1 Molecular Modeling in Mineralogy and Geochemistry
Randall T. Cygan
INTRODUCTION .................................................... 1
Historical perspective ....................................... 2
Molecular modeling tools ..................................... 3
POTENTIAL ENERGY ................................................ 6
Energy terms ................................................. 7
Atomic charges .............................................. 10
Practical concerns .......................................... 11
MOLECULAR MODELING TECHNIQUES .................................. 11
Conformational analysis ..................................... 11
Energy minimization ......................................... 13
Energy minimization and classical-based equilibrium
structures .................................................. 14
Quantum chemistry methods ................................... 15
Energy minimization and quantum-based equilibrium
structures .................................................. 18
Monte Carlo methods ......................................... 20
Molecular dynamics methods .................................. 23
Quantum dynamics ............................................ 25
FORSTERITE: THE VERY MODEL OF A MODERN MAJOR MINERAL ........... 26
Static calculations and energy minimization studies ......... 27
Lattice dynamics studies .................................... 27
Quantum studies ............................................. 27
THE FUTURE ..................................................... 28
ACKNOWLEDGMENTS ................................................ 28
GLOSSARY OF TERMS .............................................. 29
REFERENCES ..................................................... 30
2 Simulating the Crystal Structures and Properties of
Ionic Materials From Interatomic Potentials
Julian D. Gale
INTRODUCTION ................................................... 37
INTERATOMIC POTENTIAL MODELS FOR IONIC MATERIALS ............... 37
Long-range interactions ..................................... 39
Short-range interactions .................................... 40
Energy minimization ......................................... 41
CRYSTAL PROPERTIES FROM STATIC CALCULATION ..................... 44
Elastic constants ........................................... 44
Dielectric constants ........................................ 44
Piezoelectric constants ..................................... 45
Phonons ..................................................... 45
DERIVATION OF POTENTIAL PARAMETERS ............................. 47
Simultaneous fitting ........................................ 47
Relaxed fitting ............................................. 49
SIMULATING THE EFFECT OF TEMPERATURE AND PRESSURE ON CRYSTAL
STRUCTURES ..................................................... 50
FUTURE DIRECTIONS IN INTERATOMIC POTENTIAL MODELLING OF IONIC
MATERIALS ...................................................... 56
Structure solution and prediction ........................... 58
ACKNOWLEDGMENTS ................................................ 59
REFERENCES ..................................................... 59
3 Application of Lattice Dynamics and Molecular Dynamics
Techniques to Minerals and Their Surfaces
Steve C. Parker, Nora H. de Leeuw, Ekatarina Bourova,
David J. Cooke
INTRODUCTION ................................................... 63
METHODOLOGY .................................................... 63
LATTICE DYNAMICS ............................................... 64
MOLECULAR DYNAMICS ............................................. 67
SIMULATION OF MINERAL-WATER INTERFACES ......................... 74
CONCLUSIONS .................................................... 80
REFERENCES ..................................................... 81
4 Molecular Simulations of Liquid and Supercritical Water:
Thermodynamics, Structure, and Hydrogen Bonding
Audrey G. Kalinichev
INTRODUCTION ................................................... 83
CLASSICAL METHODS OF MOLECULAR SIMULATIONS ..................... 86
Molecular dynamics .......................................... 86
Monte Carlo methods ......................................... 87
Boundary conditions, long-range corrections, and
statistical errors .......................................... 89
Interaction potentials for aqueous simulations .............. 90
THERMODYNAMICS OF SUPERCRITICAL AQUEOUS SYSTEMS ................ 95
Macroscopic thermodynamic properties of simulated
supercritical water ......................................... 96
Micro-thermodynamic properties .............................. 97
STRUCTURE OF SUPERCRITICAL WATER .............................. 101
HYDROGEN BONDING IN LIQUID AND SUPERCRITICAL WATER ............ 104
MOLECULAR CLUSTERIZATION IN SUPERCRITICAL WATER ............... 109
DYNAMICS OF MOLECULAR TRANSLATIONS, LIBRATIONS, AND
VIBRATIONS IN SUPERCRITICAL WATER ............................. 113
CONCLUSIONS AND OUTLOOK ....................................... 120
ACKNOWLEDGMENTS ............................................... 121
REFERENCES .................................................... 121
5 Molecular Dynamics Simulations of Silicate Glasses and Glass
Surfaces
Stephen H. Garofalini
