Full-Dimensional Calculations of Rovibrational Levels of Five-Atom Molecules Using Two Different Strategies: Applications to CH4, CHD3, CH3D and CH3F
Zhang, Dong H.
Carrington, Tucker Jr
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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, the frame is an Eckart frame. Vibrational basis functions are products of contracted stretch and bend functions and eigen values are computed with the Lanczos algorithm. For CH4, CHD3, and CH3D, we report the ﬁrst J > 0 energy levels computed on the Wang-Carrington (WC) potential energy surface [X. G. Wang and T. Carrington, J. Chem. Phys. 141, 15 (2014)]. For CH3F the PES of Zhao et al. [J. Chem. Phys. 144, 204302 (2016)] was used. All the results are in good agreement with experimental data.