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Preprint 10-2009

Analysis of the projected Coupled Cluster Method in Electronic Structure Calculation

Source file is available as :   Portable Document Format (PDF)

Author(s) : Reinhold Schneider

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 10-2009

MSC 2000

65N25 Eigenvalue problems
65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65Z05 Applications to physics
81V55 Molecular physics
81V70 Many-body theory; quantum Hall effect

Abstract :
The electronic Schrödinger equation plays a fundamental role in molcular physics. It describes the stationary nonrelativistic behaviour of an quantum mechanical N electron system in the electric field generated by the nuclei. The (Projected) Coupled Cluster Method has been developed for the numerical computation of the ground state energy and wave function. It provides a powerful tool for high accuracy electronic structure calculations. The present paper aims to provide a rigorous analytical treatment and convergence analysis of this method. If the discrete Hartree Fock solution is sufficiently good, the quasi-optimal convergence of the projected coupled cluster solution to the full CI solution is shown. Under reasonable assumptions also the convergence to the exact wave function can be shown in the Sobolev H^1-norm. The error of the ground state energy computation is estimated by an Aubin Nitsche type approach. Although the Projected Coupled Cluster method is nonvariational it shares advantages with the Galerkin or CI method. In addition it provides size consistency, which is considered as a fundamental property in many particle quantum mechanics.

Keywords : electronic Schrödinger equation, quantum chemistry, coupled cluster method, Galerkin method, error analysis

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