Energy density analysis for second-order Møller-Plesset perturbation theory and coupled-cluster theory with singles and doubles: Application to C₂H₄ - CH₄ complexes

Grid-based energy density analysis (EDA), in which numerical integration is performed for two-electron integrals by the pseudospectral method (Imamura et al., J. Chem. Phys. 2007, 126, 034103), is extended to correlated methods: second-order Møller-Plesset (MP2) perturbation and coupled-cluster singles and doubles (CCSD). Using EDA for MP2 and CCSD, we estimate atomic correlation energy differences and correlation energy density difference maps for C₂H₄-CH₄ complexes. The analyses confirm that polarization and diffuse functions essentially contribute to the descriptions of weak interaction around the nuclei and in the area between C₂H₄ and CH₄, respectively.