| Author: |
Errol G. Lewars
|
| Published in: | Springer International Publishing |
| Release Year: | 2012 |
| ISBN: | 978-3-319-30916-3 |
| Pages: | 739 |
| Edition: | Third Edition |
| File Size: | 14 MB |
| File Type: | |
| Language: | English |
Description of Computational Chemistry
Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry. If mathematical analysis should ever hold a prominent place in chemistry-an aberration which is happily almost impossible-it would occasion a rapid and widespread degeneration of that science. Augustus Compte, French philosopher, 1798–1857; in Philosophie Positive, 1830. A dissenting view: The more progress the physical sciences make, the more they tend to enter the domain of mathematics, which is a kind of center to which they all converge. We may even judge the degree of perfection to which a science has arrived by the facility to which it may be submitted to calculation.
Adolphe Quetelet, French astronomer, mathematician, statistician, and sociologist, 1796–1874, writing in 1828. Computational Chemistry third edition differs from the second in these ways:
1. The typographical errors that were found in the first edition have been (I hope) corrected.
2. Sentences and paragraphs have on occasion been altered to clarify an explanation.
3. The biographical footnotes have been updated as necessary.
4. Significant developments since 2010 (the year of the latest references in the second edition), up to the end of 2015, have been added and referenced in the relevant places.
As might be inferred from the word Introduction, the purpose of Computational Chemistry book, like that of previous editions, is to teach the basics of the core concepts and methods of computational chemistry. Computational Chemistry is a textbook, and no attempt has been made to please every reviewer by dealing with esoteric “advanced” topics. Some fundamental concepts are the idea of a potential energy surface, the mechanical picture of a molecule as used in molecular mechanics, and the Schr€odinger equation and it's elegant taming with matrix methods to give energy levels and molecular orbitals. All the needed matrix algebra is explained before it is used.
The fundamental techniques of computational chemistry are molecular mechanics, ab initio, semiempirical, and density functional methods. Molecular dynamics and Monte Carlo methods are only mentioned; while these are important, they utilize several fundamental concepts and methods explained here, and if presented at the level of the topics treated here would require a book of their own. I wrote the first edition (2003) because there seemed to be no text quite right for an introductory course in computational chemistry for a fairly general chemical audience, and the second (2011) the edition was issued in the same belief; although there are several good books on quantum chemistry and on its disciplinary associate (“handmaiden” might seem somewhat disparaging) computational chemistry, Computational Chemistryedition is submitted in the same spirit as the first two.
I hope it will be useful to anyone who wants to learn enough about the subject to start reading the literature and to start doing computational chemistry. As implied above, there are excellent books on the field, but evidently, none that seeks to familiarize the general student of chemistry with computational chemistry in quite the same sense that standard textbooks of those subjects make organic or physical chemistry accessible. To that end the mathematics has been held on a leash; no attempt is made to prove that molecular orbitals are vectors in Hilbert space, or that a finite-dimensional inner-product space must have an orthonormal basis, and the only sections that the nonspecialist may justifiably view with some trepidation are the (outlined) derivation of the Hartree-Fock and Kohn-Sham equations. These sections should be read, if only to get the flavor of the procedures, but should not stop anyone from getting on with the rest of the book.
Computational chemistry has become a tool used in much the same spirit as infrared or NMR spectroscopy, and to use it sensibly it is no more necessary to be able to write your own programs than the fruitful use of infrared or NMR spectroscopy requires you to be able to build your own spectrometer. I have tried to give enough theory to provide a reasonably good idea of how standard procedures in the programs work. In this regard, the concept of constructing and diagonalizing a Fock matrix is introduced early, and there is little talk of computationally less relevant secular determinants (except for historical reasons in connection with the simple Hückel method). Many results of actual computations, some done specifically for Computational Chemistry book, are given. Almost all the assertions in these pages are accompanied by literature references, which should make the text useful to researchers who need to track down methods or results, and to anyone who may wish to delve deeper.
