Physical Chemistry (eBook)

How Chemistry Works

Kurt W. Kolasinski (Autor)

eBook Download: PDF

2016
John Wiley & Sons (Verlag)
978-1-118-75121-3 (ISBN)

Infos

Much of chemistry is motivated by asking 'How'? How do I make a primary alcohol? React a Grignard reagent with formaldehyde. Physical chemistry is motivated by asking 'Why'? The Grignard reagent and formaldehyde follow a molecular dance known as a reaction mechanism in which stronger bonds are made at the expense of weaker bonds. If you are interested in asking 'why' and not just 'how', then you need to understand physical chemistry.

Physical Chemistry: How Chemistry Works takes a fresh approach to teaching in physical chemistry. This modern textbook is designed to excite and engage undergraduate chemistry students and prepare them for how they will employ physical chemistry in real life. The student-friendly approach and practical, contemporary examples facilitate an understanding of the physical chemical aspects of any system, allowing students of inorganic chemistry, organic chemistry, analytical chemistry and biochemistry to be fluent in the essentials of physical chemistry in order to understand synthesis, intermolecular interactions and materials properties. For students who are deeply interested in the subject of physical chemistry, the textbook facilitates further study by connecting them to the frontiers of research.

• Provides students with the physical and mathematical machinery to understand the physical chemical aspects of any system.
• Integrates regular examples drawn from the literature, from contemporary issues and research, to engage students with relevant and illustrative details.
• Important topics are introduced and returned to in later chapters: key concepts are reinforced and discussed in more depth as students acquire more tools.
• Chapters begin with a preview of important concepts and conclude with a summary of important equations.
• Each chapter includes worked examples and exercises: discussion questions, simple equation manipulation questions, and problem-solving exercises.
• Accompanied by supplementary online material: worked examples for students and a solutions manual for instructors.
• Written by an experienced instructor, researcher and author in physical chemistry, with a voice and perspective that is pedagogical and engaging.

Professor Kurt W. Kolasinski, West Chester University, Pennsylvania, USA
Kurt Kolasinski has been a Professor of physical chemistry at West Chester University since 2014 having joined the faculty in 2006. He has held faculty positions at the University of Virginia (2004 - 2006), Queen Mary University of London (2001 - 2004), and the University of Birmingham (UK) (1995 - 2001). His research focuses on surface science, laser/surface interactions and nanoscience. A particular area of expertise is the formation of nanostructures in silicon and porous silicon using a variety of chemical and laser-based techniques. He is the author of over 100 scholarly publications as well as the widely used textbook Surface Science: Foundations of Catalysis and Nanoscience, which appeared in its third edition in 2012.

 

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Much of chemistry is motivated by asking 'How'? How do I make a primary alcohol? React a Grignard reagent with formaldehyde. Physical chemistry is motivated by asking 'Why'? The Grignard reagent and formaldehyde follow a molecular dance known as a reaction mechanism in which stronger bonds are made at the expense of weaker bonds. If you are interested in asking 'why' and not just 'how', then you need to understand physical chemistry. Physical Chemistry: How Chemistry Works takes a fresh approach to teaching in physical chemistry. This modern textbook is designed to excite and engage undergraduate chemistry students and prepare them for how they will employ physical chemistry in real life. The student-friendly approach and practical, contemporary examples facilitate an understanding of the physical chemical aspects of any system, allowing students of inorganic chemistry, organic chemistry, analytical chemistry and biochemistry to be fluent in the essentials of physical chemistry in order to understand synthesis, intermolecular interactions and materials properties. For students who are deeply interested in the subject of physical chemistry, the textbook facilitates further study by connecting them to the frontiers of research. Provides students with the physical and mathematical machinery to understand the physical chemical aspects of any system. Integrates regular examples drawn from the literature, from contemporary issues and research, to engage students with relevant and illustrative details. Important topics are introduced and returned to in later chapters: key concepts are reinforced and discussed in more depth as students acquire more tools. Chapters begin with a preview of important concepts and conclude with a summary of important equations. Each chapter includes worked examples and exercises: discussion questions, simple equation manipulation questions, and problem-solving exercises. Accompanied by supplementary online material: worked examples for students and a solutions manual for instructors. Fifteen supporting videos from the author presenting such topics as Entropy & Direction of Change; Rate Laws; Sequestration; Electrochemistry; etc. Written by an experienced instructor, researcher and author in physical chemistry, with a voice and perspective that is pedagogical and engaging.

