Tests of accuracy for computed magnetic properties via off-diagonal hypervirial relations.

Abstract

Most of the methods presently available to investigate the molecular magnetic response work extremely well for the computation of properties, such as magnetizability and nuclear magnetic shielding, but they provide insufficiently accurate current density maps, in that they do not guarantee exact conservation, leading to unphysical features in maps. The present study starts from the results obtained by Epstein and Sambe and moves forward to generalize them. An off-diagonal hypervirial relationship, connecting the matrix elements of a given differentiable function of position f(r) to its derivatives ∇f(r), via the anticommutator ∇αf,p^α + with the canonical momentum operator p^, has first been proven. Afterward, this relationship is applied to show that the equations proposed by Sambe to check the quality and conservation of computed electronic current densities can be obtained as particular cases of this general theorem, with a substantial gain in computational efficiency. Connections with previous work by Arrighini, Maestro, and Moccia are outlined, and the implications that hint at future work are discussed.