The visualization of chemical bonding motifs from many-electron wavefunctions: Dynamic Voronoi Metropolis Sampling

Abstract

Localized valence bond theory and the delocalized molecular orbital theory (MO) are always being discussed in terms of which is the better description of electronic structure. Molecular orbital theory has won out due to its algorithmic simplicity. However, the intuition of the practising chemist is based on valence bond theory. What is missing is an intuition-free method to inspect the high dimensionality electronic wavefunction to recover chemical intuition from MO calculation. A method is prevented to visualise the 3N-dimensional space of a many-electron wavefunction into hyper-regions related by permutation symmetry. These hyper-regions represent ``tiles'' of the wavefunction from which the wavefunction may be regenerated in its entirety upon application of the set of permutations of like-spin electrons. In this method, a Voronoi diagram is constructed from the average position of Monte Carlo walkers sampling |Ψ|2, determines a self-consistent partitioning of the wavefunction. When one of the identical 3N-dimensional Voronoi sites is projected onto the coordinates of each electron, chemical motifs are naturally revealed. The structures of some molecules such as nitrogen and oxygen give connections with the double quartet of Linnett. And, other molecules such as ethylene, show the chemical bonds which are satisfied by chemical sense. When this method, with multi-configurational wavefunctions, is applied to benzene, the conjugated electronic structure appears. Dicarbon’s structure, which is in terms of a near triple bond with singlet-coupled outer electrons, is arrived by this method with a configuration interaction calculation. Multi-Voronoi tiles are required to describe the electronic structures of molecules which have resonance structures or unpaired electrons. After implementation of multi-Voronoi, the two electronic configurations of methyl radical, and resonance structures of allyl cation are presented. Moreover, the analysis of the wavefunction tile along a reaction coordinate is demonstrated to reveal the electron movements depicted by the canonical ``curly-arrow'' notation for several reactions such as SN2 and the [4+2] Diels-Alder reaction. The Diels-Alder reaction is revealed to involve the separation and counter-propagation of electrons spins. This unprecedented method of extraction the movements of electrons during a chemical reaction is a breakthrough in connecting traditional depictions of chemical mechanism with state-of-the-art quantum chemical calculations.