Pinyuan Li

We investigated the various factors impacting the performance of Δ-machine learning (Δ-ML) solution phase molecular properties.

Semiclassical electrons (aka Lewis dots) have been a mainstay of chemists' thinking about molecular structure, polarizability, and reactivity for over a century. This utility has motivated the development of a corresponding quantitative description. Here we devise pairwise potentials that describe the behavior of valence electron pairs in hydrocarbons, including those in single, double, bridge, and bent bonds of linear, branched, and cyclic compounds, including anionic and cationic states. Beyond predicting structures and energies, the new subatomistic force field, dubbed LEWIS-B, efficiently simulates carbocation addition to a double bond and cation migration to a neighboring carbon. A crucial feature of the semiclassical electrons is variable spread, a fourth degree of freedom in addition to three Cartesian coordinates. In spontaneously adapting to different environments, the spread provides a signature of electron stability, with more contracted clouds where the electron interactions are favorable and expanded clouds where electrons are less tightly held. In addition, the pair potentials provide insight into the subtle trade-offs that govern isomerizations and reactions.

As very light fermions, electrons are governed by antisymmetric wave functions that lead to exchange integrals in the evaluation of the energy. Here we use the localized representation of orbitals to decompose the electronic energy in a fashion that isolates the enigmatic exchange contributions and characterizes their distinctive control over electron distributions. The key to this completely general analysis is considering the electrons in groups of three, drawing attention to the curvatures of pair potentials, rather than just their amplitudes and slopes. We show that a positive curvature at short distances is essential for the mutual distancing of electrons and a negative curvature at longer distances is essential to account for the influence of lone pairs on bond torsion. Neither curvature is available in the absence of the exchange contributions. Thus, although exchange energies are much shorter range than Coulomb energies, their influence on molecular geometry is profound and readily understood.