Molecular Modeling of Geochemical Reactions E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 1122

Veröffentlichungsjahr: 2016

Beschreibung

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.

Leseprobe

Table of Contents

Cover

Title Page

List of Contributors

Preface

1 Introduction to the Theory and Methods of Computational Chemistry

1.1 Introduction

1.2 Essentials of Quantum Mechanics

1.3 Multielectronic Atoms

1.4 Bonding in Molecules and Solids

1.5 From Quantum Chemistry to Thermodynamics

1.6 Available Quantum Chemistry Codes and Their Applications

References

2 Force Field Application and Development

2.1 Introduction

2.2 Potential Forms

2.3 Fitting Procedure

2.4 Force Field Libraries

2.5 Evolution of Force Fields for Selected Classes of Minerals

2.6 Concluding Remarks

References

3 Quantum-Mechanical Modeling of Minerals

3.1 Introduction

3.2 Theoretical Framework

3.3 Structural Properties

3.4 Elastic Properties

3.5 Vibrational and Thermodynamic Properties

3.6 Modeling Solid Solutions

3.7 Future Challenges

References

4 First Principles Estimation of Geochemically Important Transition Metal Oxide Properties

4.1 Introduction

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

4.3 Accuracy of Calculations for Observable Bulk Properties

4.4 Calculation of Surface Properties

4.5 Simulations of the Mineral–Water Interface

4.6 Future Perspectives

Acknowledgments

Appendix

A.1 Short Introduction to Pseudopotentials

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

A.3 Overview of the PAW Method

References

5 Computational Isotope Geochemistry

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

5.2 The Vibrational Eigenvalue Problem

5.3 Isotope Exchange Equilibria

5.4 Qualitative Insights

5.5 Quantitative Estimates

5.6 Relationship to Empirical Estimates

5.7 Beyond the Harmonic Approximation

5.8 Kinetic Isotope Effects

5.9 Summary and Prognosis

Acknowledgments

References

6 Organic and Contaminant Geochemistry

6.1 Introduction

6.2 Molecular Modeling Methods

6.3 Applications

6.4 Perspectives and Future Challenges

Glossary

References

7 Petroleum Geochemistry

7.1 Introduction: Petroleum Geochemistry and Basin Modeling

7.2 Technology Development of the Petroleum Geochemistry

7.3 Computational Simulations in Petroleum Geochemistry

7.4 Summary

References

8 Mineral–Water Interaction

8.1 Introduction

8.2 Brief Review of AIMD Simulation Method

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

8.4 Theoretical Methodology for Vibrational Spectroscopy and Mode Assignments

8.5 Property Calculations from AIMD: Dipoles and Polarisabilities

8.6 Illustrations from Our Recent Works

8.7 Some Perspectives for Future Works

References

9 Biogeochemistry

9.1 Introduction

9.2 Challenges and Approaches to Computational Modeling of Biomineralization

9.3 Case Studies

9.4 Concluding Remarks and Future Perspectives

Acknowledgments

References

10 Vibrational Spectroscopy of Minerals Through

Ab Initio

Methods

10.1 Introduction

10.2 Theoretical Background and Methods

10.3 Examples and Applications

10.4 Simulation of Vibrational Properties for Crystal Structure Determination

10.5 Future Challenges

Acknowledgements

References

11 Geochemical Kinetics via Computational Chemistry

11.1 Introduction

11.2 Methods

11.3 Applications

11.4 Future Challenges

References

Index

End User License Agreement

List of Tables

Chapter 01

Table 1.1

Geometry and vibrational frequencies of gas-phase water calculated using a 6-311G* basis set with different exchange–correlation functionals.

Table 1.2

Geometry and vibrational frequencies of gas-phase water calculated using a B3LYP functional with different Gaussian basis sets.

Table 1.3

Geometry and vibrational frequencies of gas-phase water calculated using a B3LYP functional with different Slater orbital basis sets.

Table 1.4

Examples of current quantum chemistry software.

Chapter 03

Table 3.1

Lattice parameter,

a

(in Å), fractional coordinates of the oxygen atom,

O

i

,

and selected distances (in Å) of three X

3

Y

2

(SiO

4

)

3

silicate garnets: pyrope (X = Mg and Y = Al), grossular (X = Ca and Y = Al), and andradite (X = Ca and Y = Fe)

.

Chapter 04

Table 4.1

Lattice parameters of the conventional cell of corundum (Å for

a, b, c;

° for

α, β, γ

) calculated using LDA, PBE, and PBE0 plane wave DFT calculations.

Table 4.2

Bond lengths and atom center distances (in Å) of corundum calculated using LDA, PBE, and PBE0 plane wave DFT calculations.

Table 4.3

Lattice parameters for the conventional cells of hematite and goethite (Å for

a, b, c;

° for

α, β, γ

) calculated using LDA, PBE, PBE+U, and PBE0 plane wave DFT calculations.

Table 4.4

Bond lengths and atom center distances (in Å) of hematite and goethite calculated using LDA, PBE, PBE+U, and PBE0 plane wave DFT calculations.

Table 4.5

Effect of cutoff energy on the lattice parameters of the conventional cell of corundum (Å for

a, b, c;

° for

α, β, γ

) in PAW and norm-conserving pseudopotential (PSPW) calculations.

Table 4.6

Band gaps (in eV) for corundum, hematite, and goethite calculated using PBE, PBE+U, and PBE0 plane wave DFT calculations.

Table 4.7

Local magnetic moment (

μ

(μB/Fe atom)) for each Fe site in hematite and goethite calculated using PBE, PBE+U, and PBE0 plane wave DFT calculations.

Table 4.8

Energy difference (in meV/Fe atom) between spin configurations of the hematite cell from PBE and PBE+U plane wave DFT calculations.

Chapter 05

Table 5.1

Frequencies (

) for CO

2

and CH

4

calculated with DFT using the exchange–correlation functional B3PW91 and basis set aug-cc-pVTZ.

Chapter 06

Table 6.1

Typical physical and chemical characteristics of kaolinite, montmorillonite, and goethite.

Table 6.2

Calculated interaction energies for complexes formed on octahedral (001) surface of kaolinite (K) and (110) surface of goethite (G).