It would be clearly inappropriate, if not impossible, to exhaustively reference each topic discussed. The choice of references has been oriented toward (besides justifying a particular assertion) reviews, and publications illustrating a topic in a general way, rather than some specialized aspect of it. In this age of the Internet, once one is aware of the existence of some subject, it is usually not hard to obtain more information about it. The material should be suitable for senior undergraduates, graduate students, and novice researchers in computational chemistry. Knowledge of the shapes of molecules, covalent and ionic bonds, spectroscopy, and some familiarity with thermodynamics at about the second- or third-year undergraduate level is assumed. Some readers may wish to review basic concepts from physical and organic chemistry.
The reader, then, should be able to acquire the basic theory of, and a fair idea of the kinds of results to be obtained from, common computational chemistry techniques. You will learn how one can calculate the geometry of (some may quibble and say “a geometry for”) a molecule, its IR and UV spectra and its thermodynamic and kinetic stability, and other information needed to make a plausible guess at its chemistry.
Computational chemistry is more accessible than ever. Hardware has become cheaper than it was even a few years ago, and powerful programs once available only for expensive workstations have been adapted to run on inexpensive personal computers. The actual use of a program is best explained by its manuals and by books written for a specific program, and the directions for setting up the various computations are not given here. Information on various programs is provided in Chap. 9. Read the book, get some programs, and go out and do computational chemistry. You may make mistakes, but they are unlikely to put you in the same kind of danger that a mistake in a wet lab might.
Adolphe Quetelet, French astronomer, mathematician, statistician, and sociologist, 1796–1874, writing in 1828. Computational Chemistry third edition differs from the second in these ways:
1. The typographical errors that were found in the first edition have been (I hope) corrected.
2. Sentences and paragraphs have on occasion been altered to clarify an explanation.
3. The biographical footnotes have been updated as necessary.
4. Significant developments since 2010 (the year of the latest references in the second edition), up to the end of 2015, have been added and referenced in the relevant places.
As might be inferred from the word Introduction, the purpose of Computational Chemistry book, like that of previous editions, is to teach the basics of the core concepts and methods of computational chemistry. Computational Chemistry is a textbook, and no attempt has been made to please every reviewer by dealing with esoteric “advanced” topics. Some fundamental concepts are the idea of a potential energy surface, the mechanical picture of a molecule as used in molecular mechanics, and the Schr€odinger equation and it's elegant taming with matrix methods to give energy levels and molecular orbitals. All the needed matrix algebra is explained before it is used.
The fundamental techniques of computational chemistry are molecular mechanics, ab initio, semiempirical, and density functional methods. Molecular dynamics and Monte Carlo methods are only mentioned; while these are important, they utilize several fundamental concepts and methods explained here, and if presented at the level of the topics treated here would require a book of their own. I wrote the first edition (2003) because there seemed to be no text quite right for an introductory course in computational chemistry for a fairly general chemical audience, and the second (2011) the edition was issued in the same belief; although there are several good books on quantum chemistry and on its disciplinary associate (“handmaiden” might seem somewhat disparaging) computational chemistry, Computational Chemistryedition is submitted in the same spirit as the first two.
I hope it will be useful to anyone who wants to learn enough about the subject to start reading the literature and to start doing computational chemistry. As implied above, there are excellent books on the field, but evidently, none that seeks to familiarize the general student of chemistry with computational chemistry in quite the same sense that standard textbooks of those subjects make organic or physical chemistry accessible. To that end the mathematics has been held on a leash; no attempt is made to prove that molecular orbitals are vectors in Hilbert space, or that a finite-dimensional inner-product space must have an orthonormal basis, and the only sections that the nonspecialist may justifiably view with some trepidation are the (outlined) derivation of the Hartree-Fock and Kohn-Sham equations. These sections should be read, if only to get the flavor of the procedures, but should not stop anyone from getting on with the rest of the book.
