Flexible water molecule in C₆₀: Intramolecular vibrational frequencies and translation-rotation eigenstates from fully coupled nine-dimensional quantum calculations with small basis sets

We present a method for efficient calculation of intramolecular vibrational excitations of H₂O inside C₆₀, together with the low-energy intermolecular translation-rotation states within each intramolecular vibrational manifold. Apart from assuming rigid C₆₀, this nine-dimensional (9D) quantum treatment is fully coupled. Following the recently introduced approach [P. M. Felker and Z. Bačić, J. Chem. Phys. 151, 024305 (2019)], the full 9D vibrational Hamiltonian of H₂O@C₆₀ is partitioned into two reduced-dimension Hamiltonians, a 6D one for the intermolecular vibrations and another in 3D for the intramolecular degrees of freedom, and a 9D remainder term. The two reduced-dimension Hamiltonians are diagonalized, and their eigenvectors are used to build up a product contracted basis in which the full vibrational Hamiltonian is diagonalized. The efficiency of this methodology derives from the insight of our earlier study referenced above that converged high-energy intramolecular vibrational excitations of weakly bound molecular complexes can be obtained from fully coupled quantum calculations where the full-dimensional product contracted basis includes only a small number of intermolecular vibrational eigenstates spanning the range of energies much below those of the intramolecular vibrational states of interest. In this study, the eigenstates included in the 6D intermolecular contacted basis extend to only 410 cm^-1 above the ground state, which is much less than the H₂O stretch and bend fundamentals, at ≈3700 and ≈1600 cm^-1, respectively. The 9D calculations predict that the fundamentals of all three intramolecular modes, as well as the bend overtone, of the caged H₂O are blueshifted relative to those of the gas-phase H₂O, the two stretch modes much more so than the bend. Excitation of the bend mode affects the energies of the low-lying H₂O rotational states significantly more than exciting either of the stretching modes. The center-of-mass translational fundamental is virtually unaffected by the excitation of any of the intramolecular vibrational modes. Further progress hinges on the experimental measurement of the vibrational frequency shifts in H₂O@C₆₀ and ab initio calculation of a high-quality 9D potential energy surface for this endohedral complex, neither of which is presently available.