Stochastic resolution of identity to CC2 for large systems: Oscillator strength and ground state gradient calculations

Abstract

An implementation of stochastic resolution of identity (sRI) approximation to CC2 oscillator strengths and ground state analytical gradients is presented. The essential four-index electron repulsion integral is contracted with a set of stochastic orbitals on the basis of the RI technique and the orbital energy difference in the denominators is decoupled by the Laplace transform. These lead to a significant scaling reduction from O(N5) to O(N3) for oscillator strengths with the number of basis functions, N. The scaling for gradients can also be reduced to O(N3) but this requires a large number of stochastic orbitals and causes a discernible loss of accuracy. Therefore, we provide an O(N4) version with better accuracy and smaller prefactor by adopting sRI partially. Such steep computational acceleration of nearly two or one order of magnitude is very attractive for large systems. This work is an extension to our previous implementations of sRI-CC2 ground and excited state energies and shows the feasibility of introducing sRI to CC2 properties beyond energies.