Untersuchung über die optischen Eigenschaften der dem Einfluss des Magnetismus ausgesetzten durchsichtigen Körper

Verdet,

doi:10.1002/andp.18541680710

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“…[1][2][3][4] Far from absorption, the Faraday effect is related to the Verdet constant, [5] a quantity characteristic of the substance which depends on concentration, temperature, and frequency. Using the response formalism, [6] it is represented as Equation (1):…”

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A Joint Theoretical–Experimental Investigation of the Faraday Effect in Benzene, Toluene, and p‐Xylene

et al. 2006

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The linear magneto-optical effect, known as the Faraday effect, consists of the rotation of the plane of polarization of linearly polarized light when it propagates through a medium placed in a magnetic field with nonzero component in the direction of light propagation. [1][2][3][4] Far from absorption, the Faraday effect is related to the Verdet constant, [5] a quantity characteristic of the substance which depends on concentration, temperature, and frequency. Using the response formalism, [6] it is represented as Equation (1):where ( m a ; m b ; iL g ) w;0 is the quadratic response function, m and L are the dipole-moment and angular-momentum operators, respectively, and e(a,b,g=x,y,z) is the Levi-Civita tensor. The Einstein summation convention over repeated indices is assumed in Equation (1); w is the circular frequency of the incident light, and C a constant [Eq. (2)]:where N is the number density and the other quantities have their usual meaning. So far, the Verdet constant has been measured for a collection of molecules, [1,7,8] and this has initiated several theoretical investigations. [9][10][11][12][13][14][15][16] In addition to linear response calculations assuming the Becquerel approximation, [9,10] V(w) is evaluated using 1) a sum-over-state expression, [11] 2) quadratic response functions, [12][13][14][15] and, more recently, 3) time-dependent density functional theory (TDDFT). [16] Gauge-independent atomic orbital (GIAO) approaches have been elaborated at both coupled cluster (CC) [14] and TDDFT [16] levels of approximation.Coriani et al. [15] employed a hierarchy of CC response theory models to assess the importance of electron correlation. They evidenced the necessity of including triple excitations for providing a correct estimate of V(w) of the nitrogen and acetylene molecules and pointed out that zero-point vibrational averaging could account for the difference between theory and experiment in the case of methane. Moreover, Krykunov et al. [16] concluded that, when a sufficiently large basis set is used, the TDDFT schemes with nonhybrid exchange-correlation functionals has a clear tendency to slightly overestimate the Verdet constant.On the other hand, little is known about structure-property relationships for organic molecules, which might be of importance in addressing molecular properties [17,18] or designing materials with outstanding magneto-optical properties. As a first step towards this goal, we have measured the dispersion of the Faraday effect for benzene, toluene, and p-xylene as pure liquids and performed theoretical calculations at the DFT level of approximation.Geometry optimizations are carried out for the three compounds at the MP2/6-31G* level of approximation. The V(w) values are evaluated by adopting the analytical quadratic response approach within the density functional theory [19] implemented in the Dalton 2.0 electronic structure program, [20] which retains the adiabatic approximation. Although this scheme allows the use of different exchange-correlation functionals for ...

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A Joint Theoretical–Experimental Investigation of the Faraday Effect in Benzene, Toluene, and p‐Xylene

et al. 2006

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“…As early as 1856 Verdet [5] showed that the Faraday effect is an additive property of matter, in the sense that the magnetic rotation (p) of a mixture is the sum of the rotations of its K components: k (p) = I (p,.,)P,.,…”

Section: The Existence Of Bond Magnetic Rotations: Experimental Evidencementioning

confidence: 99%

“…Therefore an exchange integral such as f L{(l, 2)M1L1(1, 4, 5)L:(3, 4, 5)L1(2, 3) dv will be negligible because is small. Then to calculate we may use (with a good approximation) the simple product L 1 (1, 2)L 2 (3,4,5) which gives: 2) ti M;L1(l, 2) dv + f L: (3,4,5) ~~ M1L2 (3,4,5) dv =At+ A2 But this kind of relation can also be satisfied in some other cases. In any case where this relation occurs an additivity rule will be obtained if the A 1 associated with a given type of loge (e.g.…”

Section: Introductionmentioning

confidence: 99%

On the General Theory of Molecular Additivity Rules: The Particular Case of the Faraday Effect

