Quartic scaling evaluation of canonical scaled opposite spin second-order Møller–Plesset correlation energy using Cholesky decompositions

The scaled opposite spin second-order Møller–Plesset (SOS-MP2) energy expression is reformulated using Cholesky decomposition of the amplitude matrix. The resulting algorithm requires an auxiliary basis or Cholesky representation of the two-electron integrals and shows fourth-order scaling with system size. Based on an analysis of operation counts, we estimate that the present approach is computationally advantageous compared to the analogous fourth-order algorithms that employ Laplace transforms.