050202 (2015)),” Fiz. Tverd. Tela – Collected Papers (Leningrad) II:162–176, 1959.Google Scholar
[871] Bychkov, Yu. A. and Rashba, E. I., “Properties of a 2d electron gas with a lifted spectrum degeneracy,” Sov. Phys. – JETP Lett. 39:7881, 1984.Google Scholar
[872] Stekolnikov, A. A., Furthmüller, J., and Bechstedt, F., “Absolute surface energies of group-IV semiconductors: Dependence on orientation and reconstruction,” Phys. Rev. B 65:115318, 2002.Google Scholar
[873] Healy, S. B., Filippi, C., Kratzer, P., Penev, E., and Scheffler, M., “Role of electronic correlation in the Si(100) reconstruction: A quantum Monte Carlo study,” Phys. Rev. Lett. 87:016105, 2001.Google Scholar
[874] Van de Walle, C. G. and Martin, R. M., “Theoretical study of Si/Ge interfaces,” J. Vac. Sci. Technol. B 3(4):12561259, 1985.Google Scholar
[875] Steiner, K., Chen, W., and Pasquarello, A., “Band offsets of lattice-matched semiconductor heterojunctions through hybrid functionals and G0 W0,” Phys. Rev. B 89:205309, 2014.Google Scholar
[876] Harrison, W. A., Kraut, E. A., Waldrop, J. R., and Grant, R. W., “Polar heterojunction interfaces,” Phys. Rev. B 18:44024410, 1978.Google Scholar
[877] Hwang, H. Y., Iwasa, Y., Kawasaki, M., Keimer, B., Nagaosa, N., and Tokura, Y., “Emergent phenomena at oxide interfaces,” Nat. Mater. 11:103, 2012, review article.Google Scholar
[878] Zubko, P., Gariglio, S., Gabay, M., Ghosez, P., and Triscone, J.-M., “Interface physics in complex oxide heterostructures,” Annu. Rev. Condens. Matter Phys. 2:141165, 2011.Google Scholar
[879] Bristowe, N. C., Ghosez, P., Littlewood, P. B., and Artacho, E., “The origin of two-dimensional electron gases at oxide interfaces: insights from theory,” J. Phys. Condens. Matter 26:143201, 2014.Google Scholar
[880] Bjaalie, L., Himmetoglu, B., Weston, L., Janotti, A., and Van de Walle, C. G., “Oxide interfaces for novel electronic applications,” New J. Phys. 16:025005, 2014.Google Scholar
[881] Pentcheva, R. and Pickett, W. E., “Electronic phenomena at complex oxide interfaces: insights from first principles,” J. Phys. Condens. Matter 22:043001, 2010.Google Scholar
[882] Rodel, T., et al., “Universal fabrication of 2d electron systems in functional oxides,” Adv. Mater. 28:19761980, 2016.Google Scholar
[883] Mattheiss, L. F., “Energy bands for KNiF3, SrTiO3, KMoO3, and KTaO3,” Phys. Rev. B 6:47184740, 1972.Google Scholar
[884] Zhong, Z., Tóth, A., and Held, K., “Theory of spin–orbit coupling at LaAlO3/SrTiO3 interfaces and SrTiO3 surfaces,” Phys. Rev. B 87:161102, 2013.Google Scholar
[885] Splendiani, A., Sun, L., Zhang, Y., Li, T., Kim, J., Chim, C.-Y., Galli, G., and Wang, F., “Emerging photoluminescence in monolayer MoS2 ,” Nano Lett. 10:12711275, 2010.Google Scholar
[886] Wang, G., Chernikov, A., Glazov, M. M., Heinz, T. F., Marie, X., Amand, T., and Urbaszek, B., “Colloquium: Excitons in atomically thin transition metal dichalcogenides,” Rev. Mod. Phys. 90:021001, 2018.Google Scholar
[887] Qiu, D. Y., da Jornada, F. H., and Louie, S. G., “Screening and many-body effects in two-dimensional crystals: Monolayer MoS2 ,” Phys. Rev. B 93:235435, 2016.Google Scholar
[888] Rasmussen, F. A. and Thygesen, K. S., “Computational 2d materials database: Electronic structure of transition-metal dichalcogenides and oxides,” J. Phys. Chem. C 119:13169–13183, 2015.Google Scholar
[889] Wannier, G. H., “The structure of electronic excitations in the insulating crystals,” Phys. Rev. 52:191197, 1937.Google Scholar
[890] Blount, G., in Solid State Physics, edited by H. Ehrenreich, Seitz, F., and Turnbull, D., Academic, New York, 1962, p. 305.Google Scholar
[891] Marzari, N., Mostofi, A. A., Yates, J. R., Souza, I., and Vanderbilt, D., “Maximally localized Wannier functions: Theory and applications,” Rev. Mod. Phys. 84:14191475, 2012.Google Scholar
[892] Kohn, W., “Analytic properties of Bloch waves and Wannier functions,” Phys. Rev. B 115:809– 821, 1959.Google Scholar
[893] Brouder, C., Panati, G., Calandra, M., Mourougane, C., and Marzari, N., “Exponential localization of Wannier functions in insulators,” Phys. Rev. Lett. 98:046402, 2007.Google Scholar
[894] Kohn, W., “Construction of Wannier functions and applications to energy bands,” Phys. Rev. B 7:43884398, 1973.Google Scholar
[895] Bullett, D. W., “A chemical pseudopotential approach to covalent bonding. I,” J. Phys. C: Solid State Phys. 8:26952706, 1975.Google Scholar
[896] Anderson, P. W., “Self-consistent pseudopotentials and ultralocalized functions for energy bands,” Phys. Rev. Lett. 21:13, 1968.Google Scholar
[897] McMahan, A. K., Annett, J. F., and Martin, R. M., “Cuprate parameters from numerical Wannier functions,” Phys. Rev. B 42:6268, 1990.Google Scholar
