RELATIONSHIP BETWEEN INFRARED INTENSITY FORMULATIONS

We shall limit our presentation only to defining relations between different intensity parameters and atomic polar tensors [33,108]. There are two main reasons for diis. Atomic polar tensors are evaluated from experimental infiared intensities of symmetric molecules (the directions of transition dipoles are fixed by symmetry) without any fiirther assumptions or approximations to be made. Secondly, quantum mechanical estimates of infrared intensities are presently obtained from calculations by analytical differentiation atomic polar tensors. These quantities appear in die standard output of current ab initio program packages [153,154], Thus, most intensity parameters can be interconnected by defining their relations to atomic polar tensors. 

Gussoni and Abbate [151] have derived a general formula relating atomic polar tensors and electro-optical parameters. Eq. (3.27) is an expression of die dipole moment derivatives with respect to symmetry coordinates in terms of electro-optical parameters. 

In general form atomic polar tensors are represented in terms of electro ptical parameters by die matrix equation  

As an illustration, in Table 5.1 explicit relations between APT and electro-optical parameters for CH3X molecules derived by Gussoni and Abbate [151] are shown. The expressions refer to the local Cartesian systems for X and H atoms defined in Fig. 5.1. 

The relationship between atomic polar tensors and bond polar parameters has also been analyzed by Galabov et al. [100,124]. Multiplying both sides of the equation Ps - Rs = Pb V Ags [Eq. (4.126)] by a symmetrized B matrix we obtain 

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