Analysis of Bonding by Quantum Chemistry─Resolving Delocalization Stabilization in a Mechanistic Basis and New Hückel Model

Abstract

No general and unique understanding of the mechanism of covalent bonding in physical terms is provided by current computational methods or by a consensus among experts. Bonding is studied by energy decomposition analysis but may also be related to the interatomic motion of valence electrons within the molecule. This dynamical view of the mechanism of bonding is not widely appreciated. The aim here is to make it accessible by translation into a corresponding form of quantum chemical energy analysis. The interatomic electron motion is directly related to the delocalization taking place when atomic basis functions are combined into molecular orbitals. A “tribasis method” is introduced, allowing an atomic basis set to form subsets of (1) strictly localized atomic functions and (2) interatomic bridge functions which allow delocalization. Calculations can then identify ground states without (no bridge functions) and with delocalization. The scheme is based on exact quantum mechanics but demonstrated by a minimal basis treatment of H 2 + and H 2 in Hartree–Fock and valence bond approximations which show that the bond energy is a sum of repulsive localization and more strongly attractive delocalization energies. The tribasis method is used to reconstruct the Hückel theory of π-electron delocalization in planar hydrocarbon molecules to account for the “overlap problem”. In its empirically fitted form, the new theory can accurately resolve both π → π* transition energy and aromatic stabilization energy. The picture of covalent bonding emerging from both hydrogenic and Hückel calculations is that there is a presence of a Pauli repulsion of localization which is overcome by a roughly twice as strong delocalization stabilization to form the bond.