Calculation of anharmonic intensities in vibrational spectra of raman scattering and full interpretation of the vibrational spectrum of trans-1,3-butadiene

The anharmonic model of vibrations of polyatomic molecule makes it possible, using the secondorder perturbation theory, to interpret vibrational spectra in detail with resonances taken into account and to calculate the band intensities in spectra for fundamental frequencies, overtones, and combination frequencies. For molecules possessing a center of symmetry (to which trans-1,3-butadiene belongs), many vibration modes have zero intensities of absorption in IR spectra due to the mutual exclusion rule. For meaningful analysis of vibrations of such molecules, measurement of Raman scattering (RS) spectra is necessary, as is developing a theoretical model for calculating the anharmonic intensity. Perturbation theory (PT) in the form of contact transformations (CTs) has proven applicable for calculating the anharmonic intensities in RS spectra. The FORTRAN software program ANCO has been developed, which allows the calculation of vibration frequencies and IR-RS intensities of fundamental vibrations, overtones, and combination frequencies on the basis of second-order PT in form of CTs using the polynomial representation of potential energy, dipole moment and polarizability surfaces. The obtained frequencies and modes of anharmonic vibrations are provided, as well as interpretation of the experimental spectrum of the trans-1,3-butadiene molecule. A procedure for calculating the scale factors of the anharmonic force field is proposed. We also show that within the anharmonic vibration model, these factors are close to unity.