Table 6.3

Calculated averaged total energies

, Ū,

and their standard deviations for models A–D and differences for each corresponding pair (last column)

.

Table 6.4

Calculated interaction energies and averaged distances for selected PAHs adsorbed on goethite (110) surface and lepidocrocite (010) surface.

Table 6.5

Formation enthalpies and Gibbs free energies for complexes of

with selected functional groups.

Table 6.6

Enthalpies and Gibbs free energies of exchange reactions between hydrated 2, 4-D/2, 4-D

–

moieties and selected hydrated functional groups using micro

+

global solvation approach (subscript “mgs”).

Table 6.7

Enthalpies and Gibbs free energies of exchange reactions between hydrated MCPA and hydrated functional groups using micro+global solvation approach (subscript “mgs”).

Table 6.8

Reaction enthalpies and Gibbs free energies for the formation of the cation-bridged complexes of

(Eq. 6.23) using micro+global solvation approach (“mgs” subscript).

Chapter 07

Table 7.1

Classification of kerogen types and their basic properties.

Chapter 09

Table 9.1

A list of molecular simulation methods that can be used for modeling different processes at the mineral–water–organic interface.

Chapter 10

Table 10.1

Calculated versus experimental vibrational properties of calcite using various basis sets (top part, B3LYP functional) and functionals (bottom, BS D).

Table 10.2

Calculated versus experimental structures and O—H stretching frequencies of brucite with various functionals.

Table 10.3

The IR spectrum of calcite.

Table 10.4

The Raman spectrum of calcite.

Table 10.5

Simulated isotopic analysis of vibrational modes in calcite.

Table 10.6

Calculated IR frequencies (

v,

cm

−1

) of three carbonates.

Table 10.7

The structure of brucite (

) and diaspore (

Pbnm,

right)

.

Table 10.8

Calculated versus experimental (Lutz et al. 1994) vibrational frequencies (cm

−1

) of brucite.

Table 10.9

IR- and Raman-active

bending (top part) and O—H stretching (bottom) modes of diaspore.

Table 10.10

The structure of boehmite.

List of Illustrations

Chapter 01

Figure 1.1

Wavefunctions and energy levels for a particle in a one-dimensional box.

Figure 1.2

Spherical coordinates used for solution of the hydrogen atom.

Figure 1.3

Schematic energy levels and orbital shapes for the hydrogen atom.

Figure 1.4

(a) The H

2

molecule and (b) schematic energy-level diagram for the first two one-electron molecular orbitals showing the bonding and antibonding combinations of the atomic orbitals.

Chapter 02

Figure 2.1

Lennard–Jones potential curve between two particles in red is decupled in the two contributions: the attraction in green and the repulsion in blue.

Figure 2.2

Schematic representation of the harmonic bond,

k

ij

,

distance,

r

ij

,

and angle,

θ

ijk

,

depicted on the water molecule (oxygen in red and hydrogen in white).

Figure 2.3

Schematic representation of the shell model.

Figure 2.4

Illustration of coarse grain (CG) modelling in the case of DOPC lipids: CG models of a single molecule and a self-assembled bilayer (membrane) are schematically depicted. The lamping of atomic groups into spherical CG units and the resulting CG representation are shown.

Figure 2.5

Schematic representation of the SPC and TIP3P water models (a) left and TIP4P (b). Oxygen in red and hydrogen in white.

Figure 2.6

Schematic representation of QM/MM showing three-region approach. The transparent inner region shows the adsorbed species, the second region (coloured green and red) is allowed to relax in response to the defect and the third region is held fixed.

Figure 2.7

Crystalline nanoparticles of calcite comprising of {10.4} surfaces, before (a) and after minimisation (b).

Figure 2.8

Time-averaged image of water (blue) and C

60

(yellow) densities above the pyrophyllite (001) surface (O in red, Si in blue, Al in light blue, H in white and C in gray).

Figure 2.9

Adsorption of dioxin at the water–(001) surface of pyrophyllite interface (O in red, Si in blue, Al in light blue and H in white).

Figure 2.10

Hematite (Fe

2

O

3

) nanoparticles comprising (a) the {01.2} (sides) and an oxygen terminated (00.1) (truncated corner) surfaces and (b) the {10.0} (sides) and iron-terminated (00.1) (top) surfaces.

Chapter 03

Figure 3.1

Pressure–volume relation of six silicate garnet end-members as computed with B3LYP first-principles simulations (continuous lines) and measured experimentally (symbols); see text for details on the experiments.

Figure 3.2

Elastic stiffness constants

B

vu

of pyrope (left panel), grossular (central panel), and andradite (right panel), as a function of pressure

P.

Black lines represent computed values. All experimental values are obtained from Brillouin scattering measurements (see text for details).

Figure 3.3

Directional quasitransverse and quasilongitudinal seismic wave velocities of single-crystal grossular, uvarovite, spessartine, pyrope, andradite, and almandine along an azimuthal angle

θ

(defined in the text). Computed data at different pressures (0 GPa, 4 GPa, 8 GPa, 12 GPa, 20 GPa, 30 GPa) are reported as continuous lines of increasing thickness. Experimental data are reported when available (see text for details).

Figure 3.4

Constant-volume specific heat

C

V

and entropy

S

of pyrope as a function of temperature, as computed at B3LYP level of theory (thick continuous line) with the largest SC considered (viz.,

X

27) and compared with experimental data (full circles) from Haselton and Westrum (1980) and Tequi et al. (1991). On the right scale of the two panels,

are reported that show the convergence of computed thermodynamic properties on the size of the adopted SC (n = 1, 2, 4, 8, 16). The inset of the right panel shows the shape of the first Brillouin zone of silicate garnets

.

Figure 3.5

Bulk modulus

K

of the grandite solid solution, Ca

3

Fe

2–2

x

Al

2x

(SiO

4

)

3

, as a function of its chemical composition

x.

Experimental data are reported as full and empty symbols (see text for details). When available, error bars are also shown. The solid line shows the quasilinear trend of our calculated values, whereas the thick dashed curve is drawn to provide an approximate fit to the experimental data, as suggested by Bass (1986) and O’Neill et al. (1989).

