Exactly Fragment Additive Breakdown of Polarization for Energy Decomposition Analysis Based on the Self-Consistent Field for Molecular Interactions

Energy decomposition analysis (EDA) is a useful method to unravel intermolecular interaction energy into chemically meaningful components such as geometric distortion, frozen interactions, polarization, and charge transfer. A further decomposition of the polarization (POL) and charge transfer (CT) energy into fragment-wise contributions would be useful to understand the significance of each fragment during these two processes. To complement the existing exact pairwise decomposition of the CT term, this work describes the formulation and implementation of a nonperturbative polarization analysis that decomposes the POL energy into an exactly fragment-wise additive sum based on the absolutely localized molecular orbital energy decomposition analysis (ALMO-EDA). These fragment-wise contributions can be further decomposed into chemically intuitive molecular orbital pairs using complementary occupied-virtual pair (COVP) analysis. A very useful phase convention is established for each COVP such that constructive interference of occupied and virtual corresponds to electron flow into that region, while destructive interference corresponds to electron outflow. A range of model problems are used to demonstrate that the polarization process is typically a collective behavior of the electrons that is quite different from the charge transfer process. This provides another reason in addition to their different distance dependence on fragment separation for separating these two processes in EDA.