The Coupled Cluster (CC) method is a widely used and highly successful high precision method for the solution of the stationary electronic Schrödinger equation, with its practical convergence properties being similar to that of a corresponding Galerkin (CI) scheme. This behaviour has for the discrete CC method been analyzed with respect to the discrete Galerkin solution (the “full-CI-limit”) in [Schneider, 2009]. Recently, we globalized the CC formulation to the full continuous space, giving a root equation for an infinite dimensional, nonlinear Coupled Cluster operator that is equivalent the full electronic Schrödinger equation [Rohwedder, 2011]. In this paper, we combine both approaches to prove existence and uniqueness results, quasi-optimality estimates and energy estimates for the CC method with respect to the solution of the full, original Schrödinger equation. The main property used is a local strong monotonicity result for the Coupled Cluster function, and we give two characterizations for situations in which this property holds.
Mots clés : quantum chemistry, electronic Schrödinger equation, coupled cluster method, numerical analysis, nonlinear operator equation, quasi-optimality, error estimators
@article{M2AN_2013__47_6_1553_0,
author = {Rohwedder, Thorsten and Schneider, Reinhold},
title = {Error estimates for the {Coupled} {Cluster} method},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1553--1582},
publisher = {EDP-Sciences},
volume = {47},
number = {6},
year = {2013},
doi = {10.1051/m2an/2013075},
mrnumber = {3110488},
zbl = {1297.65139},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2013075/}
}
TY - JOUR AU - Rohwedder, Thorsten AU - Schneider, Reinhold TI - Error estimates for the Coupled Cluster method JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2013 SP - 1553 EP - 1582 VL - 47 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2013075/ DO - 10.1051/m2an/2013075 LA - en ID - M2AN_2013__47_6_1553_0 ER -
%0 Journal Article %A Rohwedder, Thorsten %A Schneider, Reinhold %T Error estimates for the Coupled Cluster method %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 1553-1582 %V 47 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2013075/ %R 10.1051/m2an/2013075 %G en %F M2AN_2013__47_6_1553_0
Rohwedder, Thorsten; Schneider, Reinhold. Error estimates for the Coupled Cluster method. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 6, pp. 1553-1582. doi : 10.1051/m2an/2013075. http://www.numdam.org/articles/10.1051/m2an/2013075/
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