Chapter 04

Figure 4.1

Unit cells for bulk goethite structure (a) and corundum structure (b) (left, 30-atom cell; right, 10-atom cell). Hematite and corundum have same crystal structure (left, 30-atom cell; right, 10-atom cell). Fe and Al, blue; O, red; H, white. The “a,” “b,” and “c” are the lattice vectors.

Figure 4.2

Projected density of states (PDOS) for atoms in surface and bulk region of Al-terminated corundum (001) using PBE96. (a) Bulk corundum and (b) Al-terminated corundum (001) surface.

Figure 4.3

Projected density of states for bulk hematite using different DFT levels. The pink line represents PDOS for the Fe atoms, and the red line represents PDOS for the O atoms. The line above the middle line (

y

 = 0) is spin-up density line and below

y

 = 0 is spin-down density line. The upper, middle, and lower figures are from (a) PBE, (b) PBE+U, and (c) PBE0, respectively.

Figure 4.4

Different possible terminations of hematite and corundum (oxygen, red; iron and aluminum, blue). The “a” and “c” are the lattice vectors.

Figure 4.5

Al

2

O

3

(001) surfaces: (a) Al-terminated corundum (001) surface (top Al layer moves down to O layer). (b) O-terminated corundum (or hematite) (001) protonated surface. The “a,” “b,” and “c” are the lattice vectors.

Figure 4.6

Bulk structure and two types of (100) surface terminations of goethite. The “a,” “b,” and “c” are the lattice vectors.

Figure 4.7

Water molecule absorbed on different hydration models for hematite (012) surface. (a) and (b) are side views of Model 1, and (c) and (d) are side views of Model 2. The “a,” “b,” and “c” are the lattice vectors.

Figure 4.8

Projected density of states for Fe atoms (a) and O atoms (b) in surface and bulk region of O-terminated hematite (001) using PBE+U.

Figure 4.9

Interfacial and bulk water regions of hematite (012)–water interface. The “a,” “b,” and “c” are the lattice vectors.

Figure 4.10

Computed power spectrum of two types of OD groups on hematite (012) surface, water on interfacial region and bulk region. (a) O

I

D and O

II

D surface group (cm

−1

) and (b) bulk water molecules (cm

−1

).

Figure 4.11

(a) Highest occupied molecular orbital (HOMO) of Fe

2+

bidentate bond to the 012 hematite surface. Note little charge transfer. (b) HOMO of Fe

2+

tridentate bond to the 001 hematite surface. Note charge transfer.

Figure A.1

Comparison of the pseudo-wave functions (dashed lines) with the full-core atomic valence wave functions (solid lines) for Fe

3+

. The lower panel shows the corresponding pseudopotentials.

Chapter 05

Figure 5.1

Molecular representation of environments for carbonate ion in (a)

and (b) CaCO

3

. Both representations are “core” structures to be embedded in more extended structures which are not shown so that the core structures are more easily seen.

Figure 5.2

Two different cluster representations

for octahedrally coordinated aquo ions with explicit first and second shell water molecules.

Figure 5.3

Error over small molecules in Richet et al. (1977).

Figure 5.4

Equilibrium constant for Reaction 5.3 for various model chemistries as a function of the number of solvating waters. Dashed lines are extrapolations.

Figure 5.5

13

C/

12

C fractionation relative to calcite for a series of carbonate minerals. Solid lines with markers are calculated from first-principles, and dashed lines are estimated empirically. ara, aragonite; cer, cerussite; dol, dolomite; mag, magnesite; rho, rhodochrosite.

Chapter 06

Scheme 6.1

Skeletal formula of MCPA and 2,4-D molecules.

Figure 6.1

Structural models of kaolinite (a), montmorillonite (b), and goethite (c).

Figure 6.2

Optimized structures of hydrogen-bonded complexes of 2,4-M (a), MCPA (b), and 2,4-D (c) on the (001) surface of kaolinite.

Figure 6.3

One-dimensional density profiles for C (

groups) and Cl atoms. Basal oxygen atoms from tetrahedral sheet represent a reference plane. Density profiles of kaolinite layer are not shown

.

Figure 6.4

Optimized structures of hydrogen-bonded complexes between molecular fragment of the goethite (110) surface and water (a), 2,4-D molecule (b), and

anion (c). Distances are in Angstrom.

Figure 6.5

The most stable optimized structure of outer sphere complex of

anion formed on the (110) surface of goethite. Distances are in Angstrom

.

Figure 6.6

One-dimensional density profiles for hydrated outer sphere complex of neutral MCPA molecule on the partially protonated (110) surface of goethite obtained from AIMD simulation.

Figure 6.7

One-dimensional density profiles for hydrated inner sphere complex of neutral MCPA molecule on the partially protonated (110) surface of goethite obtained from AIMD simulation.

Figure 6.8

Snapshots from AIMD simulations on four models of partially hydrated cation-bridged complexes of

anion on the (001) surface of montmorillonite.

Figure 6.9

Ca—O radial distribution functions for models A and B (Figure 6.8) calculated from AIMD simulations.

Figure 6.10

One-dimensional density profiles for models A and B (Figure 6.8) calculated from AIMD simulations.

Figure 6.11

DFT optimized geometries for selected PAH molecules adsorbed on the (110) surface of goethite.

Figure 6.12

DFT optimized geometries for selected PAH molecules adsorbed on the (010) surface of lepidocrocite.

Figure 6.13

Structure and hydrogen bond distances (Å) in gas and solution (underlined values) of the OA5···MCPA complex. Distances are in Angstrom. Underlined values correspond to COSMO calculations.

Figure 6.14

Cation-bridged complex between

anion and OA3 oligomeric fragment of polyacrylic acid. Distances are in Angstrom. Underlined values correspond to COSMO calculations.

Figure 6.15

Free energy profile for MCPA trapping in the nanopore model of HSs with partially hydrated hydrophilic domain.

Figure 6.16

Free energy profile for naphthalene trapping in the nanopore model of HSs with partially hydrated hydrophilic domain.

Chapter 07

Figure 7.1

Hydrocarbon generations as the function of the vitrinite reflectance (VRo).

