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

Abstract

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 ...

Faraday Rotation Dispersion Measurements of Diamagnetic Organic Liquids and Simultaneous Determination of Natural Optical Rotatory Dispersion Using a Pulsed Magnetic Field

“…3 are in good agreement with those reported by other groups. 21,27,28 The observed spectra clearly separated into three groups based on their magnitude: naphthalene derivatives, benzene derivatives, and aliphatic compounds. Furthermore, it was indicated that aromatic groups have an increasing effect on the FR in the visible region.…”

Invariance of molecular response properties under a coordinate translation

“…The Verdet constant, measured in rad within the Système International (SI) of units, is a scalar, obtained by spatial averaging from a third‐rank axial tensor , referred to as Verdet tensor, also taken into account to rationalize the inverse Faraday effect, in which optical magnetization is induced by applying circularly polarized light …”

On the origin independence of the Verdet tensor†

“…The Verdet constant, measured in rad T −1 m −1 within the Système International (SI) of units, is a scalar [2][3][4][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33], obtained by spatial averaging from a third-rank axial tensor V αβγ , hereafter referred to as Verdet tensor, also taken into account to rationalise the inverse Faraday effect, in which optical magnetisation is induced by applying circularly polarised light [34,35]. A tensor with analogous properties has been considered to predict nuclear magnetic resonance (NMR) chemical shift induced by a circularly polarised laser beam [35][36][37].…”