Young - Computational chemistry

CONTENTS xiii

24.5Continuum Methods 208

24.6Recommendations 212 Bibliography 213

25. Electronic Excited States

216

25.1Spin States 216

25.2CIS 216

25.3Initial Guess 217

25.4	Block Diagonal Hamiltonians		218
25.5	Higher Roots of a CI	218
25.6	Neglecting a Basis Function		218
25.7	Imposing Orthogonality: DFT Techniques			218
25.8	Imposing Orthogonality: QMC Techniques			219
25.9	Path Integral Methods	219

25.10Time-dependent Methods 219

25.11Semiempirical Methods 220

25.12State Averaging 220

25.13 Electronic Spectral Intensities 220

25.14Recommendations 220 Bibliography 221

26. Size Consistency

223

26.1Correction Methods 224

26.2Recommendations 225 Bibliography 226

27. Spin Contamination

227

27.1How Does Spin Contamination A¨ect Results? 227

27.2 Restricted Open-shell Calculations 228

27.3 Spin Projection Methods 229

27.4 Half-electron Approximation 229

27.5 Recommendations 230

Bibliography 230

28. Basis Set Customization			231
28.1	What Basis Functions Do	231
28.2	Creating Basis Sets from Scratch 231
28.3	Combining Existing Basis Sets		232
28.4	Customizing a Basis Set	233
28.5	Basis Set Superposition Error		237
	Bibliography 238

xiv CONTENTS

29. Force Field Customization

239

29.1Potential Pitfalls 239

29.2Original Parameterization 240

29.3Adding New Parameters 240 Bibliography 241

30. Structure±Property Relationships

243

30.1QSPR 243

30.2QSAR 247

30.33D QSAR 247

30.4Comparative QSAR 249

30.5Recommendations 249 Bibliography 249

31. Computing NMR Chemical Shifts

252

31.1 Ab initio Methods 252

31.2Semiempirical Methods 253

31.3Empirical Methods 253

31.4Recommendations 254 Bibliography 254

32. Nonlinear Optical Properties

256

32.1 Nonlinear Optical Properties 256

32.2Computational Algorithms 257

32.3	Level of Theory 259
32.4	Recommendations 259
	Bibliography 260
33. Relativistic E¨ects		261
33.1	Relativistic Terms in Quantum Mechanics	261

33.2Extension of Nonrelativistic Computational Techniques 262

33.3Core Potentials 262

33.4 Explicit Relativistic Calculations 263

33.5 E¨ects on Chemistry 263

33.6 Recommendations 264

Bibliography 264

34. Band Structures		266
34.1	Mathematical Description of Energy Bands	266
34.2	Computing Band Gaps 266
34.3	Computing Band Structures 268

	CONTENTS	xv
34.4	Describing the Electronic Structure of Crystals 269
34.5	Computing Crystal Properties 270

34.6Defect Calculations 271 Bibliography 271

35.	Mesoscale Methods								273
	35.1	Brownian Dynamics				273
	35.2	Dissipative Particle Dynamics 274
	35.3	Dynamic Mean-®eld Density Functional
		Method	274
	35.4	Nondynamic Methods					275
	35.5	Validation of Results 275
	35.6	Recommendations				275
		Bibliography		276
36.	Synthesis Route Prediction								277
	36.1	Synthesis Design Systems						277
	36.2	Applications of Traditional Modeling
		Techniques		279
	36.3	Recommendations				280
		Bibliography		280
Part III.	APPLICATIONS								281
37.	The Computational Chemist's View of the Periodic Table								283
	37.1	Organic Molecules				283
	37.2	Main Group Inorganics, Noble Gases, and Alkali
		Metals	285
	37.3	Transition Metals			286
	37.4	Lanthanides and Actinides						289
		Bibliography		290
38.	Biomolecules								296
	38.1	Methods for Modeling Biomolecules 296
	38.2	Site-speci®c Interactions					297
	38.3	General Interactions				298
	38.4	Recommendations				298
		Bibliography		298
39.	Simulating Liquids								302
	39.1	Level of Theory			302
	39.2	Periodic Boundary Condition Simulations 303

