In a new paper (DOI: 10.1039/d2cp05648h), selected as a “2023 Hot PCCP article”, the Herzfeld group has shown that the “Lewis dot” representation of electrons can predict states that have otherwise been predicted only by the most advanced implementations of quantum mechanics.

Basically, the structures and reactions of molecules are controlled by the interactions of electrons with each other and with atomic nuclei. However, the process is complicated by the fact that wave properties are important for particles as light as electrons. The gold standard is to explicitly model these properties using wave mechanics. But it is convenient to have an implicit description that is more accessible and intuitive. These are the “Lewis dots” that are generally used to represent bonds and reaction mechanisms in chemistry courses and journal articles. Lewis dots are semi-classical particles: classical in the sense of being associated with a location in space, but non-classical in that they don’t stick to the oppositely charged nuclei and can have two different spin states.

In recent years, the Herzfeld group has sought to quantify this picture. A subtlety is that the interactions between electrons is spin dependent due to the antisymmetry of electron wave functions. This explains why electrons of unlike spin often form pairs. However, the charges of electrons should always repel one another and Linnett suggested already in 1961 that two electrons should only co-localize if they are both sufficiently attracted to the same inter-nuclear region. In their new paper, the Herzfeld group shows that, a careful representation of the effects of wave function anti-symmetry, leads to Linnett-like structures when there are not enough internuclear basins to induce all the electrons to form simple pairs. A striking example is given by benzene. The traditional semi-classical representation of benzene, as a resonance between two structures with alternating single and double bonds, is obviated by a structure with three electrons in each carbon-carbon bond (shown here with the six carbon kernels in teal, six hydrogen kernels in white, and 15 valence electrons of each spin in pink and magenta).

Publication: Emergence of Linnett’s “double quartets” from a model of “Lewis dots.” Judith Herzfeld. Physical Chemistry Chemical Physics, Issue 7, 2023.