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

Yvon Maday; Gabriel Turinici^{[1]}

- [1] INRIA Rocquencourt, Rocquencourt B.P. 105, 78153 Le Chesnay Cedex, France.

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

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topMaday, Yvon, and Turinici, Gabriel. "Numerical analysis of the adiabatic variable method for the approximation of the nuclear hamiltonian." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 35.4 (2001): 779-798. <http://eudml.org/doc/194073>.

@article{Maday2001,

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.},

affiliation = {INRIA Rocquencourt, Rocquencourt B.P. 105, 78153 Le Chesnay Cedex, France.},

author = {Maday, Yvon, Turinici, Gabriel},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

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},

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/194073},

volume = {35},

year = {2001},

}

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 - Modélisation Mathématique et Analyse Numérique

PY - 2001

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/194073

ER -

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