Reviews in Computational Chemistry

LIST OF CONTRIBUTORS

Pere Alemany, Departament de Química Física and Institut de Química Teòrica i Computacional (IQTCUB), Universitat de Barcelona, Martí i Franquès, Barcelona, Spain

Santiago Alvarez, Departament de Química Inorgànica and Institut de Química Teòrica i Computacional (IQTCUB), Universitat de Barcelona, Martí i Franquès, Barcelona, Spain

Edwin Antillon, School of Materials Engineering and Birck Nanotechnology Center, Purdue University, West Lafayette, IN, United States

David Avnir, Institute of Chemistry and The Lise Meitner Minerva Center for Computational Quantum Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel

David Casanova, Donostia International Physics Center (DIPC), Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), Donostia, Spain; IKERBASQUE, Basque Foundation for Science, Bilbao, Spain

Mathew J. Cherukara, School of Materials Engineering and Birck Nanotechnology Center, Purdue University, West Lafayette, IN, United States

Chaim Dryzun, Institute of Chemistry and The Lise Meitner Minerva Center for Computational Quantum Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel

Andreas Hermann, School of Physics and Astronomy, The University of Edinburgh, Edinburgh, United Kingdom

Frank Jensen, Department of Chemistry, Aarhus University, Aarhus, Denmark

Anna I. Krylov, Department of Chemistry, University of Southern California, Los Angeles, CA, United States

Dmitrii E. Makarov, Department of Chemistry and Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX, United States

Balazs Nagy, Department of Chemistry, Aarhus University, Aarhus, Denmark

Raghunathan Ramakrishnan, Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials, Department of Chemistry, University of Basel, Basel, Switzerland

Alejandro Strachan, School of Materials Engineering and Birck Nanotechnology Center, Purdue University, West Lafayette, IN, United States

O. Anatole von Lilienfeld, Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials, Department of Chemistry, University of Basel, Basel, Switzerland; General Chemistry, Free University of Brussels, Brussels, Belgium

Mitchell A. Wood, School of Materials Engineering and Birck Nanotechnology Center, Purdue University, West Lafayette, IN, United States

PREFACE

This book series traditionally includes reviews of current topics in computational chemistry and provides minitutorials for novices initiating new directions in their own research along with critical literature reviews highlighting advanced applications. Volume 30 is no exception to that longstanding tradition. While each chapter has a unique focus, two themes connect some of the chapters in this volume: modeling of phenomena under extreme conditions in Chapters 1 and 2 and quantum chemistry in Chapters 3–5.

Chapter 1 focuses on the effects of high pressure on chemical bonding, as pressure is a variable with a range of observed values spanning 50 orders of magnitude between interstellar space and the interior of a neutron star. Andreas Hermann reviews the responses of materials to pressure and provides an important tutorial describing appropriate modeling approaches applicable to the study of high-pressure phases. Applications of computational chemistry to investigate mechanical, electronic, and spectroscopic properties of molecules round out the chapter.

Chapter 2, by Mitchell Wood, Mathew Cherukara, Edwin Antillon, and Alejandro Strachan, focuses on the behavior of materials under the extreme conditions of stress and temperature induced by shock loading. Of particular benefit to the reader is that the authors present examples that can be reproduced using an online simulation tool accessible using a standard web browser that runs on computing resources at Purdue University. The authors introduce the topic through MD simulations of shockwaves in solids. This tutorial aids in understanding material responses to shock such as plastic deformation and failure. Additional attention is paid to shock-induced phase transformations, synthesis, and chemical reactions.

In Chapter 3, Balazs Nagy and Frank Jensen provide a thorough and informative review on basis sets in quantum chemistry. This chapter will be an excellent resource for graduate students new to the field of computational chemistry faced with choosing methods for their first quantum calculations and for the experienced researcher who wants to identify the most suitable property basis set for a new research question. This chapter provides a basic introduction to the basis set approximation and desirable features of a basis set before enumerating the types of basis functions in common use today. Performance comparisons of basis set size, function type, general versus segmented contraction, and core potential size provide evidence-based guidance in the selection of suitable basis sets, which the authors augment with advice for practitioners regarding the compromise between accuracy and efficiency.

Systems with unpaired electrons offer particular challenges to the computational chemistry community. Anna Krylov details these challenges and reviews methods best suited to address each of these challenges in Chapter 4. Examples illustrate applications of computational methods to simple high-spin states, charge-transfer systems, di- and triradicals, and excited states. Computation of molecular properties for comparison to spectroscopic observables has been reviewed due to the importance of such comparisons in validating and benchmarking the suitability of various methods for use on open-shell systems.

Chapter 5 rounds out the quantum chemistry theme by discussing machine learning to overcome efficiency problems hindering quantum chemical methods in the search of chemical space of synthetically accessible species in a high-throughput manner. Raghunathan Ramakrishnan and Anatole von Lilienfeld review appropriate molecular representations that relate to quantum mechanical inputs, and the application of supervised machine learning methods to generalize from large training sets of molecules and their associated quantum mechanical results to previously unobserved examples that comprise a test set or out-of-sample set. This chapter demonstrates that even quantum chemistry is moving into the regime of Big Data, in which thousands of predictions can rapidly be made using the trained machine learning model.

Chapter 6, by Dmitrii Makarov, will introduce many readers to the use of master equations to describe the time evolution of a system, with probabilistic treatment of transitions between potential states of the system. Systems modeled using master equations might be simply represented by two states, such as folded and unfolded protein conformations, or might be represented by a much more complex network of states. The use of master equations to investigate kinetic properties for both classical and quantum systems using kinetic Monte Carlo (KMC) is reviewed, and the difference in the physical meaning of the KMC scheme in these two cases is articulated.

Chapter 7 introduces a new way for chemists in general, and computational chemists specifically, to think about symmetry. Symmetry provides chemists with an important mechanism to describe chemical structures and computational chemists with simplifications that improve computing efficiency. However, we often assume ideal symmetry for chemical systems that typically deviate from the ideal case and electronic structure changes may accompany those deviations from ideal symmetry. This train of thought demonstrates the importance of being able to quantify how well a given chemical system matches various ideal symmetries. Pere Alemany, David Casanova, Santiago Alvarez, Chaim Dryzun, and David Avnir present continuous symmetry measures (CSMs) as this quantitative tool and demonstrate continuous symmetry measures in the context of the atomic framework, matrices and operators, functions, and irreproducible representations. Applications of CSMs demonstrate the value in shifting from a binary representation of symmetry (symmetric or not) toward a quantitative reflection of the degree of symmetry.

