Definition of invariant molecular tensors in an origin change. III. Comparison of the methods suitable for the obtainment of invariant tensors for refraction and the Faraday effect

Duprez-Quesnoit, C.

doi:10.1002/qua.560190202

Cited by 4 publications

(4 citation statements)

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“…A few studies on the invariance of the molecular tensor used to rationalize the Faraday effect, in a shift of origin, Eq. , have appeared . However, the first proof of the translational invariance the Verdet tensor has been reported only recently …”

Section: Translation Of Frequency‐dependent Response Tensorsmentioning

confidence: 99%

“…(122) and (124), anapole, Eqs. (138) and (144), for equations (137), (139), (140), and assuming linear response, the first line of the interaction energy, Eq. (120), can be rewritten in the alternative forms and so forth, that is,…”

Section: Tutorial Reviewsmentioning

confidence: 99%

“…(305), have appeared. [137][138][139][140] However, the first proof of the translational invariance the Verdet tensor has been reported only recently. [111] The third-rank tensors needed to rationalize contributions quadratic in the external fields and intramolecular perturbations are expressed, within the quadratic response scheme, by the response function A;B;Ĉ x1;x2 5…”

Section: Translational Invariance Of the Verdet Tensormentioning

confidence: 99%

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Invariance of molecular response properties under a coordinate translation

Lazzeretti

2014

Int J of Quantum Chemistry

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The response of a molecule to static and dynamic electromagnetic fields and intramolecular perturbations is reviewed within the framework of the Rayleigh-Schr€ odinger 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 timedependent 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.

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Section: Translation Of Frequency‐dependent Response Tensorsmentioning

confidence: 99%

Section: Tutorial Reviewsmentioning

confidence: 99%

Section: Translational Invariance Of the Verdet Tensormentioning

confidence: 99%

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Invariance of molecular response properties under a coordinate translation

Lazzeretti

2014

Int J of Quantum Chemistry

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“…A few studies on the invariance of the molecular tensor used to rationalise the Faraday effect, in a shift of origin r → r = r + d of the coordinate system, have been reported [5,[40][41][42] …”

Section: Introductionmentioning

confidence: 99%

On the origin independence of the Verdet tensor^†

et al. 2013

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The condition for invariance under a translation of the coordinate system of the Verdet tensor and the Verdet constant, calculated via quantum chemical methods using gaugeless basis sets, is expressed by a vanishing sum rule involving a third-rank polar tensor. The sum rule is, in principle, satisfied only in the ideal case of optimal variational electronic wavefunctions. In general, it is not fulfilled in non-variational calculations and variational calculations allowing for the algebraic approximation, but it can be satisfied for reasons of molecular symmetry. Group-theoretical procedures have been used to determine (i) the total number of non-vanishing components and (ii) the unique components of both the polar tensor appearing in the sum rule and the axial Verdet tensor, for a series of symmetry groups. Test calculations at the random-phase approximation level of accuracy for water, hydrogen peroxide and ammonia molecules, using basis sets of increasing quality, show a smooth convergence to zero of the sum rule. Verdet tensor components calculated for the same molecules converge to limit values, estimated via large basis sets of gaugeless Gaussian functions and London orbitals.

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