Computational chemistry has become a tool used in much the same spirit as infrared or NMR spectroscopy, and to use it sensibly it is no more necessary to be able to write your own programs than the fruitful use of infrared or NMR spectroscopy requires you to be able to build your own spectrometer. I have tried to give enough theory to provide a reasonably good idea of how standard procedures in the programs work. In this regard, the concept of constructing and diagonalizing a Fock matrix is introduced early, and there is little talk of computationally less relevant secular determinants (except for historical reasons in connection with the simple Hückel method). Many results of actual computations, some done specifically for Computational Chemistry book, are given. Almost all the assertions in these pages are accompanied by literature references, which should make the text useful to researchers who need to track down methods or results, and to anyone who may wish to delve deeper.
It would be clearly inappropriate, if not impossible, to exhaustively reference each topic discussed. The choice of references has been oriented toward (besides justifying a particular assertion) reviews, and publications illustrating a topic in a general way, rather than some specialized aspect of it. In this age of the Internet, once one is aware of the existence of some subject, it is usually not hard to obtain more information about it. The material should be suitable for senior undergraduates, graduate students, and novice researchers in computational chemistry. Knowledge of the shapes of molecules, covalent and ionic bonds, spectroscopy, and some familiarity with thermodynamics at about the second- or third-year undergraduate level is assumed. Some readers may wish to review basic concepts from physical and organic chemistry.
The reader, then, should be able to acquire the basic theory of, and a fair idea of the kinds of results to be obtained from, common computational chemistry techniques. You will learn how one can calculate the geometry of (some may quibble and say “a geometry for”) a molecule, its IR and UV spectra and its thermodynamic and kinetic stability, and other information needed to make a plausible guess at its chemistry.
Computational chemistry is more accessible than ever. Hardware has become cheaper than it was even a few years ago, and powerful programs once available only for expensive workstations have been adapted to run on inexpensive personal computers. The actual use of a program is best explained by its manuals and by books written for a specific program, and the directions for setting up the various computations are not given here. Information on various programs is provided in Chap. 9. Read the book, get some programs, and go out and do computational chemistry. You may make mistakes, but they are unlikely to put you in the same kind of danger that a mistake in a wet lab might.
Content of Computational Chemistry
1 An Outline of What Computational Chemistry Is All About ...... 1
1.1 What You Can Do with Computational Chemistry . . . ......... 1
1.2 The Tools of Computational Chemistry . . . . . . . . . . . . . . . . . . . . 2
1.3 Putting it All Together . ............................... 4
1.4 The Philosophy of Computational Chemistry . . .............. 5
1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Easier Questions ......................................... 6
Harder Questions . . . . .................................... 6
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 The Concept of the Potential Energy Surface .................. 9
2.1 Perspective ........................................ 9
2.2 Stationary Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 The Born-Oppenheimer Approximation . . . . . . . . . . . . . . . . . . . . 22
2.4 Geometry Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5 Stationary Points and Normal-Mode Vibrations. Zero
Point Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.6 Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Easier Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Harder Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3 Molecular Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.1 Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2 The Basic Principles of Molecular Mechanics . . . . . . . . . . . . . . . 54
3.2.1 Developing a Forcefield . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.2.2 Parameterizing a Forcefield . . . . . . . . . . . . . . . . . . . . . . . 59
3.2.3 A Calculation Using our Forcefield . . . . . . . . . . . . . . . . . 64
3.3 Examples of the Use of Molecular Mechanics . . . . . . . . . . . . . . . 68
3.3.1 To Obtain Reasonable Input Geometries for Lengthier
(ab Initio, Semiempirical or Density Functional) Kinds of
Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.3.2 To Obtain (Often Excellent) Geometries . . . . . . . . . . . . . . 72
3.3.3 To Obtain (Sometimes Excellent) Relative
Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.3.4 To Generate the Potential Energy Function Under Which
Molecules Move, for Molecular Dynamics or Monte
Carlo Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.3.5 As a (Usually Quick) Guide to the Feasibility of,
or Likely Outcome of, Reactions in Organic Synthesis . . . 86
3.4 Frequencies and Vibrational Spectra Calculated by MM . . . . . . . . 88
3.5 Strengths and Weaknesses of Molecular Mechanics . . . . . . . . . . . 91
3.5.1 Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.5.2 Weaknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Easier Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Harder Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4 Introduction to Quantum Mechanics in Computational
Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.1 Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.2 The Development of Quantum Mechanics. The Schr€odinger
Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.2.1 The Origins of Quantum Theory: Blackbody Radiation
and the Photoelectric Effect . . . . . . . . . . . . . . . . . . . . . . . 103
4.2.2 Radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.2.3 Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.2.4 The Nuclear Atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.2.5 The Bohr Atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.2.6 The Wave Mechanical Atom and the Schr€odinger
Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.3 The Application of the Schr€odinger Equation to Chemistry
by Hückel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.3.2 Hybridization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.3.3 Matrices and Determinants . . . . . . . . . . . . . . . . . . . . . . . . 125
4.3.4 The Simple Hückel Method–Theory . . . . . . . . . . . . . . . . . 135
4.3.5 The Simple Hückel Method–Applications . . . . . . . . . . . . . 150
4.3.6 Strengths and Weaknesses of the Simple Hückel
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
4.3.7 The Determinant Method of Calculating the Hückel c’s
and Energy Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
4.4 The Extended Hückel Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
4.4.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
4.4.2 An Illustration of the EHM: The Protonated Helium
Molecule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
4.4.3 The Extended Hückel Method–Applications . . . . . . . . . . . 182
4.4.4 Strengths and Weaknesses of the Extended Hückel
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
Easier Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
Harder Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
5 Ab initio Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
5.1 Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
5.2 The Basic Principles of the Ab initio Method . . . . . . . . . . . . . . . . 194
5.2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
5.2.2 The Hartree SCF Method . . . . . . . . . . . . . . . . . . . . . . . . . 195
5.2.3 The Hartree-Fock Equations . . . . . . . . . . . . . . . . . . . . . . . 199
5.3 Basis Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
5.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
5.3.2 Gaussian Functions; Basis Set Preliminaries;
Direct SCF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
5.3.3 Types of Basis Sets and Their Uses . . . . . . . . . . . . . . . . . 258
5.4 Post-Hartree-Fock Calculations: Electron Correlation . . . . . . . . . . 276
5.4.1 Electron Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
5.4.2 The Møller-Plesset Approach to Electron Correlation . . . . 282
5.4.3 The Configuration Interaction Approach to Electron
Correlation. The Coupled Cluster Method . . . . . . . . . . . . . 291
5.5 Applications of The Ab initio Method . . . . . . . . . . . . . . . . . . . . . 303
5.5.1 Geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
5.5.2 Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
5.5.3 Frequencies and Vibrational (IR) Spectra . . . . . . . . . . . . . 356
5.5.4 Properties Arising from Electron Distribution: Dipole
Moments, Charges, Bond Orders, Electrostatic Potentials,
Atoms-in-Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
5.5.5 Miscellaneous Properties–UV and NMR Spectra,
Ionization Energies, and Electron Affinities . . . . . . . . . . . 386
5.5.6 Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
5.6 Strengths and Weaknesses of Ab initio Calculations . . . . . . . . . . . 400
5.6.1 Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
5.6.2 Weaknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401
Easier Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402
Harder Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
6 Semiempirical Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421
6.1 Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421
6.2 The Basic Principles of SCF Semiempirical Methods . . . . . . . . . . 423
6.2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423
6.2.2 The Pariser-Parr-Pople (PPP) method . . . . . . . . . . . . . . . . 426
6.2.3 The Complete Neglect of Differential Overlap (CNDO)
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428
6.2.4 The Intermediate Neglect of Differential Overlap
(INDO) Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429
6.2.5 The Neglect of Diatomic Differential Overlap (NDDO)
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430
6.3 Applications of Semiempirical Methods . . . . . . . . . . . . . . . . . . . 445
6.3.1 Geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
6.3.2 Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452
6.3.3 Frequencies and Vibrational Spectra . . . . . . . . . . . . . . . . . 460
6.3.4 Properties Arising from Electron Distribution: Dipole
Moments, Charges, Bond Orders . . . . . . . . . . . . . . . . . . . 464
6.3.5 Miscellaneous Properties–UV Spectra, Ionization
Energies, and Electron Affinities . . . . . . . . . . . . . . . . . . . 468
6.3.6 Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471
6.3.7 Some General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . 472
6.4 Strengths and Weaknesses of Semiempirical Methods . . . . . . . . . 473
6.4.1 Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473
6.4.2 Weaknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474
