Generalized X-pol theory and charge delocalization states

The mixed molecular orbital and valence bond (MOVB) method has been used to generalize the explicit polarization (X-Pol) potential to incorporate charge delocalization resonance effects in the framework of valence bond theory. In the original X-Pol method, a macromolecular system is partitioned into individual fragments or blocks, and the molecular orbitals of the system are strictly localized within each block. Consequently, these block-localized molecular orbitals (BLMOs) are nonorthogonal across different blocks. In the generalized X-Pol (GX-Pol) theory, we construct charge delocalization VB states by expanding the localization space from monomer blocks into pairwise delocalized blocks. Thus, the expansion of the basis space leads to charge delocalization between monomer pairs, and a series of pairwise delocalization states can be constructed. In general, L-body delocalized states can be analogously defined by grouping L monomer blocks into one. The Hartree product wave function for each state can be fully antisymmetrized, which introduces explicitly exchange repulsion among all blocks. The GX-Pol wave function is a linear combination of all L-body charge transfer (valence bond) states, which incorporates charge delocalization and their resonance as well as static correlation effects. The GX-Pol method provides a general and rigorous theory to incorporate charge delocalization explicitly into these fragment-based electronic structural methods for macromolecular systems.