The value of Reviews in Computational Chemistry stems from the pedagogically driven reviews that have made this ongoing book series so popular. We are grateful to the authors featured in this volume as well as to the authors that contributed to prior volumes.

Volumes of Reviews in Computational Chemistry are available in an online form through Wiley InterScience. Please consult the Web (http://www.interscience.wiley.com/onlinebooks) or contact [email protected] for the latest information.

Abby L. Parrill

Memphis

Kenny B. Lipkowitz

Washington

August 2016

CONTRIBUTORS TO PREVIOUS VOLUMES

Volume 1 (1990)

David Feller andErnest R. Davidson, Basis Sets for Ab Initio Molecular Orbital Calculations and Intermolecular Interactions

James J. P. Stewart, Semiempirical Molecular Orbital Methods

Clifford E. Dykstra, Joseph D. Augspurger, Bernard Kirtman, and David J. Malik, Properties of Molecules by Direct Calculation

Ernest L. Plummer, The Application of Quantitative Design Strategies in Pesticide Design

Peter C. Jurs, Chemometrics and Multivariate Analysis in Analytical Chemistry

Yvonne C. Martin, Mark G. Bures, and Peter Willett, Searching Databases of Three-Dimensional Structures

Paul G. Mezey, Molecular Surfaces

Terry P. Lybrand, Computer Simulation of Biomolecular Systems Using Molecular Dynamics and Free Energy Perturbation Methods

Donald B. Boyd, Aspects of Molecular Modeling

Donald B. Boyd, Successes of Computer-Assisted Molecular Design

Ernest R. Davidson, Perspectives on Ab Initio Calculations

Volume 2 (1991)

Andrew R. Leach, A Survey of Methods for Searching the Conformational Space of Small and Medium-Sized Molecules

John M. Troyer and Fred E. Cohen, Simplified Models for Understanding and Predicting Protein Structure

J. Phillip Bowen and Norman L. Allinger, Molecular Mechanics: The Art and Science of Parameterization

Uri Dinur and Arnold T. Hagler, New Approaches to Empirical Force Fields

Steve Scheiner, Calculating the Properties of Hydrogen Bonds by Ab Initio Methods

Donald E. Williams, Net Atomic Charge and Multipole Models for the Ab Initio Molecular Electric Potential

Peter Politzer and Jane S. Murray, Molecular Electrostatic Potentials and Chemical Reactivity

Michael C. Zerner, Semiempirical Molecular Orbital Methods

Lowell H. Hall and Lemont B. Kier, The Molecular Connectivity Chi Indexes and Kappa Shape Indexes in Structure–Property Modeling

I. B. Bersuker and A. S. Dimoglo, The Electron-Topological Approach to the QSAR Problem

Donald B. Boyd, The Computational Chemistry Literature

Volume 3 (1992)

Tamar Schlick, Optimization Methods in Computational Chemistry

Harold A. Scheraga, Predicting Three-Dimensional Structures of Oligopeptides

Andrew E. Torda and Wilfred F. van Gunsteren, Molecular Modeling Using NMR Data

David F. V. Lewis, Computer-Assisted Methods in the Evaluation of Chemical Toxicity

Volume 4 (1993)

Jerzy Cioslowski, Ab Initio Calculations on Large Molecules: Methodology and Applications

Michael L. McKee and Michael Page, Computing Reaction Pathways on Molecular Potential Energy Surfaces

Robert M. Whitnell and Kent R. Wilson, Computational Molecular Dynamics of Chemical Reactions in Solution

Roger L. DeKock, Jeffry D. Madura, Frank Rioux, and Joseph Casanova, Computational Chemistry in the Undergraduate Curriculum

Volume 5 (1994)

John D. Bolcer and Robert B. Hermann, The Development of Computational Chemistry in the United States

Rodney J. Bartlett and John F. Stanton, Applications of Post-Hartree–Fock Methods: A Tutorial

Steven M. Bachrach, Population Analysis and Electron Densities from Quantum Mechanics

Jeffry D. Madura, Malcolm E. Davis, Michael K. Gilson, Rebecca C. Wade, Brock A. Luty, and J. Andrew McCammon, Biological Applications of Electrostatic Calculations and Brownian Dynamics Simulations

K. V. Damodaran and Kenneth M. Merz Jr., Computer Simulation of Lipid Systems

Jeffrey M. Blaney and J. Scott Dixon, Distance Geometry in Molecular Modeling

Lisa M. Balbes, S. Wayne Mascarella, and Donald B. Boyd, A Perspective of Modern Methods in Computer-Aided Drug Design

Volume 6 (1995)

Christopher J. Cramer and Donald G. Truhlar, Continuum Solvation Models: Classical and Quantum Mechanical Implementations

Clark R. Landis, Daniel M. Root, and Thomas Cleveland, Molecular Mechanics Force Fields for Modeling Inorganic and Organometallic Compounds

Vassilios Galiatsatos, Computational Methods for Modeling Polymers: An Introduction

Rick A. Kendall, Robert J. Harrison, Rik J. Littlefield, and Martyn F. Guest, High Performance Computing in Computational Chemistry: Methods and Machines

Donald B. Boyd, Molecular Modeling Software in Use: Publication Trends

Eiji Ōsawa and Kenny B. Lipkowitz, Appendix: Published Force Field Parameters

Volume 7 (1996)

Geoffrey M. Downs and Peter Willett, Similarity Searching in Databases of Chemical Structures

Andrew C. Good and Jonathan S. Mason, Three-Dimensional Structure Database Searches

Jiali Gao, Methods and Applications of Combined Quantum Mechanical and Molecular Mechanical Potentials

Libero J. Bartolotti and Ken Flurchick, An Introduction to Density Functional Theory

Alain St-Amant, Density Functional Methods in Biomolecular Modeling

Danya Yang and Arvi Rauk, The A Priori Calculation of Vibrational Circular Dichroism Intensities

Donald B. Boyd, Appendix: Compendium of Software for Molecular Modeling

Volume 8 (1996)

