Invariance of molecular response properties under a coordinate translation

Abstract

The response of a molecule to static and dynamic electromagnetic fields and intramolecular perturbations is reviewed within the framework of the Rayleigh-Schrödinger perturbation theory. A semiclassical approach is adopted, using quantized form of electronic operators and the nonquantized description of the electromagnetic fields via the Maxwell equations. The Bloch multipolar gauge has been used to define operators suitable to describe the molecular interaction with nonhomogneous time-dependent perturbations. It is shown that the quantum mechanical theory of magnetic properties can profitably be proposed in terms of electronic current densities induced by an external magnetic field and permanent magnetic dipole moments at the nuclei. Theoretical relationships are reported to evaluate magnetizability, nuclear magnetic shielding, and nuclear spin-spin coupling, proving that the whole theory can be reformulated via the equations of classical electromagnetism, provided that the current density is evaluated by quantum mechanical methods. Emphasis is placed on the invariance of response properties in a translation of the coordinate system as a basic requirement for measurability. The connections among translational invariance, gauge invariance, and electron charge conservation are outlined, showing that they can be illustrated via quantum mechanical sum rules. A number of relationships describing the change of static and dynamic electromagnetic properties in a translation of the reference frame are reported. © 2014 Wiley Periodicals, Inc. The magnetic dipole m and the magnetic field Bind  induced by a circular loop of electronic current density JB; below, the anapole moment A, and the confined magnetic field induced by an electronic current density flowing on the surface of a geometrical torus. The magnetic dipole m and the magnetic field Bind  associated with the circular loop are origin-independent. The magnetic dipole of the torus vanishes and the anapole moment is origin-independent. © 2014 Wiley Periodicals, Inc.