Figure 7.2

A comprehensive reaction network of the kerogen pyrolysis to generate hydrocarbon and nonhydrocarbon compounds.

Figure 7.3

A computational approach to locate the transition state of the C–C bond rupture based on the electron distribution. The C–C bond length has been fixed from 1.5 to 5.0 Å with an increment of 0.5 Å, while the rest of the atoms of the butane molecule is allowed to fully be optimized. Both the relative Gibbs free energy differences (referred to the optimized stable configuration with C–C bond length of 1.53 Å) of both the singlet and triplet configurations at room temperature

T

 = 298.13 K were determined. All calculations were conducted at DFT/B3LYP/6-31G*(d,p) level.

Figure 7.4 δ

13

C isotope fractionation of C

13

to C

21

n

-alkane as a function of final pyrolysis temperature (points) and the theoretical kinetic model using a

13

C/

12

C isotope substitution

ΔΔH

value of 230 J/mol (55 cal/mol), a frequency factory ratio (

A

*/

A

) of 1.02, and an initial

δ

13

C value of −30.35‰.

Figure 7.5 δ

D isotope fractionation of C

13

to C

22

(filled) and

C

13

–

C

15

n

-alkanes (nonfilled) as a function of final pyrolysis temperature and the theoretical kinetic model using a D/H isotope substitution

ΔΔH

value of 1340 J/mol (320 cal/mol), an initial

δ

D value of −107.8‰, and three different frequency factor ratios

A

*/

A

 = 1.02, 1.07, and 1.20.

Figure 7.6

Molecular modeling of the computed doubly substituted methane isotopologue concentrations related to the paleo gas formation conditions. In order to distinguish different methane sources, a high-resolution determination of the

13

CH

3

D at the level of 10

−9

will be required.

Chapter 08

Figure 8.1

Scheme of silanols encountered at the surface of silica: Isolated (Q

3

), geminal (Q

2

), vicinal (Q

3

) and H-bonded with a neighbouring silanol. This scheme does not take into account the presence of an aqueous interface.

Figure 8.2

Organisation of silanols, SiOH, at the dry quartz surface. The silanols are all located in plane and form a H-bonded network within the surface plane.

Figure 8.3

Left: scheme defining the angle between the (Si—)OH and the normal to the surface (denoted

Z

-axis on the scheme). Right: distribution of (Si—)OH angles (in degrees) with respect to the surface normal for aqueous (0001) quartz interface (black) and aqueous amorphous interface (red). For this latest interface, decomposition of the angles is also presented in terms of Si—OH group types: geminals belonging to a concave zone (green), geminals belonging to a convex zone (blue), ‘isolated’ (light blue) and vicinals (brown). Bottom: scheme illustrating the bimodal character of Si—OH orientations at the crystalline α-quartz–water interface.

Figure 8.4

Schematic organisation of the repeated motif of water molecules adsorbed within the first layer of aqueous water at the interface with crystalline (0001) α-quartz (left) and (0001) α-alumina (right). These motifs are repeated over the 2D surfaces.

Figure 8.5

Schematic organisation of the interfacial region between amorphous silica and water.

Figure 8.6

Scheme of the (101) boehmite interface with liquid water. Water is either explicitly represented schematically within the first adsorbed layer at the surface or is implicitly represented by the blue colour for the rest of the bulk water. The scheme presents nomenclature of the boehmite surface sites, the two terraces, the step edge and the low edge.

Figure 8.7

Top: snapshots extracted from the DFT-MD simulations illustrating the water chain formed at the step edge of (101) aqueous boehmite and the proton transfer occurring along that chain (a: before proton transfer, b: after proton transfer). Bottom: schemes of proton transfers occurring at the boehmite aqueous surface observed along the DFT-MD.

Figure 8.8

Infrared (IR) spectra of the interfacial water at the (0001) quartz–water (left) and (0001) alumina–water (right) interfaces from DFT-MD simulations. The bands are colour coded according to ‘weak’ or ‘strong’ H bonds formed between water and hydroxyl surface sites; see text for details. The schemes below the bands correspond to the assignment of the vibrational bands in terms of interfacial water molecules being H-bond acceptors or donors to the surface sites.

Figure 8.9

DFT-MD infrared (IR) spectra of bulk liquid water (blue), ice water (orange) and the water layers beyond the interfacial layer at the quartz–water interface (black).

Figure 8.10

A snapshot from the (010) pyrophyllite/water interface. Si atoms are represented in yellow, Al in green, O in red and H in white. The simulation box is also indicated (blue line), and periodic boundary conditions in all directions are used. The inset shows the deprotonable groups, namely, SiOH, AlOH

2

and AlOH.

Chapter 09

Figure 9.1

Hierarchical structure of bone form macro to atomic scale. The yellow rectangles represent HAP nanocrystals between and within the fibrils. See Section 9.3 for further details.

Figure 9.2

Schematic illustration of the complex energy landscapes of protein–mineral interactions. (a) Ordered protein shifts its free energy minimum configuration upon binding to the mineral surface. (b) Disordered protein displays a multimodal distribution of free energy minima configurations; it forms a sharp free energy minimum upon binding to the mineral surface. Note that the bound protein may be partially structured as shown or may remain disordered with a random different configuration compared to the solution state.

Figure 9.3

Basic algorithm of TREMD method. N independent replicas are spaced on a temperature “ladder” and are simulated in parallel (in HREMD, potential energies are scaled on the ladder instead of temperature). At fixed time interval, Metropolis test is applied to decide if the two adjacent replicas can be interchanged according to their potential energies (Eq. 9.1)

.

Figure 9.4

Snapshots that illustrate the interactions between

, Pi, and the peptide (SerP)

2

-(Glu)

8

in MD simulations. The peptide backbone is rendered in ribbon. (a) The peptide with a random coil structure. No apparent

or Pi network was observed. (b) The peptide with an α-helix conformation. An equilateral triangle configuration was found only with this helix backbone conformation. The side chain non-hydrogen atoms of SerP2, Glu6, and Glu9, which coordinate to three

ions in an equilateral triangle (indicated with green dotted lines, distances in Å), are highlighted in licorice representation. Color designation: blue, calcium; cyan, Glu residue; gold, SerP residue; green, sodium; red, oxygen; tan, phosphate; white, hydrogen; yellow, chloride.

