Discovering Chemistry With Natural Bond Orbitals

This book explores chemical bonds, their intrinsic energies, and the corresponding dissociation energies which are relevant in reactivity problems. It offers the first book on conceptual quantum chemistry, a key area for understanding chemical principles and predicting chemical properties. It presents NBO mathematical algorithms embedded in a well-tested and widely used computer program (currently, NBO 5.9). While encouraging a "look under the hood" (Appendix A), this book mainly enables students to gain proficiency in using the NBO program to re-express complex wavefunctions in terms of intuitive chemical concepts and orbital imagery.

Preface xi

1 Getting Started 1

1.1 Talking to your electronic structure system 1

1.2 Helpful tools 3

1.3 General $NBO keylist usage 4

1.4 Producing orbital imagery 6

Problems and exercises 8

2 Electrons in Atoms 10

2.1 Finding the electrons in atomic wavefunctions 10

2.2 Atomic orbitals and their graphical representation 13

2.3 Atomic electron configurations 18

2.4 How to find electronic orbitals and configurations in NBO output 23

2.5 Natural atomic orbitals and the natural minimal basis 29

Problems and exercises 31

3 Atoms in Molecules 34

3.1 Atomic orbitals in molecules 35

3.2 Atomic configurations and atomic charges in molecules 39

3.3 Atoms in open-shell molecules 44

Problems and exercises 49

4 Hybrids and Bonds in Molecules 51

4.1 Bonds and lone pairs in molecules 52

4.2 Atomic hybrids and bonding geometry 60

4.3 Bond polarity, electronegativity, and Bent’s rule 71

4.4 Hypovalent three-center bonds 78

4.5 Open-shell Lewis structures and spin hybrids 82

4.6 Lewis-like structures in transition metal bonding 86

Problems and exercises 89

5 Resonance Delocalization Corrections 92

5.1 The natural Lewis structure perturbative model 93

5.2 Second-order perturbative analysis of donor–acceptor interactions 96

5.3 $Del energetic analysis [integrated ESS/NBO only] 105

5.4 Delocalization tails of natural localized molecular orbitals 113

5.5 How to $CHOOSE alternative Lewis structures 117

5.6 Natural resonance theory 123

Problems and exercises 133

6 Steric and Electrostatic Effects 135

6.1 Nature and evaluation of steric interactions 136

6.2 Electrostatic and dipolar analysis 145

Problems and exercises 153

7 Nuclear and Electronic Spin Effects 155

7.1 NMR chemical shielding analysis 156

7.2 NMR J-coupling analysis 162

7.3 ESR spin density distribution 168

Problems and exercises 173

8 Coordination and Hyperbonding 176

8.1 Lewis acid–base complexes 178

8.2 Transition metal coordinate bonding 193

8.3 Three-center, four-electron hyperbonding 204

Problems and exercises 206

9 Intermolecular Interactions 209

9.1 Hydrogen-bonded complexes 210

9.2 Other donor–acceptor complexes 217

9.3 Natural energy decomposition analysis 223

Problems and exercises 227

10 Transition State Species and Chemical Reactions 231

10.1 Ambivalent Lewis structures: the transition-state limit 232

10.2 Example: bimolecular formation of formaldehyde 236

10.3 Example: unimolecular isomerization of formaldehyde 243

10.4 Example: SN2 halide exchange reaction 246

Problems and exercises 249

11 Excited State Chemistry 252

11.1 Getting to the “root” of the problem 252

11.2 Illustrative applications to NO excitations 256

11.3 Finding common ground: NBO versus MO state-to-state transferability 269

11.4 NBO/NRT description of excited-state structure and reactivity 277

11.5 Conical intersections and intersystem crossings 282

Problems and exercises 289

Appendix A: What’s Under the Hood? 297

Appendix B: Orbital Graphics: The NBOView Orbital Plotter 300

Appendix C: Digging at the Details 302

Appendix D: What If Something Goes Wrong? 304

Appendix E: Atomic Units (a.u.) and Conversion Factors 307

Index 309

“Following this text’s clear explanations, even readers with limited backgrounds in quantum mechanics will learn how to perform sophisticated explorations of modern bonding and valency concepts.” (Chimie Nouvelle, 1 March 2013)

FRANK WEINHOLD, PhD, is Emeritus Professor of Physical and Theoretical Chemistry at the University of Wisconsin–Madison. Professor Weinhold has served on the editorial advisory boards of the International Journal of Quantum Chemistry and Russian Journal of Physical Chemistry. He is the author of more than 170 technical publications and software packages, including the natural bond orbital program.

CLARK R. LANDIS, PhD, is Professor of Inorganic Chemistry at the University of Wisconsin–Madison. He has received teaching and lectureship awards for his contributions to chemical education. Dr. Landis's research focuses on catalysis in transition metal complexes.

Learn how to investigate chemical bonding questions using modern NBO computational methods

Using the latest computational technology, this practical how-to guide to chemical discovery introduces readers to natural bond orbital (NBO) concepts, strategies, and practical implementations. Without resorting to complex mathematics and programming, readers will learn how to fully leverage the NBO 5.9 computer program to re-express complex multi-electron wave functions in terms of intuitive chemical concepts and orbital imagery.

Discovering Chemistry with Natural Bond Orbitals begins with an introductory chapter that sets forth the basics, including how to produce orbital imagery. Next, the authors cover such critical topics as:

• Electrons in atoms
• Hybrids and bonds in molecules
• Steric and electrostatic effects
• Atoms in molecules
• Resonance delocalization corrections
• Nuclear and electronic spin effects

Each chapter ends with problems and exercises that enable readers to apply NBO methods to investigate chemical bonds, their intrinsic energies, and the corresponding dissociation energies that are relevant in reactivity problems. There are also worked-out examples and sample input and output throughout the text to help guide and support readers in their own investigations. In addition, the text features numerous sidebars and links to websites and other texts where more in-depth information can be found on individual topics.

There are five appendices at the end of the text filled with useful supplementary material, including Appendix D, "What if Something Goes Wrong?", to help readers solve common problems that arise in NBO investigations.

Following this text's clear explanations, even readers with limited backgrounds in quantum mechanics will learn how to perform sophisticated explorations of modern bonding and valency concepts.