Potential Energy Surfaces and the Applications to Reaction Dynamics and Molecular Vibrations Open Access

Abstract

The importance of potential energy surface cannot be overemphasized due to the role it plays in theoretical chemistry. With the potential, the kinetics and dynamics of chemical reactions can be modeled, and molecular eigenenergies and eigenstates can be calculated, which could be used to explain molecular spectroscopy.

In this work, the analytical representations of potential energy surfaces for molecules and clusters such as H7⁺ , CH3OH, and formic acid dimer were constructed by fitting to tens of thousands of scattered ab initio energies. These potential energy surfaces were employed in subsequent studies of dynamics or spectroscopy. The potential energy surfaces for hydrogen and methane clathrate hydrates were obtained by many-body expansion strategy, and the binding energies of (H2)n(H2O)20 and (H2)n(H2O)24 and barrier height of H2 diffusion in clathrates has been investigated using the many-body potential. The invariance of potential when permuting the like atoms is incorporated in the analytical expressions, following the method developed by Braams, Bowman, and co-workers.

Molecular vibrational properties of H7⁺ , formic acid dimer and CH4 confined in clathrate cages have been investigated. Diffusion Monte Carlo calculations were applied to characterize the vibrational ground state properties, while the vibrational eigenenergies and eigenstates were calculated using the vibrational self-consistent and virtual-state configuration interaction method. The treatment of the large amplitude motion and the reduction of dimensionality are highlighted in these calculations.

The analytical potential energies were also used in studies of the dynamics of chemical reactions. Molecular dynamics calculations was performed to simulate the unimolecular decomposition of methanol to estimate the branching ratio of different product channels. Similar simulations have been carried out to model the dissociation of vinyl chloride that produces cold vinylidene, however, using direct "on-the-fly" potential. In addition to these applications, the use of adiabatic switching method to prepare initial condition in quasi-classical trajectories has been investigated.

Table of Contents

Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

I Theories and Methods 4

Chapter 2 Potential Energy Surface . . . . . . . . . . . . . . . . . . . 5

2.1 Born-Oppenheimer Approximation . . . . . . . . . . . . . . . 5

2.2 Permutationally Invariant Potential Energy Surface . . 7

2.2.1 Monomial symmetrization . . . . . . . . . . . . . . . . . . . 9

2.2.2 Invariant polynomials . . . . . . . . . . . . . . . . . . . . . .10

2.2.3 Purified fitting basis . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Many-body Expansion . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4 Dipole Moment Surface . . . . . . . . . . . . . . . . . . . . . . . 14

2.5 Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Chapter 3 Molecular Vibrations . . . . . . . . . . . . . . . . . . . . . . 17

3.1 Normal Mode Analysis . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2 Vibrational Self-Consistent Field and

Configuration Interaction . . . . . . . . . . . . . . . . . . . . . . 21

3.3 The Code "Multimode" . . . . . . . . . . . . . . . . . . . . . . . . 23

3.3.1 Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.3.2 Potential representation . . . . . . . . . . . . . . . . . . . 24

3.3.3 VCI excitation space and matrix pruning . . . . . . . 25

3.3.4 Infrared intensity . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.4 Local Monomer Model . . . . . . . . . . . . . . . . . . . . . . . . 26

3.5 Diffusion Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.5.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.5.2 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Chapter 4 Dynamics Simulations . . . . . . . . . . . . . . . . . . . . . 31

4.1 Initial Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.2 Final Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.2.1 Translations and Rotations . . . . . . . . . . . . . . . . . 34

4.2.2 Vibration and Zero-point Energy Constraint . . . . .35

II Many-body Potentials for Clathrate Hydrates 37

Chapter 5 Many-body Potentials for Clathrate Hydrates . . . 38

5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.2 Fitting of Non-covalent Interactions . . . . . . . . . . . . . . 40

5.3 CH4−H2O Potential . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.3.1 Ab initio calculation and potential fitting . . . . . . . 43

5.3.2 Test of the potential . . . . . . . . . . . . . . . . . . . . . . . 45

5.3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.4 CH4(H2O)2 Potential . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.4.1 Ab initio calculation and fitting . . . . . . . . . . . . . . . 57

5.4.2 Test of the potential . . . . . . . . . . . . . . . . . . . . . . . 60

5.4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.5 H2−H2O Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.5.1 Ab initio calculation and potential fitting . . . . . . . 64

5.5.2 Test of the potential . . . . . . . . . . . . . . . . . . . . . . . 67

5.5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.6 H2−H2O−H2O Potential . . . . . . . . . . . . . . . . . . . . . . . 74

