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.

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A novel method is presented that significantly reduces the computational bottleneck of executing high-level, electronic structure calculations of the energies and their gradients for a large database that adequately samples the configuration space of importance for systems containing more than four atoms that are undergoing multiple, simultaneous reactions in several energetically open channels. The basis of the method is the high-degree of correlation that generally exists between the Hartree–Fock (HF) and higher-level electronic structure energies. It is shown that if the input vector to a neural network (NN) includes both the configuration coordinates and the HF energies of a small subset of the database, MP4(SDQ) energies with the same basis set can be predicted for the entire database using only the HF and MP4(SDQ) energies for the small subset and the HF energies for the remainder of the database. The predictive error is shown to be less than or equal to the NN fitting error if a NN is fitted to the entire database of higher-level electronic structure energies. The general method is applied to the computation of MP4(SDQ) energies of 68 308 configurations that comprise the database for the simultaneous, unimolecular decomposition of vinyl bromide into six different reaction channels. The predictive accuracy of the method is investigated by employing successively smaller subsets of the database to train the NN to predict the MP4(SDQ) energies of the remaining configurations of the database. The results indicate that for this system, the subset can be as small as 8% of the total number of configurations in the database without loss of accuracy beyond that expected if a NN is employed to fit the higher-level energies for the entire database. The utilization of this procedure is shown to save about 78% of the total computational time required for the execution of the MP4(SDQ) calculations. The sampling error involved with selection of the subset is shown to be about 10% of the predictive error for the higher-level energies. A practical procedure for utilization of the method is outlined. It is suggested that the method will be equally applicable to the prediction of electronic structure energies computed using even higher-level methods than MP4(SDQ).

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