Zdenek Slanina, Shyi-Long Lee, and Chin-hui Yu, Computations in Treating Fullerenes and Carbon Aggregates

Gernot Frenking, Iris Antes, Marlis Böhme, Stefan Dapprich, Andreas W. Ehlers, Volker Jonas, Arndt Neuhaus, Michael Otto, Ralf Stegmann, Achim Veldkamp, and Sergei F. Vyboishchikov, Pseudopotential Calculations of Transition Metal Compounds: Scope and Limitations

Thomas R. Cundari, Michael T. Benson, M. Leigh Lutz, and Shaun O. Sommerer, Effective Core Potential Approaches to the Chemistry of the Heavier Elements

Jan Almlöf and Odd Gropen, Relativistic Effects in Chemistry

Donald B. Chesnut, The Ab Initio Computation of Nuclear Magnetic Resonance Chemical Shielding

Volume 9 (1996)

James R. Damewood, Jr., Peptide Mimetic Design with the Aid of Computational Chemistry

T. P. Straatsma, Free Energy by Molecular Simulation

Robert J. Woods, The Application of Molecular Modeling Techniques to the Determination of Oligosaccharide Solution Conformations

Ingrid Pettersson and Tommy Liljefors, Molecular Mechanics Calculated Conformational Energies of Organic Molecules: A Comparison of Force Fields

Gustavo A. Arteca, Molecular Shape Descriptors

Volume 10 (1997)

Richard Judson, Genetic Algorithms and Their Use in Chemistry

Eric C. Martin, David C. Spellmeyer, Roger E. Critchlow Jr., and Jeffrey M. Blaney, Does Combinatorial Chemistry Obviate Computer-Aided Drug Design?

Robert Q. Topper, Visualizing Molecular Phase Space: Nonstatistical Effects in Reaction Dynamics

Raima Larter and Kenneth Showalter, Computational Studies in Nonlinear Dynamics

Stephen J. Smith and Brian T. Sutcliffe, The Development of Computational Chemistry in the United Kingdom

Volume 11 (1997)

Mark A. Murcko, Recent Advances in Ligand Design Methods

David E. Clark, Christopher W. Murray, and Jin Li, Current Issues in De Novo Molecular Design

Tudor I. Oprea and Chris L. Waller, Theoretical and Practical Aspects of Three-Dimensional Quantitative Structure–Activity Relationships

Giovanni Greco, Ettore Novellino, and Yvonne Connolly Martin, Approaches to Three-Dimensional Quantitative Structure–Activity Relationships

Pierre-Alain Carrupt, Bernard Testa, and Patrick Gaillard, Computational Approaches to Lipophilicity: Methods and Applications

Ganesan Ravishanker, Pascal Auffinger, David R. Langley, Bhyravabhotla Jayaram, Matthew A. Young, and David L. Beveridge, Treatment of Counterions in Computer Simulations of DNA

Donald B. Boyd, Appendix: Compendium of Software and Internet Tools for Computational Chemistry

Volume 12 (1998)

Hagai Meirovitch, Calculation of the Free Energy and the Entropy of Macromolecular Systems by Computer Simulation

Ramzi Kutteh and T. P. Straatsma, Molecular Dynamics with General Holonomic Constraints and Application to Internal Coordinate Constraints

John C. Shelley and Daniel R. Bérard, Computer Simulation of Water Physisorption at Metal–Water Interfaces

Donald W. Brenner, Olga A. Shenderova, and Denis A. Areshkin, Quantum-Based Analytic Interatomic Forces and Materials Simulation

Henry A. Kurtz and Douglas S. Dudis, Quantum Mechanical Methods for Predicting Nonlinear Optical Properties

Chung F. Wong, Tom Thacher, and Herschel Rabitz, Sensitivity Analysis in Biomolecular Simulation

Paul Verwer and Frank J. J. Leusen, Computer Simulation to Predict Possible Crystal Polymorphs

Jean-Louis Rivail and Bernard Maigret, Computational Chemistry in France: A Historical Survey

Volume 13 (1999)

Thomas Bally and Weston Thatcher Borden, Calculations on Open-Shell Molecules: A Beginner's Guide

Neil R. Kestner and Jaime E. Combariza, Basis Set Superposition Errors: Theory and Practice

James B. Anderson, Quantum Monte Carlo: Atoms, Molecules, Clusters, Liquids, and Solids

Anders Wallqvist and Raymond D. Mountain, Molecular Models of Water: Derivation and Description

James M. Briggs and Jan Antosiewicz, Simulation of pH-dependent Properties of Proteins Using Mesoscopic Models

Harold E. Helson, Structure Diagram Generation

Volume 14 (2000)

Michelle Miller Francl and Lisa Emily Chirlian, The Pluses and Minuses of Mapping Atomic Charges to Electrostatic Potentials

T. Daniel Crawford and Henry F. Schaefer III, An Introduction to Coupled Cluster Theory for Computational Chemists

Bastiaan van de Graaf, Swie Lan Njo, and Konstantin S. Smirnov, Introduction to Zeolite Modeling

Sarah L. Price, Toward More Accurate Model Intermolecular Potentials for Organic Molecules

Christopher J. Mundy, Sundaram Balasubramanian, Ken Bagchi, Mark E. Tuckerman, Glenn J. Martyna, and Michael L. Klein, Nonequilibrium Molecular Dynamics

Donald B. Boyd and Kenny B. Lipkowitz, History of the Gordon Research Conferences on Computational Chemistry

Mehran Jalaie and Kenny B. Lipkowitz, Appendix: Published Force Field Parameters for Molecular Mechanics, Molecular Dynamics, and Monte Carlo Simulations

Volume 15 (2000)

F. Matthias Bickelhaupt and Evert Jan Baerends, Kohn-Sham Density Functional Theory: Predicting and Understanding Chemistry

Michael A. Robb, Marco Garavelli, Massimo Olivucci, and Fernando Bernardi, A Computational Strategy for Organic Photochemistry

Larry A. Curtiss, Paul C. Redfern, and David J. Frurip, Theoretical Methods for Computing Enthalpies of Formation of Gaseous Compounds

Russell J. Boyd, The Development of Computational Chemistry in Canada

Volume 16 (2000)

Richard A. Lewis, Stephen D. Pickett, and David E. Clark, Computer-Aided Molecular Diversity Analysis and Combinatorial Library Design

