Self-Attractive Hartree Decomposition: Partitioning Electron Density into Smooth Localized Fragments

Chemical
bonding plays a central role in the description and understanding
of chemistry. Many methods have been proposed to extract information
about bonding from quantum chemical calculations, the majority of
them resorting to molecular orbitals as basic descriptors. Here, we
present a method called self-attractive Hartree (SAH) decomposition
to unravel pairs of electrons directly from the electron density,
which unlike molecular orbitals is a well-defined observable that
can be accessed experimentally. The key idea is to partition the density
into a sum of one-electron fragments that simultaneously maximize
the self-repulsion and maintain regular shapes. This leads to a set
of rather unusual equations in which every electron experiences self-attractive
Hartree potential in addition to an external potential common for
all the electrons. The resulting symmetry breaking and localization
are surprisingly consistent with chemical intuition. SAH decomposition
is also shown to be effective in visualization of single/multiple
bonds, lone pairs, and unusual bonds due to the smooth nature of fragment
densities. Furthermore, we demonstrate that it can be used to identify
specific chemical bonds in molecular complexes and provides a simple
and accurate electrostatic model of hydrogen bonding.