*ab initio*potential-energy surface obtained using modified novelty sampling and feedforward neural networks. II. Numerical application of the method

^{1}, L. M. Raff

^{2}, M. G. Rockley

^{2}, M. Hagan

^{3}, Paras M. Agrawal

^{4}and R. Komanduri

^{4}

### Abstract

A previously reported method for conducting molecular dynamics simulations of gas-phase chemical dynamics on *ab initio*potential-energysurfaces using modified novelty sampling and feedforward neural networks is applied to the investigation of the unimolecular dissociation of vinyl bromide. The neural network is fitted to a database comprising the MP4(SDQ) energies computed for 71 969 nuclear configurations using an extended basis set. Dissociation rate coefficients and branching ratios at an internal excitation energy of for all six open reaction channels are reported. The distribution of vibrational energy in HBr formed in three-center dissociation is computed and found to be in excellent accord with experimental measurements. Computational requirements for the electronic structure calculations, neural network training, and trajectory calculations are given. The weight and bias matrices required for implementation of the neural network potential are made available through the Supplementary Material.

We are indebted to Sergei Manzhos and Tucker Carrington for alerting us to the problems that were present in the data originally reported in Ref. 1. This project is funded by grants from the National Science Foundation (Grant Nos. DMI-0200327 and DMI-0457663). All other acknowledgments contained in Ref. 1 are appropriate for this paper.

INTRODUCTION

NEURAL NETWORK POTENTIAL-ENERGY SURFACE

DISSOCIATION DYNAMICS

SUMMARY AND CONCLUSIONS

### Key Topics

- Dissociation
- 22.0
- Databases
- 18.0
- Ab initio calculations
- 17.0
- Artificial neural networks
- 14.0
- Dissociation energies
- 13.0

## Figures

Atom numbering used to define the interparticle distances.

Atom numbering used to define the interparticle distances.

Illustration of the first cycle of the iterative novelty sampling procedure. The shaded distribution is the modified minimum distance distribution (see Ref. 1) of the 14 854 points obtained from the trajectories on the empirical potential surface. The unshaded histogram shows the distribution of minimum modified distances for the 19 821 new configurations from those in the shaded distribution. The new configurations are obtained in the first cycle of novelty sampling using a 15-140-1 NN fitted to the original 14 854 points. The failure of the two distributions to cover the same region of scaled minimum distances shows that there is not yet a sufficient sampling of configuration space to adequately represent the vinyl bromide potential surface.

Illustration of the first cycle of the iterative novelty sampling procedure. The shaded distribution is the modified minimum distance distribution (see Ref. 1) of the 14 854 points obtained from the trajectories on the empirical potential surface. The unshaded histogram shows the distribution of minimum modified distances for the 19 821 new configurations from those in the shaded distribution. The new configurations are obtained in the first cycle of novelty sampling using a 15-140-1 NN fitted to the original 14 854 points. The failure of the two distributions to cover the same region of scaled minimum distances shows that there is not yet a sufficient sampling of configuration space to adequately represent the vinyl bromide potential surface.

Illustration of the final cycle of the iterative novelty sampling procedure. The shaded distribution is the modified minimum distance distribution (see Ref. 1) of the 71 969 points obtained in the fourth cycle of the iterative procedure. The unshaded histogram shows the distribution of minimum modified distances for the new configurations from those in the shaded distribution. The new configurations are obtained in the fifth cycle of novelty sampling using a 15-140-1 NN fitted to the 71 969 points in the shaded distribution. As can be seen, the two distributions now span essentially the same region of scaled minimum distances. This is the novelty sampling criterion for convergence.

Illustration of the final cycle of the iterative novelty sampling procedure. The shaded distribution is the modified minimum distance distribution (see Ref. 1) of the 71 969 points obtained in the fourth cycle of the iterative procedure. The unshaded histogram shows the distribution of minimum modified distances for the new configurations from those in the shaded distribution. The new configurations are obtained in the fifth cycle of novelty sampling using a 15-140-1 NN fitted to the 71 969 points in the shaded distribution. As can be seen, the two distributions now span essentially the same region of scaled minimum distances. This is the novelty sampling criterion for convergence.

