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
