Gauge invariance, nuclear magnetic

The first term of (3.289) represents a translational Stark effect. A molecule with a permanent dipole moment experiences a moving magnetic field as an electric field and hence shows an interaction the term could equally well be interpreted as a Zeeman effect. The second term represents the nuclear rotation and vibration Zeeman interactions we shall deal with this more fully below. The fourth term gives the interaction of the field with the orbital motion of the electrons and its small polarisation correction. The other terms are probably not important but are retained to preserve the gauge invariance of the Hamiltonian. For an ionic species (q 0) we have the additional translational term... 

A. Ligabue, S. P. A. Sauer, P. Lazzeretti, Gauge invariant calculations of nuclear magnetic shielding constants using the continuous transformation of the origin of the current density approach. 11. Density-functional and coupled cluster theory, J. Chem. Phys. 126 (2007) 154111. 

Previously, Lazzeretti et al had shown that, within the CTOCD-DZ approach, the multipole polarizabilities (of any order) of nuclear magnetic shieldings are invariant to a gauge translation irrespective of the quality of the basis set employed. On the other hand, they depend upon the origin of the eoordinate system for multipole higher than dipole, because of the intrinsie origin dependence of the related operators. 

Invariance of magnetizability, nuclear magnetic shielding and electronic current density in a gauge translation... 

Sauer SPA, Oddershede J (1993) Correlated and gauge invariant calculations of nuclear shielding constants. In Tossell JA (eds) Nuclear magnetic shieldings and molecular structure, volume 386 of NATO ASI series C, Kluwer, Dordrecht, pp 351-365... 

Fukui, H., Miura, K., and Matsuda, H. (1992a). Calculation of nuclear magnetic shieldings. VIII. Gauge invariant many-body perturbation method. J. Chem. Phys., 96, 2039-2043. 

This substitution is, formally, easy to perform in the many-body and the Kohn-Sham Hamiltonians of SDFT, but the presence of the vector potential complicates the task of solving these equations. Maintaining gauge invariance is not trivial in approximate calculations. Moreover, in extended systems the vector potential breaks translational invariance, so Bloch s theorem cannot be used anymore.Still, couplings of external vector potentials become relevant in many situations, and ways to deal with them have been developed, e.g. for the calculation of nuclear magnetic shielding tensors and spin-spin coupling constants. 

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