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Error estimates for the Coupled Cluster method∗

Published online by Cambridge University Press:  26 August 2013

Thorsten Rohwedder  and
Reinhold Schneider
Thorsten Rohwedder
Affiliation:
Sekretariat MA 5-3, Institut für Mathematik, TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany.. rohwedder@math.tu-berlin.de
Reinhold Schneider
Affiliation:
Sekretariat MA 5-3, Institut für Mathematik, TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany.. rohwedder@math.tu-berlin.de
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Abstract

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.

Keywords

Quantum chemistryelectronic Schrödinger equationcoupled Cluster methodnumerical analysisnonlinear operator equationquasi-optimalityerror estimators
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 6 , November 2013 , pp. 1553 - 1582
Copyright
© EDP Sciences, SMAI, 2013

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