Keith L. Peterson, Artificial Neural Networks and Their Use in Chemistry

Jörg-Rüdiger Hill, Clive M. Freeman, and Lalitha Subramanian, Use of Force Fields in Materials Modeling

M. Rami Reddy, Mark D. Erion, and Atul Agarwal, Free Energy Calculations: Use and Limitations in Predicting Ligand Binding Affinities

Volume 17 (2001)

Ingo Muegge and Matthias Rarey, Small Molecule Docking and Scoring

Lutz P. Ehrlich and Rebecca C. Wade, Protein–Protein Docking

Christel M. Marian, Spin–Orbit Coupling in Molecules

Lemont B. Kier, Chao-Kun Cheng, and Paul G. Seybold, Cellular Automata Models of Aqueous Solution Systems

Kenny B. Lipkowitz and Donald B. Boyd, Appendix: Books Published on the Topics of Computational Chemistry

Volume 18 (2002)

Geoff M. Downs and John M. Barnard, Clustering Methods and Their Uses in Computational Chemistry

Hans-Joachim Böhm and Martin Stahl, The Use of Scoring Functions in Drug Discovery Applications

Steven W. Rick and Steven J. Stuart, Potentials and Algorithms for Incorporating Polarizability in Computer Simulations

Dmitry V. Matyushov and Gregory A. Voth, New Developments in the Theoretical Description of Charge-Transfer Reactions in Condensed Phases

George R. Famini and Leland Y. Wilson, Linear Free Energy Relationships Using Quantum Mechanical Descriptors

Sigrid D. Peyerimhoff, The Development of Computational Chemistry in Germany

Donald B. Boyd and Kenny B. Lipkowitz, Appendix: Examination of the Employment Environment for Computational Chemistry

Volume 19 (2003)

Robert Q. Topper, David, L. Freeman, Denise Bergin, and Keirnan R. LaMarche, Computational Techniques and Strategies for Monte Carlo Thermodynamic Calculations, with Applications to Nanoclusters

David E. Smith and Anthony D. J. Haymet, Computing Hydrophobicity

Lipeng Sun and William L. Hase, Born–Oppenheimer Direct Dynamics Classical Trajectory Simulations

Gene Lamm, The Poisson–Boltzmann Equation

Volume 20 (2004)

Sason Shaik and Philippe C. Hiberty, Valence Bond Theory: Its History, Fundamentals and Applications. A Primer

Nikita Matsunaga and Shiro Koseki, Modeling of Spin Forbidden Reactions

Stefan Grimme, Calculation of the Electronic Spectra of Large Molecules

Raymond Kapral, Simulating Chemical Waves and Patterns

Costel Sârbu and Horia Pop, Fuzzy Soft-Computing Methods and Their Applications in Chemistry

Sean Ekins and Peter Swaan, Development of Computational Models for Enzymes, Transporters, Channels and Receptors Relevant to ADME/Tox

Volume 21 (2005)

Roberto Dovesi, Bartolomeo Civalleri, Roberto Orlando, Carla Roetti, and Victor R. Saunders, Ab Initio Quantum Simulation in Solid State Chemistry

Patrick Bultinck, Xavier Gironés, and Ramon Carbó-Dorca, Molecular Quantum Similarity: Theory and Applications

Jean-Loup Faulon, Donald P. Visco, Jr., and Diana Roe, Enumerating Molecules

David J. Livingstone and David W. Salt, Variable Selection-Spoilt for Choice

Nathan A. Baker, Biomolecular Applications of Poisson–Boltzmann Methods

Baltazar Aguda, Georghe Craciun, and Rengul Cetin-Atalay, Data Sources and Computational Approaches for Generating Models of Gene Regulatory Networks

Volume 22 (2006)

Patrice Koehl, Protein Structure Classification

Emilio Esposito, Dror Tobi, and Jeffry Madura, Comparative Protein Modeling

Joan-Emma Shea, Miriam Friedel, and Andrij Baumketner, Simulations of Protein Folding

Marco Saraniti, Shela Aboud, and Robert Eisenberg, The Simulation of Ionic Charge Transport in Biological Ion Channels: An Introduction to Numerical Methods

C. Matthew Sundling, Nagamani Sukumar, Hongmei Zhang, Curt Breneman, and Mark Embrechts, Wavelets in Chemistry and Chemoinformatics

Volume 23 (2007)

Christian Ochsenfeld, Jörg Kussmann, and Daniel Lambrecht, Linear Scaling in Quantum Chemistry

Spiridoula Matsika, Conical Intersections in Molecular Systems

Antonio Fernandez-Ramos, Benjamin Ellingson, Bruce Garrett, and Donald Truhlar, Variational Transition State Theory with Multidimensional Tunneling

Roland Faller, Coarse Grain Modeling of Polymers

Jeffrey Godden and Jürgen Bajorath, Analysis of Chemical Information Content using Shannon Entropy

Ovidiu Ivanciuc, Applications of Support Vector Machines in Chemistry

Donald Boyd, How Computational Chemistry Became Important in the Pharmaceutical Industry

Volume 24 (2007)

Martin Schoen and Sabine H. L. Klapp, Nanoconfined Fluids. Soft Matter Between Two and Three Dimensions

Volume 25 (2007)

Wolfgang Paul, Determining the Glass Transition in Polymer Melts

Nicholas J. Mosey and Martin H. Müser, Atomistic Modeling of Friction

Jeetain Mittal, William P. Krekelberg, Jeffrey R. Errington, and Thomas M. Truskett, Computing Free Volume, Structured Order, and Entropy of Liquids and Glasses

Laurence E. Fried, The Reactivity of Energetic Materials at Extreme Conditions

Julio A. Alonso, Magnetic Properties of Atomic Clusters of the Transition Elements

Laura Gagliardi, Transition Metal- and Actinide-Containing Systems Studied with Multiconfigurational Quantum Chemical Methods

Hua Guo, Recursive Solutions to Large Eigenproblems in Molecular Spectroscopy and Reaction Dynamics

Hugh Cartwright, Development and Uses of Artificial Intelligence in Chemistry

Volume 26 (2009)

C. David Sherrill, Computations of Noncovalent π Interactions

Gregory S. Tschumper, Reliable Electronic Structure Computations for Weak Noncovalent Interactions in Clusters

