Polarizability derivatives

Just as the derivatives of the electric dipole with respect to normal coordinates are important in infrared spectroscopy, so the same derivatives of the polarizability play a role in Raman spectroscopy. 

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The need for a local field correction in Raman spectra was first suggested by Woodward and George [39] who, however, made no attempt to present a quantitative expression for the magnitude of the effect. Starting from Onsager s theory, Pivovarov derived an expression for the ratio between polarizability derivatives in solution and in vacuo (and then Raman intensities) [34,35] ... 

A new, more accurate electron diffraction study of gaseous mercuric chloride has been reported.159 The interatomic distances (Hg—Cl = 2.25 A, Cl—Cl = 4.48 A) are shorter than previously reported values by 0.02 to 0.09 A. A complete normal-co-ordinate analysis of bis(methylthio)mercury has also been reported.160 The Raman spectra of gaseous mercuric chloride, bromide, and iodide have been reported.161 The bond polarizability derivatives calculated from the data increase in the order Cl < Br < I, suggesting an increased degree of covalence in the mercury-halogen bond with increasing size of the halogen atom. 

In this case, as well, the first derivative, (da/dq)Q, is responsible for determining the observation of vibration fundamentals in the Raman spectrum [11], Given that the polarizability is a response function of the molecule to an external electric field, then the polarizability and the polarizability derivatives are both symmetric tensors of the second rank. Then, each vibration has six chances to be observed in the Raman spectrum. Therefore, for a vibration transition to be permitted in the Raman spectrum, it is required that at least one of the six components of the derivative tensor is different from zero. 

The authors also studied the polarization patterns associated with the intermolecular vibrational modes. Average polarizability derivatives were calculated to be quite small, yielding small scattering activities, all below 10 (xl0 " C N kg ) ... 

Swanton, D. J., Bacskay, G. B., and Hush, N. S., An ab initio SCE calculation of the polarizability ten.mr, polarizability derivatives and Raman scattering activities of the water-dimer molecule. Chem. Phys. 83, 69-75 (1984). 

Liquid Phase Calculations of the Linear Response. The data in Table 5 for the isotropic polarizability, derived formally via the Lorentz-Lorenz equation (1) from the measured refractive index, shows that the assumption that individual molecular properties are largely retained at high frequency in the liquid is very reasonable. While the specific susceptibilities for the gas and liquid phases differ, once the correction for the polarization of the surface of a spherical cavity, which is the essential feature of the Lorentz-Lorenz equation, has been applied, it is clear that the average molecular polarizabilities in the gas and liquid have values which always agree within 5 or 10%. 

The parameters C, D, E and F involve components of polarizability derivative tensors. Qjs is the displacive order parameter in the low-temperature phase and Qjq corresponds to which is present in the intermediate pseudo-phase. The damping constant T qjh) includes the effect of coupling between the hard mode and the reorientational relaxation of displaced lead atoms. 

We have also found that the molecular distortions that disobey the GMPP are not necessarily the same as those that break the GMHP. To get some insight into the origin of this discrepancy, we have started our analysis from the exact expression of the isotropic static electronic polarizability derived from perturbation theory ... 

Apart from a normal coordinate analysis, rather less information is required to perform an atom dipole interaction calculation than a bond polarizability calculation of ROA specifically, the derivatives of the local isotropic atomic polarizabilities with respect to the internal coordinates, which can be decuded from ordinary Raman intensities or else transferred from other (simpler) molecules. The anisotropic parts of the polarizability derivatives are generated automatically by the dipole-dipole interaction function. 

The most important electric properties are dipole moment and polarizability derivatives. The theory of dipole moment derivatives has been worked out by Bratoz (1958) and by Gerratt and Mills (1968). Both papers use the obvious definition of the dipole moment derivative the change of the dipole moment with nuclear coordinates. Komornicki and Mclver (1979) have pointed out, in an influential paper, that the alternative definition, namely the derivative of the geometrical force with respect to the electric field, is more useful, as there are only three field components versus 3N nuclear coordinates. Similarly, the polarizability derivatives can be defined as the second derivatives of the forces with respect to the field components. Komornicki and Mclver (1979) suggest numerical differentiation with respect to the field... 

K. M. Gough, H. K. Srivastava, K. Belohorcova. Molecular polarizability and polarizability derivatives in cyclohexane analyzed with the theory of atoms in molecules. J. Phys. Chem. -, 98, 771-776 (1994). 

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