Rotational Corrections to Polarizability Derivatives

The transfrumation of vibrational intensities in Raman spectra into molecular parameto s involves sevoal calculation stages. An essential initial step is the reduction of intensity data to polarizability derivatives with respect to symmetiy vibrational coordinates. As pointed out in previous ciutyters, the inverse electro-optical problem of vibrational intensities can be performed with success only for molecules possessing sufficient symmetry. The transformation between da/dQ and do/dSj derivatives is carried out widi die aid of the normal coordinate transformation matrix Lg according to the expression  

Polarizability derivatives with respect to symmetry coordinates obtained from Eqs. (9.1) and (9.2) are not always purely intramolecular quantities since contributions from the compensatory molecular rotation accompanying some vibrations may be present. Such contributions arise in the cases of non-totally symmetric modes of molecules having a non-spherical polarizability ellipsoid. Polarizability derivatives corrected for contributions from molecular rotation can be obtained according to the relation 

Wj is the compensatory rotation arising when a molecule undergoes particular vibrational distoition, and oq is the static molecular polarizability tensor. If the vector wj is presented in a pseudo-tensor form [Eq. (3.7)], Eq. (9.5) can be rewritten as 

The absolute compensatory molecular rotation can be evaluated, as afready discussed in Section 3.II.A, by employing the hypodiedcal isotope approach [34-36]. The hypothetical species obtained by setting the masses of some appropriately chosen atoms equal to zero [35,36] or weighted by factors of 1000 or more [34] are incorporated in the 

The superscripts r and a stand for the reference and actual molecule, respectively. More details about the matrices p and A are given in Chapters 2 and 3. Some examples of application of the hypothetical isotope approach in deriving rotational corrections to polarizability derivatives are given below. 

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