[898] Schnell, I., Czycholl, G., and Albers, R. C., “Hubbard-U calculations for Cu from first-principle Wannier functions,” Phys. Rev. B 65:075103, 2002.Google Scholar
[899] Boys, S. F., “Construction of some molecular orbitals to be approximately invariant for changes from one molecule to another,” Rev. Mod. Phys. 32:296299, 1960.Google Scholar
[900] Marzari, N. and Vanderbilt, D., “Maximally localized generalized Wannier functions for composite energy bands,” Phys. Rev. B 56:1284712865, 1997.Google Scholar
[901] Souza, I., Wilkens, T. J., and Martin, R. M., “Polarization and localization in insulators: generating function approach,” Phys. Rev. B 62:16661683, 2000.Google Scholar
[902] Silvestrelli, P. L., Marzari, N., Vanderbilt, D., and Parrinello, M., “Maximally-localized Wannier functions for disordered systems: Application to amorphous silicon,” Solid State Commun. 107:711, 1998.Google Scholar
[903] Berghold, G., Mundy, C. J., Romero, A. H., Hutter, J., and Parrinello, M., “General and efficient algorithms for obtaining maximally localized Wannier functions,” Phys. Rev. B 61:10040– 10048, 2000.Google Scholar
[904] Souza, I., Marzari, N., and Vanderbilt, D., “Maximally localized Wannier functions for entangled energy bands,” Phys. Rev. B 65:035109, 2002.Google Scholar
[905] Andersen, O. K., Liechtenstein, A. I., Jepsen, O., and Paulsen, F., “LDA energy bands, low-energy hamiltonians, t′, t′′, t (k), and J(perpendicular),” J. Phys. Chem. Solids 56:1573, 1995.Google Scholar
[906] Yates, J. R., Wang, X., Vanderbilt, D., and Souza, I., “Spectral and Fermi surface properties from Wannier interpolation,” Phys. Rev. B 75:195121, 2007.Google Scholar
[907] Lee, Y.-S., Buongiorno Nardelli, M., and Marzari, N., “Band structure and quantum conductance of nanostructures from maximally localized Wannier functions: The case of function-alized carbon nanotubes,” Phys. Rev. Lett. 95:076804, 2005.Google Scholar
[908] Landau, L. D. and Lifshitz, E. M., Electrodynamics of Continuous Media, Pergamon Press, Oxford, U.K., 1960.Google Scholar
[909] Feynman, R. P., Leighton, R. B., and Sands, M., Lectures on Physics, Vol. 2, Addison Wesley Publishing Company, Reading, MA, 1982.Google Scholar
[910] Lines, M. E. and Glass, A. M., Principles and Applications of Ferroelctrics and Related Materials, Clarendon Press, Oxford, 1977.Google Scholar
[911] Martin, R. M., “Comment on: Calculation of electric polarization in crystals,” Phys. Rev. B 9:1998, 1974.Google Scholar
[912] Tagantsev, A. K., “Review: Electric polarization in crystals and its response to thermal and eleastic perturbations,” Phase Transit. 35:119, 1991.Google Scholar
[913] Thouless, D. J., Kohmoto, M., Nightingale, M. P., and den Nijs, M., “Quantized Hall conductance in a two-dimensional periodic potential,” Phys. Rev. Lett. 49:405408, 1982.Google Scholar
[914] Thouless, D. J., “Quantization of particle transport,” Phys. Rev. B 27:60836087, 1983.Google Scholar
[915] Niu, Q. and Thouless, D. J., “Quantised adiabatic charge transport in the presence of substrate disorder and many-body interaction,” J. Phys. A 17:2453, 1984.Google Scholar
[916] Cohen, M. L. and Louie, S. G., Fundamentals of Condensed Matter Physics, Cambridge University Press, Cambridge, U.K., 2016.Google Scholar
[917] Kaxiras, E. and Joannopoulos, J. D., Quantum Theory of Materials, 2nd rev. ed., Cambridge University Press, Cambridge, U.K., 2019.Google Scholar
[918] Vanderbilt, D. H., Berry Phases in Electronic Structure Theory, Cambridge University Press, Cambridge, U.K., 2018.Google Scholar
[919] Resta, R., “The insulating state of matter: A geometric approach,” Eur. Phys. J. B 79:121137, 2011.Google Scholar
[920] Ortiz, G., Souza, I., and Martin, R. M., “The exchange–correlation hole in polarized dielectrics: Implications for the microscopic functional theory of dielectrics,” Phys. Rev. Lett. 80:353– 356, 1998.Google Scholar
[921] Kohn, W., “Theory of the insulating state,” Phys. Rev. 133:A171–181, 1964.Google Scholar
[922] Resta, R., “The quantum mechanical position operator in extended systems,” Phys. Rev. Lett. 80:18001803, 1998.Google Scholar
[923] Resta, R. and Sorella, S., “Electron localization in the insulating state,” Phys. Rev. Lett. 82:370– 373, 1999.Google Scholar
[924] Aebischer, C., Baeriswyl, D., and Noack, R. M., “Dielectric catastrophe at the Mott transition,” Phys. Rev. Lett. 86:468471, 2001.Google Scholar
[925] Arlt, G. and Quadflieg, P., “Piezoelectricity in III–V compounds with a phenomenological analysis of the piezoelectric effect,” Phys. Status Solidi 25:323, 1968.Google Scholar
[926] Martin, R. M., “Comment on: Piezoelectricity under hydrostatic pressure,” Phys. Rev. B 6:4874, 1972.Google Scholar
[927] Vanderbilt, D., “Berry-phase theory of proper piezoelectric response,” J. Phys. Chem. Solids 61:147151, 2000.Google Scholar