Easier Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475
Harder Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477
7 Density Functional Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
7.1 Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
7.2 The Basic Principles of Density Functional Theory . . . . . . . . . . . 485
7.2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
7.2.2 Forerunners to Current DFT Methods . . . . . . . . . . . . . . . . 487
7.2.3 Current DFT Methods: The Kohn-Sham
Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
7.3 Applications of Density Functional Theory . . . . . . . . . . . . . . . . . 508
7.3.1 Geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509
7.3.2 Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519
7.3.3 Frequencies and Vibrational Spectra . . . . . . . . . . . . . . . . . 527
7.3.4 Properties Arising from Electron Distribution–Dipole
Moments, Charges, Bond Orders, Atoms-in-Molecules . . . 530
7.3.5 Miscellaneous Properties–UV and NMR Spectra,
Ionization Energies and Electron Affinities,
Electronegativity, Hardness, Softness and the Fukui
Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534
7.3.6 Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552
7.4 Strengths and Weaknesses of DFT . . . . . . . . . . . . . . . . . . . . . . . 553
7.4.1 Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553
7.4.2 Weaknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553
7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554
Easier Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556
Harder Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557
8 Some “Special” Topics: (Section 8.1) Solvation, (Section 8.2)
Singlet Diradicals, (Section 8.3) A Note on Heavy Atoms
and Transition Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565
8.1 Solvation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565
8.1.1 Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566
8.1.2 Ways of Treating Solvation . . . . . . . . . . . . . . . . . . . . . . . 566
8.2 Singlet Diradicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583
8.2.1 Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584
8.2.2 Problems with Singlet Diradicals and Model
Chemistries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585
8.2.3 Singlet Diradicals, Beyond Model Chemistries . . . . . . . . . 587
8.3 A Note on Heavy Atoms and Transition Metals . . . . . . . . . . . . . . 598
8.3.1 Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599
8.3.2 Heavy Atoms and Relativistic Corrections . . . . . . . . . . . . 599
8.3.3 Some Heavy Atom Calculations . . . . . . . . . . . . . . . . . . . . 600
8.3.4 Transition Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 601
8.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604
Solvation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605
Easier Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605
Harder Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605
Singlet Diradicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606
Easier Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606
Harder Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606
Heavy Atoms and Transition Metals . . . . . . . . . . . . . . . . . . . . . . . . . . 606
Easier Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606
Harder Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607
9 Selected Literature Highlights, Books, Websites, Software
and Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613
9.1 From the Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613
9.1.1 Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613
9.1.2 Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
9.1.3 Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626
9.2 To the Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630
9.2.1 Books . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630
9.2.2 Websites for Computational Chemistry in General . . . . . . 633
9.3 Software and Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635
9.3.1 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635
9.3.2 Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 639
9.3.3 Postscript . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 641
Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715
1.1 What You Can Do with Computational Chemistry . . . ......... 1
1.2 The Tools of Computational Chemistry . . . . . . . . . . . . . . . . . . . . 2
1.3 Putting it All Together . ............................... 4
1.4 The Philosophy of Computational Chemistry . . .............. 5
1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Easier Questions ......................................... 6
Harder Questions . . . . .................................... 6
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 The Concept of the Potential Energy Surface .................. 9
2.1 Perspective ........................................ 9
2.2 Stationary Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 The Born-Oppenheimer Approximation . . . . . . . . . . . . . . . . . . . . 22
2.4 Geometry Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5 Stationary Points and Normal-Mode Vibrations. Zero
Point Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.6 Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Easier Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Harder Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3 Molecular Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.1 Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2 The Basic Principles of Molecular Mechanics . . . . . . . . . . . . . . . 54