xviCONTENTS

39.3Recommendations 305 Bibliography 305

40. Polymers

307

40.1 Level of Theory 307

40.2Simulation Construction 309

40.3Properties 310

40.4Recommendations 315 Bibliography 315

41. Solids and Surfaces

318

41.1Continuum Models 318

41.2Clusters 318

41.3Band Structures 319

41.4Defect Calculations 319

41.5Molecular Dynamics and Monte Carlo Methods 319

41.6Amorphous Materials 319

41.7Recommendations 319 Bibliography 320

Appendix.	Software Packages			322
A.1	Integrated Packages		322
A.2	Ab initio and DFT Software			332
A.3	Semiempirical Software 340
A.4	Molecular Mechanics/Molecular Dynamics/Monte
	Carlo Software	344
A.5	Graphics Packages		349
A.6	Special-purpose Programs			352
	Bibliography	358
GLOSSARY				360
Bibliography 370
INDEX				371

Preface

At one time, computational chemistry techniques were used only by experts extremely experienced in using tools that were for the most part di½cult to understand and apply. Today, advances in software have produced programs that are easily used by any chemist. Along with new software comes new literature on the subject. There are now books that describe the fundamental principles of computational chemistry at almost any level of detail. A number of books also exist that explain how to apply computational chemistry techniques to simple calculations appropriate for student assignments. There are, in addition, many detailed research papers on advanced topics that are intended to be read only by professional theorists.

The group that has the most di½culty ®nding appropriate literature are working chemists, not theorists. These are experienced researchers who know chemistry and now have computational tools available. These are people who want to use computational chemistry to address real-world research problems and are bound to run into signi®cant di½culties. This book is for those chemists.

We have chosen to cover a large number of topics, with an emphasis on when and how to apply computational techniques rather than focusing on theory. Each chapter gives a clear description with just the amount of technical depth typically necessary to be able to apply the techniques to computational problems. When possible, the chapter ends with a list of steps to be taken for di½cult cases.

There are many good books describing the fundamental theory on which computational chemistry is built. The description of that theory as given here in the ®rst few chapters is very minimal. We have chosen to include just enough theory to explain the terminology used in later chapters.

The core of this book is the description of the many computation techniques available and when to use them. Prioritizing which techniques work better or worse for various types of problems is a double-edged sword. This is certainly the type of information that is of use in solving practical problems, but there is no rigorous mathematical way to prove which techniques work better than others. Even though this prioritization cannot be proven, it is better to have an approximate idea of what works best than to have no idea at all. These suggestions are obtained from a compilation of information based on lessons from our own experience, those of colleagues, and a large body of literature covering chemistry from organic to inorganic, from polymers to drug design. Unfortunately, making generalizations from such a broad range of applications means

xvii

xviii PREFACE

that there are bound to be exceptions to many of the general rules of thumb given here.

The reader is advised to start with this book and to then delve further into the computational literature pertaining to his or her speci®c work. It is impossible to reference all relevant works in a book such as this. The bibliography included at the end of each chapter primarily lists textbooks and review articles. These are some of the best sources from which to begin a serious search of the literature. It is always advisable to run several tests to determine which techniques work best for a given project.

The section on applications examines the same techniques from the standpoint of the type of chemical system. A number of techniques applicable to biomolecular work are mentioned, but not covered at the level of detail presented throughout the rest of the book. Likewise, we only provide an introduction to the techniques applicable to modeling polymers, liquids, and solids. Again, our aim was to not repeat in unnecessary detail information contained elsewhere in the book, but to only include the basic concepts needed for an understanding of the subjects involved.

We have supplied brief reviews on the merits of a number of software packages in the appendix. Some of these were included due to their widespread use. Others were included based on their established usefulness for a particular type of problem discussed in the text. Many other good programs are available, but space constraints forced us to select a sampling only. The description of the advantages and limitations of each software package is again a generalization for which there are bound to be exceptions. The researcher is advised to carefully consider the research task at hard and what program will work best in addressing it. Both software vendors and colleagues doing similar work can provide useful suggestions.

Although there are now many problems that can be addressed by occasional users of computational tools, a large number of problems exist that only career computational chemists, with the time and expertise, can e¨ectively solve. Some of the readers of this book will undoubtedly decide to forego using computational chemistry, thus avoiding months of unproductive work that they cannot a¨ord. Such a decision in and of itself is a valuable reason for doing a bit of reading rather than blindly attempting a di½cult problem.