INTRODUCTION .................................................. 131
MOLECULAR DYNAMICS COMPUTER SIMULATION TECHNIQUE .............. 131
Interatomic potentials ..................................... 135
Periodic boundary conditions ............................... 137
MD SIMULATIONS OF OXIDE GLASSES ............................... 140
Bulk glasses ............................................... 140
Bulk SiO2 .................................................. 141
Multicomponent silicate glasses ............................ 145
MD SIMULATIONS OF OXIDE GLASS SURFACES ........................ 147
SiO2 ....................................................... 147
Multicomponent silicate surfaces ........................... 162
SUMMARY ....................................................... 162
ACKNOWLEDGMENTS ............................................... 164
REFERENCES .................................................... 164
6 Molecular Models of Surface Relaxation, Hydroxylation,
and Surface Charging at Oxide-Water Interfaces
James R. Rustad
INTRODUCTION .................................................. 169
SCOPE ......................................................... 170
THE STILLINGER-DAV1D WATER MODEL .............................. 172
IRON-WATER AND SILICON-WATER POTENTIALS AND THE BEHAVIOR
OF FE3+ AND SI4+ IN THE GAS PHASE AND IN AQUEOUS SOLUTION ..... 174
CRYSTAL STRUCTURES ............................................ 177
VACUUM-TERMINATED SURFACES .................................... 179
HYDRATED AND HYDROXYLATED SURFACES ............................ 183
Neutral surfaces ........................................... 183
Surface charging ........................................... 188
SOLVATED INTERFACES ........................................... 191
REMARKS ....................................................... 193
ACKNOWLEDGMENTS ............................................... 193
REFERENCES .................................................... 194
7 Structure and Reactivity of Semiconducting Mineral
Surfaces: Convergence of Molecular Modeling and
Experiment
Kevin M. Rosso
INTRODUCTION .................................................. 199
BACKGROUND CONCEPTS ........................................... 200
Experimental approaches .................................... 200
Semiconductors and their surfaces .......................... 201
THEORETICAL METHODS ........................................... 212
Theory-Hartree-Fock versus density functional theory ....... 213
Basis sets-Gaussian orbital versus plane waves ............. 216
Surface model-Cluster versus periodic ...................... 221
Codes-Crystal vs. CASTEP ................................... 223
APPLICATIONS .................................................. 226
Sulfides ................................................... 226
Oxides ..................................................... 248
CONCLUDING REMARKS AND OUTLOOK ................................ 260
ACKNOWLEDGMENTS ............................................... 262
REFERENCES .................................................... 262
8 Quantum Chemistry and Classical Simulations of Metal
Complexes in Aqueous Solutions
David M. Sherman
INTRODUCTION .................................................. 273
Experimental methods ....................................... 273
Continuum models ........................................... 274
Atomistic computational methods ............................ 274
QUANTUM CHEMISTRY OF METAL COMPLEXES: THEORETICAL BACKGROUND
AND METHODOLOGY ............................................... 275
Quantum mechanics of many-electron systems ................. 275
Bonding in molecules and complexes ......................... 280
Calculating thermodynamic quantities from first
principles ................................................. 283
Simulations of solvent effects ............................. 284
APPLICATIONS OF QUANTUM CHEMISTRY TO METAL COMPLEXES IN
AQUEOUS SOLUTIONS ............................................. 285
Group IIB cations Zn, Cd and Hg ............................ 285
Group IB cations Cu, Ag, and Au ............................ 292
Iron and manganese ......................................... 296
Alkali earth and alkali metal cations ...................... 299
Post-transition metals ..................................... 299
CLASSICAL ATOMISTIC SIMULATIONS OF METAL COMPLEXES IN
AQUEOUS SOLUTIONS ............................................. 301
Background ................................................. 301
Interatomic potentials ..................................... 302
Molecular dynamics ......................................... 304
Metropolis Monte Carlo simulations ......................... 305
Applications ............................................... 305
THE NEXT ERA: AB INITIO MOLECULAR DYNAMICS .................... 310
Application to copper(I) chloride solutions ................ 311
SUMMARY AND FUTURE DIRECTIONS ................................. 311
ACKNOWLEDGMENTS ............................................... 312
REFERENCES .................................................... 312
9 First Principles Theory of Mantle and Core Phases
Lars Stixrude
INTRODUCTION .................................................. 319
