Quasiclassical trajectory studies using 3D spline interpolation of a b i n i t i o surfaces

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Abstract
The accuracy of spline fitting procedures has been investigated for Morse potentials, Lennard‐Jones potentials, a collinear D–Cl–H potential surface, and for three dimensional DIM (He–H+2) and a valence‐bond D–Cl–H surface. The adequacy of 3D spline surfaces in quasiclassical trajectory studies has been examined for both the He–H+2 and D+HCl systems. It is found that while one dimensional spline fits are very accurate, this accuracy decreases substantially for a two‐dimensional spline fit. There is an additional, but smaller, decrease in accuracy for three‐dimensional splines. The surface gradients are found to be less accurately fitted than the corresponding function values. In general, (15×15×15) cubic spline fits are found to lack the necessary accuracy to produce a point‐by‐point match of a quasiclassical trajectory to that obtained on the original analytic surface. However, total reaction cross sections, energy partitioning distributions, and spatial scattering distributions computed on spline surfaces are found to be in good accord with those obtained from the full analytic surface. This suggests that in spite of their limited accuracy, spline fits may provide a very useful tool for interpolation of ab initio surfaces. The computer time requirements for use of 3D cubic splines in quasiclassical trajectory calculations are found to be within range of present computational facilities.