THE UTILITY OF HIGHER-ORDER DERIVATIVES IN CONSTRUCTING MOLECULAR-POTENTIAL ENERGY SURFACES BY INTERPOLATION

In this paper we evaluate the use of higher order derivatives in the c onstruction of an interpolated potential energy surface for the OH+H-2 -->H2O+H reaction. The surface construction involves interpolating bet ween local Taylor expansions about a set of known data points. We exam ine the use of first, second, third, and fourth order Taylor expansion s in the interpolation scheme. The convergence of the various interpol ated surfaces is evaluated in terms of the probability of reaction. We conclude that first order Taylor expansions (and by implication zerot h order expansions) are not suitable for constructing potential energy surfaces for reactive systems. We also conclude that it is inefficien t to use fourth order derivatives. The factors differentiating between second and third order Taylor expansions are less clear. Although thi rd order surfaces require substantially fewer data points to converge than second order surfaces, this faster convergence does not offset th e large cost incurred in calculating numerical third derivatives. We t herefore conclude that, without an efficient means for calculating ana lytic third derivatives, second order derivatives provide the most cos t-effective means of constructing a global potential energy surface by interpolation. (C) 1995 American Institute of Physics.