Ab Initio Dot Structures Beyond the Lewis Picture

Identifying a real space measure of charge-shift bonding with probability density analysis

Charge-shift bonds have been hypothesized as a third type of chemical bonds in addition to covalent and ionic bonds. They have first been described with valence bond theory where they are identified by the resonance energy resulting from ionic contributions. While other indicators have been described, a clear real space fingerprint for charge-shift bonding is still lacking. Probability density analysis has been developed as a real space method, allowing chemical bonding to be identified from the many-electron probability density |Ψ|2 where the wave function Ψ can be obtained from any quantum chemical method. Recently, barriers of a probability potential, which depends on this density, have proven to be good measures for delocalization and covalent bonding. In this work, we employ many examples to demonstrate that a well-suited measure for charge-shift bonding can be defined within the framework of probability density analysis. This measure correlates well with the charge-shift resonance energy from valence bond theory and thus strongly supports the charge-shift bonding concept. It is, unlike the charge-shift resonance energy, not dependent on a reference state. Moreover, it is independent of the polarity of the bond, suggesting to characterize bonds in molecules by both their polarity and their charge-shift character.

Multi-center bonds as resonance hybrids: A real space perspective

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 that 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.

Atomic shell structure from Born probabilities: Comparison to other shell descriptors and persistence in molecules

Real space chemical bonding descriptors, such as the electron localization function or the Laplacian of the electron density, have been widely used in electronic structure theory thanks to their power to provide chemically intuitive spatial images of bonded and non-bonded interactions. This capacity stems from their ability to display the shell structure of atoms and its distortion upon molecular formation. Here, we examine the spatial position of the N electrons of an atom at the maximum of the square of the wavefunction, the so-called Born maximum, as a shell structure descriptor for ground state atoms with Z = 1-36, comparing it to other available indices. The maximization is performed with the help of variational quantum Monte Carlo calculations. We show that many electron effects (mainly Pauli driven) are non-negligible, that Born shells are closer to the nucleus than any other of the examined descriptors, and that these shells are very well preserved in simple molecules.

Real space electron delocalization, resonance, and aromaticity in chemistry

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 concept of delocalization, resonance and aromaticity are commonly discussed within electronic structure frameworks relying on specific wave function expansions. Here the authors propose a redefinition of these concepts from first-principles by investigating saddle points of the all-electron probability density.

Valence Bond Theory-Its Birth, Struggles with Molecular Orbital Theory, Its Present State and Future Prospects

This essay describes the successive births of valence bond (VB) theory during 1916–1931. The alternative molecular orbital (MO) theory was born in the late 1920s. The presence of two seemingly different descriptions of molecules by the two theories led to struggles between the main proponents, Linus Pauling and Robert Mulliken, and their supporters. Until the 1950s, VB theory was dominant, and then it was eclipsed by MO theory. The struggles will be discussed, as well as the new dawn of VB theory, and its future.