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

We propose a compression of the opposite-spin coupled cluster doubles amplitudes of the form τ_ij ^ab≡U_ia ^VT^VWU_jb ^W, where U_ia ^V 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 λ_ab ^ij≡U_ia ^VL^VWU_jb ^W, this yields a fully self-consistent parameterization of reduced-rank coupled cluster equations in terms of the Lagrangian L₀T^VW,L^VW. 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.