A Chemically Meaningful Measure of Electron Localization

Abstract

Electron localization and delocalization are commonly invoked in the day-to-day rationalization of chemistry. This work addresses the challenges of quantifying this elusive concept in a chemically useful manner. A general principle, requiring the simultaneous quantification of (1) a limited physical volume (classical criterion) and (2) same-spin loneliness (quantum criterion), is introduced. It is demonstrated how, by beginning with the Electron Localization Function (ELF) scalar field, one can choose to discard all points in space where the same-spin loneliness is lower than a certain value. Such a partitioning approach ensures that both criteria for quantifying localization (1 and 2) are simultaneously met. The most chemically instructive results arise when the dividing boundary condition is set by the local behavior of a homogeneous electron gas. The High Electron Localization domain Population (HELP) is introduced and applied for quantifying the localization of individual domains within molecules, as well as a measure of total electron localization in atoms and molecules. Several striking agreements with chemical intuition, experimental measurable quantities, and quantum chemical constructs are demonstrated along with understandable differences. Studies of diatomic molecules agree with current ideas on chemical bonding. The size-dependence and magnitude of localization in linear hydrocarbons is studied and compared to cyclic systems, such as benzene. The proposed methodology offers a straightforward measure for direct and quantitative comparisons between atoms, molecules, and extended condensed matter.

Atomic and Ionic Radii of Elements 1–96

“…The electron density in the tail of Group 1 atoms is special in this sense, because it arises from only one s‐electron, which is isolated or separate relative to same spin‐counterparts. Same‐spin loneliness is one measure of electron localization, and can be viewed as the primary cause behind steric strain in and between molecules. This qualitatively explains how a given outer electron density in Group 1 atoms can generate a larger repulsion toward the electrons of neighboring atom, compared to the same (mixed‐spin) density of other atoms.…”

“…There are variations to be avoided (see the Li curve) until the density settles down to its expected exponential falloff. The Boyd density cutoff has been used as a practical outer boundary for quantum chemical topology domains . Other limiting values have been proposed, and variable isodensity surfaces have been used for the construction of solvation spheres in implicit solvation models …”

Spatially resolved characterization of electron localization and delocalization in molecules: Extending the Kohn‐Resta approach

“…The intuitive concept of electron localization and delocalization is widely used in chemistry to qualitatively interpret various properties of molecules, molecular systems, and solids . It is commonly associated with specific distribution of electrons which are accumulated in the certain spatial regions or are spread out over some atomic groups.…”

The bonding picture in hypervalent XF3 (X = Cl, Br, I, At) fluorides revisited with quantum chemical topology

“…The physical foundations of the VSEPR model have been extensively researched in the framework of the electron‐pair density and, moreover, numerous studies based on the gradient field of density functions have supported its original principles . Indeed, these works brought knowledge on the role of the electron‐pair domains, defined as regions of space in which the probability of finding two opposite‐spin electrons is high . Among the density functions, the so‐called electron localization function (ELF) helped for the good application of the VSEPR model, in particular to hypervalent molecules .…”