A neural network/trajectory approach is presented for the development of accurate potential-energy hypersurfaces that can be utilized to conduct ab initio molecular dynamics (AIMD) and Monte Carlo studies of gas-phase chemical reactions, nanometric cutting, and nanotribology, and of a variety of mechanical properties of importance in potential microelectromechanical systems applications. The method is sufficiently robust that it can be applied to a wide range of polyatomic systems. The overall method integrates ab initio electronic structure calculations with importance sampling techniques that permit the critical regions of configuration space to be determined. The computed ab initio energies and gradients are then accurately interpolated using neural networks (NN) rather than arbitrary parametrized analytical functional forms, moving interpolation or least-squares methods. The sampling method involves a tight integration of molecular dynamics calculations with neural networks that employ early stopping and regularization procedures to improve network performance and test for convergence. The procedure can be initiated using an empirical potential surface or direct dynamics. The accuracy and interpolation power of the method has been tested for two cases, the global potential surface for vinyl bromide undergoing unimolecular decomposition via four different reaction channels and nanometric cutting of silicon. The results show that the sampling methods permit the important regions of configuration space to be easily and rapidly identified, that convergence of the NN fit to the ab initio electronic structure database can be easily monitored, and that the interpolation accuracy of the NN fits is excellent, even for systems involving five atoms or more. The method permits a substantial computational speed and accuracy advantage over existing methods, is robust, and relatively easy to implement.

The reaction dynamics of the thermal, gas-phase decomposition of vinyl bromide has been investigated using classical trajectory methods on a global, analytic potential-energy surface fitted to the results of ab initio electronic structure calculations and experimental thermochemical, spectroscopic, and structural data. The saddle-point geometries and energies for several decomposition channels are determined using 6-3 lG(d,p) basis sets for carbon and hydrogen and Huzinaga's (4333/433/4) basis set augmented with split outer s and p orbitals and an f orbital for bromine. Electron correlation is incorporated using Mtiller-Plesset fourthorder perturbation theory with all single, double, triple, and quadruple excitations included. The calculated transition-state energies without zero-point energy corrections relative to vinyl bromide are four-center HBr elimination (3.530 eV), three-center HBr elimination (3.196 eV), four-center H2 elimination (4.159 eV), and three-center HZ elimination (4.618 eV). The global potential is written as a sum of the different reaction channel potentials connected by parametrized switching functions. The average absolute difference between AE values for the various decomposition channels obtained from the global surface and experimental measurement is 0.076 eV. Predicted equilibrium geometries for reactants and products are in good to excellent accord with experiment. The average absolute difference between the fundamental harmonic vibrational frequencies predicted by the global surface and those obtained from Raman and IR spectra varies from 10.2 cm-' for HzC=CHBr to 81.3 cm-' for H2C=CH. The potential barriers for six decomposition channels agree with the ab initio calculations to within an average difference of 0.124 eV. The dissociation dynamics of vinyl bromide on the ground-state surface is investigated at several excitation energies in the range 4.0-6.44 eV. The results show the following: (1) The decomposition dynamics follows a first-order rate law.(2) At thermal energies, the only brominated decomposition product is HBr. The results indicate that a previously reported activation energy for this process is too small. (3) As the excitation energy increases, other decomposition channels become important. At E = 6.44 eV, the reaction channels are, in order of importance, HZ elimination (48.1%), HBr formation (44.5%), Br atom elimination (4.6%), and C-H bond fission (2.6%). (4) The percentage of the total excitation energy partitioned into product relative translational motion and HBr internal energy upon HBr elimination is nearly independent of the total excitation energy. (5) Comparison of the calculated and measured relative translational energy distributions for product Br atoms upon C-Br bond fission and time-of-flight spectra for C2H2 upon HBr elimination indicates that in previously reported photolysis experiments Br atom dissociation is occurring on an excited electronic surface but HBr elimination is taking place on the ground-state surface subsequent to internal conversion....

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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This monograph presents recent advances in neural network (NN) approaches and applications to chemical reaction dynamics. Topics covered include: (i) the development of ab initio potential-energy surfaces (PES) for complex multichannel systems using modified novelty sampling and feedforward NNs; (ii) methods for sampling the configuration space of critical importance, such as trajectory and novelty sampling methods and gradient fitting methods; (iii) parametrization of interatomic potential functions using a genetic algorithm accelerated with a NN; (iv) parametrization of analytic interatomic potential functions using NNs; (v) self-starting methods for obtaining analytic PES from ab inito electronic structure calculations using direct dynamics; (vi) development of a novel method, namely, combined function derivative approximation (CFDA) for simultaneous fitting of a PES and its corresponding force fields using feedforward neural networks; (vii) development of generalized PES using many-body expansions, NNs, and moiety energy approximations; (viii) NN methods for data analysis, reaction probabilities, and statistical error reduction in chemical reaction dynamics; (ix) accurate prediction of higher-level electronic structure energies (e.g. MP4 or higher) for large databases using NNs, lower-level (Hartree-Fock) energies, and small subsets of the higher-energy database; and finally (x) illustrative examples of NN applications to chemical reaction dynamics of increasing complexity starting from simple near equilibrium structures (vibrational state studies) to more complex non-adiabatic reactions. The monograph is prepared by an interdisciplinary group of researchers working as a team for nearly two decades at Oklahoma State University, Stillwater, OK with expertise in gas phase reaction dynamics; neural networks; various aspects of MD and Monte Carlo (MC) simulations of nanometric cutting, tribology, and material properties at nanoscale; scaling laws from atomistic to continuum; and neural networks applications to chemical reaction dynamics. It is anticipated that this emerging field of NN in chemical reaction dynamics will play an increasingly important role in MD, MC, and quantum mechanical studies in the years to come.

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