[928] Kallin, C. and Halperin, B. I., “Surface-induced charge disturbances and piezoelectricity in insulating crystals,” Phys. Rev. B 29:21752189, 1984.Google Scholar
[929] Resta, R., “Theory of the electric polarization in crystals,” Ferroelectrics 136:51, 1992.Google Scholar
[930] Resta, R., “Towards a quantum theory of polarization in ferroelectrics: The case of KNbO3,” Europhys. Lett. 22:133138, 1993.Google Scholar
[931] Ortiz, G. and Martin, R. M., “Macroscopic polarization as a geometric quantum phase: Many-body formulation,” Phys. Rev. B 49:1420214210, 1994.Google Scholar
[932] Gonze, X., Allan, D. C., and Teter, M. P., “Dielectric tensor, effective charges, and phonons in α-quartz by variational density-functional perturbation theory,” Phys. Rev. Lett. 68:3603– 3606, 1992.Google Scholar
[933] Dal Corso, A. and Mauri, F., “Wannier and Bloch orbital computation of the nonlinear susceptibility,” Phys. Rev. B 50:57565759, 1994.Google Scholar
[934] Kleemann, W., Schäfer, F. J., and Fontana, M. D., “Crystal optical studies of spontaneous and precursor polarization in KNbO3 ,” Phys. Rev. B 30:11481154, 1984.Google Scholar
[935] Resta, R., “Why are insulators insulating and metals conducting?,” J. Phys. Condens. Matter 14:R625–R656, 2002.Google Scholar
[936] Kudinov, E. K., “Difference between insulating and conducting states,” Sov. Phys. Solid State 33:1299–1304, 1991, [Fiz. Tverd. Tela 33, 2306 (1991)].Google Scholar
[937] Callen, H. B. and Welton, T. A., “Irreversibility and generalized noise,” Phys. Rev. 83:3440, 1951.Google Scholar
[938] Callen, H. B. and Greene, R. F., “On a theorem of irreversible thermodynamics,” Phys. Rev. 86:702710, 1952.Google Scholar
[939] Kubo, R., “A general expression for the conductivity tensor,” Can. J. Phys. 34:1274, 1956.Google Scholar
[940] Martin, P. C., Measurement and Correlation Functions, Gordon and Breach, New York, 1968.Google Scholar
[941] Penn, D. R., “Wave-number-dependent dielectric function of semiconductors,” Phys. Rev. 128:20932097, 1962.Google Scholar
[942] Sgiarovello, C., Peressi, M., and Resta, R., “Electron localization in the insulating state: Application to crystalline semiconductors,” Phys. Rev. B 64:115202, 2001.Google Scholar
[943] Hasan, M. Z. and Kane, C. L., “Colloquium: Topological insulators,” Rev. Mod. Phys. 82:3045– 3067, 2010.Google Scholar
[944] Qi, X.-L. and Zhang, S.-C., “Topological insulators and superconductors,” Rev. Mod. Phys. 83:10571110, 2011.Google Scholar
[945] Asboth, J. K., Oroszlany, L., and Palyi, A., Lecture Notes in Physics, vol. 919, A Short Course on Topological Insulators: Band Structure and Edge States in One and Two Dimensions, Springer, Heidelburg, Germany, 2016.Google Scholar
[946] Bernevig, A., Topological Insulators and Topological Superconductors, Princeton University Press, Princeton, NJ, 2013.Google Scholar
[947] Bansil, A., Lin, H., and Das, T., “Colloquium: Topological band theory,” Rev. Mod. Phys. 88:021004, 2016.Google Scholar
[948] Fu, L., “Topological crystalline insulators,” Phys. Rev. Lett. 106:106802, 2011.Google Scholar
[949] Haldane, F. D. M., “Nobel lecture: Topological quantum matter,” Rev. Mod. Phys. 89:040502, 2017.Google Scholar
[950] Thouless, D. J., Topological Quantum Numbers in Nonrelativistic Physics, World Scientific, Singapore, 1988.Google Scholar
[951] Kogut, J. B. and Stephanov, M. A., The Phases of Quantum Chromodynamics: From Confinement to Extreme Environments, Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology, Cambridge University Press, Cambridge, U.K., 2003.Google Scholar
[952] Wilczek, Frank, “Particle physics and condensed matter: the saga continues,” Phy. Scr. 2016:014003, 2016.Google Scholar
[953] Jackiw, R. and Rebbi, C., “Solitons with fermion number 1/2,” Phys. Rev. D 13:33983409, 1976.Google Scholar
[954] Su, W. P., Schrieffer, J. R., and Heeger, A. J., “Solitons in polyacetylene,” Phys. Rev. Lett. 42:16981701, 1979.Google Scholar
[955] Soluyanov, A. A. and Vanderbilt, D., “Wannier representation of Z2 topological insulators,” Phys. Rev. B 83:035108, 2011.Google Scholar
[956] Yu, R., Qi, X.-L., Bernevig, A., Fang, Z., and Dai, X., “Equivalent expression of Z2 topological invariant for band insulators using the non-Abelian Berry connection,” Phys. Rev. B 84:075119, 2011.Google Scholar
[957] Gresch, D., Autès, Gabriel, Yazyev, O. V., Troyer, M., Vanderbilt, D., Bernevig, B. A., and Soluyanov, Alexey A., “Z2Pack: Numerical implementation of hybrid Wannier centers for identifying topological materials,” Phys. Rev. B 95:075146, 2017.Google Scholar
[958] Bradlyn1, B., Elcoro, L., Cano1, J., Vergniory, M. G., Wang, Z., Felser, C., Aroyo, M. I., and Bernevig, B. A., “Topological quantum chemistry,” Nature 547:298–305, 2017.Google Scholar
