Efficient equation-of-motion coupled-cluster theory using low-rank factorization

Abstract

Density functional theory in the Kohn-Sham framework is the most common and widespread method in computational material science. However, the necessity for highly accurate electronic structure theory calculations gives rise to the continued exploration of alternative techniques. Within these approaches, quantum chemical wave function based methods such as the equation of motion coupled cluster theories show remarkable potential. In conjunction with these methods, the biggest drawback stems from the significantly larger computational cost, which scales polynomially with the system size. The aim of this work is the implementation of several electronic structure algorithms culminating in the improvement of the computational efficiency of the equation of motion coupled cluster singles and doubles theory by applying low-rank factorization techniques to the Coulomb integrals. As proof of principle, we employ a model of two electrons in one dimension confined within a harmonic potential. We can validate the successful implementation of this approach and we are able to verify that the overall computational expenses are reduced through the approximation of the Coulomb integrals via six small matrices using tensor contraction. The low-rank factorized Coulomb integrals prove effective in calculating excited state energies without significant loss of accuracy. We find that adjusting two parameters of our low-rank approximation techniques allows for a systematic trade-off between accurate results and computational expenses. The results of our work make us optimistic that, building on this proof of principle, we can go a step beyond and develop efficient methods for calculating linear absorption spectra of real materials.