Inhalt

Physical Chemistry 3
Contents 9
Preface 17
About the companion website 19
1 Introduction 21
1.1 Atoms and molecules 21
1.2 Phases 22
1.2.1 Directed practice 23
1.3 Energy 23
1.3.1 Directed practice 23
1.4 Chemical reactions 24
1.4.1 Directed practice 25
1.5 Problem solving 25
1.5.1 Directed practice 27
1.5.2 Performing calculations 27
1.5.3 Units and reporting data 27
1.6 Some conventions 27
Exercises 31
Further reading 34
2 Ideal gases 35
2.1 Ideal gas equation of state 36
2.1.1 Example 37
2.1.2 Directed practice 37
2.2 Molecular degrees of freedom 38
2.2.1 Directed practice 39
2.3 Translational energy: Distribution and relation to pressure 41
2.3.1 Example 42
2.4 Maxwell distribution of molecular speeds 43
2.5 Principle of equipartition of energy 44
2.6 Temperature and the zeroth law of thermodynamics 45
2.7 Mixtures of gases 47
2.7.1 Directed practice 47
2.8 Molecular collisions 47
2.8.1 Directed practice 49
Exercises 49
Further reading 50
3 Non-ideal gases and intermolecular interactions 51
3.1 Non-ideal behavior 51
3.2 Interactions of matter with matter 52
3.2.1 Directed practice 54
3.3 Intermolecular interactions 54
3.3.1 Long-range interactions 54
3.3.2 Short-range energies 57
3.3.3 The hydrogen bond, halogen bond, and related interactions 58
3.4 Real gases 59
3.4.1 Virial expansion 59
3.4.2 Empirical equations of state 60
3.4.3 Example 61
3.4.4 Example 61
3.5 Corresponding states 62
3.5.1 Directed practice 62
3.6 Supercritical fluids 63
Exercises 63
Further reading 64
4 Liquids, liquid crystals, and ionic liquids 65
4.1 Liquid formation 65
4.2 Properties of liquids 65
4.3 Intermolecular interaction in liquids 67
4.3.1 Directed practice 70
4.4 Structure of liquids 70
4.4.1 Directed practice 72
4.5 Internal energy and equation of state of a rigid sphere liquid 72
4.5.1 General equations of state for liquids 73
4.6 Concentration units 73
4.7 Diffusion 75
4.7.1 Ficks first law of diffusion 75
4.7.2 Ficks second law of diffusion 75
4.7.3 Non-Fickian diffusion 77
4.8 Viscosity 77
4.9 Migration 79
4.10 Interface formation 80
4.11 Liquid crystals 82
4.11.1 Directed practice 84
4.12 Ionic liquids 84
Exercises 86
Further reading 87
5 Solids, nanoparticles, and interfaces 88
5.1 Solid formation 88
5.2 Electronic structure of solids 90
5.2.1 Directed practice 92
5.3 Geometrical structure of solids 92
5.3.1 Miller indices 95
5.4 Interface formation 96
5.4.1 Surface structure and adsorption sites 96
5.4.2 Surface defects 97
5.5 Glass formation 98
5.6 Clusters and nanoparticles 98
5.6.1 Directed practice 100
5.7 The carbon family: Diamond, graphite, graphene, fullerenes, and carbon nanotubes 100
5.7.1 Directed practice 103
5.8 Porous solids 103
5.8.1 Directed practice 104
5.9 Polymers and macromolecules 104
Exercises 106
Endnotes 106
Further reading 106
6 Statistical mechanics 107
6.1 The initial state of the universe 108
6.2 Microstates and macrostates of molecules 109
6.2.1 Directed practice 111
6.3 The connection of entropy to microstates 111
6.3.1 Example 113
6.4 The constant a: Introducing the partition function 113
6.4.1 The value of ?????? 114
6.5 Using the partition function to derive thermodynamic functions 114
6.5.1 Example 116
6.6 Distribution functions for gases 116
6.6.1 Directed practice 117
6.7 Quantum statistics for particle distributions 118
6.7.1 The distribution function for fermions 119
6.7.2 The distribution function for bosons 119
6.7.3 Distributions in the dilute gas limit 120
6.8 The Maxwell–Boltzmann speed distribution 122
6.9 Derivation of the ideal gas law 123
6.10 Deriving the Sackur–Tetrode equation for entropy of a monatomic gas 124
6.10.1 Directed practice 125
