Rank reduced coupled cluster theory. I. Ground state energies and wavefunctions

Abstract

We propose a compression of the opposite-spin coupled cluster doubles amplitudes of the form τijabUiaVTVWUjbW, where UiaV are the n V -highest magnitude eigenvectors of the MP2 or MP3 doubles amplitudes. Together with a corresponding parameterization of the opposite-spin coupled cluster Lagrange multipliers of the form λabijUiaVLVWUjbW, this yields a fully self-consistent parameterization of reduced-rank coupled cluster equations in terms of the Lagrangian L0TVW,LVW. Making this Lagrangian stationary with respect to the L VW parameters yields a perfectly determined set of equations for the T VW equations and coupled cluster energy. These equations can be solved using a Lyapunov equation for the first-order amplitude updates. We test this "rank-reduced coupled cluster" method for coupled cluster singles and doubles in medium sized molecules and find that substantial compression of the T^2 amplitudes is possible with acceptable accuracy.