ERROR ESTIMATES FOR THE COUPLED CLUSTER METHOD

作者：Rohwedder Thorsten^*; Schneider Reinhold

来源：ESAIM: Mathematical Modelling and Numerical Analysis , 2013, 47(6): 1553-1582.

DOI：10.1051/m2an/2013075

• Quantum chemistry
• electronic Schrodinger equation
• coupled Cluster method
• numerical analysis
• non-linear operator equation
• quasi-optimality
• error estimators

The Coupled Cluster (CC) method is a widely used and highly successful high precision method for the solution of the stationary electronic Schrodinger 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 %26quot;full-CI-limit%26quot;) 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 Schrodinger 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 Schrodinger 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.

• 出版日期2013-11