Molecular Rydberg states

M. S. Child

doi:10.1017/CBO9780511994814.002

1 - Molecular Rydberg states

Published online by Cambridge University Press: 07 October 2011

M. S. Child

Show author details

M. S. Child: Affiliation:
University of Oxford

Book contents

Get access

Summary

The nature of Rydberg states

The nature of atomic Rydberg states is well described by Gallagher, though with less emphasis on theory [1]. Those of molecules are severely complicated by the additional nuclear degrees of freedom, in a way that gives them quite different properties from those treated in most spectroscopic texts [2, 3, 4, 5]. The essential difference is that established spectroscopic theory is rooted in the Born–Oppenheimer approximation, whereby the frequencies of the electronic motion are assumed to be so high compared with the vibrational and rotational ones that the nuclear motions may be treated as moving under an adiabatic electronic energy (or potential energy) surface. In addition the vibrational frequency usually far exceeds that of the rotations, which means that every vibrational state has an approximate rotational constant. Such considerations provide the basis for a highly successful systematic theory. Modern ab-initio methods allow the calculation of very reliable potential energy surfaces and there are a variety of efficient methods for diagonalizing the resulting Hamiltonian matrix within a functional or numerical basis. Electronically non-adiabatic interactions between a small number of electronic states can also be handled by this matrix diagonalization approach, even including fragmentation processes, if complex absorbing potentials are added to the molecular Hamiltonian.

The difficulty in applying such techniques to highly excited molecular electronic states is that the Rydberg spectrum of every molecule includes 100 electronic states with principal quantum number n = 10, separated from the n = 11 manifold by only 100 cm-1, which is small compared with most vibrational spacings and comparable to rotational spacings for small hydride species.

Type: Chapter
Information: Theory of Molecular Rydberg States , pp. 1 - 16

DOI: https://doi.org/10.1017/CBO9780511994814.002 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] T., Gallagher, Rydberg Atoms (Cambridge University Press, 1994).Google Scholar

[2] G., Herzberg, Spectra of Diatomic Molecules, 2nd edn (Van Nostrand, 1950).Google Scholar

[3] G., Herzberg, Infrared and Raman Spectra (Van Nostrand, 1945).Google Scholar

[4] G., Herzberg, Electronic Spectra of Polyatomic Molecules (Van Nostrand, 1967).Google Scholar

[5] P. R., Bunker and P., Jensen, Molecular Symmetry and Spectroscopy (NRC Research Press, 1998).Google Scholar

[6] U., Fano, Phys. Rev. 2, 353 (1970).

[7] M. J., Seaton, Rep. Prog. Phys. 46, 167–257 (1983).

[8] C. H., Greene and C., Jungen, Adv. At. Mol. Phys. 21, 51 (1985).

[9] C., Jungen, Molecular Applications of Quantum Defect Theory (IOP Publishing, 1996).Google Scholar

[10] A., Szabo and N. S., Ostlund, Modern Quantum Chemistry (Dover Publishing, 1996).Google Scholar

[11] P. G., Burke and K. A., Berrington, Atomic and Molecular Processes: An R-Matrix Approach (IOP, 1993).Google Scholar

[12] P. G., Burke, R-Matrix Theory of Atomic Collisions: Application to Atomic, Molecular and Optical Processes (Springer, 2011).Google Scholar

[13] M., Aymar, C. H., Greene and E., Luc-Koenig, Rev. Mod. Phys. 68, 1015 (1996).

[14] M. S., Child, Semiclassical Mechanics with Molecular Applications (Oxford University Press, 1991).Google Scholar

[15] H., Lefebvre-Brion and R. W., Field, Perturbations in the Spectra of Diatomic Molecules (Academic Press, 1986).Google Scholar

[16] E. P., Eisbud and L., Eisbud, Phys. Rev. 72, 29 (1947).

[17] P. J. A., Buttle, Phys. Rev. 160, 719 (1967).

[18] R. N., Zare, Angular Momentum (Wiley Interscience, 1988).Google Scholar

[19] H., Lefebvre-Brion and R. W., Field, The Spectra and Dynamics of Diatomic Molecules (Academic Press, 2005).Google Scholar

[20] M., Larsson and A. E., Orel, Dissociative Recombination of Molecular Ions (Cambridge University Press, 2008).Google Scholar

[21] V., Kokoouline and C. H., Greene, Phys. Rev. A 68, 012703 (2003).

[22] C., Jungen and S. T., Pratt, Phys. Rev. Lett. 102, 023201 (2009).

[23] M., Göppert-Mayer, Ann. Physik. 9, 273 (1931).

[24] R. N., Dixon, J. M., Bayley and M. N. R., Ashfold, Chem. Phys. 84, 21 (1984).

[25] A. D., Buckingham, B. J., Orr and J. M., Sichel, Phil. Trans. Roy. Soc. London, A 268, 147 (1970).

[26] U., Fano and D., Dill, Phys. Rev. A 6, 185 (1972).

[27] D., Dill and U., Fano, Phys. Rev. Lett. 29, 1203 (1972).

[28] D., Dill, J. Chem. Phys. 65, 1130 (1976).

[29] R. R., Lucchese, A., Lafosse, J. C., Brenotet al., Phys. Rev. A 65, 020702 (2002).

[30] K., Blum, Density Matrix Theory and Applications (Plenum Press, 1981).Google Scholar

[31] D. J., Leahy, K. L., Reid, H., Park and R. N., Zare, J. Chem. Phys. 97, 4948 (1992).

[32] C. H., Greene and R. N., Zare, Phys. Rev. A 25, 2031 (1982).

[33] G., Raseev and N. A., Cherepkov, Phys. Rev. A 49, 3948 (1990).

[34] I. S., Averbukh and N. F., Perelman, Phys. Lett. A 139, 449 (1989).

[35] H. H., Fielding, Ann. Rev. Phys. Chem. 56, 91 (2005).

[36] F., Texier and C., Jungen, Phys. Rev. A 59, 412 (1999).

[37] K., Müller-Dethlefs and E. W., Schlag, Ann. Rev. Phys. Chem. 42, 109 (1991).

[38] D., Park, Z. Physik 159, 155 (1960).

[39] U., Fano, Phys. Rev. A 24, 619 (1981).

[40] W. E., Milne, Phys. Rev. 35, 863 (1930).

[41] W. E., Milne, Am. Math. Mon. 40, 863 (1933).

[42] C., Jungen and F., Texier, J. Phys. B 33, 2495 (2000).

Book contents

1 - Molecular Rydberg states

Summary

Access options

References

Save book to Kindle

Save book to Dropbox

Save book to Google Drive