Non-orthogonal and orthogonal valence bond wavefunctions in the hydrogen molecule: the diabatic view

Abstract

The ability of the valence bond (VB) approach to describe a molecular system in ‘chemical terms’ finds its theoretical justification in the fact that the VB wavefunctions are supposed to be diabatic, i.e. with a well-defined nature, not depending on the nuclear geometry. The intimate nature of the VB wavefunctions is here analysed by computing the non-adiabatic coupling for the simple, paradigmatic case of the hydrogen (H₂) molecule. This analysis reveals that the neutral and ionic VB wavefunctions cannot be considered as diabatic states, given that they present a large non-adiabatic coupling. The diabatic states, obtained by a suitable transformation of the VB wavefunctions, are found to be the wavefunctions of the orthogonal VB (OVB) approach, which therefore gains a legitimacy in the analysis of the composition of the adiabatic wavefunctions. Such an analysis has some bearing on the description of the nature of the chemical bond in H₂: the neutral structure gives a dissociative curve and the bond is due to the stabilisation brought by the ionic structure that mixes together with the neutral structure in the ground state wavefunction at short internuclear distances. The ability of the (at first glance) neutral VB wavefunction based on the 1s orbitals to describe in a compact way the ground state (and therefore the chemical bond) is ascribed to an almost optimal mixing in this wavefunction of the diabatic neutral and ionic states at all internuclear distances.

Keywords:

• valence bond
• orthogonal valence bond
• diabatic states
• chemical bond
• non-adiabatic coupling

Acknowledgements

The authors thank G. Corongiu for bringing to their attention Majorana’s work and C. Landis for helpful discussion. This work has been financed by the Italian MIUR through its PRIN 2009 funds.