Peter Elliott, Filip Furche, and Kieron Burke, Excited States from Time-Dependent Density Functional Theory

Thomas Vojta, Computing Quantum Phase Transitions

Thomas L. Beck, Real-Space Multigrid Methods in Computational Chemistry

Francesca Tavazza, Lyle E. Levine, and Anne M. Chaka, Hybrid Methods for Atomic-Level Simulations Spanning Multi-Length Scales in the Solid State

Alfredo E. Cárdenas and Eric Bath, Extending the Time Scale in Atomically Detailed Simulations

Edward J. Maginn, Atomistic Simulation of Ionic Liquids

Volume 27 (2011)

Stefano Giordano, Allessandro Mattoni, and Luciano Colombo, Brittle Fracture: From Elasticity Theory to Atomistic Simulations

Igor V. Pivkin, Bruce Caswell, and George Em Karniadakis, Dissipative Particle Dynamics

Peter G. Bolhuis and Christoph Dellago, Trajectory-Based Rare Event Simulation

Douglas L. Irving, Understanding Metal/Metal Electrical Contact Conductance from the Atomic to Continuum Scales

Max L. Berkowitz and James Kindt, Molecular Detailed Simulations of Lipid Bilayers

Sophya Garaschuk, Vitaly Rassolov, and Oleg Prezhdo, Semiclassical Bohmian Dynamics

Donald B. Boyd, Employment Opportunities in Computational Chemistry

Kenny B. Lipkowitz, Appendix: List of Computational Molecular Scientists

Volume 28 (2015)

Giovanni Bussi and Davide Branduardi, Free-Energy Calculations with Metadynamics: Theory and Practice

Yue Shi, Pengyu Ren, Michael Schnieders, and Jean-Philip Piquemal, Polarizable Force Fields for Biomolecular Modeling

Clare-Louise Towse and Valerie Daggett, Modeling Protein Folding Pathways

Joël Janin, Shoshana J. Wodak, Marc F. Lensink, and Sameer Velankar, Assessing Structural Predictions of Protein-Protein Recognition: The CAPRI Experiment

C. Heath Turner, Zhongtao Zhang, Lev D. Gelb, and Brett I. Dunlap, Kinetic Monte Carlo Simulation of Electrochemical Systems

Ilan Benjamin, Reactivity and Dynamics at Liquid Interfaces

John S. Tse, Computational Techniques in the Study of the Properties of Clathrate Hydrates

John M. Herbert, The Quantum Chemistry of Loosely Bound Electrons

Volume 29 (2016)

Gino A. DiLabio and Alberto Otero-de-la-Roza, Noncovalent Interactions in Density Functional Theory

Akbar Salam, Long-Range Interparticle Interactions: Insights from Molecular Quantum Electrodynamic (QED) Theory

Joshua Pottel and Nicolas Moitessier, Efficient Transition State Modeling Using Molecular Mechanics Force Fields for the Everyday Chemistry

Tim Mueller, Aaron Gilad Kusne, and Rampi Ramprasad, Machine Learning in Materials Science: Recent Progress and Emerging Applications

Eva Zurek, Discovering New Materials via A Priori Crystal Structure Prediction

Alberto Ambrosetti and Pier Luigi Silvestrelli, Introduction to Maximally Localized Wannier Functions

Zhanyong Guo and Dieter Cremer, Methods for Rapid and Automated Description of Proteins: Protein Structure, Protein Similarity, and Protein Folding

CHAPTER 1

CHEMICAL BONDING AT HIGH PRESSURE

Andreas Hermann

School of Physics and Astronomy, The University of Edinburgh, Edinburgh, United Kingdom

HIGH-PRESSURE SCIENCE

Motivation

We, as humans, are very accustomed to the conditions of atmospheric pressure. By climbing high mountains, we can experience reduced pressure conditions (down to about c01-math-0001 atmosphere at the top of Mt Everest), and by diving down into the sea, we can experience high-pressure conditions (up to about 20 atmospheres for world-record free divers). Our experiences of pressure are thus restricted to a range of 1–2 orders of magnitude. Yet this is simply a consequence of our environmental conditions, and pressure is in fact a variable with one of the largest observable ranges in nature—about 50 orders of magnitude separate the pressure in empty interstellar space (at c01-math-0002 bar) from that at the center of a neutron star (at c01-math-0003 bar). Closer to home, the pressure at the center of Earth is about 360 Gigapascals (GPa), which is 3.6 Mbar.

These examples hint at some of the scientific fields interested in high-pressure science. There is also a fundamental interest in how matter interacts when it is compressed—our entire chemical intuition is built around how molecular and extended compounds form at atmospheric pressure. It is not clear at all (and, as we shall see, often wrong) that the same rules that guide structure formation are valid if the constituent atoms were, say, at separations 50% smaller than we are used to. In the geo- and planetary science community, for example, the properties of minerals can be very different at the conditions found in Earth's core than when we study them in samples collected on the surface. There is also a significant interest in exploiting high pressure to synthesize new materials with interesting properties—pressure can change reaction barriers and relative stabilities of different allotropes of a material, and phase transitions under pressure are very commonplace. The challenge in this application is to recover the synthesized product back to atmospheric conditions, and such efforts therefore tend to concentrate on covalently bound systems; the high-pressure production of synthetic diamond is a prime example: it involves significant structural changes at the atomic level and the transformation from c01-math-0004 - to c01-math-0005 -bonded carbon.¹ We should mention that there is strong interest from the defense industry in understanding high-pressure effects—blast waves and shock waves from impacts are some of the primary results of explosives, and understanding their behavior and materials' responses to them is of natural concern to defense agencies around the world. In a crude generalization, dynamic compression research is often strong in countries that build large bombs.

Pressure in Industrial Processes

We mentioned the synthesis of diamonds in high-pressure chambers. There are other much more relevant industry processes that rely on elevated pressures. Arguably, the most important is the Haber–Bosch process, which produces about 450 million tons of ammonia-based fertilizer, annually, worldwide. The dramatic increase in crop yields enabled by the Haber–Bosch process has allowed the population explosion on Earth; about 80% of the nitrogen atoms in an average human's body have been inside a Haber–Bosch plant.², ³ The industrial process itself, the conversion c01-math-0006 + 3H c01-math-0007 c01-math-0008 c01-math-0009 , relies on high pressure and temperature, the former usually being around 200 bar. Pressures in large-scale processes, chemical or otherwise, cannot be much larger than this, in order to allow high throughputs in large-volume vessels. This is the case, for example, in coal pyrolysis and oil refinement, which use pressures that are (by the standards of this review) rather low. However, one can conversely define what high pressure is, as the conditions where something interesting or unexpected happens: a chemical reaction, a structural transformation, etc. In that sense, tens or hundreds of bars can be just as exciting in one context as millions of bars in another.