[959] Beenakker, C. W. J., “Search for majorana fermions in superconductors,” Ann. Rev. Condens. Matter Phys. 4:113136, 2013.Google Scholar
[960] Mong, R. S. K. and Shivamoggi, V., “Edge states and the bulk-boundary correspondence in Dirac Hamiltonians,” Phys. Rev. B 83:125109, 2011.Google Scholar
[961] Schnyder, A. P., Ryu, S., Furusaki, A., and Ludwig, A. W. W., “Classification of topological insulators and superconductors in three spatial dimensions,” Phys. Rev. B 78:195125, 2008.Google Scholar
[962] Qi, X.-L., Hughes, T. L., and Zhang, S.-C., “Topological field theory of time-reversal invariant insulators,” Phys. Rev. B 78:195424, 2008.Google Scholar
[963] Kitaev, A., “Periodic table for topological insulators and superconductors,” AIP Conf. Proc. 1134:2230, 2009.Google Scholar
[964] Ryu, S., Schnyder, A. P., Furusaki, A., and Ludwig, A. W. W., “Topological insulators and superconductors: Tenfold way and dimensional hierarchy,” New J. Phy. 12:065010, 2010.Google Scholar
[965] Mele, E. J. and Rice, M. J., “Vibrational excitations of charged solitons in polyacetylene,” Phys. Rev. Lett. 45:926929, 1980.Google Scholar
[966] Rice, M. J. and Mele, E. J., “Elementary excitations of a linearly conjugated diatomic polymer,” Phys. Rev. Lett. 49:14551459, 1982.Google Scholar
[967] Pershoguba, S. S. and Yakovenko, V. M., “Shockley model description of surface states in topological insulators,” Phys. Rev. B 86:075304, 2012.Google Scholar
[968] Zak, J., “Berry’s phase for energy bands in solids,” Phys. Rev. Lett. 62:27472750, 1989.Google Scholar
[969] Jadaun, P., Xiao, D., Niu, Q., and Banerjee, K., S, “Topological classification of crystalline insulators with space group symmetry,Phys. Rev. B 88:085110, 2013.Google Scholar
[970] Alexandradinata, A., Dai, X., and Bernevig, B. A., “Wilson-loop characterization of inversion-symmetric topological insulators,” Phys. Rev. B 89:155114, 2014.Google Scholar
[971] Qi, X.-L., Wu, Y.-S., and Zhang, S.-C., “Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors,” Phys. Rev. B 74:085308, 2006.Google Scholar
[972] Fu, L. and Kane, C. L., “Topological insulators with inversion symmetry,” Phys. Rev. B 76:045302, 2007.Google Scholar
[973] Bernevig, B. A., Hughes, T. L., and Zhang, S.-C., “Quantum spin Hall effect and topological phase transition in HgTe quantum wells,” Science 314:17571761, 2006.Google Scholar
[974] König, M., Wiedmann, S., Brüne, C., Roth, A., Buhmann, H., Molenkamp, L. W., Qi, X.-L., and Zhang, S.-C., “Quantum spin Hall insulator state in HgTe quantum wells,” Science 318:766– 770, 2007.Google Scholar
[975] Nicklas, J. W. and Wilkins, J. W., “Accurate electronic properties for (Hg,Cd)Te systems using hybrid density functional theory,” Phys. Rev. B 84:121308, 2011.Google Scholar
[976] Kane, E. O., “Band structure of indium antimonide,” J. Phy. Chem. of Solids 1:249261, 1957.Google Scholar
[977] Haldane, F. D. M., “Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the ‘parity anomaly,”‘ Phys. Rev. Lett. 61:20152018, 1988.Google Scholar
[978] Nakada, K., Fujita, M., Dresselhaus, G., and Dresselhaus, M. S., “Edge state in graphene ribbons: Nanometer size effect and edge shape dependence,” Phys. Rev. B 54:1795417961, 1996.Google Scholar
[979] Reis, F., Li, G., Dudy, L., Bauernfeind, M., Glass, S., Hanke, W., Thomale, R., Schäfer, J., and Claessen, R., “Bismuthene on a SiC substrate: A candidate for a high-temperature quantum spin Hall material,” Science 357:287290, 2017.Google Scholar
[980] Fu, L., Kane, C. L., and Mele, E. J., “Topological insulators in three dimensions,” Phys. Rev. Lett. 98:106803, 2007.Google Scholar
[981] Nielsen, H. B. and Ninomiya, M., “Absence of neutrinos on a lattice: (I). Proof by homotopy theory,” Nucl. Phys. B 185:2040, 1981.Google Scholar
[982] Xia, Y., Qian, D., Hsieh, D., Wray, L., Pal, A., Lin, H., Bansil, A., Grauer, D., Hor, Y. S., Cava, R. J., and Hasan, M. Z., “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5:398, 2009.Google Scholar
[983] Larson, P., Greanya, V. A., Tonjes, W. C., Rong Liu, Mahanti, S. D., and Olson, C. G., “Electronic structure of Bi2 X3 (X = S,Se,T) compounds: Comparison of theoretical calculations with photoemission studies,” Phys. Rev. B 65:085108, 2002.Google Scholar
[984] Herring, W. C., “Accidental degeneracy in the energy bands of crystals,” Phys. Rev. 52: 365373, 1937.Google Scholar
[985] Weyl, H., “Elektron und gravitation. I,” Z. Phys. 56:330352, 1929.Google Scholar
[986] Armitage, N. P., Mele, E. J., and Vishwanath, A., “Weyl and Dirac semimetals in three-dimensional solids,” Rev. Mod. Phys. 90:015001, 2018.Google Scholar
[987] Zahid Hasan, M., Su-Yang Xu, Ilya Belopolski, and Shin-Ming Huang, “Discovery of Weyl fermion semimetals and topological Fermi arc states,Ann. Rev. Condens. Matter Phys. 8:289309, 2017.Google Scholar
