The vibrational spectrum of TpRhH2(H2): a computational and inelastic neutron scattering study

We report extensive density functional theory studies of the structures and vibrational frequencies of Tp^3,5-MeRhH₂(H₂) in its ground and various transition states as well as the first direct comparison of observed and calculated inelastic neutron scattering (INS) vibrational spectra on this type of compound. Geometry optimizations produced canted η²-dihydrogen dihydride local minima of C₁ symmetry; with HH distances for the C₁ minimum energy structure of 0.842 and 0.898 Å and barriers to rotation of 0.34 and 0.50 kcal mol⁻¹, respectively for B3LYP/BS1 and BP86/BS1 calculations of Tp^3,5-MeRhH₂(H₂). The latter results from one transition state rotated approximately 60° away (a second lower energy transition state which is a few hundreds of a kcal mol⁻¹ above the C₁ MIN is rotated approximately 30° away). With these calculated d(HH) values for the C₁ MIN the previously reported experimental data on the rotation of the dihydrogen ligand yields an experimental barrier to rotation of 1 kcal mol⁻¹ and places the torsional transition at 200 cm⁻¹ in the INS spectrum. Optimization of the Rh structure, that is analogous to the related Ir(V) C_s minimum found for TpIrH₄, generates a high-energy (>4 cal mol⁻¹) C_s transition state TpRh^IIIH₄ structure with an η³-H₃ ⁻ ligand. This transition state (C_s TSE) exchanges the hydrogen in the mirror plane between two chiral C₁ MIN structures. Comparisons between observed and computed INS spectra suggests that the experimental INS spectrum be viewed as resulting from a quantum-averaged ground state encompassing at least two of the low energy structures found in our calculations.