5.6.1 Ab initio calculation and PES fitting . . . . . . . . . . 74

5.6.2 Test of the potential . . . . . . . . . . . . . . . . . . . . . . . 76

5.6.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

5.7 Many-body "Plug and Play" Potential for Clathrate

Hydrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

5.8 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . 83

Chapter 6 Storage Capacity and H2 Diffusion in Clathrate

Hydrates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

6.2 Potential Energy Surface . . . . . . . . . . . . . . . . . . . . . . 88

6.3 Storage Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

6.4 H2 Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

6.5 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . 97

III Molecular Vibrations 98

Chapter 7 Ground State Properties and Vibrational

Spectra of H7⁺ . . . . . . . . . . . . . . . . . . . . . . . . . . 99

7.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

7.2 Potential Energy and Dipole Moment Surface . . . . . 101

7.2.1 Ab initio calculations for PES II . . . . . . . . . . . . . 102

7.2.2 Potential energy and dipole moment surfaces

fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

7.2.3 Properties of the potential energy and dipole

moment surfaces . . . . . . . . . . . . . . . . . . . . . . . 103

7.3 Diffusion Monte Carlo Calculations . . . . . . . . . . . . . 107

7.3.1 Computational details . . . . . . . . . . . . . . . . . . . . 107

7.3.2 Results and discussions . . . . . . . . . . . . . . . . . . 108

7.4 IR Spectrum of H7+ . . . . . . . . . . . . . . . . . . . . . . . . . 117

7.4.1 Computational detail . . . . . . . . . . . . . . . . . . . . . 117

7.4.2 Results and discussions . . . . . . . . . . . . . . . . . . 118 7.5 Conclusions and Remarks . . . . . . . . . . . . . . . . . . . . 121 Chapter 8 Tunneling Splitting and Fundamentals of Formic Acid Dimer . . . . . . . . . . . . . . . . . . . . . . 123 8.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 8.2 Potential Energy Surface . . . . . . . . . . . . . . . . . . . . . 126 8.3 Computational Details and Results . . . . . . . . . . . . . 133 8.3.1 Tunneling splittings . . . . . . . . . . . . . . . . . . . . . . 133 8.3.2 Anharmonic frequencies . . . . . . . . . . . . . . . . . . 136 8.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . 140 Chapter 9 Vibrations of Methane Confined in Clathrate Cages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 9.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .141 9.2 Potential energy surface . . . . . . . . . . . . . . . . . . . . . 144 9.3 Local monomer model . . . . . . . . . . . . . . . . . . . . . . . 146 9.4 VSCF+VCI calculations . . . . . . . . . . . . . . . . . . . . . . 148 9.4.1 Fundamental frequencies . . . . . . . . . . . . . . . . . 149 9.4.2 Overtones and combination bands . . . . . . . . . . 153 9.5 Diffusion Monte Carlo calculations . . . . . . . . . . . . . 155 9.6 Summary and conclusions . . . . . . . . . . . . . . . . . . . . 159 IV Dynamics in Gas-phase Molecules 161 Chapter 10 Thermal Decomposition of Methanol . . . . . . . 162 10.1 Overview . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 162 10.2 Potential Energy Surface . . . . . . . . . . . . . . . . . . . . 164 10.2.1 Sampling of configuration space . . . . . . . . . . . 164 10.2.2 Ab initio calculations and potential fitting . . . . 166 10.2.3 Properties of the potential energy surface . . . 168 10.3 Molecular Dynamics Simulations . . . . . . . . . . . . . . 175 10.3.1 Computational details . . . . . . . . . . . . . . . . . . . 175 10.3.2 Results and discussions . . . . . . . . . . . . . . . . . 176 10.4 Summary, Conclusions, and Remarks . . . . . . . . . . 178 Chapter 11 Dissociation of Vinyl Chloride . . . . . . . . . . . . . 179 11.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 11.2 Computational Details . . . . . . . . . . . . . . . . . . . . . . 182 11.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . 182 11.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . 187 Chapter 12 Adiabatic Switching Method for Initial Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 12.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 12.2 Theory and Computational Details . . . . . . . . . . . . 193 12.2.1 Adiabatic switching . . . . . . . . . . . . . . . . . . . . . 193 12.2.2 Quantization of H0 . . . . . . . . . . . . . . . . . . . . . .195 12.2.3 Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . 196 12.2.4 Computational details . . . . . . . . . . . . . . . . . . . 197 12.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . 197 12.3.1 CH4 zero-point energy . . . . . . . . . . . . . . . . . . 197 12.3.2 Excited states . . . . . . . . . . . . . . . . . . . . . . . . . 200 12.3.3 Implementation in quasiclassical trajectory calculations . . . . . . . . . . . . . . . . . . . 201 12.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . 203

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

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