10.4.2 Virtual Orbital Localization

Virtual orbitals can be advantageous to be localized in many scenarios. One scenario where this is useful is generalized valence bond (GVB) methods, where each bonding orbital is paired with its antibonding orbital through Sano procedure. Currently this is done in GVBMAN when PP or CCVB is run. An improved guess has been proposed that has been shown to converge faster^{Aldossary:2020}. The new subroutine is a stand-alone version that can generate these antibonding orbitals and exit without initiating a GVB calculation. It can do Boys, Pipek-Mezey, or Edmiston-Rudenberg localization for the occupied space depending on GVB_LOCAL = 1, 2, or 3, respectively, while 0 performs it on the canonical orbitals. The subroutine also prints out each occupied orbital’s Mulliken charge, delocalization measure, and variance, in which it automatically detects the bonding orbitals and generates an antibonding guess for each. A population analysis based on this effective minimal basis can also be done using EDA_POP_ANAL = 1. The number of bonds can be enforced by taking the highest GVB_N_PAIRS specified, with no guarantee of them being bonding, i.e. they can be core or lone pairs. This is currently implemented for Restricted and Restricted Open-Shell, while Unrestricted case is underway.