Employing Diffusion Monte Carlo to Study Ro-vibrational Excited States and Minimized Energy Paths of Partially Deuterated Methane

Using Diffusion Monte Carlo, vibrational and rotational excited states of CH5+ and its deuterated isotopologues are evaluated and analyzed. A method for evaluating anharmonic corrections to energies along a minimized energy path for the reaction CH3+ + H2 → CH5+ → CH3+ + H2 is also discussed. For the vibrational excited states, the fundamentals in the five modes for CH5+ and CD5+ are calculated. The fundamentals are generated by requiring that the wave functions change sign at specified values of the five Symmetry Adapted Linear Combinations (SALC's) of the CH or CD bond lengths. While the definitions of these modes are based on displacements of the CH or CD bond lengths, the frequencies are found to be low compared to previously calculated CH vibrational frequencies of CH5+. The totally symmetric mode, with A1+ symmetry, has a calculated frequency of 2164 and 1551 cm-1 for CH5+ and CD5+. The frequencies of the four fundamentals that arise from excitation of the four SALC's that transform under G1+ symmetry have frequencies that range from 1039 to 1383 and 628 to 893 cm-1 in CH5+ and CD5+, respectively. The origins of the broken degeneracy are investigated and are found to reflect extensive coupling to the two low-frequency modes that lead to isomerization of CH5+. For the rotational excited states, the J=1, |K|=0,1 rotationally excited states of CH5+ and its deuterated isotopologues are calculated. The calculated J=1, |K|=0,1 rotationally excited state energies are high in energy when compared to the rotational energies calculated from vibrationally averaged rotational constants. The energy of a low-lying inversion mode that corresponds to a low-energy tunneling doublet is also calculated. When the inversion energy is subtracted from that of the J=1, |K|=0,1 rotational energy, the energies are in good agreement with those calculated from the vibrationally averaged rotational constants. The low-lying inversion mode cannot be removed from the calculations because of the extremely high symmetry of CH5+. The participation ratios are also calculated. These ratios are found to be reduced from those of the ground state, and identical for the inversion and rotationally excited states. The low-lying inversion mode may help with assigning the high resolution spectra of CH5+. By using Jacobi coordinates, the evaluation of anharmonic corrections to the energies along a minimum energy path are straightforward to implement using Diffusion Monte Carlo. The CH3+ + H2 → CH5+ reaction and its deuterated and partially tritiated analogues are investigated. In addition to exploring how the energetics of this reaction change upon deuteration or partial tritiation, projections of the probability amplitude onto various internal coordinates are evaluated and used to provide a quantum mechanical description of how deuteration affects the orientation of the two fragments as they combine to form the molecular ion. Different regions of interaction are reported and analyzed. Regardless of deuteration or partial tritiation or location of deuterium or tritium atoms, the distances at which different regions of interaction are observed do not change. Comparisons between quantum mechanical and classical mechanical calculations are also discussed.