Löwdin Population Analysis With and Without Rotational Invariance

Theoretical arguments and calculations are presented concerning atomic orbital-based population analyses, as well as the way they are affected by rigid rotation of the molecule. It was recently shown that the Löwdin distribution of atomic charges (atomic populations computed in a Löwdin-orthogonalized basis) is, in general, not rotationally invariant unless an initial atom-centered basis of pure spherical harmonics is used or the atomic orbitals on the same atom are pre-orthogonalized. In the present work, we compare the effect of linear transformations of the initial basis on charges within a series of organic, transition metal, and actinide compounds that have been computed in a basis containing either the Cartesian 6d and 10f orbitals or the pure spherical harmonics (5d, 7f components), respectively. Löwdin populations obtained without pre-orthogonalization are orientationally dependent when computed in the 6d-, 10f-component basis and the asymmetric distribution of the Löwdin atomic charges among symmetry-equivalent atoms is observed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem 106: 2065–2072, 2006