The atomic polar tensor APT model

Polar tensors have been developed by Biarge et al. (1961) to aid in the calculation of vibrational intensities (see also Sec. 5.2.9.1.2). They are derived for each atom by displacing the atom in small increments along the cartesian coordinates and noting the change in dipole moment. 

Here q(a) is the change in the dipole moment of the molecule for the displacement of the a atom. 

Nafie and Friedman (1983) have used this formalism to arrive at a simple expression for the rotatory strength of a vibrational transition  

Here the components of (dfildR ) are the elements of the atomic polar tensor for the n atom in the molecule. 

As the method readily lends itself to implementation into a quantum chemical program, the authors also give the appropriate formulation for the CNDO method and report calculations on L-alanine and (-i-)-(3/ )-methylcyclohexanone, which, as they state, compare favorably with experiment and simpler theories. 

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An approximate form of the NMO model, the atomic polar tensor (APT) model, has also proved effective (42). Rather than considering local contributions, this model considers contributions from the derivative of the total molecular dipole moment with respect to Cartesian displacement of a given nucleus, (3p/9R )o. The latter ate the elements of the atomic polar tensor for atom n. 

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