Comparison of the output from the 15-140-1 NN for the 64 773 configurations in the training set with *ab initio* energies computed using MP4(SDQ) methods and the basis set described in the text. If the fit was perfect, all points would lie on a 45° line. The average absolute deviation is . The energy zero is taken to be the atoms of vinyl bromide when separated at infinite distance.

Comparison of the output from the 15-140-1 NN for the 64 773 configurations in the training set with *ab initio* energies computed using MP4(SDQ) methods and the basis set described in the text. If the fit was perfect, all points would lie on a 45° line. The average absolute deviation is . The energy zero is taken to be the atoms of vinyl bromide when separated at infinite distance.

Comparison of the output from the 15-140-1 NN for the 7196 configurations in the testing set with *ab initio* energies computed using MP4(SDQ) methods and the basis set described in the text. If the fit was perfect, all points would lie on a 45° line. The average absolute deviation is . The energy zero is taken to be the atoms of vinyl bromide when separated at infinite distance.

Comparison of the output from the 15-140-1 NN for the 7196 configurations in the testing set with *ab initio* energies computed using MP4(SDQ) methods and the basis set described in the text. If the fit was perfect, all points would lie on a 45° line. The average absolute deviation is . The energy zero is taken to be the atoms of vinyl bromide when separated at infinite distance.

Histogram showing the distribution of the deviations of the predicted energies obtained from the 15-140-1 NN and those resulting from electronic structure calculations at MP4(SDQ) level using the basis set described in the text. The results for all 71 969 configurations are included in the histogram. The energy zero is taken to be the atoms of vinyl bromide when separated at infinite distance.

Histogram showing the distribution of the deviations of the predicted energies obtained from the 15-140-1 NN and those resulting from electronic structure calculations at MP4(SDQ) level using the basis set described in the text. The results for all 71 969 configurations are included in the histogram. The energy zero is taken to be the atoms of vinyl bromide when separated at infinite distance.

Computed decay curve for vinyl bromide at internal excitation randomly distributed over all 12 vibrational degrees of freedom. The line is a least-squares fit to the data. Its slope yields a total decay rate coefficient of .

Computed decay curve for vinyl bromide at internal excitation randomly distributed over all 12 vibrational degrees of freedom. The line is a least-squares fit to the data. Its slope yields a total decay rate coefficient of .

Distribution of vibrational energy in HBr subsequent to three-center dissociation. The points are the results obtained from 320 trajectories. The curve is a least-squares fit of a Boltzmann distribution. This fit corresponds to a HBr vibrational temperature of , which is in very good accord with the experimentally reported result in Ref. 24 of .

Distribution of vibrational energy in HBr subsequent to three-center dissociation. The points are the results obtained from 320 trajectories. The curve is a least-squares fit of a Boltzmann distribution. This fit corresponds to a HBr vibrational temperature of , which is in very good accord with the experimentally reported result in Ref. 24 of .

## Tables

Configurations stored in each cycle of the iterative, novelty sampling process.

Configurations stored in each cycle of the iterative, novelty sampling process.

Range of input and target output variables for the 15-140-1 neural network. The atom numbers for the input bond distances are given in Fig. 6.

Range of input and target output variables for the 15-140-1 neural network. The atom numbers for the input bond distances are given in Fig. 6.

Comparison of predicted potential-energy barrier heights for three-center HBr and dissociation reactions.

Comparison of predicted potential-energy barrier heights for three-center HBr and dissociation reactions.

Comparison of harmonic vibrational frequencies for vinyl bromide obtained from MP4(SDQ) and MP2 calculations with results from a previously reported analytic surface and experiment. The frequencies are reported in equivalent wave numbers.

Comparison of harmonic vibrational frequencies for vinyl bromide obtained from MP4(SDQ) and MP2 calculations with results from a previously reported analytic surface and experiment. The frequencies are reported in equivalent wave numbers.

Branching ratios on the *ab initio* NN potential and an analytic potential surface at internal excitation energy.

Branching ratios on the *ab initio* NN potential and an analytic potential surface at internal excitation energy.

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