Molecular Modeling of Geochemical Reactions An Introduction

Molecular processes in nature affect human health, the availability of resources and the Earth’s climate. Molecular modelling is a powerful and versatile toolbox that complements experimental data and provides insights where direct observation is not currently possible.

Molecular Modeling of Geochemical Reactions: An Introduction applies computational chemistry to geochemical problems. Chapters focus on geochemical applications in aqueous, petroleum, organic, environmental, bio- and isotope geochemistry, covering the fundamental theory, practical guidance on applying techniques, and extensive literature reviews in numerous geochemical sub-disciplines.

Topics covered include:
• Theory and Methods of Computational Chemistry
• Force Field Application and Development
• Computational Spectroscopy
• Thermodynamics
• Structure Determination 
• Geochemical Kinetics

This book will be of interest to graduate students and researchers looking to understand geochemical processes on a molecular level. Novice practitioners of molecular modelling, experienced computational chemists, and experimentalists seeking to understand this field will all find information and knowledge of use in their research.

List of Contributors xi

Preface xiii

1 Introduction to the Theory and Methods of Computational Chemistry 1
David M. Sherman

1.1 Introduction 1

1.2 Essentials of Quantum Mechanics 2

1.2.1 The Schrödinger Equation 4

1.2.2 Fundamental Examples 4

1.3 Multielectronic Atoms 7

1.3.1 The Hartree and Hartree–Fock Approximations 7

1.3.2 Density Functional Theory 13

1.4 Bonding in Molecules and Solids 17

1.4.1 The Born–Oppenheimer Approximation 17

1.4.2 Basis Sets and the Linear Combination of Atomic Orbital Approximation 18

1.4.3 Periodic Boundary Conditions 20

1.4.4 Nuclear Motions and Vibrational Modes 21

1.5 From Quantum Chemistry to Thermodynamics 22

1.5.1 Molecular Dynamics 24

1.6 Available Quantum Chemistry Codes and Their Applications 27

References 28

2 Force Field Application and Development 33
Marco Molinari, Andrey V. Brukhno, Stephen C. Parker, and Dino Spagnoli

2.1 Introduction 33

2.2 Potential Forms 35

2.2.1 The Non-bonded Interactions 35

2.2.2 The Bonded Interactions 37

2.2.3 Polarisation Effects 37

2.2.4 Reactivity 39

2.2.5 Fundamentals of Coarse Graining 40

2.3 Fitting Procedure 42

2.3.1 Combining Rules Between Unlike Species 42

2.3.2 Optimisation Procedures for All-Atom Force Fields 43

2.3.3 Deriving CG Force Fields 45

2.3.4 Accuracy and Limitations of the Fitting 47

2.3.5 Transferability 48

2.4 Force Field Libraries 48

2.4.1 General Force Fields 48

2.4.2 Force Field Libraries for Organics: Biomolecules with Minerals 49

2.4.3 Potentials for the Aqueous Environment 50

2.4.4 Current CGFF Potentials 51

2.4.5 Multi-scale Methodologies 53

2.5 Evolution of Force Fields for Selected Classes of Minerals 54

2.5.1 Calcium Carbonate 54

2.5.2 Clay Minerals 56

2.5.3 Hydroxides and Hydrates 60

2.5.4 Silica and Silicates 60

2.5.5 Iron-Based Minerals 61

2.6 Concluding Remarks 63

References 64

3 Quantum-Mechanical Modeling of Minerals 77
Alessandro Erba and Roberto Dovesi

3.1 Introduction 77

3.2 Theoretical Framework 79

3.2.1 Translation Invariance and Periodic Boundary Conditions 79

3.2.2 HF and KS Methods 80

3.2.3 Bloch Functions and Local BS 81

3.3 Structural Properties 82

3.3.1 P–V Relation Through Analytical Stress Tensor 83

3.3.2 P–V Relation Through Equation of State 85

3.4 Elastic Properties 86

3.4.1 Evaluation of the Elastic Tensor 86

3.4.2 Elastic Tensor-Related Properties 89

3.4.3 Directional Seismic Wave Velocities and Elastic Anisotropy 89

3.5 Vibrational and Thermodynamic Properties 91

3.5.1 Solid-State Thermodynamics 93

3.6 Modeling Solid Solutions 95

3.7 Future Challenges 98

References 99

4 First Principles Estimation of Geochemically Important Transition Metal Oxide Properties: Structure and Dynamics of the Bulk, Surface, and Mineral/Aqueous Fluid Interface 107
Ying Chen, Eric Bylaska, and John Weare