High-Pressure Experiments

The field of high-pressure laboratory physics owes most of its early successes to Percy W. Bridgman, recipient of the 1946 Nobel Prize in physics for his pioneering work at high pressures. He developed the first high-pressure apparatus, which enabled him to reach 10 GPa in the 1920s, and developments since then have increased the pressure range accessible to so-called static compression in laboratory experiments up to 1 TPa, or 1000 GPa—several times the pressure at the center of the Earth.⁴ An alternative method to generate pressure is through the creation of shock waves traveling through the sample material, and such dynamic compression has been possible since the 1950s. In this section, we discuss briefly the different methods available to generate high pressure, and the consequences this has on making measurements; these, in turn, affect the requirements put on computational approaches.

Static Pressure Generation

Pressure is force per area, so to exert high pressure on a sample one needs to maximize the force and/or minimize the area said force acts upon. Both avenues will test the material strength of the entire apparatus, but mostly the parts that are in direct contact with the sample. To transmit the pressure without loss to the sample, the sample enclosure is made of very hard and incompressible materials. Bridgman's own apparatus used two opposed anvils made of tungsten carbide (WC), which are brought together in a piston and compress the sample in the middle by operating a large lever. One of his early breakthroughs was the development of the Bridgman seal in the piston that would be at higher pressure than the sample chamber itself and therefore prevent any leakage of sample material.

Bridgman's main experimental observables were macroscopic: compressibilities (volume discontinuities at phase transitions), viscosities, electrical and thermal conductivities. To do X-ray diffraction measurements on the sample, the enclosing cylinder holding the pistons, anvils, and sample must be transparent to X-ray radiation. This is how diamonds got first introduced into high-pressure science, and the split diamond cell by Lawson and Tang was the first pressure cell that allowed collection of X-ray data from the sample.⁵ Developed in 1950, it consists of two diamond halves with a cylindrical tube bored along their touching surfaces. In the tube, the sample would be compressed by thin WC wire pistons. The weakest point of the setup is obviously the huge interfacial area between the diamond halves. John C. Jamieson, Lawson's student, and (independently) van Valkenburg and Weir at the National Bureau of Standards, then developed the drilled diamond cell: a large single crystal of diamond had a thin tube drilled into it, which took the sample and the WC pistons.¹, ⁶ These pressure cells were able to reach pressures of 2–3 GPa.

Various improvements could be made to the cells, but the need for (and large cost of) large single-crystal diamonds and the difficulty in drilling accurate tubes would limit their applicability. Therefore, instead of using diamond as the confinement material of the cell, why not use it as the active pressure-generating component? This idea resulted in the diamond anvil cell (DAC), the most versatile instrument of high-pressure science for the last 50 years. The groups around Jamieson and Lawson as well as van Valkenburg and Weir developed DACs independently at their respective institutions in the late 1950s. They consisted of opposing anvils made of beveled diamonds which, when pushed together through screw or lever setups, crushed a sample at a small contact point in between.⁷–⁹ These cells could immediately reach pressures around 10 GPa. Due to diamond's transparency, high-pressure phase transitions could for the first time be observed visually and also allowed all kinds of spectroscopic analyses (see the following discussion). By using a gasket (usually a thin metal sheet with a hole) to hold the sample and a pressure-mediating medium, hydrostatic or nearly hydrostatic pressure conditions could be generated, and single-crystal samples (instead of powders) could be studied in diffraction experiments (Figure 1).

Figure 1 Schematics of static high-pressure cells. Left: Piston cylinder cell with Bridgman seal (dark gray); diamond anvil cell (DAC); and double-stage DAC. In all cases, samples are shown in black.

Since the inception of the DAC, various modifications were introduced to increase the maximum pressure attainable, manipulate sample conditions (like temperature and external fields), and perform different types of measurements (like neutron diffraction or electrical conductivity). A double-stage DAC has been introduced that can approach pressures of 1000 GPa by placing a sample between microscopic hemispheres of superhard nanodiamond, which are in turn placed inside a conventional DAC.¹⁰, ¹¹ A dynamic DAC has been developed that reversibly and at high rates, through electromechanical actuators, changes the load profile on a sample, thus allowing the study of dynamical processes in a quasi-static background.¹² Laser- and resistive heating of DACs allow the study of materials under combined high-pressure and high-temperature conditions. In addition, DACs developed for neutron diffraction measurements enable detailed studies of light element and magnetic materials, almost up to 100 GPa.¹³, ¹⁴

Dynamic Pressure Generation

An entirely different way to generate high pressures is in dynamical processes, usually by generation of shock waves. This has been used as an experimental technique since about the 1950s. A shock wave traveling through a sample will, behind the shock front, create a region of high pressure and high temperature.¹⁵, ¹⁶ The latter cannot be avoided but can be tuned to some degree through the design of the wave front. Dynamic compression events generally last about 1 c01-math-0010 s–1 ps and can reach pressures in the TPa or even Gbar regime. Shock waves are usually generated in one of the following three ways: (i) with explosive acceleration of projectiles or flyers—where a metal plate is accelerated by a chemical explosion and impacts at high velocity on a target containing the sample (the sample might be attached to a coupler material to enable a cleaner propagation of the shock wave and to achieve higher pressures in the sample); (ii) with capacitor discharges, where huge current pulses create magnetic acceleration of a metal plate that forms part of the circuit; or (iii) with pulses of electromagnetic radiation (for instance from strong laser sources) that transiently create a plasma on the surface of the target, the expansion of which drives a pressure wave into the target (Figure 2).

Figure 2 Schematics of shock-wave generation. From left: chemical (guns), electrical discharge (capacitor banks), or optical means (laser-generated plasmas). Flyer plates are drawn in black, shocked and unshocked sample material are shown in gray and white, and the direction of flight and the shock wave is indicated by arrows.

