Nowadays, the Coupled Cluster (CC) method is the probably most widely used high precision method for the solution of the main equation of electronic structure calculation, the stationary electronic Schrödinger equation. Traditionally, the equations of CC are formulated as a nonlinear approximation of a Galerkin solution of the electronic Schrödinger equation, i.e. within a given discrete subspace. Unfortunately, this concept prohibits the direct application of concepts of nonlinear numerical analysis to obtain e.g. existence and uniqueness results or estimates on the convergence of discrete solutions to the full solution. Here, this shortcoming is approached by showing that based on the choice of an N-dimensional reference subspace R of H1(ℝ3 × {± 1/2}), the original, continuous electronic Schrödinger equation can be reformulated equivalently as a root equation for an infinite-dimensional nonlinear Coupled Cluster operator. The canonical projected CC equations may then be understood as discretizations of this operator. As the main step, continuity properties of the cluster operator S and its adjoint S† as mappings on the antisymmetric energy space H1 are established.
Mots clés : quantum chemistry, electronic Schrödinger equation, coupled cluster method, numerical analysis, nonlinear operator equation
@article{M2AN_2013__47_2_421_0,
author = {Rohwedder, Thorsten},
title = {The continuous {Coupled} {Cluster} formulation for the electronic {Schr\"odinger} equation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {421--447},
publisher = {EDP-Sciences},
volume = {47},
number = {2},
year = {2013},
doi = {10.1051/m2an/2012035},
mrnumber = {3021693},
zbl = {1269.82032},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2012035/}
}
TY - JOUR AU - Rohwedder, Thorsten TI - The continuous Coupled Cluster formulation for the electronic Schrödinger equation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2013 SP - 421 EP - 447 VL - 47 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2012035/ DO - 10.1051/m2an/2012035 LA - en ID - M2AN_2013__47_2_421_0 ER -
%0 Journal Article %A Rohwedder, Thorsten %T The continuous Coupled Cluster formulation for the electronic Schrödinger equation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 421-447 %V 47 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2012035/ %R 10.1051/m2an/2012035 %G en %F M2AN_2013__47_2_421_0
Rohwedder, Thorsten. The continuous Coupled Cluster formulation for the electronic Schrödinger equation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 2, pp. 421-447. doi : 10.1051/m2an/2012035. http://archive.numdam.org/articles/10.1051/m2an/2012035/
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