Classification of bonds is essential for understanding and predicting the reactivity of chemical compounds. This classification mainly manifests in the bond order and the contribution of different Lewis resonance structures....

Chemists explaining a molecule’s stability and reactivity often refer to the concepts of delocalization, resonance, and aromaticity. Resonance is commonly discussed within valence bond theory as the stabilizing effect of mixing different Lewis structures. Yet, most computational chemists work with delocalized molecular orbitals, which are also usually employed to explain the concept of aromaticity, a ring delocalization in cyclic planar systems which abide certain number rules. However, all three concepts lack a real space definition, that is not reliant on orbitals or specific wave function expansions. Here, we outline a redefinition from first principles: delocalization means that likely electron arrangements are connected via paths of high probability density in the many-electron real space. In this picture, resonance is the consideration of additional electron arrangements, which offer alternative paths. Most notably, the famous 4n + 2 Hückel rule is generalized and derived from nothing but the antisymmetry of fermionic wave functions.

The empirical Lewis picture of the chemical bond dominates the view chemists have of molecules, of their stability and reactivity. Within the mathematical framework of quantum mechanics, all this chemical information is hidden in the many-particle wave function Ψ. Thus, to reveal and understand it, there is great interest in enhancing the Lewis model and connecting it to computable quantities. As has previously been shown, the Lewis picture can often be recovered from the probability density |Ψ|2 with probabilities in agreement with valence bond weights: the structures appear as most likely positions in the all-electron configuration space. Here, we systematically expand this topological probability density analysis to molecules with multiple bonds and lone pairs, employing correlated Slater-Jastrow wave functions. In contrast to earlier studies, non-Lewis structures are obtained that disagree with the prevalent picture and have a potentially better predictive capability. While functional groups are still recovered with these ab initio structures, the boundary between bonds and lone pairs is mostly blurred or non-existent. In order to understand the newly found structures, the Lewis electron pairs are replaced with spin-coupled electron motifs as the fundamental electronic fragment. These electron motifs—which coincide with Lewis’ electron pairs for many single bonds—arise naturally from the generally applicable analysis presented. An attempt is made to rationalize the geometry of the newly-found structures by considering the Coulomb force and the Pauli repulsion.

The concept of distinct bonds within molecules has proven to be successful in rationalizing chemical reactivity. However, bonds are not a well-defined physical concept, but rather vague entities, described by different and often contradicting models. With probability density analysis, which can---in principle---be applied to any wave function, bonds are recovered as spin-coupled positions within most likely electron arrangements in coordinate space. While the wave functions of many systems are dominated by a single electron arrangement which is built from two-center two-electron bonds, some systems require several different arrangements to be well described. In this work, a range of these multi-center bonded molecules are classified and investigated with probability density analysis. The results are compared with valence bond theory calculations and data from collision-induced dissociation experiments.