On the origin independence of the Verdet tensor†

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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, satisfi...

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Autores principales:	Caputo, M.C., Coriani, S., Pelloni, S., Lazzeretti, P.
Formato:	JOUR
Materias:	Faraday effect sum rule for origin independence symmetry unique components Verdet constant Verdet tensor Algebraic approximation Electronic wave functions Gaussian functions Quantum-chemical methods Random phase approximations Sum rule Variational calculation Molecules Quantum chemistry Variational techniques Tensors
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_00268976_v111_n9-11_p1405_Caputo
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_00268976_v111_n9-11_p1405_Caputo
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spelling	todo:paper_00268976_v111_n9-11_p1405_Caputo2023-10-03T14:37:17Z On the origin independence of the Verdet tensor† Caputo, M.C. Coriani, S. Pelloni, S. Lazzeretti, P. Faraday effect sum rule for origin independence symmetry unique components Verdet constant Verdet tensor Algebraic approximation Electronic wave functions Gaussian functions Quantum-chemical methods Random phase approximations Sum rule Variational calculation Verdet constant Sum rule Verdet constant Faraday effect Molecules Quantum chemistry Variational techniques Tensors Faraday effect 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. © 2013 Copyright Taylor and Francis Group, LLC. Fil:Caputo, M.C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00268976_v111_n9-11_p1405_Caputo
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Faraday effect sum rule for origin independence symmetry unique components Verdet constant Verdet tensor Algebraic approximation Electronic wave functions Gaussian functions Quantum-chemical methods Random phase approximations Sum rule Variational calculation Verdet constant Sum rule Verdet constant Faraday effect Molecules Quantum chemistry Variational techniques Tensors Faraday effect
spellingShingle	Faraday effect sum rule for origin independence symmetry unique components Verdet constant Verdet tensor Algebraic approximation Electronic wave functions Gaussian functions Quantum-chemical methods Random phase approximations Sum rule Variational calculation Verdet constant Sum rule Verdet constant Faraday effect Molecules Quantum chemistry Variational techniques Tensors Faraday effect Caputo, M.C. Coriani, S. Pelloni, S. Lazzeretti, P. On the origin independence of the Verdet tensor†
topic_facet	Faraday effect sum rule for origin independence symmetry unique components Verdet constant Verdet tensor Algebraic approximation Electronic wave functions Gaussian functions Quantum-chemical methods Random phase approximations Sum rule Variational calculation Verdet constant Sum rule Verdet constant Faraday effect Molecules Quantum chemistry Variational techniques Tensors Faraday effect
description	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. © 2013 Copyright Taylor and Francis Group, LLC.
format	JOUR
author	Caputo, M.C. Coriani, S. Pelloni, S. Lazzeretti, P.
author_facet	Caputo, M.C. Coriani, S. Pelloni, S. Lazzeretti, P.
author_sort	Caputo, M.C.
title	On the origin independence of the Verdet tensor†
title_short	On the origin independence of the Verdet tensor†
title_full	On the origin independence of the Verdet tensor†
title_fullStr	On the origin independence of the Verdet tensor†
title_full_unstemmed	On the origin independence of the Verdet tensor†
title_sort	on the origin independence of the verdet tensor†
url	http://hdl.handle.net/20.500.12110/paper_00268976_v111_n9-11_p1405_Caputo
work_keys_str_mv	AT caputomc ontheoriginindependenceoftheverdettensor AT corianis ontheoriginindependenceoftheverdettensor AT pellonis ontheoriginindependenceoftheverdettensor AT lazzerettip ontheoriginindependenceoftheverdettensor
_version_	1807324646398230528

On the origin independence of the Verdet tensor†

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