Computing rovibrational levels of methane with curvilinear internal vibrational coordinates and an Eckart frame

We present a new procedure for computing a rovibrational spectrum of a polyatomic molecule and apply it to methane. The Schrodinger equation is solved, numerically exactly, by using a nested contracted basis. Rovibrational wavefunctions are computed in a vertical bar v >vertical bar J K M > basis, where vertical bar v > is a vibrational wavefunction and vertical bar JKM > is a symmetric top wavefunction. In turn, the vertical bar v > are obtained by solving a vibrational Schrodinger equation with basis functions that are products of contracted bend and stretch functions. At all stages of the calculation we exploit parity symmetry. The calculations are done in internal coordinates that facilitate the treatment of large amplitude motion. An Eckart molecule-fixed frame is used by numerically computing coefficients of the kinetic energy operator. The efficacy of the method is demonstrated by calculating a large number of converged J = 10 methane rovibrational levels in the Tetradecad polyad. No previous calculation of rovibrational levels of methane includes as many levels as we report in this paper. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4793474]