NEURAL-NETWORK MODELS OF POTENTIAL-ENERGY SURFACES

Neural networks provide an efficient, general interpolation method for nonlinear functions of several variables. This paper describes the us e of feed-forward neural networks to model global properties of potent ial energy surfaces from information available at a limited number of configurations. As an initial demonstration of the method, several fit s are made to data derived from an empirical potential model of CO ads orbed on Ni(111). The data are error-free and geometries are selected from uniform grids of two and three dimensions. The neural network mod el predicts the potential to within a few hundredths of a kcal/mole at arbitrary geometries. The accuracy and efficiency of the neural netwo rk in practical calculations are demonstrated in quantum transition st ate theory rate calculations for surface diffusion of CO/Ni(111) using a Monte Carlo/path integral method. The network model is much faster to evaluate than the original potential from which it is derived. As a more complex: test of the method, the interaction potential of H-2 Wi th the Si(100)-2X1 surface is determined as a function of 12 degrees o f freedom from energies calculated with the local density functional m ethod at 750 geometries. The training examples are not uniformly space d and they depend weakly on variables not included in the fit. The neu ral net model predicts the potential at geometries outside the trainin g set with a mean absolute deviation of 2.1 kcal/mole. (C) 1995 Americ an institute of Physics.