Second-Generation Energy Decomposition Analysis of Intermolecular Interaction Energies from the Second-Order Mo̷ller–Plesset Theory: An Extensible, Orthogonal Formulation with Useful Basis Set Convergence for All Terms

Energy decomposition analysis (EDA) based on density functional theory (DFT) and self-consistent field (SCF) calculations has become widely used for understanding intermolecular interactions. This work reports a new approach to EDA for post-SCF wave functions based on closed-shell restricted second-order Mo̷ller–Plesset (MP2) together with an efficient implementation that generalizes the successful SCF-level second-generation absolutely localized molecular orbital EDA approach, ALMO-EDA-II, and improves upon MP2 ALMO-EDA-I. The new MP2 ALMO-EDA-II provides distinct energy contributions for a frozen interaction energy containing permanent electrostatics and Pauli repulsions, polarized energy-yielding induced electrostatics, dispersion-corrected energy, and the fully relaxed energy, which describes charge transfer. All terms have useful complete basis set limits due to the design of the theory, corroborated by a range of test calculations on model systems, and the S22 and the Ionic43 data sets of weak and strong intermolecular interactions, respectively. Comparisons with the DFT-based ALMO-EDA-II suggest that the new MP2 EDA yields quite a consistent interpretation of intermolecular interactions when the total interaction energies are consistent. To begin to address the limitations of the MP2 theory itself, the MP2 ALMO-EDA-II was also implemented for κ-regularized MP2 and the size-consistent second-order Brillouin–Wigner (BW-s2) method, both of which are more accurate for dispersion-dominated interactions. The principal limitation of MP2 ALMO-EDA-II is associated with the need to obtain orthogonal fragment-localized virtual orbitals, which leads to clearly poorer results when using atomic orbital basis sets that contain diffuse functions. We therefore recommend using nonaugmented basis sets.