The weak-overlap bond: An SGF (Simplified Group Function) analysis

Substituent and solvent effects in reactivity and spectroscopy, as well as bonding in Van der Waals and/or hydrogen-bonded dimers, fall within the weak-to-zero-overlap regime. The simplified group function (SGF) approach coupled with a fixed spin (FS) electronic representation is shown to lead to a systematic theoretical development of the wave function in this bonding region in a manner paralleling intuitive chemical thinking; i.e. in terms of labelled electrons of fixed spin “jumping” between specific-group orbitals (FS activity). The readily visualizable resolution into types of FS activity is shown to also underlie the formal theoretical resolution of the SGF wave function, and thus any observables derived from it. In particular, the energetics of the weak-overlap bond (the SGF potential) is developed in the perturbative limit of mixing excitation structures, leading to additive long-range (overlap independent: static, inductive, dispersive) and short-range (overlap dependent: dative, codative, covalent and Pauli-induced) contributions. An important feature of SGF methodology in analytic application to substituent and solvent effects is that simplification of the wave function is achieved through systematic suppression of interchange activity, thereby retaining the full form of the Hamiltonian including, e.g., electron-electron repulsion). This is demonstrated in a range of applications: viz. (i) to a justification for frontier-orbital theory and the angular-overlap model; (ii) to a description of substituent effects in aromatic electrophilic substitution; and (iii) to the development of a simple framework for discussing solvent/ligand effects on solute/metal transition energies.