Gauge-invariant calculation of static and dynamical magnetic properties from the current density.
In this work we solve two problems related to the calculation of static and dynamical magnetic properties with ab initio theories. First, we show that the dependence of the dynamical magnetic dipole moment on the reference point of the multipole expansion and on the gauge origin of the vector potential have a clear physical significance. They are due to a dynamical electric dipole moment and an electric field, respectively. Both are fully determined by the experimental setup and do not pose any fundamental problem, contrary to what is commonly assumed. Second, in the static case, any dependence on the gauge origin is an artifact of the computational method. We show that the artificial dependence on the gauge origin can be removed in an elegant way by the introduction of a sum rule that puts the diamagnetic and paramagnetic contributions on equal footing. Our approach can be applied to calculate any magnetic observable that can be derived from the current density, and can be used in combination with any ab initio theory from which it can be obtained. To illustrate our method we apply it here to time-dependent current-density-functional theory for the calculation of static and dynamical magnetizabilities of molecules.
Laboratoire de Chimie et Physique Quantiques, IRSAMC, Université Toulouse III - Paul Sabatier, CNRS and European Theoretical Spectroscopy Facility (ETSF), 118 Route de Narbonne, 31062 Toulouse Cedex, France and Laboratoire de Physique Théorique, CNRS, IRSAMC, Université Toulouse III - Paul Sabatier and European Theoretical Spectroscopy Facility (ETSF), 118 Route de Narbonne, 31062 Toulouse Cedex, France.
Nathaniel
N
Raimbault
Scientific Computing & Modeling NV, Vrije Universiteit, Theoretical Chemistry, De Boelelaan 1083, 1081 HV Amsterdam, Netherlands.
Paul L
PL
de Boeij
Laboratoire de Physique Théorique, CNRS, IRSAMC, Université Toulouse III - Paul Sabatier and European Theoretical Spectroscopy Facility (ETSF), 118 Route de Narbonne, 31062 Toulouse Cedex, France.
Pina
P
Romaniello
Laboratoire de Chimie et Physique Quantiques, IRSAMC, Université Toulouse III - Paul Sabatier, CNRS and European Theoretical Spectroscopy Facility (ETSF), 118 Route de Narbonne, 31062 Toulouse Cedex, France.
J A
JA
Berger