6.11 The partition function of a diatomic molecule 126
6.12 Contributions of each degree of freedom to thermodynamic functions 126
6.12.1 Translations 126
6.12.2 Rotations 126
6.12.3 Vibrations 129
6.12.4 Electronic excitation 130
6.13 The total partition function and thermodynamic functions 131
6.14 Polyatomic molecules 133
Exercises 135
Endnotes 136
Further reading 136
7 First law of thermodynamics 137
7.1 Some definitions and fundamental concepts in thermodynamics 138
7.2 Laws of thermodynamics 138
7.3 Internal energy and the first law 139
7.3.1 State versus path functions and reversibility 140
Reversible process 141
Irreversible process 141
7.4 Work 141
7.4.1 Example 142
7.4.2 Example 143
7.4.3 Directed practice 143
7.5 Intensive and extensive variables 143
7.6 Heat 144
7.6.1 Example 144
7.6.2 Example 145
7.7 Non-ideal behavior changes the work 145
7.7.1 Directed practice 146
7.8 Heat capacity 146
7.8.1 Example 147
7.9 Temperature dependence of Cp 147
7.9.1 Example 148
7.10 Internal energy change at constant volume 149
7.10.1 Example 149
7.11 Enthalpy 150
7.11.1 Example 150
7.11.2 Example 151
7.11.3 Directed practice 151
7.12 Relationship between CV and Cp and partial differentials 151
7.12.1 Example 153
7.12.2 Directed practice 153
7.13 Reversible adiabatic expansion/compression 153
7.13.1 Example 155
Exercises 156
Endnotes 158
Further reading 158
8 Second law of thermodynamics 159
8.1 The second law of thermodynamics 160
8.2 Thermodynamics of a hurricane 161
8.2.1 Carnot cycle 162
8.3 Heat engines, refrigeration, and heat pumps 165
8.3.1 Heat engine efficiency 165
8.3.2 Heat pumps and refrigerators 166
8.4 Definition of entropy 168
8.4.1 Thermodynamic definition 168
8.4.2 Statistical mechanical definition 168
8.4.3 Equivalence of thermodynamic and statistical mechanical definitions 169
8.5 Calculating changes in entropy 170
8.5.1 DS for isothermal processes and phase transitions 170
8.5.2 Entropy change during heating at constant pressure or constant volume 171
8.5.3 Entropy change when changing T and V 171
8.6 Maxwells relations 172
8.6.1 Example 174
8.6.2 Directed practice 174
8.7 Calculating the natural direction of change 174
8.7.1 Clausius inequality 176
Exercises 177
Endnotes 179
Further reading 179
9 Third law of thermodynamics and temperature dependence of heat capacity, enthalpy and entropy 180
9.1 When and why does a system change? 180
9.2 Natural variables of internal energy 181
9.3 Helmholtz and Gibbs energies 182
9.3.1 Example 182
9.4 Standard molar Gibbs energies 183
9.4.1 Example 184
9.4.2 Directed practice 184
9.5 Properties of the Gibbs energy 184
9.5.1 Gibbs–Helmholtz equation 185
9.5.2 Gibbs energy of an ideal gas at arbitrary pressure 187
9.5.3 Gibbs energy and electrical work 187
9.6 The temperature dependence of ??????rCp and H 188
9.7 Third law of thermodynamics 190
9.8 The unattainability of absolute zero 191
9.9 Absolute entropies 192
9.10 Entropy changes in chemical reactions 193
9.10.1 Example 194
9.10.2 Directed practice 194
9.11 Calculating at any temperature 195
Exercises 197
Further reading 200
10 Thermochemistry: The role of heat in chemical and physical changes 201
10.1 Stoichiometry and extent of reaction 201
10.2 Standard enthalpy change 202
10.2.1 Example 203
10.2.2 Directed practice 204
10.2.3 Temperature dependence of enthalpy of reaction 204
10.3 Calorimetry 204
10.3.1 Example 205
10.3.2 Example 206
10.3.3 Directed practice 207
10.4 Phase transitions 207
10.4.1 Example 209
10.4.2 Example 209
10.5 Bond dissociation and atomization 210
10.6 Solution 211
10.6.1 Directed practice 211
10.7 Enthalpy of formation 212
10.8 Hesss law 212
10.8.1 Example 212
10.8.2 Example 212