Daudel¹,

Gallais

Smet

1967

Int J of Quantum Chemistry

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A set of requirements which allows a clear understanding of the origin of molecular additivity rules is presented. These requirements are: (a) to find good decompositions into loges of the molecules concerned; (b) to associate with each loge i a fraction Ai of the molecular property under consideration in such a way that the molecular property A satisfies the relation: (c) to show that the various Ai remain approximately constant in the family of molecules studied. This possibility of satisfying these requirements is discussed in the case of the Faraday effect. It is shown that in this case from the experimental viewpoint molecular additivity rules are observed at least within certain limits which are carefully specified. Furthermore, starting from a variational theory of the Faraday effect it is shown that it is always possible to satisfy requirement (b) when requirement (a) is satisfied. Therefore the additive properties of the Faraday effect are clearly understood when it is possible to satisfy both requirements (a) and (c). On présente un nombre de conditions pour expliquer l'origine des règles d'additivité moléculaire. Il est nécessaire: (a) de trouver de bonnes decompositions en loges des molecules en question; (b) d'associer à chaque loge i une fraction Ai de la propriété moléculaire considéréé de sorte que la propriété moléculaire A satisfait is à relation (c) de montrer qu'approximativement les Ai restent constantes dans la famille de molécules étudiée. On discute la possibilité de satisfaire à ces conditions dans le cas de l'effet Faraday. On montre que dans ce cas‐ci du point de vue expérimental les règles d'additivité moléculaire sont observées au moins entre certaines limites, qui sont bien précisées. De plus, partant d'une théorie de variations de l'effet Faraday on montre qu'il est toujours possible de satisfaire a la condition (b) quand la condition (a) est remplie. Les proprétés additives de l'effet Faraday sont donc bien comprises quand it est possible de remplir les conditions (a) et (c). Eine Reihe von Forderungen fair die Erklarung der Ursprung molekularer Additivitätsregeln wurde darstellt. Dafür ist es notwendig: (a) gute Zerlegungen der Moleküle in Logen zu fulden; (b) zu jeder Loge i ein Bruchteil Ai der molekularen Eigenschaft A so dass (c) zu zeigen dass die Ai ungefähr konstant in der studierten Molektülfamilie bleiben. Die Möglichkeit diesen Forderungen zu befriedigen wurde im Falle des Faradayeffekts diskutiert. Es wurde gezeigt, dass in diesem Fall, vom experimentalen Standpunkte aus, die molekulare Additivitätsregeln wenigstens innerhalb gewisser, wohl spezifizierter Grenzen beobachtet sind. Ferner wurde es gezeigt, dass es immer möglich ist, Forderung (b) zu befriedigen, wenn (a) befriedigt ist. Darum sind die additiven Eigenschaften des Faraday‐effekts wohl verstanden, wenn es möglich ist sowohl Forderung (a) als Forderung (c) zu befriedigen.

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“…It manifests itself in certain substances as the rotation of the plane of polarisation of a light beam when a magnetic field is applied parallel to it. The rotation angle, φ, is proportional to the modulus of the magnetic flux density B, the length l of the material in the field and its Verdet constant, v, named after the French physicist Marcel Verdet (1824-66) [8][9][10][11], who used the name 'pouvoir rotatoire magnetique' for the first time in 1858 [10,12]. The sense of rotation with respect to the magnetic field's direction does not depend on the direction of light propagation, due to conservation of parity [13,14].…”

Section: Introductionmentioning

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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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Untersuchung über die optischen Eigenschaften der dem Einfluss des Magnetismus ausgesetzten durchsichtigen Körper

Cited by 5 publications

References 0 publications

A Joint Theoretical–Experimental Investigation of the Faraday Effect in Benzene, Toluene, and p‐Xylene

A Joint Theoretical–Experimental Investigation of the Faraday Effect in Benzene, Toluene, and p‐Xylene

On the General Theory of Molecular Additivity Rules: The Particular Case of the Faraday Effect

On the origin independence of the Verdet tensor^†

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Untersuchung über die optischen Eigenschaften der dem Einfluss des Magnetismus ausgesetzten durchsichtigen Körper

Cited by 5 publications

References 0 publications

A Joint Theoretical–Experimental Investigation of the Faraday Effect in Benzene, Toluene, and p‐Xylene

A Joint Theoretical–Experimental Investigation of the Faraday Effect in Benzene, Toluene, and p‐Xylene

On the General Theory of Molecular Additivity Rules: The Particular Case of the Faraday Effect

On the origin independence of the Verdet tensor†

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On the origin independence of the Verdet tensor^†