Cotton-Mouton constant

Table 2.8 Cotton-Mouton constant mC(co,T) (1 020 G-2 cm3 moi 1) for liquid water. Atj(0) and Q(co) in atomic units. T = 293.15 K, X = 632.8 nm. aug-cc-pVTZ basis set. See refs. [23,24] for further details...

Cotton-Mouton studies are discussed extensively by Beams. Measurements of the Cotton-Mouton constant in the gas phase permit determinations of the diamagnetic anisotropy of molecules when performed in condensed phase, they yield the angular correlations between molecules. ... 

By means of Eqs. (85a)-(85c), (92), (93), (104), and (106) for the three contributions to the molecular Cotton-Mouton constant arising from the orientational mechanism of birefringence in the magnetic field, we obtain... 

It can easily be seen that in the absence of the vibronic coupling all the parameters 0G3/2(r, p), Q%n(T, /3), and Q n(T, P) are equal to one, and the Cotton-Mouton constant in this approximation is a quadratic function of the inverse temperature, similar to that inherent to molecules with nonzero magnetic moments and with anisotropic polarizability and magnetic susceptibility. The vibronic interaction modifies the temperature dependence by means of the temperature-dependent reduction factors, a part of which was discussed in the investigation of the Kerr effect. 

Ionization constants of hydroxy- and mercaptopyridazines, ° of amino- and diaminopyridazines and their quaternization products,of methylsulfinylpyridazines," and of pyridazinium ylides have been recorded. The basicities of a series of pyridazines have been determined and correlated with substituent constants using the Hammett free-energy relationship. The magnetic susceptibility of pyridazine was measured, and the rate constant for the reaction of hydrogen atoms with pyridazine was determined. The experimental dipole moment, Kerr constant, and molar Cotton-Mouton constant, obtained at 298 K and 633 nm, are reported. The magnetic circular dichroism spectrum of pyridazine has been measured. ... 

The Cotton-Mouton effect, magnetic anisotropy, and charge localization of 2,4,6-tris(dimethyl-amino)-1,3,5-triazine compared with 1,3,5-triazine have been examined <91JST(248)20l>. Dilute solution Kerr and Cotton-Mouton constants were measured for both 1,3,5-triazine and 2,4,6-tris(dimethylamino)-l,3,5-triazine. These constants were then used to derive experimental values for the optical-frequency polarizability anisotropies, and more importantly the magnetic anisotropies of... 

The experimental parameter that may give quantitative information on the magnetizability polarizability to second order in the electric field is the Cotton-Mouton constant, responsible for the Cotton-Mouton effect (CME), i.e., the birefringence of light in gases in a static magnetic field [15-19],... 

A theoretical interpretation of CME has been given by Buckingham and Pople, who showed that the Cotton-Mouton constant can be expressed in terms of the anisotropy of the fourth-rank hypermagnetizability, the electric polarizability, and the magnetizability [20], and by Atkins and Miller [21],... 

Fig. 16. Compari son of experimental values of the Cotton-Mouton constant CM (darkened circles) with theoretical (lines) and independently measured values (open symbols) of the persistence length Ip. The left and right axes have been shifted so that measured values of CM can be referenced against Ip. Theory curves are for the OSF model with lo between 50 and 70 nm, and Zg values from independent measurements were adjusted to the plotted Ip values by adding 50 nm. Adapted from Ref. 247.

The key is the Cotton-Mouton, or magnetically induced birefringence experiment. If the multipole analysis of induced effects, as outlined in 2 is justified then it may be shown ) that the Cotton-Mouton constant (jJZ) is proportional to g2 in fact... 

The experimental quantity connected to the hypermagnetizabUity is the molar Cotton-Mouton constant m C. Semiclassically, for fluids composed of closed-shell systems (Buckingham and Pople 1956 Fowler and Buckingham 1989 Jamieson 1991) ... 

In O Eq. 11.185, a is the (frequency-dependent) electric polarizability tensor, and i, the magne-tizabUity tensor. The two contributions to the molar Cotton-Mouton constant in O Eq. 11.183 are, therefore, a temperature-independent term related to the hypermagnetizabUity and a temperature-dependent molecular orientational part - the Langevin term. ... 

Thorvaldsen, A. J., Ruud, K., Rizzo, A., 8c Coriani, S. (2008). Analytical calculations of frequency-dependent hypermagnetizabilities and Cotton-Mouton constants using London atomic orbitals. Journal of Chemical Physics, 129, 164110. 

Although interesting from the theoretical point of view, no third-order properties (134) and (135) have been measured so far. On the other hand, the fourth-order hypermagnetizability enters the Cotton-Mouton constant available from studies of birefringence of gases. To fourth-order, the CT(X1D-DZ expression properties are most easily established using the quantum mechanical resolution of the identity via equations (38) and (41), using equations (132), (133), (140), and (141). They are ... 

The Cotton-Mouton constant (magnetic double refraction) is 111 —na AX,... 

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