DISTRIBUTED APPROXIMATING FUNCTIONAL FIT OF THE H-3 AB-INITIO POTENTIAL-ENERGY DATA OF LIU AND SIEGBAHN

We report a distributed approximating functional (DAF) fit of the nb i nitio potential-energy data of Liu [J. Chem. Phys. 58, 1925 (1973)] an d Siegbahn and Liu [ibid. 68, 2457 (1978)]. The DAF-fit procedure is b ased on a variational principle, and is systematic and general. Only t wo adjustable parameters occur in the DAF leading to a fit which is bo th accurate (to the level inherent in the input data; RMS error of 0.2 765 kcal/mol) and smooth (''well-tempered,'' in DAF terminology). In a ddition, the LSTH surface of Truhlar and Horowitz based on this same d ata [J. Chem. Phys. 68, 2466 (1978)] is itself approximated using only the values of the LSTH surface on the same,grid coordinate points as the at initio data, and the same DAF parameters. The purpose of this e xercise is to demonstrate that the DAF delivers a well-tempered approx imation to a known function that closely mimics the true potential-ene rgy surface. As is to be expected, since there is only roundoff error present in the LSTH input data, even more significant figures of fitti ng accuracy are obtained. The RMS error of the DAF fit, of the LSTH su rface at the input points, is 0.0274 kcal/mol, and a smooth fit, accur ate to better than I cm(-1), can be obtained using more than 287 input data points. (C) 1997 American Institute of Physics.