Figure 9.5

Construction of high-resolution collagen molecules self-assembled in the pseudohexagonal structure of a fibril. Each molecule is composed of three peptides in a triple helix (colored ribbons). The colored lines represent chemical bonds between backbone and side chain atoms. The numbers in the right panel of (d) indicate the designated molecular segments in the original 2-D collagen packing model, inferred from TEM results (Petruska and Hodge, 1964).

Figure 9.6

Binding of the charged side chains of statherin to the HAP (001) surface. Left:  Schematic drawing of the proposed “lattice matching” pattern from N-terminus of statherin across the surface (white parallelograms). Inset:  close-up view. Right:  four basic amino acids comprise the recognition motif to the pattern on the surface. Amino acid side chains are represented by licorice model and HAP surface is represented by ball model. Color designation: blue, nitrogen; gray, carbon; green, calcium; orange, phosphate; red, oxygen; white, hydrogen.

Figure 9.7

Structural, dynamical, and energetic properties of CaCO

3

clusters. (a) Snapshots taken from REMD showing the stoichiometric evolution of polymeric cluster configurations. (b) Plot showing the diffusion coefficient (D) of

ions within the clusters compared with calcite and ACC (dashed curve, from simulation) and the self- diffusion coefficients (solid lines, experimental) of several common solvents. (c) The free energy of the solvated ions as a function of cluster size determined at

.

Chapter 10

Figure 10.1

Polarised IR reflectance spectra of single crystal calcite. The two datasets correspond to the electric field of the incident radiation being parallel and perpendicular to the

c

axis, respectively. Arrow points to the experimental extra peak at 848 cm

−1

(see text).

Figure 10.2

Polarised Raman spectra of single crystal calcite. The three datasets correspond to XX, ZZ and XZ polarisations, respectively. Damping factors

γ

here correspond to the peak full width at half maximum (FWHM). Arrows point to the experimental extra peaks discussed in the text.

Figure 10.3

Calculated adsorption IR spectra of three carbonates: zoom on the low-frequency region. Peaks labelled according to Table 10.6.

Figure 10.4

Polarised IR reflectance spectrum along the

c

axis of single crystal ortho-enstatite. Experimental (full line) and calculated (dashed line) curves both from figure 3 Demichelis et al. (2012).

Figure 10.5

Polyhedra, ball and stick representation of Mg(OH)

2

brucite (left) and α-AlOOH diaspore (right). Mg atoms are coloured in green, Al in grey, O in red and H in white. Green dot lines represent hydrogen bonds in diaspore.

Figure 10.6

Ball and stick and polyhedral representation of boehmite structures. The

Cmcm

arrangement is shown, together with the arrangements exhibiting parallel (

Cmc

2

1

) and antiparallel (

P

2

1

/

b

) HB chains. Al atoms are coloured in grey and H atoms in white. O atoms involved in HBs are shown in dark red and the others in light red.

Figure 10.7

Schematic representation of hydrogen flipping between two positions through the

Cmcm

configuration. Kinetic constants for each reaction are shown. Only atoms involved in the process are represented.

Chapter 11

Figure 11.1

(a) Potential energy surface (PES—contours in kilojoule per mole) and (b) cross section for Si(OH)

4

 + F

−

 → Si(OH)

3

F + OH

−

illustrate how reactions may proceed via the minimum-energy pathway between two states. In this case, the Si—F distance (i.e., the reaction coordinate) is decreased by constraining the Si and F atomic coordinates during the energy minimization and the Si—O distance is the dependent parameter that relaxes as the Si—F bond is formed. The difference between the stable configurations (i.e., reactants and products) and the highest energy point along the reaction coordinate (i.e., the transition state) is an estimate of the activation energy (

ΔE

a

) of the reaction.

Figure 11.2

(a) Implicit (i.e., polarized continuum) and (b) explicit (i.e., addition of H

2

O or other solvent molecules) solvation methods result in significantly different bond distances for HPO

4

2−

. The continuum solvation method is a better approximation for low dielectric constant organic solvents, but when strong H-bonds form, the continuum approximation does not account as well for these specific interactions. These changes affect calculated structures, energies, and spectroscopic properties. (c) Addition of H

2

O molecules to include second or third solvation shells can make the calculations significantly more time-consuming, but comparison of (b) and (c) shows that the P—O bond distances change with addition of the extra H

2

O molecules. Molecules drawn with Materials Studio 7 (Accelrys Inc., San Diego, CA). (H, white; H-bonds, dashed blue lines; O, green; P, pink).

Figure 11.3

Potential energy surfaces for an electron transfer process from donor to acceptor (D···A), where the initial (

ψ

A

) and final (

ψ

B

) electronic states are parabolic with respect to collective nuclear coordinates (

q

).

ΔG

° is the energy difference between the initial state in its equilibrium nuclear configuration (

q

A

) and that (

q

B

) of the final state.

λ

is the reorganization energy required to distort the nuclear coordinates from

q

A

to

q

B

while keeping the electron on the donor.

ΔG

*′

prime is the diabatic activation energy to distort nuclear coordinates from

q

A

to that of the crossing point configuration

q

C

, whereas Δ

G

*

is that energy reduced by the magnitude of the electronic coupling (

V

AB

) between

ψ

A

and

ψ

B

at

q

C

.

Figure 11.4

The imaginary mode (i.e., the vibrational mode associated with a negative frequency) of the reaction CO

2

 + OH

−

 → HCO

3

−

is illustrated. A configuration from the highest energy point along the reaction pathway defined by the C···O distance was subjected to a frequency analysis. The presence of one and only one imaginary mode at the highest point along the reaction coordinate helps to identify the configuration as a transition state. In addition, the atomic motions defined by this mode should lead back and forth between the reactants and products. In this example, as the C···OH

−

distance extends and contracts, the products, HCO

3

−

, and reactants (CO

2

 + OH

−

) are formed, respectively. Molecules drawn with Materials Studio 7 (Accelrys Inc., San Diego, CA). (C, gray; H, white; Na, purple; O, green).

