Universal observable chemical bond analysis: gradient bundle decomposition of the electron charge density

Abstract

Our curiosity-driven desire to "see" chemical bonds dates back at least one-hundred years, perhaps to antiquity.Sweeping improvements in the accuracy of measured and predicted electron charge densities, alongside our largely bondcentric understanding of molecules and materials, heighten this desire with means and significance. Energetic analysis of arbitrary regions of charge density is problematic, however, because electronic kinetic energy is ambiguous over such regions. If the flux of the charge density gradient is zero across the boundary of a region, then the ambiguity vanishes and such a region is found to possess a well-defined kinetic energy. Such regions are called gradient bundles. Here we present gradient bundle decomposition, a method for the infinitesimal partitioning of a three-dimensional charge density that results in a two-dimensional projected space in which kinetic—and thus total—energy is everywhere well-defined; a space called the condensed charge density (P). Bond "silhouettes" in P can be reverse-projected to reveal precise three-dimensional bonding regions we call bond bundles, and P enables direct inspection of the energy distribution within a bond. We show that delocalized metallic bonds and organic covalent bonds alike can be objectively analyzed, the formation of bonds observed, and that the crystallographic structure of simple metals can be rationalized in terms of bond bundle structure.We demonstrate that gradient bundle decomposition also reveals the charge density's intrinsic ridge structure indicative of regions of energetic—hence chemical—significance. Bond bundle analysis also effortlessly resolves many concerns regarding the chemical significance of bond critical points and bond paths in The Quantum Theory of Atoms in Molecules. Our method also reproduces the expected results of organic chemistry, enabling the recontextualization of existing bond models from a charge density perspective. Gradient bundles had been successfully demonstrated previously as a proof of concept in systems with linear symmetry. The complexity of a generalized gradient bundle decomposition—to systems of any symmetry—necessitated a programmatic approach. Here we also outline the resulting novel algorithms.