Ab initio Molecular Potential Energy Surface Constructionand Molecular Dynamics Simulation for Small Molecules Open Access

Abstract

For the theoretical study of the chemical reactions, potential energy surface (PES) plays a crucial role. High quality PESs are always desired; however, there are many challenges in constructing these surfaces, and one of them is caused by the molec- ular permutation symmetry. In this dissertation, several methods targeting at the invariant property of the PES are addressed, especially the most advanced approach using the invariant polynomials. Based on the high quality PESs constructed with intrinsic permutation symmetry, extensive quasiclassical trajectory simulations of the small molecule reactions H + 2 + H3 , H + CH4, CH+ 5 /CH5 and H3O+/H3O including their isotopomers are performed to understand the underlying microscopic reaction mechanism. In addition to the study of the dynamics of chemical reactions, some static properties of H+ 5 and CH+ 5 are also investigated based upon diffusion Monte Carlo methods. By the good agreement between the theoretical simulation results and the available experimental data, it indicates that quasiclassical trajectory simu- lation based on accurate potential energy surface is a powerful method to investigate and further understand the microscopic chemical reaction mechanism.

Table of Contents

1 Introduction 1

1.1 Chemical Reactions, Quasiclassical Trajectory Simulation and Potential Energy Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

I Theory and Methods 3

2 Ab initio Molecular Potential Energy Construction 4

2.1 Molecule Symmetry and Representation . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 Molecular PES Least Squares Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Invariant Fitting Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3.1 Straightforward Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.2 Restricted Coefficients Approach . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.4 Invariant Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.5 Normal Mode Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32

2.6 Molecular Geometry Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3 Molecular Dynamics Simulation 48

3.1 Initial Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48

3.1.1 Normal Mode Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.1.2 Rotational Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49

3.1.3 Relative Position and Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.2 Zero Point Energy Constraint in Quasiclassical Trajectory . . . . . . . . . . . 56

3.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.2.2 Method and Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.2.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.3 Final Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.3.1 Relative Velocity and Translation Energy . . . . . . . . . . . . . . . . . . . . . 65

3.3.2 Velocity Scattering Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.3.3 Internal Vibrational Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.3.4 Rotational Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.4 Propagation Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.4.1 Verlet Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

II Applications 70

4 Ab initio Global Potential Energy Surface for H5 ⁺ ⟶ CH3 ⁺ + H2 71

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.2 Fitting Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.2.1 Sampling Strategy and ab initio Calculation . . . . . . . . . . 73

4.2.2 Fitting ab initio Data . . . . . . . . . . . . . . . . . . . . . . 74

4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.3.1 Properties of Stationary Points on the PES . . . . . . . . . . . 76

4.3.2 Dissociation Properties . . . . . . . . . . . . . . . . . . . . . . 85

4.4 Long Range Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . 94

4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

5 Theoretical Study of the Formation and Destruction of H2D⁺ via Reactions HD + H3 ⁺ ⟷ H2 + H2D⁺ 98

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5.2 Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.2.1 Reaction Channels . . . . . . . . . . . . . . . . . . . . . . . . 102

5.2.2 Potential Energy Surface with Long Range Interaction . . . . 104

5.2.3 Initial Conditions for Quasiclassical Trajectory . . . . . . . . 107

5.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.3.1 Forward Reaction: Forming of H2D⁺ . . . . . . . . . . . . . . 109

5.3.2 Reverse Reaction: Destructing of H2D⁺ . . . . . . . . . . . . . 116

5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

6 Vibrational Ground State Properties of H5 ⁺ and its Isotopomers from Diffusion Monte Carlo Calculations 127

6.1 DMC Study of the Ground State Structure of H5 ⁺ and its Isotopomers 128

6.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

6.1.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

6.1.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 131

6.1.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . 144

6.2 Additional Information . . . . . . . . . . . . . . . . . . . . . . . . . . 145

7 Quasiclassical Trajectory Study of the Reaction H + CH4(ν 3 = 0, 1) ⟶ CH3 + H2 Using a New ab initio Potential Energy Surface 155

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

7.2 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

7.2.1 Potential Energy Surface . . . . . . . . . . . . . . . . . . . . . 158

7.2.2 Trajectory Calculations . . . . . . . . . . . . . . . . . . . . . . 164

7.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 167

7.3.1 CH3 Angular Distribution . . . . . . . . . . . . . . . . . . . . 167

7.3.2 H2 and CH3 Rotational Distributions . . . . . . . . . . . . . . 171

7.3.3 Cross Section Enhancement Ratio . . . . . . . . . . . . . . . . 171

7.3.4 CH3 Vibrational Energy Distribution . . . . . . . . . . . . . . 175

7.3.5 Lab Speed Distribution . . . . . . . . . . . . . . . . . . . . . . 177

7.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 180

8 Quasiclassical Trajectory Study of the Reaction of Fast H Atoms with C-H Stretch Excited CHD3 181

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

8.2 Potential Energy Surface and Calculation Details . . . . . . . . . . . 183

8.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 185

8.3.1 Reaction Probabilities and Cross Sections . . . . . . . . . . . 186

8.3.2 CD3 and CHD2 Angular Distributions . . . . . . . . . . . . . 189

8.3.3 H2 and HD Rotational Distributions . . . . . . . . . . . . . . 189

8.3.4 CD3 and CHD2 Vibrational Energy Distributions . . . . . . . 191

8.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 192

9 CH5 ⁺/CH5 195

9.1 Probing the Structure of CH5 ⁺ by Dissociative Charge Exchange . . . 196

9.2 Supporting Information . . . . . . . . . . . . . . . . . . . . . . . . . . 203

9.2.1 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

9.2.2 Theoretical . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

9.3 Additional Information . . . . . . . . . . . . . . . . . . . . . . . . . . 212

9.3.1 Semi-Rigid Sampling . . . . . . . . . . . . . . . . . . . . . . . 213

9.3.2 Direct Jumping . . . . . . . . . . . . . . . . . . . . . . . . . . 214

9.3.3 Resonant Case . . . . . . . . . . . . . . . . . . . . . . . . . . 219

9.3.4 Non-Resonant Case . . . . . . . . . . . . . . . . . . . . . . . . 220

9.4 DMC Calculation on CH5 ⁺ and its Isotopomers . . . . . . . . . . . . 227

9.5 PIMC Study of the Geometry of CD3H2 ⁺ . . . . . . . . . . . . . . . . 232

10 H3O⁺/H3O 237

10.1 Experimental Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

10.2 H3O⁺ Potential Energy Surface . . . . . . . . . . . . . . . . . . . . . 240

10.3 H3O Potential Energy Surface . . . . . . . . . . . . . . . . . . . . . . 243

10.4 Direct Dynamics Simulation . . . . . . . . . . . . . . . . . . . . . . . 244

11 Summary 259

References 260

About this Dissertation

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School	Laney Graduate School
Department	Chemistry
Degree	PhD
Submission	Dissertation
Language	English
Research Field	Chemistry, Physical
Keyword	potential energy surface quasiclassical trajectory molecular dynamics
Committee Chair / Thesis Advisor	Bowman, Joel M, Emory University
Committee Members	Heaven, Michael, Emory University Kindt, James, Emory University

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