ANALYTICAL FORMULAE FOR POLYATOMIC POTENTIAL ENERGY SURFACES

Abstract

Analytical expressions for the complete potential energy surface of a polyatomic molecule have been formulated, containing parameters which can be adjusted to reproduce: (i) the total energy and geometry of the molecules in equilibrium (ii) the harmonic (and anharmonic) force field of the molecules about the equilibrium configuration (iii) the total energy, geometry, and force constants of all dissociation products (e.g. $ABC \rightarrow AB+C, AC+B, BC+A, A+B+C$) (iv) ab initio calculations of the energy for particular geometries. The resulting expression man then be used to predict the shape of the potential energy surface over all of the (3N-6) dimensional coordinate space. The value of such a formula is similar to the value of the Morse function for a diatomic molecule. Thus it may be used to gain insight into the shape of the energy surface, to predict metastable minima, to predict the paths of chemical reactions, and to make classical trajectory calculations. Examples of results will be shown for various molecules: e.g. $^{H_{\backslash}}O-F$ (metastable minima $O-F^{H}$ and $O\ldots $HF), HCN (HNC), $C_{3}$ and $O_{3}$ (three equivalent minima), and $H_{2}CO$ (HCOH, and interesting dissociations to H+HCO and $H_{2}$ + CO etc.) The difficulties of this approach will also be discussed. In addition to the problem of assessing the reliability of the surface, there are considerable difficulties associated with reproducing the effects of surface intersections where these play and important role.