Abstract
The neural network (NN) procedure to interpolate ab initio data for the purpose of molecular dynamics (MD) simulations has been tested on the system. Unlike other similar NN studies, here, we studied the dissociation of without the initial use of any empirical potential. During the dissociation of into or , the spin multiplicity of the system changes from singlet to triplet in the first reaction and from singlet to pentet in the second. This paper employs four potential surfaces. The first is a NN fit [NN(STP)] to a database comprising the lowest of the singlet, triplet, and pentet energies obtained from density functional calculations in 6673 nuclear configurations. The other three potential surfaces are obtained from NN fits to the singlet, triplet, and pentet-state energies. The dissociationdynamics on the singlet-state and NN(STP) surfaces are reported. The results obtained using the singlet surface correspond to those expected if the reaction were to occur adiabatically. The dynamics on the NN(STP) surface represent those expected if the reaction follows a minimum-energy pathway. This study on a small system demonstrates the application of NNs for MD studies using ab initio data when the spin multiplicity of the system changes during the dissociation process.
This project is funded by grants from the National Science Foundation (DMI-0200327 and DMI-0457663). We thank Dr. W. DeVries, Dr. G. Hazelrigg, Dr. J. Cao, and Dr. D. Durham of the Division of Design, Manufacturing, and Industrial Innovation, Dr. B. M. Kramer, Engineering Centers Division, and Dr. J. Larsen Basse, Tribology and Surface Engineering program for their interest and support of this work. This project was also sponsored in part by a DEPSCoR grant on the Multiscale Modeling and Simulation of Material Processing (F49620-03-1-0281). The authors thank Dr. Craig S. Hartley and Dr. J. Tiley, Program Managers of the Metallic Materials Program, of the Air Force Office of Scientific Research (AFOSR) for their interest in and support of this work. One of the authors (R.K.) also thanks A. H. Nelson, Jr., endowed chair in engineering for additional support.
I. INTRODUCTION
II. COMPUTATIONAL PROCEDURE
A. Ab initio data
B. Neural networks
C. Molecular dynamics simulations
III. RESULTS AND DISCUSSION
A. Energetics and geometry
B. Trajectories
IV. ADIABATIC/NONADIABATIC PROCESSES
V. SUMMARY AND CONCLUSIONS
Key Topics
- Dissociation
- 34.0
- Ab initio calculations
- 24.0
- Dissociation energies
- 16.0
- Databases
- 13.0
- Potential energy surfaces
- 11.0
Figures
The potential energy in eV given by the NN(STP) neural network vs the corresponding ab initio potential energy for the data used for (a) training and (b) testing.
The potential energy in eV given by the NN(STP) neural network vs the corresponding ab initio potential energy for the data used for (a) training and (b) testing.
The potential energy in eV given by the NN(S) neural network vs the corresponding ab initio potential energy for the data used for (a) training and (b) testing.
The potential energy in eV given by the NN(S) neural network vs the corresponding ab initio potential energy for the data used for (a) training and (b) testing.
The potential energy of as a function of on the NN(STP) surface corresponding to the minimum reaction path, as described in the text for the reaction given by Eq. (7).
The potential energy of as a function of on the NN(STP) surface corresponding to the minimum reaction path, as described in the text for the reaction given by Eq. (7).
The potential energy of as a function of corresponding to the minimum reaction path on the NN(STP) surface, as described in the text for the reaction given by Eq. (8).
The potential energy of as a function of corresponding to the minimum reaction path on the NN(STP) surface, as described in the text for the reaction given by Eq. (8).
The potential energy of as a function of corresponding to the minimum reaction path on the NN(STP) surface, as described in the text for the reaction given by Eq. (9).
The potential energy of as a function of corresponding to the minimum reaction path on the NN(STP) surface, as described in the text for the reaction given by Eq. (9).
The variation of as a function of time in picoseconds at computed on the NN(STP) surface.
The variation of as a function of time in picoseconds at computed on the NN(STP) surface.
RRK plot for the dissociation rate in for the dissociation of into . The circles and solid line correspond to the data obtained using the NN(STP) potential with . The triangles and the dotted line correspond to the data obtained using the NN(S) potential surface with .
RRK plot for the dissociation rate in for the dissociation of into . The circles and solid line correspond to the data obtained using the NN(STP) potential with . The triangles and the dotted line correspond to the data obtained using the NN(S) potential surface with .
The location of the atoms during the combination-dissociation reaction given by Eq. (14) for a typical trajectory at time steps: (a) 1, (b) 200, (c) 400, (d) 500, (e) 600, (f) 800, (g) 1000, (h) 1200, and (i) 1600; 1 time . Each of the nine boxes shown here is of size in the plane in which the reaction occurs.
The location of the atoms during the combination-dissociation reaction given by Eq. (14) for a typical trajectory at time steps: (a) 1, (b) 200, (c) 400, (d) 500, (e) 600, (f) 800, (g) 1000, (h) 1200, and (i) 1600; 1 time . Each of the nine boxes shown here is of size in the plane in which the reaction occurs.
The variation of , , and (in Å) as a function of time for a typical trajectory undergoing a combination-dissociation reaction given by Eq. (14).
The variation of , , and (in Å) as a function of time for a typical trajectory undergoing a combination-dissociation reaction given by Eq. (14).
Variation of the four potentials along the reaction coordinate. The results for the singlet, triplet, pentet, and minimum-energy reaction pathways are labeled in the figure as NN(S), NN(T), NN(P), and NN(STP), respectively. The crossing point of the NN(S) and NN(STP) potentials is seen at a Si–O distance of . The energy at the crossing point relative to that for equilibrium is .
Variation of the four potentials along the reaction coordinate. The results for the singlet, triplet, pentet, and minimum-energy reaction pathways are labeled in the figure as NN(S), NN(T), NN(P), and NN(STP), respectively. The crossing point of the NN(S) and NN(STP) potentials is seen at a Si–O distance of . The energy at the crossing point relative to that for equilibrium is .
Tables
The maximum and minimum values of input and output parameters.
The maximum and minimum values of input and output parameters.
Reaction rate coefficients for the reaction .
Reaction rate coefficients for the reaction .
Article metrics loading...
Full text loading...
Commenting has been disabled for this content