4.1 Introduction 107

4.2 Overview of the Theoretical Methods and Approximations Needed to Perform AIMD Calculations 109

4.3 Accuracy of Calculations for Observable Bulk Properties 113

4.3.1 Bulk Structural Properties 113

4.3.2 Bulk Electronic Structure Properties 118

4.4 Calculation of Surface Properties 123

4.4.1 Surface Structural Properties 123

4.4.2 Electronic Structure in the Surface Region 127

4.4.3 Water Adsorption on Surface 129

4.5 Simulations of the Mineral–Water Interface 130

4.5.1 CPMD Simulations of the Vibrational Structure of the Hematite (012)–Water Interface 130

4.5.2 CPMD Simulations of Fe2+ Species at the Mineral–Water Interface 132

4.6 Future Perspectives 134

Acknowledgments 134

Appendix 134

A.1 Short Introduction to Pseudopotentials 135

A.1.1 The Spin Penalty Pseudopotential 137

A.1.2 Projected Density of States from Pseudo-Atomic Orbitals 138

A.2 Hubbard-Like Coulomb and Exchange (DFT+U) 138

A.3 Overview of the PAW Method 139

References 143

5 Computational Isotope Geochemistry 151
James R. Rustad

5.1 A Brief Statement of Electronic Structure Theory and the Electronic Problem 152

5.2 The Vibrational Eigenvalue Problem 154

5.3 Isotope Exchange Equilibria 156

5.4 Qualitative Insights 159

5.5 Quantitative Estimates 160

5.6 Relationship to Empirical Estimates 169

5.7 Beyond the Harmonic Approximation 171

5.8 Kinetic Isotope Effects 172

5.9 Summary and Prognosis 172

Acknowledgments 173

References 173

6 Organic and Contaminant Geochemistry 177
Daniel Tunega, Martin H. Gerzabek, Georg Haberhauer, Hans Lischka, and Adelia J. A. Aquino

6.1 Introduction 177

6.1.1 Review Examples of Molecular Modeling Applications in Organic and Contaminant Geochemistry 179

6.2 Molecular Modeling Methods 184

6.2.1 Molecular Mechanics: Brief Summary 184

6.2.2 Quantum Mechanics: Overview 187

6.2.3 Molecular Modeling Techniques: Summary 192

6.2.4 Models: Clusters, Periodic Systems, and Environmental Effects 195

6.3 Applications 196

6.3.1 Modeling of Surface Complexes of Polar Phenoxyacetic Acid-Based Herbicides with Iron Oxyhydroxides and Clay Minerals 197