3.2.1 Developing a Forcefield . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.2.2 Parameterizing a Forcefield . . . . . . . . . . . . . . . . . . . . . . . 59
3.2.3 A Calculation Using our Forcefield . . . . . . . . . . . . . . . . . 64
3.3 Examples of the Use of Molecular Mechanics . . . . . . . . . . . . . . . 68
3.3.1 To Obtain Reasonable Input Geometries for Lengthier
(ab Initio, Semiempirical or Density Functional) Kinds of
Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.3.2 To Obtain (Often Excellent) Geometries . . . . . . . . . . . . . . 72
3.3.3 To Obtain (Sometimes Excellent) Relative
Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.3.4 To Generate the Potential Energy Function Under Which
Molecules Move, for Molecular Dynamics or Monte
Carlo Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.3.5 As a (Usually Quick) Guide to the Feasibility of,
or Likely Outcome of, Reactions in Organic Synthesis . . . 86
3.4 Frequencies and Vibrational Spectra Calculated by MM . . . . . . . . 88
3.5 Strengths and Weaknesses of Molecular Mechanics . . . . . . . . . . . 91
3.5.1 Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.5.2 Weaknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Easier Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Harder Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4 Introduction to Quantum Mechanics in Computational
Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.1 Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.2 The Development of Quantum Mechanics. The Schr€odinger
Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.2.1 The Origins of Quantum Theory: Blackbody Radiation
and the Photoelectric Effect . . . . . . . . . . . . . . . . . . . . . . . 103
4.2.2 Radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.2.3 Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.2.4 The Nuclear Atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.2.5 The Bohr Atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.2.6 The Wave Mechanical Atom and the Schr€odinger
Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.3 The Application of the Schr€odinger Equation to Chemistry
by Hückel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.3.2 Hybridization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.3.3 Matrices and Determinants . . . . . . . . . . . . . . . . . . . . . . . . 125
4.3.4 The Simple Hückel Method–Theory . . . . . . . . . . . . . . . . . 135
4.3.5 The Simple Hückel Method–Applications . . . . . . . . . . . . . 150
4.3.6 Strengths and Weaknesses of the Simple Hückel
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
4.3.7 The Determinant Method of Calculating the Hückel c’s
and Energy Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
4.4 The Extended Hückel Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
4.4.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
4.4.2 An Illustration of the EHM: The Protonated Helium
Molecule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
4.4.3 The Extended Hückel Method–Applications . . . . . . . . . . . 182
4.4.4 Strengths and Weaknesses of the Extended Hückel
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
Easier Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
Harder Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
5 Ab initio Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
5.1 Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
5.2 The Basic Principles of the Ab initio Method . . . . . . . . . . . . . . . . 194
5.2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
5.2.2 The Hartree SCF Method . . . . . . . . . . . . . . . . . . . . . . . . . 195
5.2.3 The Hartree-Fock Equations . . . . . . . . . . . . . . . . . . . . . . . 199
5.3 Basis Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
5.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
5.3.2 Gaussian Functions; Basis Set Preliminaries;
Direct SCF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
5.3.3 Types of Basis Sets and Their Uses . . . . . . . . . . . . . . . . . 258
5.4 Post-Hartree-Fock Calculations: Electron Correlation . . . . . . . . . . 276
5.4.1 Electron Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
5.4.2 The Møller-Plesset Approach to Electron Correlation . . . . 282
5.4.3 The Configuration Interaction Approach to Electron
Correlation. The Coupled Cluster Method . . . . . . . . . . . . . 291
5.5 Applications of The Ab initio Method . . . . . . . . . . . . . . . . . . . . . 303
5.5.1 Geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
5.5.2 Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
5.5.3 Frequencies and Vibrational (IR) Spectra . . . . . . . . . . . . . 356
5.5.4 Properties Arising from Electron Distribution: Dipole
Moments, Charges, Bond Orders, Electrostatic Potentials,
Atoms-in-Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
5.5.5 Miscellaneous Properties–UV and NMR Spectra,
Ionization Energies, and Electron Affinities . . . . . . . . . . . 386
5.5.6 Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
5.6 Strengths and Weaknesses of Ab initio Calculations . . . . . . . . . . . 400
5.6.1 Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
5.6.2 Weaknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401
Easier Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402
Harder Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
6 Semiempirical Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421
6.1 Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421
6.2 The Basic Principles of SCF Semiempirical Methods . . . . . . . . . . 423
6.2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423
