Compensatory molecular rotation

Vibrations belonging to Bi and B2 have to be treated for contributions from compensatory molecular rotation. The geometric parameters and the definition of symmetry coordinates are given in Table 3.4. Cartesian reference system and definition of internal coordinates are shown in Fig. 3.3(A). 

The problem with rotational contributions to intensities is dealt with by eliminating the rotational terms from both sides of the resulting linear equations. As a consequence, the parameters obtained are determined from purely vibrational distortions in the molecules. As noted in an early review Overend [16], subtraction of contributions to dipole moment derivatives arising from the compensatory molecular rotation present in particular modes of polar molecules is required to consider tire quantities obtained as purely intramolecular parameters that depend solely on the electronic structure of molecules. A satisfactory treatment of rotational contributions is implicit in the valence optical scheme. In contrast, in atomic polar tensors and bond charge tensors, due to the requirement that intensities are expressed on the basis of parameters referring to space-fixed Cartesian systems, a considerable amount of rotational intensity is introduced into the respective tensor elements, as shown by Person and Kubulat [86]. 

If experimental data are treated, Vx is calculated from die relation (4.93). hi Eq. (4.93) Ps is the array of dipole nuMiient derivatives with respect to symmetry coordinates [Eq. (3.4)]. As underlined earlier, Vx refers to a molecule-fixed reference cocHrdinate system as also do the experimental dp /dQj derivatives ( = x, y, z). The array Vx may contain implicidy contributions originating from die compensatory molecular rotation in the case of polar molecules. These contributions are also present in the P matrix. RotatirmaUy corrected P may, however, be used to derive a fully rotation-free atomic polar tensor matrix. This is achieved through the equation... 

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... 

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... 

Methyl chloride has Raman-active vibrations belonging to A and the doubly degenerate E, syimnetry species. The E-vibrations are non-totally synunetric and contain contributions from compensatory molecular rotation. Geometry parameters, definition of synunetry coordinates and the orientation of the molecule in Cartesian space are given in Table 3.8 and Fig. 3.7. The equilibrium molecular polarizability tensor of CH3CI employed in the calculations has the following form [289] ... 

The heavy-isotope approach to evaluate rotational contributions to polarizability derivatives [288] will be illustrated with calculations on a series of molecules consisting of acetonitrile (C3V synunetiy), dichloromethane (C2v symmetry) and acetone (C2v symmetry). Structural parameters and polarizability tensors employed in die calculations are surtunarized in Table 9.1. Since the axes of the Cartesian reference systems (Fig. 9.1) are chosen to coincide with the respective inertial axes, the static polarizability tensors acquire sirtqile diagonal form. The symmetry coordinates corresponding to vibrations which may crmtain contributions from compensatory molecular rotation for the three molecules are given in Tables 9.2, 9.3 and 9.4, respectively. The following heavy isotopes are employed ... 

Dichloromethane The dichloromethane molecule possesses C2v synunetry and has two groups of vibrations belonging to B] and B2 symmetry classes that contain contributions from compensatory molecular rotation. Two heavy isotopes are created in this case C H2Cl2 in evaluating rotational corrections to B] class (weighting factor of 1(P) and C H2 Cl2 in the case of B2 vibrations (weighting factor of 10 ). The asterisks mark die heavy atoms in the isotopes. 

Section 9.1. After removing the polarizability tensor associated with the compensatory molecular rotation p B , Eq. (9.97) reads... 

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... 

Within the zero-mass approach the reference hypothetical isotope contains atoms with zero masses. Typically, the respective atoirrs do not lie on the main molecular symmetry axis. As an example, the CH3CI molecule will be considered. In this case, it is appropriate to set all hydrogen-masses equal to zero. Thus, the C-Cl bond will maintain fixed direction during vibrational motion and this hypothetical isotope species will have negligibly small compensatory rotations. 

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