Figure 11.5

A TiO

2

nanoparticle with a Ti

4+

(H

2

O)

6

ion is illustrated to provide an example of the classical crystal growth theory where macroscopic crystals are assumed to grow via addition of monomers from a supersaturated solution. Recently, this theory has been shown to be incorrect in some cases where oligomers or molecular clusters form in the supersaturated solution, and these become the building blocks for crystal growth. The difference in size of the monomer and nanocluster shown is intended to provide a graphical representation of why the monomeric growth model can be problematic. Even this small nanoparticle is made up of over 100 atoms, so it becomes hard to imagine that the system is bimodally distributed between monomers and nanoparticles or critical nuclei. A distribution of molecular sizes is more reasonable in most cases.

Guide

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Dedication

To see a World in a grain of sand…

—William Blake

To my wife, Doris, and son, Cody, who bring much joy to my life.

Molecular Modeling of Geochemical Reactions

An Introduction

Edited by

JAMES D. KUBICKI

University of Texas at El Paso, USA

This edition first published 2016© 2016 John Wiley & Sons, Ltd.

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List of Contributors

Adelia J. A. Aquino Institute for Soil Research, University of Natural Resources and Life Sciences, Vienna, Austria and Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, TX, USA

Andrey V. Brukhno Department of Chemistry, University of Bath, Bath, UK

Eric Bylaska Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, WA, USA

Ying Chen Chemistry and Biochemistry Department, University of California, San Diego, La Jolla, CA, USA

Marco De La Pierre Nanochemistry Research Institute, Curtin Institute for Computation, and Department of Chemistry, Curtin University, Perth, Western Australia, Australia

Raffaella Demichelis Nanochemistry Research Institute, Curtin Institute for Computation, and Department of Chemistry, Curtin University, Perth, Western Australia, Australia

Roberto Dovesi Dipartimento di Chimica, Università degli Studi di Torino and NIS Centre of Excellence “Nanostructured Interfaces and Surfaces”, Torino, Italy

Alessandro Erba Dipartimento di Chimica, Università degli Studi di Torino, Torino, Italy

Marie-Pierre Gaigeot LAMBE CNRS UMR 8587, Université d’Evry val d’Essonne, Evry, France and Institut Universitaire de France, Paris, France

Martin H. Gerzabek Institute for Soil Research, University of Natural Resources and Life Sciences, Vienna, Austria

Georg Haberhauer Institute for Soil Research, University of Natural Resources and Life Sciences, Vienna, Austria

James D. Kubicki Department of Geological Sciences, University of Texas at El Paso, El Paso, TX, USA

Hans Lischka Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, TX, USA and Institute for Theoretical Chemistry, University of Vienna, Vienna, Austria

Qisheng Ma Department of Computational and Molecular Simulation, GeoIsoChem Corporation, Covina, CA, USA

Marco Molinari Department of Chemistry, University of Bath, Bath, UK

Stephen C. Parker Department of Chemistry, University of Bath, Bath, UK

Kevin M. Rosso Physical Sciences Division, Pacific Northwest National Laboratory, Richland, WA, USA

James R. Rustad Corning Incorporated, Corning, NY, USA

Nita Sahai Department of Polymer Science, Department of Geology, and Integrated Bioscience Program, University of Akron, Akron, OH, USA

David M. Sherman School of Earth Sciences, University of Bristol, Bristol, UK

Dino Spagnoli School of Chemistry and Biochemistry, University of Western Australia, Crawley, Western Australia, Australia

Marialore Sulpizi Department of Physics, Johannes Gutenberg Universitat, Mainz, Germany

Yongchun Tang Geochemistry Division, Power Environmental Energy Research Institute, Covina, CA, USA

Daniel Tunega Institute for Soil Research, University of Natural Resources and Life Sciences, Vienna, Austria

John Weare Chemistry and Biochemistry Department, University of California, San Diego, La Jolla, CA, USA

Zhijun Xu Department of Polymer Science, University of Akron, Akron, OH, USA and Department of Chemical Engineering, Nanjing University, Nanjing, China

Weilong Zhao Department of Polymer Science, University of Akron, Akron, OH, USA

Preface

Humility is an underrated scientific personality characteristic. When I think of William Blake’s famous lithograph of Sir Isaac Newton toiling away at the bottom of a dark ocean, I am always reminded of how much we do not know. Science is a humbling enterprise because even our most notable achievements will likely be replaced by greater understanding at some date in the future. I am allowing myself an exception in the case of publication of this volume, however. I am proud of this book because so many leaders in the field of computational geochemistry have agreed to be a part of it. We all know that the best people are so busy with projects that it is difficult to take time away from writing papers and proposals to dedicate time to a chapter. The authors who have contributed to this volume deserve a great deal of appreciation for taking the time to help explain computational geochemistry to those who are considering using these techniques in their research or trying to gain a better understanding of the field in order to apply its results to a given problem. I am proud to be associated with this group of scientists.

When my scientific career began in 1983, computational geochemistry was just getting a toehold in the effort to explain geochemical reactions at an atomic level. People such as Gerry V. Gibbs and John (Jack) A. Tossell were applying quantum chemistry to model geologic materials, and C. Austen Angell and coworkers were simulating melts with classical molecular dynamics. As an undergraduate, I had become interested in magmatic processes, especially the generation of magmas in subduction zones and the nucleation of crystals from melts. Organic chemistry exposed me to the world of reaction mechanisms which were not being studied extensively at the time in geochemistry. When the opportunity arose in graduate school to use MD simulations to model melt and glass behavior, I jumped at the chance to combine these interests in melts and mechanisms naïve to the challenges that lie ahead. Fortunately, through the guidance of people such as Russell J. Hemley, Ron E. Cohen, Anne M. Hofmeister, Greg E. Muncill, and Bjorn O. Mysen at the Geophysical Laboratory, I was able to complement the computational approach with experimental data on diffusion rates and vibrational spectra. This approach helped benchmark the simulations and provide insights into the problems at hand that were difficult to attain with computation alone. This strategy has worked throughout my career and has led to numerous fascinating collaborations.

