APZT An Example of Application

In this section an example of calculations employing the APZT formalism is presented. Atomic polarizability tensors for formaldehyde-do and foimaldehyde-d2 are evaluated. The initial data are taken from RHF/6-31G(d,p) db initio MO calculations [332]. Molecular geometry, static polarizability tensor and definition of symmetry coordinates are given in Table 9.11. The orientation of the molecule in the Cartesian space, definition of internal coordinates and numbering of atoms are shown in Fig. 3.1. 

The ag matrices comprising molecular polarizability derivatives with respect to symmetry coordinates for H2CO and D2CO are given below. 

Molecular geometry, static polarizability and definition of symmetry vibrational coordinates for formaldehyde  

It can be seen fi-om Eqs. (9.86) and (9.87), diat polarizability derivatives with respect to symmetry coordinates belonging to non-totally symmetric modes are different for the two isotopic species. This is expected since the do/dSj derivatives are mass-dependent quantities. The Op tensor is evaluated from Eq. (9.81)  

The atomic polarizability tensors for H2CO and D2CO are obtained from Eq. (9.76). The elements of Bg and P matrices need to be rearranged to match the dimensions of a and Op, respectively. The ag Bg, Op p and ax tensors obtained for the two species are given in Tables 9.12 and 9.13. It can be seen that the atomic polarizability tensors ax for formaldehyde-do formaldehyde-d2 are, as expected, identical. 

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