Young - Computational chemistry
.pdfCONTENTS 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 |
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25.5 |
Higher Roots of a CI |
218 |
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25.6 |
Neglecting a Basis Function |
218 |
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25.7 |
Imposing Orthogonality: DFT Techniques |
218 |
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25.8 |
Imposing Orthogonality: QMC Techniques |
219 |
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25.9 |
Path Integral Methods |
219 |
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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 |
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231 |
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28.1 |
What Basis Functions Do |
231 |
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28.2 |
Creating Basis Sets from Scratch 231 |
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28.3 |
Combining Existing Basis Sets |
232 |
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28.4 |
Customizing a Basis Set |
233 |
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28.5 |
Basis Set Superposition Error |
237 |
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Bibliography 238 |
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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 |
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32.4 |
Recommendations 259 |
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Bibliography 260 |
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33. Relativistic E¨ects |
261 |
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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 |
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34.1 |
Mathematical Description of Energy Bands |
266 |
34.2 |
Computing Band Gaps 266 |
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34.3 |
Computing Band Structures 268 |
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CONTENTS |
xv |
34.4 |
Describing the Electronic Structure of Crystals 269 |
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34.5 |
Computing Crystal Properties 270 |
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34.6Defect Calculations 271 Bibliography 271
35. |
Mesoscale Methods |
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273 |
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35.1 |
Brownian Dynamics |
273 |
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35.2 |
Dissipative Particle Dynamics 274 |
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35.3 |
Dynamic Mean-®eld Density Functional |
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Method |
274 |
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35.4 |
Nondynamic Methods |
275 |
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35.5 |
Validation of Results 275 |
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35.6 |
Recommendations |
275 |
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Bibliography |
276 |
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36. |
Synthesis Route Prediction |
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277 |
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36.1 |
Synthesis Design Systems |
277 |
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36.2 |
Applications of Traditional Modeling |
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Techniques |
279 |
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36.3 |
Recommendations |
280 |
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Bibliography |
280 |
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Part III. |
APPLICATIONS |
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281 |
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37. |
The Computational Chemist's View of the Periodic Table |
283 |
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37.1 |
Organic Molecules |
283 |
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37.2 |
Main Group Inorganics, Noble Gases, and Alkali |
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Metals |
285 |
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37.3 |
Transition Metals |
286 |
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37.4 |
Lanthanides and Actinides |
289 |
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Bibliography |
290 |
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38. |
Biomolecules |
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296 |
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38.1 |
Methods for Modeling Biomolecules 296 |
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38.2 |
Site-speci®c Interactions |
297 |
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38.3 |
General Interactions |
298 |
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38.4 |
Recommendations |
298 |
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Bibliography |
298 |
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39. |
Simulating Liquids |
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302 |
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39.1 |
Level of Theory |
302 |
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39.2 |
Periodic Boundary Condition Simulations 303 |
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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 |
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322 |
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A.1 |
Integrated Packages |
322 |
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A.2 |
Ab initio and DFT Software |
332 |
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A.3 |
Semiempirical Software 340 |
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A.4 |
Molecular Mechanics/Molecular Dynamics/Monte |
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Carlo Software |
344 |
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A.5 |
Graphics Packages |
349 |
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A.6 |
Special-purpose Programs |
352 |
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Bibliography |
358 |
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GLOSSARY |
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360 |
Bibliography 370 |
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INDEX |
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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 |
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`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 |
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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 |