A key step in this process occurred while I was working as a postdoc at Caltech under Geoffrey A. Blake and Edward M. Stolper. I met another postdoc, Dan G. Sykes, who also shared a passion for melt and glass structure. As I was learning how to apply quantum mechanics to geochemistry, Dan and I discussed his models for explaining the vibrational spectra of silica and aluminosilicate glasses. Dan’s model differed from the prevailing interpretations of IR and Raman spectra, but his hypotheses were testable via construction of the three- and four-membered ring structures he thought gave rise to the observed trends in vibrational frequencies with composition. We argued constantly over the details of his model and came up with several tests to disprove it, but, in the end, the calculations and observed spectra agreed well enough that we were able to publish a series of papers over the objections of reviewers who were skeptical of the views of two young postdocs. Among these papers, a key study was published with the help of George R. Rossman whose patience and insight inspired more confidence in me that the path we were following would be fruitful. This simple paper comparing calculated versus observed H-bond frequencies ended up being more significant than I had known at the time because this connection is critical in model mineral–water interactions that became a theme later in my career.

When I could not find work any longer doing igneous-related research, I turned to a friend from undergraduate chemistry at Cal State Fullerton, Sabine E. Apitz, to employ me as a postdoc working on environmental chemistry. Fortunately, the techniques I had learned were transferable to studying organic–mineral interactions. This research involving mineral surfaces eventually led to contacts with Susan L. Brantley and Carlo G. Pantano who were instrumental in landing a job for me at Penn State. Numerous collaborations blossomed during my tenure in the Department of Geosciences, and all these interdisciplinary projects kept me constantly excited about learning new disciplines in science. Recently, I made the decision to move to the University of Texas at El Paso to join a team of people who are creating an interdisciplinary research environment while simultaneously providing access to excellent education and social mobility.

The rapid developments in hardware, software, and theory that have occurred since 1983 have propelled research in computational geochemistry. All of us appreciate the efforts of all those developing new architectures and algorithms that make our research possible. We offer this book as a stepping stone for those interested in learning these techniques to get started in their endeavors, and we hope the reviews of literature and future directions offered will help guide many new exciting discoveries to come.

James D. KubickiDepartment of Geological SciencesThe University of Texas at El PasoOctober 3, 2015

1Introduction to the Theory and Methods of Computational Chemistry

David M. Sherman

School of Earth Sciences, University of Bristol, Bristol, UK

1.1 Introduction

The goal of geochemistry is to understand how the Earth formed and how it has chemically differentiated among the different reservoirs (e.g., core, mantle, crust, hydrosphere, atmosphere, and biosphere) that make up our planet. In the early years of geochemistry, the primary concern was the chemical analysis of geological materials to assess the overall composition of the Earth and to identify processes that control the Earth’s chemical differentiation. The theoretical underpinning of geochemistry was very primitive: elements were classified as chalcophile, lithophile, and siderophile (Goldschmidt, 1937), and the chemistry of the lithophile elements was explained in terms of simple models of ionic bonding (Pauling, 1929). It was not possible to develop a predictive quantitative theory of how elements partition among different phases.

In the 1950s, experimental studies began to measure how elements are partitioned between coexisting phases (e.g., solid, melt, and fluid) as a function of pressure and temperature. This motivated the use of thermodynamics so that experimental results could be extrapolated from one system to another. Equations of state were developed that were based on simple atomistic (hard-sphere) or continuum models (Born model) of liquids (e.g., Helgeson and Kirkham, 1974). This work continued on into the 1980s. By this time, computers had become sufficiently fast that atomistic simulations of geologically interesting materials were possible. However, the computational atomistic simulations were based on classical or ionic models of interatomic interactions. Minerals were modeled as being composed of ions that interact via empirical or ab initio-derived interatomic potential functions (e.g., Catlow et al., 1982; Bukowinski, 1985). Aqueous solutions were composed of ions solvated by (usually) rigid water molecules modeled as point charges (Berendsen et al., 1987). Many of these simulations have been very successful and classical models of minerals and aqueous solutions are still in use today. However, ultimately, these models will be limited in application insofar as they are not based on the real physics of the problem.

The physics underlying geochemistry is quantum mechanics. As early as the 1970s, approximate quantum mechanical calculations were starting to be used to investigate bonding and electronic structure in minerals (e.g., Tossell et al., 1973; Tossell and Gibbs, 1977). This continued into the 1980s with an emphasis on understanding how chemical bonds dictate mineral structures (e.g., Gibbs, 1982) and how the pressures of the deep earth might change chemical bonding and electronic structure (Sherman, 1991). Early work also applied quantum chemistry to understand geochemical reaction mechanisms by predicting the structures and energetics of reactive intermediates (Lasaga and Gibbs, 1990). By the 1990s, it became possible to predict the equations of state of simple minerals and the structures and vibrational spectra of gas-phase metal complexes (Sherman, 2001). As computers have become faster, it now possible to simulate liquids, such as silicate melts or aqueous solutions, using ab initio molecular dynamics.

We are now at the point where computational quantum chemistry can be used to provide a great deal on insight on the mechanisms and thermodynamics of chemical reactions of interest in geochemistry. We can predict the structures and stabilities of metal complexes on mineral surfaces (Sherman and Randall, 2003; Kwon et al., 2009) that control the fate of pollutants and micronutrients in the environment. We can predict the complexation of metals in hydrothermal fluids that determine the solubility and transport of metals leading to hydrothermal ore deposits (Sherman, 2007; Mei et al., 2013, 2015). We can predict the phase transitions of minerals that may occur in the Earth’s deep interior (Oganov and Ono, 2004; Oganov and Price, 2005). Computational quantum chemistry is now becoming a mainstream activity among geochemists, and investigations using computational quantum chemistry are now a significant contribution to work presented at major conferences on geochemistry.

Many geochemists want to use these tools, but may have come from a traditional Earth science background. The goal of this chapter is to give the reader an outline of the essential concepts that must be understood before using computational quantum chemistry codes to solve problems in geochemistry. Geochemical systems are usually very complex and many of the high-level methods (e.g., configuration interaction) that might be applied to small molecules are not practical. In this chapter, I will focus on those methods that can be usefully applied to earth materials. I will avoid being too formal and will emphasize what equations are being solved rather than how they are solved. (This has largely been done for us!) It is crucial, however, that those who use this technology be aware of the approximations and limitations. To this end, there are some deep fundamental concepts that must be faced, and it is worth starting at fundamental ideas of quantum mechanics.