THEORY ........................................................ 321
Overview ................................................... 321
Total energy, forces, and stresses ......................... 324
Statistical mechanics ...................................... 326
SELECTED APPLICATIONS ......................................... 332
Overview ................................................... 332
Phase transformations in silicates ......................... 332
High temperature properties of transition metals ........... 336
CONCLUSIONS AND OUTLOOK ....................................... 339
Scale ...................................................... 339
Duration ................................................... 339
Materials .................................................. 340
ACKNOWLEDGMENTS ............................................... 340
REFERENCES .................................................... 340
10 A Computational Quantum Chemical Study of the Bonded
Interactions in Earth Materials and Structurally and
Chemically Related Molecules
G.V. Gibbs, Monte B. Boisen, Jr., Lesa L. Beverly,
Kevin M. Rosso
INTRODUCTION .................................................. 345
BOND LENGTH AND BOND STRENGTH CONNECTIONS FOR OXIDE,
FLUORIDE, NITRIDE, AND SULFIDE MOLECULAR AND CRYSTALLINE
MATERIALS ..................................................... 345
Bond lengths and crystal radii ............................. 345
Bonded interactions ........................................ 346
Pauling bond strength and bond length variations ........... 347
Brown and Shannon bond strength and bond length
variations ................................................. 348
Bond strength p and bond length variations ................. 348
Bond number and bond length variations ..................... 350
Nitride, fluoride and sulfide bond strength and bond
length variations .......................................... 351
Bond strength and crystal radii ............................ 352
FORCE CONSTANTS, COMPRESSIBILITIES OF COORDINATED POLYHEDRA,
AND POTENTIAL ENERGY MODELS ................................... 353
Force constants and bond length variations ................. 353
Force constants and polyhedral compressibilities ........... 354
Force fields and bond length and angle variations .......... 355
Generation of new and viable structure types for silica .... 357
CALCULATED ELECTRON DENSITY DISTRIBUTIONS FOR EARTH
MATERIALS AND RELATED MOLECULES ............................... 358
Bond critical point properties and electron density
distributions .............................................. 358
Bond critical point properties calculated for molecules .... 359
Bond critical point properties calculated for earth
materials .................................................. 361
Variable radius of the oxide anion ......................... 362
BOND STRENGTH, ELECTRON DENSITY, AND BOND TYPE CONNECTIONS .... 365
SITES OF POTENTIAL ELECTROPHILIC ATTACK IN EARTH MATERIALS .... 367
Bonded and nonbonded electron pairs ........................ 367
Bonded and nonbonded electron lone pairs for a silicate
molecule ................................................... 369
Localization of the electron density for the silica
polymorphs ................................................. 370
Nonbonded lone pair electrons for low albite ............... 372
CONCLUDING REMARKS ............................................ 373
ACKNOWLEDGMENTS ............................................... 375
REFERENCES .................................................... 376
11 Modeling the Kinetics and Mechanisms of Petroleum
and Natural Gas Generation: A First Principles Approach
Yitian Xiao
INTRODUCTION .................................................. 383
AB INITIO METHOD .............................................. 385
KEROGEN DECOMPOSITION AND OIL AND GAS GENERATION .............. 390
Introduction ............................................... 390
The kinetics and mechanisms of hydrocarbon thermal
cracking ................................................... 394
Computational methods ...................................... 396
Initiation reaction (homolytic scission) ................... 397
Hydrogen transfer reaction ................................. 400
Radical decomposition (P scission) ......................... 403
Elementary reactions versus overall hydrocarbon cracking ... 406
Summary .................................................... 407
ISOTOPIC FRACTIONATION AND NATURAL GAS GENERATION ............. 408
Introduction ............................................... 408
Transition state theory and gas isotopic fractionation ..... 409
Natural gas plot ........................................... 410
Carbon kinetic isotope effect: homolytic scission verses
β scission ................................................. 411
Biogenic gas versus thermogenic gas ........................ 415
Summary .................................................... 416
POSSIBLES ROLES OF MINERALS AND TRANSITION METALS IN OIL AND
GAS GENERATION ................................................ 416
Introduction ............................................... 416
Acid catalyzed isomerization of C7 alkanes and light HC
