Benzene-H₂O and benzene-HDO: Fully coupled nine-dimensional quantum calculations of flexible H₂O/HDO intramolecular vibrational excitations and intermolecular states of the dimers, and their infrared and Raman spectra using compact bases

We present a rigorous and comprehensive theoretical treatment of the vibrational dynamics of benzene-H₂O and benzene-HDO dimers, where the quantum bound-state calculations of the coupled intra- A nd intermolecular vibrational states of the dimers are complemented by the quantum simulations of their infrared (IR) and Raman spectra utilizing the computed eigenstates. Apart from taking benzene to be rigid, the methodology for the nine-dimensional (9D) vibrational quantum calculations introduced in this study is fully coupled. The approach yields the intramolecular vibrational fundamentals and the bend (ν₂) overtone of H₂O and HDO in the complex, together with the low-lying intermolecular vibrational states in each of the intramolecular vibrational manifolds considered. Following the recently introduced general procedure [P. M. Felker and Z. Bačić, J. Chem. Phys. 151, 024305 (2019)], the full 9D vibrational Hamiltonian of the dimer is divided into a 6D intermolecular Hamiltonian, a 3D intramolecular Hamiltonian, and a 9D remainder term. A 9D contracted product basis is constructed from the low-energy eigenstates of the two reduced-dimension Hamiltonians, and the full vibrational dimer Hamiltonian is diagonalized in it. The symmetry present in the dimers is exploited to reduce the Hamiltonian matrix to a block diagonal form. Guided by the findings of our earlier study referenced above, the 6D intermolecular contracted bases for each symmetry block include only 40 eigenstates with energies up to about 225 cm^-1, far below the stretch and bend fundamentals of H₂O and HDO, which range between 1400 cm^-1 and 3800 cm^-1. As a result, the matrices representing the symmetry blocks of the 9D Hamiltonian are small for the high-dimensional quantum problem, 1360 and 1680 for the H₂O and HDO complexes, respectively, allowing for direct diagonalization. These calculations characterize in detail the H₂O/HDO intramolecular vibrations, their frequency shifts, and couplings to the large-amplitude-motion intermolecular vibrational sates. The computed IR spectra of the two complexes in the OH-stretch region, as well as the intermolecular Raman spectra, are compared to the experimental spectra in the literature.