6.3.2 Modeling of Adsorption Processes of Polycyclic Aromatic Hydrocarbons on Iron Oxyhydroxides 217

6.3.3 Modeling of Interactions of Polar and Nonpolar Contaminants in Organic Geochemical Environment 220

6.4 Perspectives and Future Challenges 227

Glossary 229

References 231

7 Petroleum Geochemistry 245
Qisheng Ma and Yongchun Tang

7.1 Introduction: Petroleum Geochemistry and Basin Modeling 245

7.2 Technology Development of the Petroleum Geochemistry 246

7.2.1 Thermal Maturity and Vitrinite Reflectance 246

7.2.2 Rock-Eval Pyrolysis 247

7.2.3 Kerogen Pyrolysis and Gas Chromatography Analysis 248

7.2.4 Kinetic Modeling of Kerogen Pyrolysis 249

7.2.5 Natural Gases and C/H Isotopes 253

7.3 Computational Simulations in Petroleum Geochemistry 253

7.3.1 Ab Initio Calculations of the Unimolecular C–C Bond Rapture 253

7.3.2 Quantum Mechanical Calculations on Natural Gas 13C Isotopic Fractionation 256

7.3.3 Deuterium Isotope Fractionations of Natural Gas 258

7.3.4 Molecular Modeling of the 13C and D Doubly Substituted Methane Isotope 260

7.4 Summary 262

References 262

8 Mineral–Water Interaction 271
Marie-Pierre Gaigeot and Marialore Sulpizi

8.1 Introduction 271

8.2 Brief Review of AIMD Simulation Method 275

8.2.1 Ab Initio Molecular Dynamics and Density Functional Theory 275

8.3 Calculation of the Surface Acidity from Reversible Proton Insertion/Deletion 280

8.4 Theoretical Methodology for Vibrational Spectroscopy and Mode Assignments 282

8.5 Property Calculations from AIMD: Dipoles and Polarisabilities 284

8.6 Illustrations from Our Recent Works 286

8.6.1 Organisation of Water at Silica–Water Interfaces: (0001) α-Quartz Versus Amorphous Silica 286

8.6.2 Organisation of Water at Alumina–Water Interface: (0001) α-Alumina Versus (101) Boehmite 291

8.6.3 How Surface Acidities Dictate the Interfacial Water Structural Arrangement 293

8.6.4 Vibrational Spectroscopy at Oxide–Liquid Water Interfaces 295

8.6.5 Clay–Water Interface: Pyrophyllite and Calcium Silicate 299

8.7 Some Perspectives for Future Works 302

References 304

9 Biogeochemistry 311
Weilong Zhao, Zhijun Xu, and Nita Sahai

9.1 Introduction 311

9.1.1 Mineral–Water Interactions 313

9.1.2 Mineral–Organic Interactions 313

9.2 Challenges and Approaches to Computational Modeling of Biomineralization 314

9.2.1 Biominerals: Structure, Nucleation, and Growth 314

9.2.2 Conformational Sampling in Modeling Biomineralization 317

9.2.3 Force Field Benchmarking 324

9.2.4 Ab Initio MD and Hybrid QM/MM Approaches 325

9.3 Case Studies 326

9.3.1 Apatite 327

9.3.2 Calcite 331

9.4 Concluding Remarks and Future Perspectives 334

Acknowledgments 335

References 335

10 Vibrational Spectroscopy of Minerals Through Ab Initio Methods 341
Marco De La Pierre, Raffaella Demichelis, and Roberto Dovesi

10.1 Introduction 341

10.2 Theoretical Background and Methods 342

10.2.1 Calculation of Vibrational Frequencies 344

10.2.2 Splitting of the Longitudinal Optical (LO) and Transverse Optical (TO) Modes 346

10.2.3 Calculation of Infrared (IR) and Raman Peak Intensities and of the IR Dielectric Function 347

10.2.4 Estimation of the Anharmonic Constant for X–H Stretching Modes 349

10.2.5 Accuracy of Basis Set and Hamiltonian 350

10.3 Examples and Applications 352

10.3.1 Vibrational Properties of Calcium and Magnesium Carbonates 353

10.3.2 A Complex Mineral: The IR Spectra of Ortho-enstatite 359

10.3.3 Treatment of the O─H Stretching Modes: The Vibrational Spectra of Brucite and Diaspore 360

10.4 Simulation of Vibrational Properties for Crystal Structure Determination 363

10.4.1 Proton Disorder in γ-AlOOH Boehmite 364

10.5 Future Challenges 368

Acknowledgements 368

References 368

11 Geochemical Kinetics via Computational Chemistry 375
James D. Kubicki and Kevin M. Rosso

11.1 Introduction 375

11.2 Methods 379

11.2.1 Potential Energy Surfaces 379

11.2.2 Choice of Solvation Methods 384

11.2.3 Activation Energies and Volumes 386

11.2.4 Transition States and Imaginary Frequencies 390

11.2.5 Rate Constants 391

11.2.6 Types of Reaction Mechanisms 393

11.3 Applications 394

11.3.1 Diffusion 394

11.3.2 Ligand Exchange Aqueous Complexes 395

11.3.3 Adsorption 396

11.3.4 Dissolution 396

11.3.5 Nucleation 398

11.4 Future Challenges 399

11.4.1 Femtosecond Spectroscopy 399

11.4.2 H-Bonding 400

11.4.3 Roaming 400

11.4.4 Large-Scale Quantum Molecular Dynamics 401

11.4.5 Reactive Force Fields 401

References 403

Index 415

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