origin ..................................................... 417
Transition metal catalysis and natural gas generation ...... 420
WATER-ORGANIC INTERACTIONS AND THEIR IMPLICATIONS ON
PETROLEUM FORMATION ........................................... 423
Introduction ............................................... 423
Why don't oil and water mix? ............................... 424
The kinetics and mechanisms of water-organic (kerogen)
interaction ................................................ 425
Hydrolysis of ether linkages ............................... 425
Hydrolysis of ester linkages ............................... 427
Water-hydrocarbon radical interactions ..................... 428
Hydrolytic disproportionate and kerogen oxidation .......... 430
CONCLUSIONS ................................................... 431
ACKNOWLEDGMENTS ............................................... 431
REFERENCES .................................................... 431
12 Calculating the NMR Properties of Minerals, Glasses,
and Aqueous Species
John D. Tossell
INTRODUCTION .................................................. 437
BASIC THEORY OF NMR SHIELDING ................................. 437
A BRIEF HISTORY OF NMR CALCULATIONS ON MOLECULES .............. 439
PRESENT STATUS OF NMR CALCULATIONS ON MOLECULES ............... 439
CALCULATION OF SI NMR SHIELDINGS IN ALUMINOSILICATES .......... 443
CALCULATIONS OF SHIELDINGS FOR OTHER ELECTROPOSITIVE
ELEMENTS: B, P, SE, NA AND RB ................................. 446
CALCULATION OF ELECTRIC FIELD GRADIENTS AT О IN
ALUMINOSILICATES .............................................. 448
CALCULATION OF NMR SHIELDING OF О IN OXIDES ................... 449
CALCULATION OF NMR SHIELDINGS FOR TRANSITION METAL COMPOUNDS
AND HEAVY MAIN-GROUP METAL COMPOUNDS .......................... 450
CALCULATIONS OF С NMR SHIELDINGS IN ORGANIC GEOCHEMISTRY ...... 450
APPLICATIONS OF NMR SHIELDING CALCULATIONS IN GEOCHEMISTRY
AND MINERALOGY ................................................ 451
A FINAL WORD ON INTERPRETATION OF CALCULATED NMR SHIELDINGS ... 453
CONCLUSION .................................................... 454
ACKNOWLEDGMENTS ............................................... 454
REFERENCES .................................................... 454
13 Interpretation of Vibrational Spectra Using Molecular
Orbital Theory Calculations
James D. Kubicki
INTRODUCTION .................................................. 459
ENERGY MINIMIZATIONS .......................................... 460
CALCULATION OF SPECTRA ........................................ 461
CALCULATION OF FREQUENCIES .................................... 462
CALCULATION OF IR AND RAMAN INTENSITIES ....................... 463
Infrared intensities ....................................... 463
Raman intensities .......................................... 465
VIBRATIONAL BANDWIDTHS ........................................ 466
EXAMPLES AND COMPARISON TO EXPERIMENT ......................... 467
Gas-phase .................................................. 467
Aqueous-phase .............................................. 469
Mineral surfaces ........................................... 473
Minerals ................................................... 475
Glasses .................................................... 475
CONCLUSIONS AND FUTURE DIRECTIONS ............................. 478
ACKNOWLEDGMENTS ............................................... 478
REFERENCES .................................................... 479
14 Molecular Orbital Modeling and Transition State Theory
in Geochemistry
Mihali A. Felipe, Titian Xiao, James D. Kubicki
INTRODUCTION .................................................. 485
TRANSITION STATE THEORY ....................................... 486
Conventional transition state theory ....................... 486
Potential energy surfaces and MO calculations .............. 490
Other rate theories ........................................ 494
DETERMINATION OF ELEMENTARY STEPS AND REACTION MECHANISMS ..... 496
Stationary-point searching schemes ......................... 496
Transition state initial guesses ........................... 498
Optimization to stationary points .......................... 501
MO-TST STUDIES IN THE GEOSCIENCES ............................. 504
Introduction and definitions ............................... 504
Reaction pathways of mineral-water interaction ............. 505
Atmospheric reactions of global significance ............... 511
ACCURACY ISSUES ............................................... 517
Basis sets ................................................. 517
Basis set superposition error .............................. 518
Methods .................................................... 518
Long-range interactions .................................... 519
Activation energies and zero point energies ................ 519
Quantum tunneling .......................................... 520
CONCLUSIONS AND FUTURE DIRECTIONS ............................. 521
ACKNOWLEDGMENTS ............................................... 522
LIST OF SYMBOLS ............................................... 522
REFERENCES .................................................... 524
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