ABSTRACT
An improved neural network (NN) approach is presented for the simultaneous development of accurate potential-energy hypersurfaces and corresponding force fields that can be utilized to conduct ab initio molecular dynamics and Monte Carlo studies on gas-phase chemical reactions. The method is termed as combined function derivative approximation (CFDA). The novelty of the CFDA method lies in the fact that although the NN has only a single output neuron that represents potential energy, the network is trained in such a way that the derivatives of the NN output match the gradient of the potential-energy hypersurface. Accurate force fields can therefore be computed simply by differentiating the network. Both the computed energies and the gradients are then accurately interpolated using the NN. This approach is superior to having the gradients appear in the output layer of the NN because it greatly simplifies the required architecture of the network. The CFDA permits weighting of function fitting relative to gradient fitting. In every test that we have run on six different systems, CFDA training (without a validation set) has produced smaller out-of-sample testing error than early stopping (with a validation set) or Bayesian regularization (without a validation set). This indicates that CFDA training does a better job of preventing overfitting than the standard methods currently in use. The training data can be obtained using an empirical potential surface or any ab initio method. The accuracy and interpolation power of the method have been tested for the reaction dynamics of H+HBr using an analytical potential. The results show that the present NN training technique produces more accurate fits to both the potential-energy surface as well as the corresponding force fields than the previous methods. The fitting and interpolation accuracy is so high (rms error=1.2 cm(-1)) that trajectories computed on the NN potential exhibit point-by-point agreement with corresponding trajectories on the analytic surface.
ABSTRACT
Previous methods proposed for obtaining analytic potential-energy surfaces (PES) from ab initio electronic structure calculations are not self-starting. They generally require that the sampling of configuration space important in the reaction dynamics of the process being investigated be initiated by using chemical intuition or a previously developed semiempirical potential-energy surface. When the system under investigation contains four or more atoms undergoing three- and four-center reactions in addition to bond scission processes, obtaining a sufficiently converged initial sampling can be very difficult due to the extremely large volume of configuration space that is important in the reaction dynamics. It is shown that by combining direct dynamics (DD) with previously reported molecular dynamics (MD), novelty sampling (NS), and neural network (NN) methods, an analytical surface suitable for MD computations for large systems may be obtained. Application of the method to the investigation of N-O bond scission and cis-trans isomerization reactions of HONO followed by comparison of the resulting neural network potential-energy surface to one obtained by using a semiempirical potential to initiate the sampling shows that the two potential surfaces are the same within the fitting accuracy of the surfaces. It is concluded that the combination of direct dynamics, molecular dynamics, novelty sampling, and neural network fitting provides a self-starting, robust, and accurate DD/MD/NS/NN method for the execution of first-principles, ab initio, molecular dynamics studies in systems containing four or more atoms which are undergoing simultaneous two-, three-, and four-center reactions.