REFINED APPROACH FOR MATRIX ELEMENT CALCULATION IN THE THEORY OF ELECTRONIC VIBRATIONAL-SPECTRA OF POLYATOMIC-MOLECULES

The approximate method suggested previously for computing the overlap integrals of vibrational wavefunctions in the theory of polyatomic mol ecule vibronic spectra is refined in an effort to account for the Dush insky effect as exactly as possible. The exact expressions obtained fo r the multi-dimensional overlap integrals present them as a finite ser ies in products of one-dimensional overlap integrals for displaced har monic oscillators with the coefficients expressed as the derivatives o f some ''generating'' functions. These are present as polynomial funct ions of the Dushinsky transformation parameters. With the help of thes e expressions we analyse the physical meaning of these parameters and the characteristics of their spectral manifestations, as well as the p ossibility for different approximations and the resulting errors. An e fficient calculation scheme, which includes a preliminary estimation o f integral values without their calculation, is also put forward. It i s shown that this method provides sufficient accuracy of vibronic spec tra calculations together with a high speed of operation. This extends the possibility of exact and reliable interpretation and prediction o f vibrational structures of electronic spectra as well as the solution of inverse vibronic problems.