Empirical Determination of the Harmonic Force Constants in Benzene. 3. The Harmonic Frequencies

Abstract

The aim of this work is to present a full set of 34 empirically determined harmonic force constants F i,k for benzene (in symmetrized Whiffen's coordinates), as well as the corresponding set of 20 harmonic normal mode (NM) frequencies for all four D 6 h isotopomers: C6H6, C6D6, 13C6H6, 13C6D6. The reliability of the obtained harmonic force constant values is reinforced by their ability to reproduce satisfactorily the experimentally measured fundamental vibrational frequencies of the four D 6 h benzene isotopomers. A specific combined LM (local mode)/SM (symmetrized modes) complex symmetrized nonperturbative vibrational model, developed in our previous work, has been employed for calculations on the vibrational energy levels in benzene, using the harmonic force constants F i,k and a few diagonal anharmonic parameters, as input data. A set of local (valence) harmonic force constants has also been derived from the empirically determined symmetrized force constants F i,k , and their physical meaning was discussed. The set of 20 harmonic NM frequencies ω k for all four D 6 h benzene isotopomers, calculated in the present work using the empirically determined set of F i,k values, have been analyzed and compared to previous empirical and ab initio determinations by other authors.

Geometry distortion of the benzene molecule in a strong magnetic field

“…The electric hypershielding has dimension V m −1 T −2 ≡ kg −1 m s A in the SI system of units. The calculations were carried out using the following base units: [27] mass m e = 9.10938188×10 and density-functional calculations [29][30][31]. With k CH = 5.547×10 2 N m −1 , and k CC = 6.616×10 2 N m −1 [29], the displacement of H and C nuclei due to the strong external magnetic field produces a change Table IV and the numerical derivatives in Table V …”

Empirical Determination of the Harmonic Force Constants in Benzene. 4. The Fermi Resonances

“…It was found that, for F 1,6,8 = −0.3, the two levels were at 1591.6 and 1609.7 cm -1 , in very good accord with the experimentally measured frequencies: 34 1591.327 and 1609.518 cm -1 . As already pointed out, to achieve this agreement, we also had to introduce minor changes in the values of some of the harmonic force constants that were established in our previous work . Thus, F 6,6 was changed from 0.671 to 0.660 and F 8.8 was changed from 6.670 to 6.660 (aJ and Angstrom).…”

“…The conventional notation for the normal mode (NM) whose frequency is 1484 cm -1 in C 6 H 6 is ν 19 . However, this notation is obviously not consistent and leads to some confusion when trying to relate the SM to NM . In fact, in terms of the SM treatment, mode no.…”

“…In the present work, we shall concentrate on the energy levels that are involved in Fermi resonance interactions. For this purpose, we introduce a number of anharmonic (cubic and quartic) Hamiltonian interaction terms in our formalism. ,, The calculation explicitly includes all 30 molecular vibrational degrees of freedom. The values of some important anharmonic force constants will be determined by fitting the calculated to the experimentally observed levels.…”

“…In a recent series of articles, − we attempted to further refine the values of the harmonic force constants for benzene by making use of a full scale vibrational model and algorithms that were designed for calculating the fundamental frequencies from a set of input values for the harmonic as well as the most important anharmonic force constants F i , k , F i , j , k , ... Meanwhile, the available rich database of experimental spectroscopic evidence for benzene and for some of its isotopomers − ,− was further extended.…”