We present a new procedure for computing a rovibrational spectrum of a polyatomic molecule and apply it to methane. The Schrödinger equation is solved, numerically exactly, by using a nested contracted basis. Rovibrational wavefunctions are computed in a |v>|JKM> basis, where |v> is a vibrational wavefunction and |JKM> is a symmetric top wavefunction. In turn, the |v> are obtained by solving a vibrational Schrödinger 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.
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