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Numerical Analysis of the Adiabatic Variable Method for the Approximation of the Nuclear Hamiltonian

Published online by Cambridge University Press:  15 April 2002

Yvon Maday  and
Gabriel Turinici
Yvon Maday
Affiliation:
ASCI, UPR 9029, bâtiment 506, Université Paris-Sud, 91405 Orsay. (turinici@asci.fr) Analyse numérique, Université Paris VI, place Jussieu, 75252 Paris Cedex 05, France. (maday@ann.jussieu.fr)
Gabriel Turinici
Affiliation:
ASCI, UPR 9029, bâtiment 506, Université Paris-Sud, 91405 Orsay. (turinici@asci.fr)
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Abstract

Many problems in quantum chemistry deal with the computation of fundamental or excited states of molecules and lead to the resolution of eigenvalue problems. One of the major difficulties in these computations lies in the very large dimension of the systems to be solved. Indeed these eigenfunctions depend on 3n variables where n stands for the number of particles (electrons and/or nucleari) in the molecule. In order to diminish the size of the systems to be solved, the chemists have proposed many interesting ideas. Among those stands the adiabatic variable method; we present in this paper a mathematical analysis of this approximation and propose, in particular, an a posteriori estimate that might allow for verifying the adiabaticity hypothesis that is done on some variables; numerical simulations that support the a posteriori estimators obtained theoretically are also presented.

Keywords

A posteriori estimatoradiabatic variable methodcomputational quantum chemistrynuclear Hamiltonian.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 4 , July 2001 , pp. 779 - 798
Copyright
© EDP Sciences, SMAI, 2001

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