  We apply a stochastic resolution of identity approximation (sRI) to the CC2
method for 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 our sRI-CC2 method can accurately reproduce the
results of deterministic CC2 approach. Our sRI-CC2 exhibits an experimental
scaling of O(N^2.88) for a hydrogen dimer chain, allowing us to calculate
systems with nearly thousands of electrons.
