Exact vibration-rotation kinetic energy operators in two sets of valence coordinates for centrally connected penta-atomic molecules

General internal coordinate gradient vectors and the vibrational kinetic energy operator of centrally-connected penta-atomic systems. Part I

New internal coordinate gradients, s-vectors, are derived using geometric algebra. The internal coordinates are based on a completely general description of the molecular geometry in terms of internal vectors. The internal coordinate gradients allow kinetic energy operators to be easily expressed in terms of orthogonal or non-orthogonal coordinate systems. Using this approach, a new exact vibrational kinetic energy operator for centrally-connected penta-atomic systems is derived for an internal polyspherical coordinate system based on orthogonal internal vectors. Difficulties associated with the well known coordinate redundancy in centrally-connected penta-atomic systems are discussed and overcome.

A perturbative calculation of the rovibrational energy levels of methane

The rovibrational energy levels of methane are determined from a quartic ab initio potential energy force field where the expansion coordinates are the Morse coordinates for the stretches and extension coordinates for the bends. Energies are calculated using canonical Van Vleck perturbation theory. Results are obtained for both rotation-vibration Hamiltonians expressed as functions of curvilinear and rectilinear normal coordinates. Second, fourth, and sixth order curvilinear results are compared with experimental results, and fourth order results for the rectilinear and curvilinear Hamiltonian are compared to each other. The calculated rovibrational levels are in good agreement with the experimental values for low J levels. The calculated rotational level splittings are in even better agreement with the experiment. In particular, the ground state tetrahedral splittings, which are as small as 10(-4) cm(-1), are well reproduced by our calculations at sixth order.

Fourier Transform Infrared Spectra of CH(2)DF: The nu(5) and nu(6) Bands

Results of a high-resolution infrared study of the spectroscopy of monodeuterated methyl fluoride, CH(2)DF, are reported for the first time. Spectra ranging from 500 to 3300 cm(-1) have been obtained and cover all the fundamental bands at resolutions down to 0.005 cm(-1). The two lowest energy fundamentals, the nu(5) and nu(6) bands, have been analyzed in detail. Since the molecule has C(s) symmetry, in principle both these bands are AB hybrids, since they belong to the irreducible representation A'. However, it was found that both are almost pure A-type bands. A total of 597 A-type lines of the nu(5) band and 619 A-type lines of the nu(6) band have been assigned. Vibrational and rotational spectroscopic constants have been determined by least-squares fitting to the data. An improved band center for nu(7) is also reported. Copyright 2001 Academic Press.