Analysis of the projected Coupled Cluster Method in Electronic Structure Calculation

The electronic Schrödinger equation plays a fundamental role in molecular physics. It describes the stationary nonrelativistic behaviour of a 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 talk 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 (Configuration Interaction) 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.