Error estimates for the Coupled Cluster method
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 6, p. 1553-1582
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.
DOI : https://doi.org/10.1051/m2an/2013075
Classification:  65Z05,  81-08,  70-08
Keywords: 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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {6},
     year = {2013},
     pages = {1553-1582},
     doi = {10.1051/m2an/2013075},
     zbl = {1297.65139},
     mrnumber = {3110488},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2013__47_6_1553_0}
}
Rohwedder, Thorsten; Schneider, Reinhold. Error estimates for the Coupled Cluster method. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 6, pp. 1553-1582. doi : 10.1051/m2an/2013075. http://www.numdam.org/item/M2AN_2013__47_6_1553_0/

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