Pipek–Mezey Orbital Localization Using Various Partial Charge Estimates

The Pipek-Mezey scheme for generating chemically intuitive, localized molecular orbitals is generalized to incorporate various ways of estimating the atomic charges, instead of the ill-defined Mulliken charges used in the original formulation, or Löwdin charges, which have also been used. Calculations based on Bader, Becke, Voronoi, Hirshfeld, and Stockholder partial charges, as well as intrinsic atomic orbital charges, are applied to orbital localization for a variety of molecules. While the charges obtained with these various estimates differ greatly, the resulting localized orbitals are found to be quite similar and properly separate σ and π orbitals, as well as core and valence orbitals. The calculated results are only weakly dependent on the basis set, unlike those based on Mulliken or Löwdin charges. The effect of varying the penalty exponent on the charge in the objective function was studied briefly and was found to lead to some changes in the localized orbitals when degeneracies are present. The various localization methods have been implemented in ERKALE, an open source program for electronic structure calculations.