Abstract
General constraints for invariance of magnetic properties in a gauge transformation are analyzed. Sum rules relative to the transformation from Coulomb to Landau gauges are examined in particular. Numerical tests for hydrogen fluoride, water, ammonia, and methane molecule have been carried out in large basis set calculations, using random-phase approximation. The conditions for invariance are severe conditions for accuracy of variational molecular wave functions.
Highlights
The quality of an approximate variational wave function, describing a given electronic state of an atom or a molecule, can be assessed a priori, by checking the degree to which certain sum rules are satisfied, independently of any comparison between experimental data and corresponding quantitiesi.e., electronic propertiesestimated via the same wave function, which might be misleading in a number of cases
They lead to insights as to when the Landau gauge transformation will affect the accuracy of the approximations retained in a calculation of magnetic properties
Numerical results relative to sum rule47͒ for susceptibility evaluated assuming the origin on a hydrogen nucleus, compare for Tables I, V, IX, and XIII demonstrate that basis sets of high quality are necessary to guarantee gauge invariance in a Landau transformation
Summary
The quality of an approximate variational wave function, describing a given electronic state of an atom or a molecule, can be assessed a priori, by checking the degree to which certain sum rules are satisfied, independently of any comparison between experimental data and corresponding quantitiesi.e., electronic propertiesestimated via the same wave function, which might be misleading in a number of cases. In addition to direct comparison of total magnetic properties within Coulomb and Landau gauges, the accuracy of theoretical estimates can be checked by analyzing sum rules for origin independence of magnetic properties in a change of coordinate system, which can be described as a gauge transformation of the Landau vector potential.[5,6]. They lead to insights as to when the Landau gauge transformation will affect the accuracy of the approximations retained in a calculation of magnetic properties
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