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Manuscript Title: Particles-on-a-sphere method for computing the rotational-vibrational spectrum of H2O.
Authors: D.M. Leitner, G.A. Natanson, R.S. Berry, P. Villarreal, G. Delgado-Barrio
Program title: SP2D
Catalogue identifier: ABDU_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 51(1988)207
Programming language: Fortran.
Computer: CRAY XMP-48.
Operating system: CTSS.
RAM: 17K words
Keywords: Molecular, Vibration.
Classification: 16.3.

Nature of problem:
An adiabatic separation of fast stretching from slow bending and overall rotational motion is made for the water molecule. This program performs a two dimensional integration over the two radial coordinates to obtain the stretching levels. In addition, an effective radius, mass of the heavy atom, and bending potential are calculated for input into the second program, which computes the bending and rotational levels. The effective bending potential can be obtained in one of two ways. One method (Method I) is performing the two dimensional integration at only one angle, the equilibrium bending angle, and using the wavefunctions to average over the radial coordinates at many bending angles. In the case of H2O, which places two identical particles on the sphere, the Hamiltonian is diagonalized separately for symmetric and antisymmetric wavefunctions. The second way (Method II) is to solve the two dimensional Schrodinger equation for vibration at several angles, treating the angle parametrically, and then to use the eigenvalues as the effective bending potential. The former method has the advantage of being computationally faster, since only one diagonalization is performed. However, the latter method provides more accuracy necessary for calculating highly excited vibrational states. One further stage of refinement, not included in this discussion, is required to account for interaction of the stretching modes with bending and rotation.

Solution method:
A basis set of harmonic oscillator functions is used, and the Hamiltonian is diagonalized to obtain the energy levels and the wavefunction coefficients. Integration over the radial coordinates to obtain the effective radius, mass, and bending potential is performed using Gaussian quadrature.

Running time:
Using 9 harmonic oscillator basis functions and 9 points of integration, the cpu time required on the Cray is about 2 seconds.