Computing energy levels of CH₄, CHD₃, CH₃D, and CH₃F with a direct product basis and coordinates based on the methyl...

Quantum mechanical calculations of ro-vibrational energies of CH₄, CHD₃, CH₃D, and CH₃F were made with two different numerical approaches. Both use polyspherical coordinates. The computed energy levels agree, confirming the accuracy of the methods. In the first approach, for all the molecules, the coordinates are defined using three Radau vectors for the CH₃ subsystem and a Jacobi vector between the remaining atom and the centre of mass of CH₃. Euler angles specifying the orientation of a frame attached to CH₃ with respect to a frame attached to the Jacobi vector are used as vibrational coordinates. A direct product potential-optimized discrete variable vibrational basis is used to build a Hamiltonian matrix. Ro-vibrational energies are computed using a re-started Arnoldi eigensolver. In the second approach, the coordinates are the spherical coordinates associated with four Radau vectors or three Radau vectors and a Jacobi vector, and the frame is an Eckart frame. Vibrational basis functions are products of contracted stretch and bend functions, and eigenvalues are computed with the Lanczos algorithm. For CH₄, CHD₃, and CH₃D, we report the first J > 0 energy levels computed on the Wang-Carrington potential energy surface [X.-G. Wang and T. Carrington, J. Chem. Phys. 141(15), 154106 (2014)]. For CH₃F, the potential energy surface of Zhao et al. [J. Chem. Phys. 144, 204302 (2016)] was used. All the results are in good agreement with experimental data.