Error estimates for the Coupled Cluster method∗
Sekretariat MA 5-3, Institut für Mathematik, TU Berlin, Straße des 17. Juni
136, 10623 Berlin, Germany.
Revised: 26 November 2012
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.
Mathematics Subject Classification: 65Z05 / 81-08 / 70-08
Key words: Quantum chemistry / electronic Schrödinger equation / coupled Cluster method / numerical analysis / nonlinear operator equation / quasi-optimality / error estimators
© EDP Sciences, SMAI, 2013