Mayer’s orthogonalization: relation to the Gram-Schmidt and Löwdin’s symmetrical scheme

Abstract

A method introduced by Mayer (Theor Chem Acc 104:163, 2000) for generating an orthogonal set of basis vectors, perpendicular to an arbitrary start vector, is examined. The procedure provides the complementary vectors in closed form, expressed with the components of the start vector. Mayer’s method belongs to the family of orthogonalization schemes, which keep an arbitrary vector intact without introducing any non-physical sequence-dependence. It is shown that Mayer’s orthogonalization is recovered by performing a two-step combination of the Gram-Schmidt and Lowdin’s symmetrical orthogonalization. Processor time requirement of constructing Mayer’s orthonormal set is proportional to ∼N2, in contrast to the rough ∼N3 CPU requirement of performing either a full Gram-Schmidt or Lowdin’s symmetrical orthogonalization. Utility of Mayer’s orthogonalization is demonstrated on an electronic structure application using perturbation theory to improve multiconfigurational wavefunctions.