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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 precisionmethod for the solution of the stationary electronic Schrödingerequation, with its practical convergence properties being similar to that of acorresponding Galerkin (CI) scheme. This behaviour has for the discrete CC method beenanalyzed with respect to the discrete Galerkin solution (the “full-CI-limit”) in[Schneider, 2009]. Recently, we globalized the CC formulation to the full continuousspace, giving a root equation for an infinite dimensional, nonlinear Coupled Clusteroperator that is equivalent the full electronic Schrödinger equation [Rohwedder, 2011]. Inthis paper, we combine both approaches to prove existence and uniqueness results,quasi-optimality estimates and energy estimates for the CC method with respect to thesolution of the full, original Schrödinger equation. The main property used is a localstrong monotonicity result for the Coupled Cluster function, and we give twocharacterizations for situations in which this property holds.

Keywords

Quantum chemistryelectronic Schrödinger equationcoupled Cluster methodnumerical analysisnonlinear operator equationquasi-optimalityerror estimators

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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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