This book was designed to aid in research, rather than as a primary text on the subject. However, students may ®nd some sections helpful. Advanced undergraduate students and graduate students will ®nd the basic topics and applications useful. Beginners are advised to ®rst become familiar with the use of computational chemistry software before delving into the advanced topics section. It may even be best to come back to this book when problems arise during computations. Some of the information in the advanced topics section is not expected to be needed until postgraduate work.

The availability of easily used graphic user interfaces makes computational chemistry a tool that can now be used readily and casually. Results may be

PREFACE xix

obtained often with a minimum amount of work. However, if the methods used are not carefully chosen for the project at hand, these results may not in any way re¯ect reality. We hope that this book will help chemists solve the realworld problems they face.

David C. Young

Acknowledgments

This book grew out of a collection of technical-support web pages. Those pages were also posted to the computational chemistry list server maintained by the Ohio Supercomputer Center. Many useful comments came from the subscribers of that list. In addition, thanks go to Dr. James F. Harrison at Michigan State University for providing advice born of experience.

The decision to undertake this project was prompted by Barbara Goldman at John Wiley & Sons, who was willing to believe in a ®rst-time author. Her suggestions greatly improved the quality of the ®nished text. Darla Henderson and Jill Roter were also very helpful in bringing the project to completion and making the existence of bureaucracy transparent.

Thanks go to Dr. Michael McKee at Auburn University and the Alabama Research and Education Network, both of which allowed software to be tested on their computers. Thanks are also due the Nichols Research Corporation and Computer Sciences Corporation and particularly Scott von Laven and David Ivey for being so tolerant of employees engaged in such job-related extracurricular activities.

A special acknowledgment also needs to be made to my family, who have now decided that Daddy will always be involved in some sort of big project so they might as well learn to live with it. My 14-year-old son observed that the computer intended for creating this book's illustrations was the best gameplaying machine in the neighborhood and took full advantage of it. Our third child was born half-way through this book's writing. Much time was spent at 2:00 a.m. with a bottle in one hand and a review article in the other.

xxi

Symbols Used in This Book

Note: A few symbols are duplicated. Although this is at times confusing, it does re¯ect common usage in the literature. Thus, it is an important notation for the reader to understand. Acronyms are de®ned in the glossary at the end of the book.

h i	expectation value
Ê	Angstroms
A
`2	Laplacian operator

aa constant, or polarizability

ba constant, or hyperpolarizability

wsusceptibility tensor, or Flory±Huggins parameter

e0	vacuum permitivity constant
es	relative permitivity

felectrostatic potential

Ga point in phase space, or a point in k-space

g	overlap between orbitals, or second hyperpolarizability
^	Hamiltonian operator
H

kdielectric constant

nfrequency of light

relectron density, also called the charge density

rdensity of states

ssurface tension

ybond angle

Cwave function

jan orbital

zexponent of a basis function

Anumber of active space orbitals, preexponential factor, a con-

stant, surface area, or a point in k-space

aa constant

amu	atomic mass units

Ba constant

Cmolecular orbital coe½cient, contraction coe½cient, or a constant

C0	weight of the HF reference determinant in the CI
Cp	heat capacity

ca constant

Da derminant, bond dissociation energy, or number of degrees of freedom

xxiii

xxiv SYMBOLS USED IN THIS BOOK

da descriptor

Eenergy, or electric ®eld

Ea	activation energy
eV	electron volts

Fforce

f … †

correlation function

GGibbs free energy

g…r†	radial distribution function
^	Hamiltonian operator or matrix
H
H…1†	®rst-order transition matrix

JJoules

KKelvin, or a point in k-space

ka constant

kB	Boltzmann constant
kg	kilograms
kx; ky; kz	coordinates in k-space

Llength of the side of a periodic box

lbond length

Mnumber of atoms, number of angles

mmass

Nnumber of molecules, particles, orbitals, basis functions, or bonds

nnumber of cycles in the periodicity

O… †	time complexity

Ppolarization

Qpartition function

qcharge

Rideal gas constant

R… †	radial function

rdistance between two particles, or reaction rate

Stotal spin

sspin

Ttemperature, or CPU time

Tg	glass transition temperature

Vvolume

w… †	probability used for a weighted average

Xa point in k-space

Ya point in k-space

Ylm	angular function
x; y; z	Cartesian coordinates