Population analyses that utilize projection operators

Several different methods have been explored that partition the 3-D space of a molecule into its atomic components using Hermitian one-electron position-space projection operators, P-A. Previously, we defined P-A so that hard interatomic boundaries between atoms are observed. This idea has been extended to allow softer boundaries that have a region of overlap between atoms that can be controlled through an iterative process. Functions that determine the shape of the atomic volume are also discussed. The atomic electron populations of 17 different systems are presented as a function of these two factors. (C) 2003 Wiley Periodicals, Inc.