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 molecule vibronic spectra is refined in an effort to account for the Dushinsky effect as exactly as possible. The exact expressions obtained for the multi-dimensional overlap integrals present them as a finite series in products of one-dimensional overlap integrals for displaced harmonic oscillators with the coefficients expressed as the derivatives of some ''generating'' functions. These are present as polynomial functions of the Dushinsky transformation parameters. With the help of these expressions we analyse the physical meaning of these parameters and the characteristics of their spectral manifestations, as well as the possibility for different approximations and the resulting errors. An efficient calculation scheme, which includes a preliminary estimation of integral values without their calculation, is also put forward. It is shown that this method provides sufficient accuracy of vibronic spectra calculations together with a high speed of operation. This extends the possibility of exact and reliable interpretation and prediction of vibrational structures of electronic spectra as well as the solution of inverse vibronic problems.