ИСТИНА

For a polyatomic molecule, second-order canonical perturbation theory (CPT2) [1] expresses spectroscopic constants such as ωe and ωexe in the form of analytical expressions using parameters of the original vibrational Hamiltonian and readily supports the calculation of energy levels for fundamentals, overtones and combination bands. The problem remains that the treatment of resonances is complicated and analytic expressions for spectroscopic constants for higher orders of perturbation theory are almost impossible to deduce. A powerful technique of using ladder operators significantly simplifies the procedure of canonical transformations for high orders of perturbation theory [2]. Combination of this technique with the one of normal ordering of operators allows developing an efficient computational algorithm for solving the anharmonic problem for a polyatomic molecule [3,4]. Within this method, the ladder operator representation of the transformed Hamiltonian is preserved during the whole algorithmic procedure until the stage of evaluation of diagonal matrix elements, while numerical coefficients are kept as real numbers. In our Fortran computer implementation of the general scheme suggested by Sibert [3,4], we lifted some limitations of the original program, including the maximum size of a molecule. Evaluation of vibrational transition probabilities in IR and Raman spectra could be efficiently accomplished using transformation S-functions obtained during canonical transformations. This technique allows obtaining reliable values of vibrational intensities in IR and Raman spectra in high orders of perturbation theory. In the traditional way of conducting CPT2 calculations using analytical formulas, the resonances are treated using a simple variational procedure, for which matrix elements of first (Fermi-type) and second-order (Darling-Dennison type) resonances are required. Analytical expressions for the latter ones are quite difficult to evaluate free of errors [5]. In the framework of the method employed by us, it is straightforward to introduce the uniform procedure of both detecting resonances, taking them into account in the final variational procedure, and presenting the final perturbative Hamiltonian in the form of a sum of the main diagonal Dunham-type expansion in powers of (vr+½) plus resonance-type expansions of the special general form, the number of which is equal to the number of resonances. It is shown that for molecules studied the coefficients of perturbative Dunham-type Hamiltonians at 4th and 6th orders of CPT conform to the same rules as for diatomic molecules. Namely, at 4th order coefficients Y0 and ωexe coincide with ones at CPT2 level, while at 6th order coefficients ωe and ωeye coincide with ones at CPT4 level. The advantages and limitations of this method are illustrated by results of vibrational analysis of several molecules, including trans- and cis-1,2-difluoethylene. [1] H.H. Nielsen, Encyclopedia of Physics, Ed. S.Flügge, XXXVII/1 (1959) 173-313 [2] Y.S.Makushkin, V.G. Tyuterev, "Methods of Perturbations and Effective Hamiltonians in Molecular Spectroscopy", Novosibirsk (1984) [3] E.L. Sibert III, J. Chem. Phys., 88 (1988) 4378-4390 [4] E.L. Sibert III, Comput. Chem. Commun., 51 (1988) 149-160 [5] D.A. Matthews, J. Vázquez, J.F. Stanton, Mol. Phys., 105 (2007) 2659-2666