Empirical determination of the harmonic force constants in benzene. 4. The Fermi resonances

In this article, we present a continuation of our work on the refinement of the harmonic force constants F-i,F-k in benzene (in symmetrized Whiffen's coordinates) and on a growing number of higher order (anharmonic) force constants, F-i,F-j,F-k and F-i,F-j,F-k,F-l, that are of importance for the benzene isotopomer invariant potential energy surface. The refined set of harmonic and anharmonic force constants improves the agreement between the experimental levels and those calculated theoretically. The emphasis of the present work is on the analysis of the two notable Fermi resonances in benzene (nu(8) + n nu(1) <-> (n + 1)nu(1) + nu(6), where n = 0, 1, ... m, and nu(20) <-> nu(8) + nu(19) <-> nu(1) + nu(6) + nu(19)). For this purpose, we have further extended our fully dimensional, fully symmetrized, and nonperturbative vibrational procedure to the vibrational structure of the benzene isotopic species with D-6h symmetry.