[988] Yan, H. and Felser, C., “Topological materials: Weyl semimetals,” Ann. Rev. Condens. Matter Phys. 8:337354, 2017.Google Scholar
[989] Vishwanath, A., “Viewpoint: Where the Weyl things are,” Physics 8:8485, 2015.Google Scholar
[990] Volovik, G. E., The Universe in a Helium Droplet, Oxford University Press, Oxford, U.K., 2009.Google Scholar
[991] Lv, B. Q., et al., “Experimental discovery of Weyl semimetal TaAs,” Phys. Rev. X 5:031013, 2015.Google Scholar
[992] Xu, S.-Y., et al., “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349:613617, 2015.Google Scholar
[993] Yan, H. and Zhang, S.-C., “Topological materials,” Rep. Prog. Phy. 75:096501, 2012.Google Scholar
[994] Evans, G. C., Functionals and Their Applications, Dover, New York, 1964.Google Scholar
[995] Landau, L. D. and Lifshitz, E. M., Quantum Mechanics: Non-relativistic Theory, Pergamon Press, Oxford, U.K., 1977.Google Scholar
[996] Shankar, R., Principles of Quantum Mechanics, Plenum Publishing, New York, 1980.Google Scholar
[997] Kittel, C., Quantum Theory of Solids, 2nd rev. ed., John Wiley & Sons, New York, 1964.Google Scholar
[998] Jones, W. and March, N. H., Theoretical Solid State Physics, vol. 2, John Wiley & Sons, New York, 1976.Google Scholar
[999] Mori, H., “A continued-fraction representation of the time-correlation functions,” Prog. Theor. Phys. 34:399, 1965.Google Scholar
[1000] Kubo, R, “Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems,” Rep. Prog. Phys. 12:570, 1957.Google Scholar
[1001] Greenwood, D. A., “The Boltzmann equation in the theory of electrical conduction in metals,” Proc. Phys. Soc. (London) 71:585, 1958.Google Scholar
[1002] Nozières, P. and Pines, D., “Electron interaction in solids. collective approach to the dielectric constant,” Phys. Rev. 109:762777, 1959.Google Scholar
[1003] Ehrenreich, H. and Cohen, M. H., “Self-consistent field approach to the many-electron problem,” Phys. Rev. 115:786790, 1959.Google Scholar
[1004] Doniach, S. and Sondheimer, E. H., Green’s Functions for Solid State Physicists, W. A. Benjamin, Reading, MA, 1974. Reprinted in Frontiers in Physics Series, no. 44.Google Scholar
[1005] Wigner, E. P., “Über eine Verschärfung des Summensatzes,” Phys. Z. 32:450, 1931.Google Scholar
[1006] Kramers, H., Jonker, C. C., and Koopmans, T., “Wigners Erweiterung des Thomas-Kuhnschen Summensatzes für ein Elektron in einem Zentralfeld,” Z. Phys. 80:178, 1932.Google Scholar
[1007] Wiser, N., “Dielectric constant with local field effects included,” Phys. Rev. 129:6269, 1963.Google Scholar
[1008] Cochran, W. and Cowley, R. A., “Dielectric constants and lattice vibrations,” J. Phys. Chem. Solids 23:447, 1962.Google Scholar
[1009] Zallen, R., “Symmetry and reststrahlen in elemental crystals,” Phys. Rev. 173:824832, 1968.Google Scholar
[1010] Zallen, R., Martin, R. M., and Natoli, V., “Infrared activity in elemental crystals,” Phys. Rev. B 49:70327035, 1994.Google Scholar
[1011] Cady, W. F., Piezoelectricity, McGraw-Hill, New York, 1946.Google Scholar
[1012] Martin, R. M., “Piezolectricity,” Phys. Rev. B 5(4):16071613, 1972.Google Scholar
[1013] Ewald, P. P., “Die Berechnung optischer und electrostatischer Gitterpotentiale,” Ann. Phy. 64:253, 1921.Google Scholar
[1014] Kornfeld, H., “Die Berechnung electrostatischer Potentiale und der Energie von Dipole- und Quadrupolgittern,” Z. Phys. 22:27, 1924.Google Scholar
[1015] Fuchs, K., “A quantum mechanical investigation of the cohesive forces of metallic copper,” Proc. Roy. Soc. 151:585, 1935.Google Scholar
[1016] Coldwell-Horsfall, R. A. and Maradudin, A. A., “Zero-point energy of an electron lattice,” J. Math. Phys. 1:395, 1960.Google Scholar
[1017] Tosi, M. P., in Solid State Physics, edited by Ehrenreich, H., Seitz, F., and Turnbull, D., Academic, New York, 1964.Google Scholar
[1018] Fraser, L. M., Foulkes, W. M. C., Rajagopal, G., Needs, R. J., Kenny, S. D., and Williamson, A. J., “Finite-size effects and coulomb interactions in quantum Monte Carlo calculations for homogeneous systems with periodic boundary conditions,” Phys. Rev. B 53:1814, 1996.Google Scholar
[1019] Lennard-Jones, J. E. and Dent, B. M., “Cohesion at a crystal surface,” Trans. Faraday Soc. 24:92108, 1928.Google Scholar
[1020] Schultz, P. A., “Local electrostatic moments and periodic boundary conditions,” Phys. Rev. B 60:15511554, 1999.Google Scholar
[1021] Makov, G. and Payne, M. C., “Periodic boundary conditions in ab initio calculations,” Phys. Rev. B 51:40144022, 1995.Google Scholar
[1022] Kantorovich, L. N., “Elimination of the long-range dipole interaction in calculations with periodic boundary conditions,” Phys. Rev. B 60:15476, 1999.Google Scholar
