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EDP Sciences, ESAIM: Mathematical Modelling and Numerical Analysis, 4(35), p. 779-798, 2001

DOI: 10.1051/m2an:2001136

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Numerical analysis of the adiabatic variable method for the approximation of the nuclear hamiltonian

Journal article published in 2001 by Yvon Maday, Gabriel Turinici ORCID
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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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.