Variational Energy Decomposition Analysis of Chemical Bonding. 1. Spin-Pure Analysis of Single Bonds

We have designed an energy decomposition analysis (EDA) to gain a deeper understanding of single chemical bonds, that is, those in which the interacting fragments are doublet open-shell systems but the supersystem is closed-shell. The method is a spin-pure extension of the absolutely localized molecular orbital (ALMO) EDA to the one-pair perfect pairing energy (equivalently to an active space of two electrons in two orbitals). The total interaction energy is broken up into four terms: frozen interactions, spin-coupling, polarization, and charge-transfer. A variety of single bonds are analyzed and, in addition, we use this method to show how solvation changes the nature of bonds, producing different results in the gas-phase and with explicit solvent molecules.