Use of the virial theorem in modeling the potential energy surfaces for triatomic collinear reactions

Abstract

The new model potential energy surface for triatomic collinear reactions, WT(R), is presented. The surface is generated via the integral virial theorem from the “normalized” electronic kinetic energy surface, TM(R), satisfying along each uniform scaling path the condition (A): S0∞[TM(SR)—T(∞)] ds = Vnn(R); Vnn is the nuclear repulsion energy, s is a scale factor, and ∞ corresponds to the separated atoms limit. The TM(R) surface is approximated by the Morse function rotating around the united atom axis. For a given Rs = sR, the corresponding WT(Rs) cut has the form of the modified Morse function: WT(Rs) = (a/2cRs){exp[-2c(Rs — b)]-4exp[-c(Rs — b)]}, parameters of which can be determined from the condition (A) and the coordinates and energy of the corresponding point on the zero-virial path (ZVP, locus of minima along the uniform scaling directions). Illustrative examples of the TM(R) and WT(R) surfaces, generated from the BEBO ZVP for the symmetrical (H—H + H H + H—H) and unsymmetrical (F—H + H F + H—H) reactions are presented. These preliminary results suggest that the present model offers an efficient way to use the virial theorem in an a priori determining the valleys curvature variations during reaction.