Atomic Polarizability Tensor Formulation APZT

In the APZT approach die changes in molecular polarizability a of a molecule having N atoms are represented as a function of atomic displacement vectors r,  

Aya and Aza are the Cartesian displacement coordinates of atom a in a space fixed Cartesian coordinate system, and i, j and k are the respective unit vectors. Atomic polarizability tensors ax are third-rank tensor quantities which can be written 3 9 rectangular arrays  

As can be seen from Eq. (9.73) 27 intensity parameters are assigned to each atom of the molecule. If the frequency of incident light lies far from any electronic absorption frequency of die molecule, the number of independent parameters for each atom a reduces to 18 since the polarizability tensor is symmetric under die frr-frmn-resonance conditions. 

Arranged in a row all ax tensors give the atomic polarizability tensor ax of the molecule 

The elements of the atomic polarizability tensor can be evaluated by applying an ejqnession analogous to that used for dipole moment derivatives [Eq. (4.12)] [299] 

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