Experimental Probes

We have already alluded to specific measurements in high-pressure experiments earlier—as in other scientific fields, technological advances to manipulate samples beget developments of diagnostics, and vice versa. The ability to describe either through appropriate computational approaches is then extremely important. In both static and dynamic compression experiments, a wide suite of diagnostics is used routinely. Diffraction experiments (using X-rays or neutrons) can solve structures of high-pressure phases; measurements include diffraction patterns from the crystalline or magnetic structure, inelastic scattering, and structure factors in amorphous materials or liquids. Hence, it is paramount to have computational approaches that describe materials' structures at given pressure and temperature conditions well. Spectroscopic analyses are widely used (utilizing infrared (IR), Raman, Mössbauer, X-ray, and occasionally nuclear magnetic resonance (NMR) spectroscopy) and sometimes, for very small samples, these are preferred to diffraction experiments. The vibrational properties of materials should thus be accessible from calculations, as should their electronic structure. Less often, conductivity (normal and Hall), magnetic susceptibilities, and optical properties (linear and nonlinear) are measured; again, information about the electronic structure of relevant high-pressure phases from accurate computations is important.

In all cases, computations are certainly helpful to interpret experimental results. Equally, they should be able to motivate further experiments—either by predicting intriguing properties of confirmed high-pressure phases or by predicting completely new high-pressure phase transitions and their respective properties.

PRESSURE EFFECTS IN MATERIALS

External pressure leads to a variety of interesting and, at first sight, unexpected effects in materials, which oftentimes involve changes to the chemical bonding of their constituents. We highlight here some examples of those effects, either originating in experiment and thus motivating atomistic computations for more insights or originating in calculations and thus motivating experimental studies.

Close Packing and Metallicity—or Not

There is a long-standing notion that if any material is compressed (and kept reasonably cold), it will eventually turn into a close-packed metal. The argument goes that whatever a material's bonding characteristics at ambient conditions, the much reduced interatomic separations at high pressure will enforce such strong overlaps of valence electron orbitals that the electrons will completely delocalize, forming a degenerate Fermi gas. In response, the arrangement of the strongly screened nuclei would then strive to maximize the packing density.¹⁷–²⁰

The idea of increased coordination under pressure has merit and is very often found in molecular crystals (which tend to polymerize when compressed) and systems with strong ionic bonding. Examples for the latter include minerals, where c01-math-0011 polyhedra show increases such as c01-math-0012 , while examples of the former include water, nitrogen, carbon dioxide, or the halogens—all of which form extended network structures under pressure, when the intermolecular separations approach the intramolecular bond distances. In case of halogens, such polymerization coincides with (actually, is slightly preceded by) a metallization of the compounds. In molecular systems with charge transfer, the polymerized state often retains an electronic band gap to much higher pressures.

However, high-pressure science has also shown us that nature seemingly wants to avoid the simple metallic state, and a slew of rather unexpected phases with unusual chemical, structural, and electronic properties have been discovered—or at least predicted in electronic structure calculations. Consider the simple alkali metals: at ambient conditions, all of them (from lithium to cesium) crystallize in a body-centered cubic (bcc) structure and, upon compression, transform into the close-packed face-centered cubic (fcc) structure (transition pressures vary from 2.4 GPa in cesium to 65 GPa in sodium).²¹ Conventionally, this should be the end of high-pressure effects. But, quite to the contrary, the alkalis exhibit extraordinary polymorphism at high pressures, arguably headlined by the transformation of sodium (by all accounts a very good metal) into an insulating phase above 200 GPa.²² Not less intriguing is the presence of melting point maxima in all alkalis²³–²⁶—which infers that at high pressures and temperatures, the alkali liquids are denser than the close-packed solids; and the appearance of complex crystal structures such as incommensurate host–guest phases, at high pressures,²⁷–³² which are accompanied by drastic changes of the electronic properties and come with reduced atomic coordination. Figure 3 shows one of those phases, Rb-IV, and also illustrates that this effect of complex structure formation is not limited to the alkali metals.

Figure 3 (a) Incommensurate host–guest phase Rb-IV at 16.8 GPa; (b) Incommensurate phase Ca-VII at 241 GPa. Guest atoms arrange in channels provided by the host, which is drawn as connected network.

Neither the occurrence of host–guest structures nor reduction of coordination numbers is a prerogative of the elements. LiB, which could be a Zintl compound, instead forms as slightly boron-deficient c01-math-0013 with c01-math-0014 , and with incommensurate boron chains running along channels in a hexagonal lithium host network.³³–³⁵ Under pressure, the boron chains form graphitic sheets (increasing coordination), which was predicted in calculations and recently confirmed in experiment.³⁴–³⁷ On the other end, hydrogen-bonded hydroxyl groups in potassium and rubidium hydroxides, KOH and RbOH, reduce network dimensionality under pressure: at ambient conditions, c01-math-0015 groups form infinite chains, while at pressure, they localize in well-separated (OH c01-math-0016 ) c01-math-0017 units.³⁸, ³⁹

Hydrogen and Hydrogen-Rich Compounds

One of the holy grails of high-pressure science, certainly among solid-state physicists, is the promised atomic and metallic phase of compressed hydrogen. A crystalline solid of hydrogen atoms, which should be one of the simplest condensed systems, has stimulated researchers' imagination (and withstood their most valiant experimental efforts) for almost a century: from the first proposal of metallic hydrogen by Wigner and Huntington,¹⁷ via Ashcroft's prediction of superconductivity in hydrogen's metallic phase,⁴⁰ the field has seen a plethora of electronic structure calculations and experiments.⁴¹–⁴⁷ The latter now reach over 350 GPa at room temperature, and several new high-pressure phases were found in recent years.⁴⁸–⁵⁰ However, it has become clear that the atomization of compressed hydrogen is much more difficult to achieve in static compression experiments than envisaged early on, and c01-math-0018 molecules remain intact (albeit with weakened bonds) up to very high pressures. Conductive hydrogen has been seen in shock compression experiments, at pressures around 140 GPa and temperatures around 3000 K,⁵¹ while studies of absorption properties and temperature profiles in laser-heated DAC and dynamic ramp-compression experiments have also been interpreted in terms of liquid–liquid transitions toward a (semi-)metallic phase.⁵²–⁵⁴

