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E-raamat: Neural Networks in Chemical Reaction Dynamics

, (Regents Professor, Department of Chemistry, Oklahoma State University), (Professor, School of Elec), (Professor & A. H. Nelson, Jr. Endowed Chair in Engineering, School of Mechanical and Aerospace Engineering, Oklahoma State University)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 18-Jan-2012
  • Kirjastus: Oxford University Press Inc
  • Keel: eng
  • ISBN-13: 9780199909889
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Neural Networks in Chemical Reaction DynamicsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 18-Jan-2012
  • Kirjastus: Oxford University Press Inc
  • Keel: eng
  • ISBN-13: 9780199909889
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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.
Preface xi
Acronyms xiii
1 Fitting Potential-Energy Hypersurfaces
1.1 Introduction
1(1)
1.2 Empirical and Semi-Empirical Potential Surfaces
2(1)
1.3 Ab Initio Potential-Energy Surfaces (PESs)
3(1)
1.4 Other Fitting Methods for Potential-Energy Surfaces
4(3)
1.5 Neural Network (NN) Approach
7(1)
1.6 Essential Steps in a Molecular Dynamics Simulations
7(1)
1.7 Organization of the Monograph
8(5)
2 Overview of Some Non-Neural Network Methods for Fitting Ab Initio Potential-Energy Databases
2.1 Introduction
13(1)
2.2 Moving Shepard Interpolation (MSI) Methods
13(11)
2.2.1 Required Input Data
13(1)
2.2.2 MSI Method for Molecules with Four or Fewer Atoms
14(2)
2.2.3 MSI Method for Molecules with More than Four Atoms
16(5)
2.2.4 MSI Configuration Space Sampling
21(2)
2.2.5 Applications and Results
23(1)
2.3 Interpolative Moving Least-Squares Methods (IMLS)
24(7)
2.3.1 General Method
24(4)
2.3.2 Cutoff Function, Basis Sets, and Data Sampling
28(2)
2.3.3 Applications and Results
30(1)
2.4 Invariant Polynomial (IP) and Reproducing Kernel Hilbert Space (RKHS) Methods
31(6)
2.4.1 Invariant Polynomial Methods
31(2)
2.4.2 Applications and Results of IP Methods
33(1)
2.4.3 Reproducing Kernal Hilbert Space (RKHS)
34(3)
2.5 Hybrid Methods
37(3)
2.5.1 Application to H3 System
37(1)
2.5.2 Application to the O(1D) + H2 System
38(2)
2.6 Neural Networks Applications to Reaction Dynamics
40(2)
3 Feedforward Neural Networks
3.1 Introduction
42(1)
3.2 Neuron Model
42(2)
3.3 Network Architectures
44(1)
3.4 Approximation Capabilities of Multilayer Networks
45(3)
3.5 Training Multilayer Networks
48(3)
3.6 Generalization (Interpolation and Extrapolation)
51(2)
3.7 Data Preprocessing
53(1)
3.8 Practical Aspects of NN Training Issues
54(6)
3.8.1 Database, Local Minima, Sampling Bias, Committees, and Derivatives
54(1)
3.8.2 Input Vector Optimization and Fitting Accuracy
55(5)
3.9 Example Training Process (MATLAB)
60(3)
3.10 The Combined Function Derivative Approximation (CFDA) NN Method
63(4)
3.11 Combined Function Derivative Approximation Pruning
67(10)
3.11.1 Two-Layer Network Response
68(3)
3.11.2 Two-Layer Network Response
71(1)
3.11.2.1 Type-A Overfitting
71(2)
3.11.2.2 Type-B Overfitting
73(2)
3.11.3 Pruning Algorithm Summary
75(2)
4 Configuration Space Sampling Methods
4.1 Introduction
77(1)
4.2 Trajectory and Novelty Sampling (NS) Methods
78(9)
4.3 Self-Starting Method Using Direct Dynamics (DD)
87(7)
4.4 Configuration Sampling Using a Gradient Fitting Method
94(6)
5 Applications of Neural Network Fitting of Potential-Energy Surfaces
5.1 Introduction
100(4)
5.2 Near Equilibrium Structures---Vibrational State Studies
104(4)
5.2.1 The H+3 Molecular Ion
104(1)
5.2.2 H2O, HOOH, and H2CO
105(3)
5.3 CFDA Fitting---The H + H'Br → HBr + H' and H2 + Br Reactions
108(8)
5.4 Cis-Trans Isomerization And N-O Dissociation Reactions Of Hono
116(8)
5.5 Gradient Sampling---Unimolecular Dissociation of HOOH to 2 OH
