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Analysis of the projected coupled cluster method in electronic structure calculation

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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.

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Authors and Affiliations

  1. TU Berlin, Sekretariat MA 5-3, Straße des 17. juni 136, 10623, Berlin, Germany

    Reinhold Schneider

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  1. Reinhold Schneider
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Correspondence to Reinhold Schneider.

Additional information

This research was supported by DFG priority program SSP 1145 Modern and universal first-principles methods for many-electron systems in chemistry and physics.

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Schneider, R. Analysis of the projected coupled cluster method in electronic structure calculation. Numer. Math. 113, 433–471 (2009). https://doi.org/10.1007/s00211-009-0237-3

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  • DOI: https://doi.org/10.1007/s00211-009-0237-3

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