[1023] Sommerfeld, A., Mechanics of Deformable Bodies, Academic Press, New York, 1950.Google Scholar
[1024] Born, M., Heisenberg, W., and Jordan, P., “Zur Quantenmechanik, II,” Z. Phys. 35:557, 1926.Google Scholar
[1025] Finkelstein, B., “Uber den Virialsatz in der Wellenmechanik,” Z. Phys. 50:293, 1928.Google Scholar
[1026] Slater, J. C., “The virial and molecular structure,” J. Chem. Phys. 1:687, 1933.Google Scholar
[1027] Schrödinger, E., “The energy-impulse hypothesis of material waves,” Ann. Phys. (Leipzig) 82:265, 1927.Google Scholar
[1028] Feynman, R. P., Undergraduate thesis, unpublished, Massachusetts Institute of Technology, 1939.Google Scholar
[1029] Martin, P. C. and Schwinger, J., “Theory of many particle systems. I,” Phys. Rev. 115: 13421373, 1959.Google Scholar
[1030] Rogers, C. and Rappe, A., “Unique quantum stress fields,” AIP Conf. Proc. 582, pp. 9196, 2001.Google Scholar
[1031] Chetty, N. and Martin, R. M., “First-principles energy density and its applications to selected polar surfaces,” Phys. Rev. B 45:60746088, 1992.Google Scholar
[1032] Chetty, N. and Martin, R. M., “GaAs (111) and (-1-1-1) surfaces and the GaAs/AlAs (111) heterojunction studied using a local energy density,” Phys. Rev. B 45:60896100, 1992.Google Scholar
[1033] Rapcewicz, K., Chen, B., Yakobson, B., and Bernholc, J., “Consistent methodology for calculating surface and interface energies,” Phys. Rev. B 57:72817291, 1998.Google Scholar
[1034] Martin, R. M., unpublished, 2002.Google Scholar
[1035] Savin, A., “Expression of the exact electron-correlation-energy density functional in terms of first-order density matrices,” Phys. Rev. A 52:R1805–R1807, 1995.Google Scholar
[1036] Levy, M. and Gorling, A., “Correlation-energy density-functional formulas from correlating first-order density matrices,” Phys. Rev. A 52:R1808–R1810, 1995.Google Scholar
[1037] Stoll, H., Golka, E., and Preuss, H., “Correlation energies in the spin-density functional formalism. II. Applications and empirical corrections,” Theor. Chim. Acta 55:29, 1980.Google Scholar
[1038] Becke, A. D., “Hartree–Fock exchange energy of an inhomogeneous electron gas,” Int. J. Quantum Chem. 23:1915, 1983.Google Scholar
[1039] Luken, W. L. and Culbertson, J. C., “Localized orbitals based on the Fermi hole,” Theor. Chim. Acta 66:279, 1984.Google Scholar
[1040] Dobson, J. F., “Interpretation of the Fermi hole curvature,” J. Chem. Phys. 94:43284333, 1991.Google Scholar
[1041] Cohen, M. H., Frydel, D., Burke, K., and Engel, E., “Total energy density as an interperative tool,” J. Chem. Phys. 113:29902994, 2000.Google Scholar
[1042] Hammer, B. and Scheffler, M., “Local chemical reactivity of a metal alloy surface,” Phys. Rev. Lett. 74:34873490, 1995.Google Scholar
[1043] Godfrey, M. J., “Stress field in quantum systems,” Phys. Rev. B 37:1017610183, 1988.Google Scholar
[1044] Filippetti, A. and Fiorentini, V., “Theory and applications of the stress density,” Phys. Rev. B 61:84338442, 2000.Google Scholar
[1045] Rogers, C. and Rappe, A., “Geometric formulation of quantum stress fields,” Phys. Rev. B 65:224117, 2002.Google Scholar
[1046] Pettifor, D. G., “Pressure-cell boundary relation and application to transition-metal equation of state,” Commun. Phys. 1:141, 1976.Google Scholar
[1047] Becke, A. D. and Edgecombe, K. E., “A simple measure of electron localization in atomic and molecular systems,” J. Chem. Phys. 92:53975403, 1990.Google Scholar
[1048] Savin, A., Nesper, R., Wengert, Steffen, and Fssler, T. F., “ELF: The Electron Localization Function,” Angew. Chem., Int. Ed. 36:1808–1832, 1997.Google Scholar
[1049] Methfessel, M. and van Schilfgaarde, M., “Derivation of force theorems in density-functional theory: Application to the full-potential LMTO method,” Phys. Rev. B 48:49374940, 1993.Google Scholar
[1050] Grafenstein, J. and Ziesche, P., “Andersen’s force theorem and the local stress field,” Phys. Rev. B 53:71437146, 1996.Google Scholar
[1051] Condon, E. U. and Shortley, G. H., Theory of Atomic Spectra, Cambridge University Press, New York, 1935.Google Scholar
[1052] Gaunt, J. A., “Triplets of helium,” Phil. Trans. Roy. Soc. (London) 228:151–196, 1929.Google Scholar
[1053] Numerov, B., “Note on the numerical integration of d2 x/dt2 = f(x,t),” Astron. Nachr. 230:359364, 1927.Google Scholar
[1054] Heath, M. T., Scientific Computing: An Introductory Survey, McGraw-Hill, New York, 1997.Google Scholar
[1055] Gill, P. E., Murray, W., and Wright, M. H., Practical Optimization, Academic Press, London, 1981.Google Scholar
[1056] Kresse, G. and Furthmüller, J., “Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set,” Phys. Rev. B 54:1116911186, 1996.Google Scholar
[1057] Pulay, P., “Convergence acceleration of iterative sequences. The case of SCF iteration,” Chem. Phys. Lett. 73:393397, 1980.Google Scholar
