A theoretical study of vibrational mode coupling in H5O2+

Abstract

The vibrational mode coupling in the protonated water dimer is investigated by performing two types of quantum calculations of the vibrational levels of H5O2+ and D5O2+, utilizing the OSS3(p) potential energy surface by Ojamaë et al. [L. Ojamaë, I. Shavitt, and S. J. Singer, J. Chem. Phys. 109, 5547 (1998)]. One is four-dimensional (4D), treating only the central O⋯H(D)+⋯O moiety. Three of the four modes considered, the asymmetric stretch and the two bends, are largely the vibrations of the central proton, while the fourth mode is essentially the O⋯O stretching vibration. The vibrational levels of O⋯H(D)+⋯O are calculated rigorously, as fully coupled (FC), and also in an adiabatic (3+1)D approximation, where the proton asymmetric stretch is treated as adiabatically separated from the other three degrees of freedom. The second set of calculations, designated VCI, is full-dimensional, 15D; it is performed by the code MULTIMODE, which does configuration interaction (CI) calculations using a basis determined from a vibrational self-consistent field Hamiltonian. The FC 4D and 15D VCI calculations give very similar fundamental frequencies of the two bending modes of the central proton, as well as the O⋯O stretch. They differ substantially only for the fundamental of the proton asymmetric stretch, the VCI value being about 25% lower than the FC 4D result. This shows that the asymmetric stretch is strongly coupled to the vibrations outside the O⋯H(D)+⋯O fragment, in contrast to the two proton bending modes and the O⋯O stretching vibration. The FC 4D and 15D VCI calculations predict the same frequency ordering of the four vibrational modes of the O⋯H(D)+⋯O moiety, and are in excellent agreement with respect to the H–D shift of the fundamentals of the shared proton modes. The adiabatic (3+1)D treatment is not quantitatively accurate, yielding fundamental frequencies of the proton vibrational modes which are considerably different from the FC 4D results. Our results have potentially significant implications for the assignment of the bands associated with shared proton vibrations in the recently reported infrared multiphoton photodissociation spectrum of the protonated water dimer.