Valence Bond Based Energy Decomposition Analysis Scheme and Its Application to Cation-π Interactions.

A new energy decomposition analysis (EDA) scheme based on valence bond (VB) wave function, called VB-EDA, is presented. In VB-EDA, the total interaction energy is decomposed into frozen, charge transfer, polarization and dynamic correlation terms based on valence bond calculations. The frozen term is the energy variation of the unrelaxed VB wave function according to the change of an interaction distance. The charge transfer term is the contribution of the additional VB structures while the polarization term is due to the relaxation of VB orbitals. Dynamic correlation term is computed by post-VBSCF methods. Different from other existing VB based EDA schemes, which were used to analyze noncovalent interactions for some specific complexes, the newly developed VB-EDA is designed for the general use. Using VB-EDA, the bonding nature of cation-π interactions in a series of cation-π complexes (cations = Li+, Na+, K+, Mg2+, and Ca2+; π systems = ethylene and benzene) is explored. Furthermore, a new covalency index, which demonstrates the covalency of cation-π interactions, is presented based on the VB-EDA results. The VB-EDA analysis reveals that the cation-π interactions in the Li+, Na+, and K+ complexes belong to the typical ionic bonds while the Mg2+ and Ca2+ complexes have the relatively large covalent characteristics. However, only the C2H4-Mg2+ complex can be regarded as a covalent bonding complex while the other complexes belong to the typical ionic complexes. Thereupon, it must be careful in the cognition for the covalency of intermolecular interaction. Large nonelectrostatic interaction component does not always correspond to a covalent bond.