Simultaneous Determination of Force Constants and Dipole Moment Derivatives of Methane

The expressions of the effective Hamiltonian and dipole moment spectroscopic parameters in the tetrahedral formalism are used simultaneously to fit the force field and dipole moment derivatives of the methane molecule. Data, the so-called “observed parameters,” are the values of the spectroscopic parameters determined from the frequencies and line strengths analyses. The ambiguities of most parameters (in the polyad scheme) are treated consistently with the Hamiltonian reduction chosen in the frequency analyses. As an illustration, the method is applied to the tetrahedralXY₄isotopic species only. The quadratic and cubic force field constants have been determined in addition to the linear and six of the seven quadratic dipole moment derivatives. The observed parameters are reproduced with a standard deviation of 4%. The results are compared with previous works and it is moreover shown that the introduction of the dipole moment data removes some correlations between the force constants.