Separability of H2O molecular potential surfaces in hyperspherical coordinates via adiabatic approximation

Abstract

An adiabatic scheme for separation of the three-dimensional (3D) nuclear dynamics on the ground electronic Born-Oppenheimer potential energy surface of an ${\mathrm{H}}_{2}\mathrm{O}$ molecule in hyperspherical coordinates is presented. It is found that the three vibrational modes are weakly coupled and the 3D vibrational wave function can be approximated as a product of three separable functions: one represented by the hyperradius and two by the two hyperangles individually. This framework is then used for investigation of the formation and the role of a saddlelike barrier arising in the two hyperspherical angles that is to moderate the OH $+$ H dissociation process. In order to test the validity of the framework, vibrational states with energies up to 19 500 ${\mathrm{cm}}^{\ensuremath{-}1}$ are constructed under the assumptions of adiabaticity and separability and compared to full three-dimensional high-precision numerical calculations yielding remarkable correspondence. As a result we present a simple construction scheme for separated molecular vibration states as the first step towards theoretical investigation of laser-driven molecular dynamics of triatomic molecules.