[1058] Pulay, P., “Improved SCF convergence acceleration,” J. Comp. Chem. 3:556560, 1982.Google Scholar
[1059] van Lenthe, J. H. and Pulay, P., “A space-saving modification of Davidson’s eigenvector algorithm,” J. Comp. Chem. 11:11641168, 1990.Google Scholar
[1060] Thirring, H., “Space lattices and specific heat,” Phys. Zeit. 14:867, 1913.Google Scholar
[1061] Lanczos, C., Applied Analysis, Printice Hall, New York, 1956.Google Scholar
[1062] Akhiezer, N. I., The Classical Moment Problem, Oliver and Boyd, Edinburgh, 1965.Google Scholar
[1063] Roder, H., Silver, R. N., Dong, J. J., and Drabold, D. A., “Kernel polynomial method for a nonorthogonal electronic-structure calculation of amorphous diamond,” Phys. Rev. B 55:15382, 1997.Google Scholar
[1064] Skilling, J., in Maximum Entropy and Bayesian Methods, edited by Skilling, J., Kluwer, Dordrecht, 1989, p. 455.Google Scholar
[1065] Mead, L. R., “Approximate solution of Fredholm integral equations by the maximum-entropy method,” J. Math. Phys. 27:2903, 1986.Google Scholar
[1066] Goedecker, S., “Linear scaling electronic structure methods,” Rev. Mod. Phys. 71:10851123, 1999.Google Scholar
[1067] Arias, T. A., “Multiresolution analysis of electronic structure: Semicardinal and wavelet bases,” Rev. Mod. Phys. 71:267311, 1999.Google Scholar
[1068] Jacobi, C. G. J., “Über ein leichtes Verfahren die in der Theorie der Säculärstörrungen vorkommenden Gleichungen numerisch aufzulösen,” Crelle’s J. 30:5194, 1846.Google Scholar
[1069] Martins, J. L. and Cohen, M. L., “Diagonalization of large matrices in pseudopotential band-structure calculations: Dual-space formalism,” Phys. Rev. B 37:61346138, 1988.Google Scholar
[1070] Nex, C. M. M., “A new splitting to solve large hermitian problems,” Comp. Phys. Comm. 53:141, 1989.Google Scholar
[1071] Teter, M. P., Payne, M. C., and Allan, D. C., “Solution of Schrödinger’s equation for large systems,” Phys. Rev. B 40:1225512263, 1989.Google Scholar
[1072] Seitsonen, A. P., Puska, M. J., and Nieminen, R. M., “Real-space electronic-structure calculations: Combination of the finite-difference and conjugate-gradient methods,” Phys. Rev. B 51:1405714061, 1995.Google Scholar
[1073] Parlett, B. N., The Symmetric Eigenvalue Problem, Prentice Hall, Engelwood Cliffs, NJ, 1980.Google Scholar
[1074] Saad, Y., Iterative Methods for Sparse Linear Systems, 2nd ed., SIAM, Philadelphia, PA, 2003.Google Scholar
[1075] Davidson, E. R., “The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices,” J. Comp. Phys. 17:87, 1975.Google Scholar
[1076] Lanczos, C., “An iteration method for the solution of the eigenvalue problem of linear differential and intergral operators,” J. Res. Natl. Bur. Stand. 45:255, 1950.Google Scholar
[1077] Lin, H. Q. and Gubernatis, J. E., “Exact diagonalization methods for quantum systems,” Comp. Phys. 7:400407, 1993.Google Scholar
[1078] Wang, L.-W. and Zunger, A., “Large scale electronic strucuture calculations using the Lanczos method,” Comp. Mat. Sci. 2:326340, 1994.Google Scholar
[1079] Davidson, E. R., in Methods in Computational Molecular Physics, edited by Diercksen, H. F. and Wilson, S., D. Reidel Publishing Co., Dordrecht, 1983, pp. 95113.Google Scholar
[1080] Davidson, E. R., “Monster matrices: Their eigenvalues and eigenvectors,” Comp. Phys. 7:519, 1993.Google Scholar
[1081] Booten, A. and van der Vorst, H., “Cracking large scale eigenvalue problems. Part I: Algorithms,” Comp. Phys. 10:239242, 1996.Google Scholar
[1082] Wood, D. M. and Zunger, A., “A new method for diagonalizing large matrices,” J. Phys. A 18:13431359, 1985.Google Scholar
[1083] Kim, H., Yu, B. D., and Ihm, J., “Modification of the DIIS method for diagonalizing large matrices,” J. Phys. A 27:11991204, 1994.Google Scholar
[1084] Stich, I., Car, R., Parrinello, M., and Baroni, S., “Conjugate gradient minimization of the energy functional: A new method for electronic structure calculation,” Phys. Rev. B 39:4997, 1989.Google Scholar
[1085] Bylander, D. M., Kleinman, L., and Lee, S., “Self-consistent calculations of the energy bands and bonding properties of B12 C3,” Phys. Rev. B 42:13941403, 1990.Google Scholar
[1086] Arias, T. A., Payne, M. C., and Joannopoulos, J. D., “Ab initio molecular dynamics: Analytically continued energy functionals and insights into iterative solutions,” Phys. Rev. Lett. 69:1077– 1080, 1992.Google Scholar
[1087] Canning, A., Wang, L. W., Williamson, A., and Zunger, A., “Parallel empirical pseudopotential electronic structure calculations for million atom systems,” J. Comp. Phys. 160:29, 2000.Google Scholar
[1088] Ericsson, T. and Ruhe, A., “The spectral transformation Lanczos method for the numerical solution of large sparse generalized symmetric eigenvalue problems,” Math. Comp. 35:1251– 1268, 1980.Google Scholar