124(3)
5.6 Unimolecular Dissociation of Vinyl Bromide (H2C = CHBr)
127(6)
5.7 Non-Adiabatic Reactions: SiO2 → SiO + O and SiO2 → Si + O2
133(8)
5.8 Generalized NN Representation of High-Dimensional Potential-Energy Surfaces
141(7)
6 Potential-Energy Surfaces Using Expansion Methods and Neural Networks
6.1 Introduction and Overview of Expansion Methods
148(3)
6.2 High-Dimensional Model Representation (HDMR) and NNs
151(4)
6.3 Many-Body Expansions, Moiety Energy Approximations, and NNs
155(10)
7 Genetic Algorithm (GA) and Internal Energy Transfer Calculations Using Neural Network (NN) Methods
7.1 Genetic Algorithm (GA) Calculations Using NN Methods
165(16)
7.1.1 Introduction
165(1)
7.1.2 Brief Overview of GA
166(1)
7.1.3 Application of NNs for GA Acceleration
167(1)
7.1.4 Interatomic Potential Functions for Si
168(2)
7.1.5 GA-NN Approach
170(3)
7.1.6 Application to Fitting of PES for Si
173(8)
7.1.7 Summary
181(1)
7.2 Internal Energy Transfer Calculations Using NN Methods
181(9)
7.2.1 Introduction to Internal Energy Transfer Calculations
181(2)
7.2.2 Applications for Acceleration of IVR Calculations: H2O2 System
183(1)
7.2.2.1 NN for Conversion of Cartesian Velocities and Kinetic Mode Energies
183(7)
8 Empirical Potential-Energy Surfaces Fitting Using Feedforward Neural Networks
8.1 Fitting to Ab Initio Electronic Structure Data
190(9)
8.1.1 Introduction
190(1)
8.1.2 General Method
191(2)
8.1.3 Application to Fitting an Ab Initio Database for Si5 Clusters
193(6)
8.2 Fitting Emp irical Potentials to Vibrational Spectral Data
199(5)
8.2.1 Introduction
199(1)
8.2.2 Application to Macromolecules
200(4)
9 Neural Network Methods for Data Analysis and Statistical Error Reduction
9.1 Introduction
204(1)
9.2 Interaction of Carbon (C2) Dimer with Diamond---MD Simulations
205(1)
9.3 Statistical Data Analysis and Results
205(7)
9.4 Conclusions
212(3)
10 Other Applications of Neural Networks to Quantum Mechanical Problems
10.1 Solving the Molecular Vibrational Schrodinger Equation
215(8)
10.1.1 Introduction and General Theory
215(5)
10.1.2 Application to H2O
220(1)
10.1.3 Summary
221(2)
10.2 Prediction of High-Level Electronic Structure Energies from Hartree-Fock Energies
223(21)
10.2.1 Introduction
223(2)
10.2.2 Concepts and General Procedures
225(4)
10.2.3 Illustrative Application to Vinyl Bromide Database
229(4)
10.2.4 Application to Equilibrium Energies of Molecular Systems
233(4)
10.2.5 Discussion and Evaluation of the Method
237(5)
10.2.6 Summary
242(2)
11 Summary, Conclusions, and Future Trends
11.1 Introduction
244(3)
11.2 Other Methods for Obtaining PESs from Ab Initio Data
247(1)
11.3 Configuration-Space Sampling Methods
247(1)
11.4 Feedforward NN Fitting of Ab Initio PESs
248(1)
11.5 Expansion Methods and NNs
249(1)
11.6 Genetic Algorithm and IVR Calculations Using NN Methods
250(1)
11.7 NN Methods for Parameter Determination of Empirical PESs
251(1)
11.8 Combined Function Derivative Approximation (CFDA) NN Method
252(1)
11.9 NN Methods for Data Analysis and Statistical Error Reduction
253(1)
11.10 Other Applications of NNs to Quantum Mechanical Problems
254(1)
11.11 Future Trends
255(2)
References 257(18)
About the Authors 275(4)
Subject Index 279
Lionel Raff is Regents Professor in the Department of Chemistry at Oklahoma State University.

Ranga Komanduri is Professor & A. H. Nelson, Jr. Endowed Chair in Engineering in the School of Mechanical and Aerospace Engineering at Oklahoma State University. Martin Hagan is Professor in the School of Electrical and Computer Engineering, Oklahoma State University

Satish Bukkapatnam is Assistant Professor in the School of Industrial Engineering and Management at Oklahoma State University.
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