Adiabatic separations of stretching and bending vibrations: Application to H2O

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Abstract
A detailed investigation is made into the use of adiabatic approximations for describing excited stretching and bending vibrations of the water molecule. The goal is to determine precisely how effective this approach can be in a fully quantum mechanical triatomic calculation which incorporates anharmonicities to all orders in each of the modes. Great care is taken to avoid introducing unnecessary limitations or approximations: (i) Curvilinear coordinates are used rather than the Cartesian coordinates which form the starting point for normal mode calculations; (ii) the exact quantum kinetic energy operator in these coordinates is used as the basis for both the adiabatic and full three‐dimensional calculations; (iii) a Sorbie–Murrell‐type potential energy surface is used, giving a reasonable representation of the ground electronic surface for large excursions from the equilibrium configuration. In addition to the bond and bond‐angle variables of earlier local mode investigations, a slightly different set of fully curvilinear coordinates is also investigated. These coordinates are shown to provide a more nearly separable description in both the exact and adiabatic treatments of this specific problem. The conventional adiabatic approach, in which the slower bending mode experiences an effective force due to averaging over the faster stretching modes, is reaffirmed to be accurate for excited stretching states. For states with any appreciable bending excitation, however, it turns out that the adiabatic calculations quickly erode in reliability. In answer to this problem, the reverse adiabatic procedure (with the bend treated first) is also implemented here. While counterintuitive, this latter method is found to yield a significant improvement for the calculated bending overtones, as well as many of the combination bands. Thus, by thorough consideration of both the coordinates and order of averaging employed, the adiabatic method is shown to be very effective for either bending or stretching overtones in a realistic, fully anharmonic, triatomic vibrational problem. In addition, introduction of a new orthonormal set of basis functions for the bending angle overcomes some of the problems associated with use of the less flexible Legendre basis.