1.2 Essentials of Quantum Mechanics

By the late nineteenth and early twentieth centuries, it was established that matter comprised atoms which, in turn, were made up of protons, neutrons, and electrons. The differences among chemical elements and their isotopes were beginning to be understood and systematized. Why different chemical elements combined together to form compounds, however, was still a mystery. Theories of the role of electrons in chemical bonding were put forth (e.g., Lewis, 1923), but these models had no obvious physical basis. At the same time, physicists were discovering that classical physics of Newton and Maxwell failed to explain the interaction of light and electrons with matter. The energy of thermal radiation emitted from black bodies could only be explained in terms of the frequency of light and not its intensity (Planck, 1900). Moreover, light (viewed as a wave since Young’s experiment in 1801) was found to have the properties of particles with discrete energies and momenta (Einstein, 1905). This suggests that light was both a particle and a wave. Whereas a classical particle could have any value for its kinetic and potential energies, the electrons bound to atoms were found to only have discrete (quantized) energies (Bohr, 1913). It was then hypothesized that particles such as electrons could also be viewed as waves (de Broglie, 1925); this was experimentally verified by the discovery of electron diffraction (Davisson and Germer, 1927). Readers can find an accessible account of the early experiments and ideas that led to quantum mechanics in Feynman et al. (2011).

The experimentally observed wave–particle duality and quantization of energy were explained by the quantum mechanics formalism developed by Heisenberg (1925), Dirac (1925), and Schrodinger (1926). The implication of quantum mechanics for understanding chemical bonding was almost immediately demonstrated when Heitler and London (1927) developed a quantum mechanical model of bonding in the H2 molecule. However, the real beginning of computational quantum chemistry occurred at the University of Bristol in 1929 when Lennard-Jones presented a molecular orbital theory of bonding in diatomic molecules (Lennard-Jones, 1929).

The mathematical structure of quantum mechanics is based on set of postulates:

Postulate 1:

A system (e.g., an atom, molecule or, really, anything) is described by a wavefunction Ψ(r1, r2, …, rN, t) over the coordinates , the N-particles of the system, and time t. The physical meaning of this wavefunction is that the probability of finding the system at a set of values for the coordinates r1, r2, …, rN at a time t is |Ψ(r1, r2, …, rN, t)|2.

Postulate 2:

For every observable (measurable) property λ of the system, there corresponds a mathematical operator that acts on the wavefunction.

Mathematically, this is expressed as follows:

(1.1)

Ψ is an eigenfunction of the operator with eigenvalue λ. An eigenfunction is a function associated with an operator such that if the function is operated on by the operator, the function is unchanged except for being multiplied by a scalar quantity λ. This is very abstract, but it leads to the idea of the states of a system (the eigenfunctions) that have defined observable properties (the eigenvalues). Observable properties are quantities such as energy, momentum, or position. For example, the operator for the momentum of a particle moving in the x-direction is

(1.2)

where i is , is Planck’s constant divided by 2π, and is the unit vector in the x-direction. Since the kinetic energy of a particle with mass m and momentum p is

the operator for the kinetic energy of a particle of mass m that is free to move in three directions (x, y, z) is

(1.3)

In general, the operator for the potential energy of a system is a scalar operator such that . That is, we multiply the wavefunction by the function that defines the potential energy. The operator Ê for the total energy E of a system is

(1.4)

It is important to recognize whether or not a quantity is a “quantum mechanical observable.” Chemists (and geochemists) often invoke quantities such as “ionicity,” “bond valence,” “ionic radius,” etc., that are not observables. These quantities are not real; they exist only as theoretical constructs. They cannot be measured.

1.2.1 The Schrödinger Equation

In classical mechanics, we express the concept of conservation of energy in terms of the Hamiltonian H of the system:

(1.5)

In quantum mechanics, we express the Hamiltonian in terms of the operators corresponding to E, T, and V:

(1.6)

or

(1.7)

This is the time-dependent Schrödinger equation. If the kinetic T and potential V energies of the system are not varying with time, then we can write:

(1.8)

Substituting this into the Hamiltonian gives:

(1.9)

This is the time-independent Schrödinger equation, and it is what we usually seek to solve in order to obtain a quantum mechanical description of the system in terms of the wavefunction and energy of each state.

1.2.2 Fundamental Examples

At this point, it is worthwhile to briefly explore several fundamental examples that illustrate the key aspects of quantum mechanics.

1.2.2.1 Particle in a Box

This is, perhaps the simplest problem yet it illustrates some of the fundamental features of quantum reality. Consider a particle of mass m inside a one-dimensional box of length L (Figure 1.1). The potential energy V of the system is 0 inside the box but infinite outside the box. Therefore, inside the box, the Schrödinger equation is

(1.10)

Figure 1.1Wavefunctions and energy levels for a particle in a one-dimensional box.

The solution to this differential equation is of the form:

(1.11)

Since the potential energy is infinite outside the box, the particle cannot be at x = 0 or at x = L. That is, we have . Hence,

(1.12)

which implies that B = 0. However, since

we find that , where

If we substitute Ψ(x) back into the Schrödinger equation, we find that

(1.13)

That is, the energy is quantized to have only specific allowed values because n can only take on integer values. The quantization results from putting the particle in a potential energy well (the box). However, the quantization is only significant if the dimensions of the box and the mass of the particle are on the order of Planck’s constant (h = 6.6262 × 10−34 J/s, i.e., if the box is angstroms to nanometers in size). The formalism of quantum mechanics certainly applies to our macroscopic world, but the quantum spacing of a 1 g object in a box of, say, 10 cm in length is too infinitesimal to measure.

1.2.2.2 The Hydrogen Atom

Now, let’s consider the hydrogen atom consisting of one electron and one proton as solved by Schrödinger (1926). We will consider only the motion of the electron relative to the position of the proton and not consider the motion of the hydrogen atom as a whole. Hence, our wavefunction for the system is Ψ(r) where r