Vibrations of H+(D+) in stoichiometric LiNbO3 single crystal

A first principles quantum mechanical calculation of the vibrational energy levels and transition frequencies associated with protons in stoichiometric LiNbO(3) single crystal has been carried out. The hydrogen contaminated crystal has been approximated by a model one obtains by translating a supercell, i.e., a cluster of LiNbO(3) unit cells containing a single H(+) and a Li(+) vacancy. Based on the supercell model an approximate Hamiltonian operator describing vibrations of the proton sublattice embedded in the host crystal has been derived. It is further simplified to a sum of uncoupled Hamiltonian operators corresponding to different wave vectors (ks) and each describing vibrations of a quasi-particle (quasi-proton). The three dimensional (3D) Hamiltonian operator of k=0 has been employed to calculate vibrational levels and transition frequencies. The potential energy surface (PES) entering this Hamiltonian operator has been calculated point wise on a large set of grid points by using density functional theory, and an analytical approximation to the PES has been constructed by non-parametric approximation. Then, the nuclear motion Schrödinger equation has been solved by employing the method of discrete variable representation. It has been found that the (quasi-)H(+) vibrates in a strongly anharmonic PES. Its vibrations can be described approximately as a stretching, and two orthogonal bending vibrations. The theoretically calculated transition frequencies agree within 1% with those experimentally determined, and they have allowed the assignment of one of the hitherto unassigned bands as a combination of the stretching and the bending of lower fundamental frequency.