6.2.2 The Pariser-Parr-Pople (PPP) method . . . . . . . . . . . . . . . . 426
6.2.3 The Complete Neglect of Differential Overlap (CNDO)
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428
6.2.4 The Intermediate Neglect of Differential Overlap
(INDO) Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429
6.2.5 The Neglect of Diatomic Differential Overlap (NDDO)
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430
6.3 Applications of Semiempirical Methods . . . . . . . . . . . . . . . . . . . 445
6.3.1 Geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
6.3.2 Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452
6.3.3 Frequencies and Vibrational Spectra . . . . . . . . . . . . . . . . . 460
6.3.4 Properties Arising from Electron Distribution: Dipole
Moments, Charges, Bond Orders . . . . . . . . . . . . . . . . . . . 464
6.3.5 Miscellaneous Properties–UV Spectra, Ionization
Energies, and Electron Affinities . . . . . . . . . . . . . . . . . . . 468
6.3.6 Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471
6.3.7 Some General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . 472
6.4 Strengths and Weaknesses of Semiempirical Methods . . . . . . . . . 473
6.4.1 Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473
6.4.2 Weaknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474
Easier Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475
Harder Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477
7 Density Functional Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
7.1 Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
7.2 The Basic Principles of Density Functional Theory . . . . . . . . . . . 485
7.2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
7.2.2 Forerunners to Current DFT Methods . . . . . . . . . . . . . . . . 487
7.2.3 Current DFT Methods: The Kohn-Sham
Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
7.3 Applications of Density Functional Theory . . . . . . . . . . . . . . . . . 508
7.3.1 Geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509
7.3.2 Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519
7.3.3 Frequencies and Vibrational Spectra . . . . . . . . . . . . . . . . . 527
7.3.4 Properties Arising from Electron Distribution–Dipole
Moments, Charges, Bond Orders, Atoms-in-Molecules . . . 530
7.3.5 Miscellaneous Properties–UV and NMR Spectra,
Ionization Energies and Electron Affinities,
Electronegativity, Hardness, Softness and the Fukui
Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534
7.3.6 Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552
7.4 Strengths and Weaknesses of DFT . . . . . . . . . . . . . . . . . . . . . . . 553
7.4.1 Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553
7.4.2 Weaknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553
7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554
Easier Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556
Harder Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557
8 Some “Special” Topics: (Section 8.1) Solvation, (Section 8.2)
Singlet Diradicals, (Section 8.3) A Note on Heavy Atoms
and Transition Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565
8.1 Solvation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565
8.1.1 Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566
8.1.2 Ways of Treating Solvation . . . . . . . . . . . . . . . . . . . . . . . 566
8.2 Singlet Diradicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583
8.2.1 Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584
8.2.2 Problems with Singlet Diradicals and Model
Chemistries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585
8.2.3 Singlet Diradicals, Beyond Model Chemistries . . . . . . . . . 587
8.3 A Note on Heavy Atoms and Transition Metals . . . . . . . . . . . . . . 598
8.3.1 Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599
8.3.2 Heavy Atoms and Relativistic Corrections . . . . . . . . . . . . 599
8.3.3 Some Heavy Atom Calculations . . . . . . . . . . . . . . . . . . . . 600
8.3.4 Transition Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 601
8.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604
Solvation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605
Easier Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605
Harder Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605
Singlet Diradicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606
Easier Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606
Harder Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606
Heavy Atoms and Transition Metals . . . . . . . . . . . . . . . . . . . . . . . . . . 606
Easier Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606
Harder Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607
9 Selected Literature Highlights, Books, Websites, Software
and Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613
9.1 From the Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613
9.1.1 Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613
9.1.2 Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
9.1.3 Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626
9.2 To the Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630
9.2.1 Books . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630
9.2.2 Websites for Computational Chemistry in General . . . . . . 633
9.3 Software and Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635
9.3.1 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635
9.3.2 Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 639
9.3.3 Postscript . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 641
Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715
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