The proposed superconductivity of atomic hydrogen within the Bardeen–Cooper–Schrieffer (BCS) theory would originate from a significant electronic density of states (DOS) at the Fermi energy, combined with a large Debye temperature (due to large sound velocity) in the atomic condensed phase of hydrogen.⁴⁰, ⁵⁵ The difficulties in studying pressurized hydrogen (which compresses 12-fold at 200 GPa) and the continuous upward trend in metallization pressure needed has led Ashcroft to propose, in 2004, an alternative route to metallic high-pressure compounds with high- c01-math-0019 superconductivity.⁵⁶ He suggested studies of hydrogen-rich compounds, such as group-14 hydrides, which involve covalently bonded hydrogen that is chemically precompressed—hydrogen atoms are closer than in the pure solid due to the strong and short bonds to a main group atom. Thus, with increasedaverage electron density, metallization should be achievable at lower pressures. Experimental studies into group-14 hydrides failed, after initially promising results, to deliver high- c01-math-0020 superconductivity.⁵⁷–⁵⁹ However, recent results indicate that sulfur and phosphorus hydrides become superconducting under pressure, with c01-math-0021 as high as 203 K—the highest known value among any material under any condition.⁶⁰, ⁶¹ Intriguingly, electronic structure calculations suggest that not the known hydrides (H c01-math-0022 S and c01-math-0023 ) but other stoichiometries (H c01-math-0024 S and c01-math-0025 , respectively, see Figure 4) are the superconducting species under high pressure.⁶²–⁶⁸ The deviation from expected stoichiometries (and thus the octet rule per formula unit) contributes to the metallic character of both compounds. Theory remains an extremely important component in this area, as structural (and stoichiometric) details of the pressurized samples are sparse, despite sophisticated measurements of resistances and the Meissner effect.

Figure 4 Predicted crystal structures of cubic c01-math-0026 S (a) and tetragonal c01-math-0027 (b), both drawn to the same scale at c01-math-0028 GPa.

Molecular Crystals

Molecules at high pressures are usually densely packed and often form crystals. Their description can be a challenge for computational investigations, due to the ladder of interactions involved: covalent bonds, ionic bonds, hydrogen bonding, and dispersion interactions all can play a role in stabilizing their condensed phases. In general, as mentioned, molecular crystals also have a tendency to polymerize under pressure; this is not unexpected. Water forms the atomic ice-X phase around 60 GPa (where the hydrogen-bond length O–H c01-math-0029 O equals the covalent OH bond length); carbon dioxide forms covalently bonded phases as low as 35 GPa (with a strong temperature dependence); nitrogen forms a three-dimensional high-energy solid with single N–N bonds at 110 GPa; and halogen dimers dissociate to form atomic phases and metallize as well (before dissociation).⁶⁹–⁷⁵

But also in these systems, we find more exotic phenomena. Ammonia, a regular hydrogen-bonded solid at ambient conditions, self-ionizes at 120 GPa, as the proton transfer reaction 2NH c01-math-0030 c01-math-0031 c01-math-0032 + c01-math-0033 is energetically beneficial—the ionic bonding component and (presumably) more compact packing of the ionized constituents outweighs the energetic cost of breaking one covalent N–H bond per ammonia pair.⁷⁶–⁷⁸ Note that density functional calculations (more on those in the following section) were indeed accurate enough to predict the stabilization of ionic ammonia phases before their experimental synthesis. Similar stabilization of ionic phases has been predicted in ammonia hydrates, where the formation of c01-math-0034 /OH c01-math-0035 pairs is energetically beneficial compared to neutral ammonia and water molecules, for the same reasons as in ammonia itself; these results await experimental confirmation.⁷⁹, ⁸⁰

Closed-Shell Reactivity

A remarkable feature of high pressure is its ability to unlock chemical reactivity in what usually appear as inert closed electronic shells. This area is dominated by computational predictions, and these exhibit some extraordinary chemistry, but experimental confirmations are still sparse (usually, stabilization is predicted above 100 GPa). There are charge transfer compounds involving noble gas constituents: for instance xenon oxides and nitrides,⁸¹–⁸⁴ sodium-helium c01-math-0036 He,⁸⁵ lithium-argon LiAr and c01-math-0037 Ar,⁸⁶ and magnesium-(Xe,Kr,Ar) compounds.⁸⁷ One reason for their stabilization is the different pressure dependence of atomic s- and d-orbitals, where the latter rise more slowly in energy as a function of confinement than the former.⁸⁸ As a consequence, with sufficient compression, an electron transfer from alkali or alkaline earth atoms to the noble gas atom is beneficial and the formation of compounds with ionic character is possible. This argument does not only hold for noble gases—cesium, for instance, can be either oxidized beyond the +1 state by fluorination or reduced beyond c01-math-0038 1 by lithiation.⁸⁹, ⁹⁰

Unusual Chemistry

A related area is the emergence of new stable stoichiometries in seemingly well-known chemical compound systems under pressure. We have just discussed this for the superconducting phases of sulfur and phosphorus hydrides, which are likely not the same stoichiometry as the conventional molecular species at ambient conditions. Many more examples exist, a lot in computational studies, and some with experimental backing. Sodium chloride, for instance, is an archetypal ionic compound, yet under pressure both sodium- and chlorine-rich compounds (Na c01-math-0039 Cl and c01-math-0040 ) have been synthesized, and the stability of others is predicted.⁹¹ A similar outcome is seen in the magnesium oxide system, where high pressures seem to stabilize both magnesium- and oxygen-rich compounds (Mg c01-math-0041 O c01-math-0042 and c01-math-0043 ); the latter has been seen in experiment.⁹², ⁹³ In both systems, the formation of anionic molecular units within the highly compressed phases (Cl c01-math-0044 and c01-math-0045 ) aids in the stabilization of some of the new stoichiometries.

A lot of unusual chemistry happens if hydrogen is involved (again, see the earlier discussion on group XV and XVI hydrides). For example, water is predicted to decompose into hydrogen peroxide and a hydrogen-rich intercalation compound at terapascal pressures;⁹⁴ novel hydronitrogens (N–H phases) are predicted to emerge;⁹⁵ and closer to home, a whole slew of hydrogen-containing minerals serve as water carriers and storage agents in Earth's mantle, upholding an equilibrium with surface water on