Stochastic Resolution of Identity to CC2 for Large Systems: Excited State Properties.

We apply a stochastic resolution of identity approximation (sRI) to the CC2 method for the excitation energy calculations. A set of stochastic orbitals are employed to decouple the crucial 4-index electron repulsion integrals and optimize the contraction steps in CC2 response theory. The CC2 response for excitations builds upon sRI-CC2 ground-state calculations, which scales as O ( N 3 ), where N is a measure for the system size. Overall, the current algorithm for excited states also allows a sharp scaling reduction from original O ( N 5 ) to O ( N 3 ). We test the sRI-CC2 for different molecular systems and basis sets, and we show that our sRI-CC2 method can accurately reproduce the results of the deterministic CC2 approach. Our sRI-CC2 exhibits an experimental scaling of O ( N 2.59 ) for a series of olefin chains, allowing us to calculate systems with nearly thousands of electrons.