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

Yvon Maday; Gabriel Turinici

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 35, Issue: 4, page 779-798
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Maday, Yvon, and Turinici, Gabriel. "Numerical Analysis of the Adiabatic Variable Method for the Approximation of the Nuclear Hamiltonian." ESAIM: Mathematical Modelling and Numerical Analysis 35.4 (2010): 779-798. <http://eudml.org/doc/197514>.

@article{Maday2010,
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. },
author = {Maday, Yvon, Turinici, Gabriel},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {A posteriori estimator; adiabatic variable method; computational quantum chemistry; nuclear Hamiltonian.; a posteriori error control; chemical kinetics; Jacobi variables method; eigenelements; nuclear Hamiltonian; multi-body problem; numerical results},
language = {eng},
month = {3},
number = {4},
pages = {779-798},
publisher = {EDP Sciences},
title = {Numerical Analysis of the Adiabatic Variable Method for the Approximation of the Nuclear Hamiltonian},
url = {http://eudml.org/doc/197514},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Maday, Yvon
AU - Turinici, Gabriel
TI - Numerical Analysis of the Adiabatic Variable Method for the Approximation of the Nuclear Hamiltonian
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 4
SP - 779
EP - 798
AB - 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.
LA - eng
KW - A posteriori estimator; adiabatic variable method; computational quantum chemistry; nuclear Hamiltonian.; a posteriori error control; chemical kinetics; Jacobi variables method; eigenelements; nuclear Hamiltonian; multi-body problem; numerical results
UR - http://eudml.org/doc/197514
ER -

References

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