Pipek-Mezey localization of occupied and virtual orbitals

Recent advances in orbital localization algorithms are used to minimize the Pipek-Mezey localization function for both occupied and virtual Hartree-Fock orbitals. Virtual Pipek-Mezey orbitals for large molecular systems have previously not been considered in the literature. For this work, the Pipek-Mezey (PM) localization function is implemented for both the Mulliken and a Löwdin population analysis. The results show that the standard PM localization function (using either Mulliken or Löwdin population analyses) may yield local occupied orbitals, although for some systems the occupied orbitals are only semilocal as compared to state-of-the-art localized occupied orbitals. For the virtual orbitals, a Löwdin population analysis shows improvement in locality compared to a Mulliken population analysis, but for both Mulliken and Löwdin population analyses, the virtual orbitals are seen to be considerably less local compared to state-of-the-art localized orbitals.