Finite Field Calculations of Raman Intensities

Hush et al. [336,337,342] have employed finite field perturbation treatment to derive molecular polarizabilities and polarizability gradients from SCF and correlated wave functions. 

In an uniform electric field f the induced dipole moment of a molecule Pinj(f) is given by [336,343] 

In the framework of the finite field formalism the perturbation to the Hamiltonian by an uniform electric field is expressed as [175] 

Ho is die Hamiltonian for the unperturbed system and p is the dipole moment operator. From the perturbed wave functions evaluated at SCF or Cl level the dipole moment value p(f) is obtained. From the Taylor series expansion [ q. (10.1)] the coefficients a, p and y can be derived from calculations at a number of distortions along particular coordinate and field direcdons. Molecular polarizability is then obtained from the expression 

Komonucki and Mclw [178] have provided an efficient method for deriving polarizability derivatives from die energy gradient Following expressions (7.2)-(7.4) do /dqj are presented as 

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