[1089] Sharma, R. R., “General expressions for reducing the Slater–Koster linear combination of atomic orbitals integrals to the two-center approximation,” Phys. Rev. B19:28132823, 1979.Google Scholar
[1090] Cohen-Tannoudji, C., Diu, B., and Laloë, F., Quantum Mechanics, Wiley-Interscience, Paris, 1977.Google Scholar
[1091] Dirac, P. A. M., The Principles of Quantum Mechanics, Oxford University Press, Oxford, 1930.Google Scholar
[1092] Ziman, J.M., Principles of the Theory of Solids, Cambridge University Press, Cambridge, 1989.Google Scholar
[1093] Bjorken, J. D. and Drell, S. D., Relativistic Quantum Mechanics, McGraw-Hill, New York, 1964.Google Scholar
[1094] Koelling, D. D. and Harmon, B. N., “A technique for relativistic spin-polarized calculations,” J. Phys. C 10:31073114, 1977.Google Scholar
[1095] MacDonald, A. H., Pickett, W. E., and Koelling, D., “A linearised relativistic augmented-plane-wave method utilising approximate pure spin basis functions,” J. Phys. C: Solid State Phys. 13:26752683, 1980.Google Scholar
[1096] Aharonov, Y. and Bohm, D., “Further discussion of the role of electromagnetic potentials in the quantum theory,” Phys. Rev. 130:16251632, 1963.Google Scholar
[1097] Simon, B., “Holonomy, the quantum adiabatic theorem, and Berry’s phase,” Phys. Rev. Lett. 51:21672170, 1983.Google Scholar
[1098] Advanced Series in Mathematical Physics, vol. 5, Geometric Phases in Physics, edited by Wilczek, F. and Shapere, A., World Prss, Singapore, 1989.Google Scholar
[1099] Dirac, P. A. M., “Quantised singularities in the electromagnetic field,” Proc. R. Soc. A 133:60– 72, 1931.Google Scholar
[1100] Prange, R. E. and Girvin, S. M., The Quantum Hall Effect, Springer-Verlag, New York, 1990.Google Scholar
[1101] Halperin, B. I., “Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential,” Phys. Rev. B 25:21852190, 1982.Google Scholar
[1102] Laughlin, R. B., “Quantized Hall conductivity in two dimensions,” Phys. Rev. B 23:5632– 5633, 1981.Google Scholar
[1103] Hall, E. H., “On a new action of the magnet on electric currents,” Am. J. Math. 2:287292, 1879.Google Scholar
[1104] Gonze, X., et al., “Recent developments in the ABINIT software package,” Comput. Phys. Commun. 205:106131, 2016.Google Scholar
[1105] Clark, S. J., Segall, M. D., Pickard, C. J., Hasnip, P. J., Probert, M. J., Refson, K., and Payne, M. C., “First principles methods using CASTEP,” Z. Kristallographie 220:567570, 2005.Google Scholar
[1106] Giannozzi, P., et al., “QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials,” J. Phys. Condens. Matter 21:395502, 2009.Google Scholar
[1107] Dovesi, R., et al., “Quantum-mechanical condensed matter simulations with CRYSTAL,” Wiley Interdiscip. Rev. Comput. Mol. Sci. 8:e1360, 2018.Google Scholar
[1108] Castro, A., Appel, H., Oliveira, M., Rozzi, C. A., Andrade, X., Lorenzen, F., Marques, M. A. L., Gross, E. K. U., and Rubio, A., “OCOTOPUS: A tool for the application of time-dependent density functional theory,” Phys. Stat. Sol. B 243:24652488, 2006.Google Scholar
[1109] Bowler, D. R., Choudhury, R., Gillan, M. J., and Miyazaki, T., “Recent progress with large-scale ab initio calculations: the conquest code,” Phys. Stat. Sol. B 243:9891000, 2006.Google Scholar
[1110] Skylaris, C.-K., Haynes, P. D., Mostofi, A. A., and Payne, M. C., “Introducing ONETEP: Linear-scaling density functional simulations on parallel computers,” J. Chem. Phys. 122:084119, 2005.Google Scholar
[1111] Haynes, P. D., Mostof, A. A., Skylaris, C.-K., and Payne, M. C., “ONETEP: Linear-scaling density-functional theory with plane-waves,” J. Phys. Conf. Ser. 26:143148, 2006.Google Scholar
[1112] Mostofi, A. A., Yates, J. R., Pizzi, G., Lee, Y.-S., Souza, I., Vanderbilt, D., and Marzari, N., “An updated version of wannier90: A tool for obtaining maximally-localised Wannier functions,” Comput. Phys. Commun. 185:23092310, 2014.Google Scholar
[1113] Wang, Y., Lv, J., Zhu, L., and Ma, Y., “CALYPSO: A method for crystal structure prediction,” Comput. Phys. Commun. 183(10):20632070, 2012.Google Scholar

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  • References
  • Richard M. Martin, University of Illinois, Urbana-Champaign
  • Book: Electronic Structure
  • Online publication: 18 September 2020
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  • Richard M. Martin, University of Illinois, Urbana-Champaign
  • Book: Electronic Structure
  • Online publication: 18 September 2020
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  • References
  • Richard M. Martin, University of Illinois, Urbana-Champaign
  • Book: Electronic Structure
  • Online publication: 18 September 2020
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