10.9 Reaction enthalpy from enthalpies of formation 213
10.9.1 Example 214
10.9.2 Example 214
10.10 Calculating enthalpy of reaction from enthalpies of combustion 214
10.10.1 Directed practice 215
10.11 The magnitude of reaction enthalpy 215
10.11.1 Directed practice 216
Exercises 216
Further reading 220
11 Chemical equilibrium 221
11.1 Chemical potential and Gibbs energy of a reaction mixture 221
11.2 The Gibbs energy and equilibrium composition 222
11.2.1 Gibbs energy and chemical potential determine the direction of change 222
11.2.2 Ideal gas equilibria 223
11.3 The response of equilibria to change 224
11.3.1 Response to temperature 225
11.3.2 Response to pressure 227
11.4 Equilibrium constants and associated calculations 229
11.4.1 Use of activities and concentrations 229
11.4.2 Heterogeneous/solution phase equilibria 230
11.4.3 Biochemical standard state 230
11.5 Acid–base equilibria 232
11.5.1 Ionization of water 232
11.5.2 Dissociation of weak acids 234
11.6 Dissolution and precipitation of salts 236
11.6.1 Solubility of sparingly soluble salts 237
11.6.2 Precipitation 238
11.7 Formation constants of complexes 239
11.8 Thermodynamics of self-assembly 242
11.8.1 Directed practice 242
Exercises 244
Endnote 248
Further reading 248
12 Phase stability and phase transitions 249
12.1 Phase diagrams and the relative stability of solids, liquids, and gases 249
12.2 What determines relative phase stability? 252
12.2.1 Directed practice 254
12.3 The p–T phase diagram 254
12.4 The Gibbs phase rule 257
12.5 Theoretical basis for the p–T phase diagram 258
12.6 Clausius–Clapeyron equation 260
12.6.1 Directed practice 261
12.6.2 Directed practice 262
12.7 Surface tension 262
12.7.1 Meniscus formation and capillary condensation 264
12.8 Nucleation 266
12.8.1 Classical nucleation theory 266
12.8.2 Classical versus nonclassical nucleation 268
12.8.3 Cloud formation: Heterogeneous versus homogeneous nucleation 269
12.9 Construction of a liquid–vapor phase diagram at constant pressure 270
12.10 Polymers: Phase separation and the glass transition 272
12.10.1 Directed practice 274
Exercises 274
Endnotes 275
Further reading 276
13 Solutions and mixtures: Nonelectrolytes 277
13.1 Ideal solution and the standard state 278
13.2 Partial molar volume 278
13.3 Partial molar Gibbs energy chemical potential 279
13.3.1 Chemical potential of a one-component system 279
13.3.2 Chemical potential of a multicomponent system 280
13.4 The chemical potential of a mixture and DmixG 281
13.5 Activity 283
13.5.1 Fugacity 284
13.6 Measurement of activity 284
13.6.1 Raoults law 285
13.6.2 Henrys law 286
13.6.3 Solubility of gases in liquids 288
13.7 Classes of solutions and their properties 289
13.7.1 Ideal solution/mixture 289
13.7.2 Gibbs energy of mixing: Ideal solutions 290
13.7.3 Entropy of mixing: Ideal solution 291
13.7.4 Enthalpy of mixing: Ideal solution 291
13.7.5 Real solutions (non-ideal solutions) 291
13.7.6 Gibbs energy of mixing: Real solutions 291
13.7.7 Entropy of mixing: Real solution 292
13.7.8 Enthalpy of mixing: Real solution 292
13.7.9 Subclassifications of real solutions 292
13.7.10 Excess functions 293
13.8 Colligative properties 293
13.8.1 Boiling point elevation 293
13.8.2 Freezing point depression 294
13.8.3 Osmosis 294
13.9 Solubility of polymers 297
13.10 Supercritical CO2 299
Exercises 301
Endnote 302
Further reading 302
14 Solutions of electrolytes 303
14.1 Why salts dissolve 303
14.2 Ions in solution 304
14.2.1 Directed practice 306
14.2.2 Directed practice 306
14.3 The thermodynamic properties of ions in solution 307
14.3.1 Enthalpy of hydration 307
14.3.2 Enthalpy, entropy and gibbs energy of ion formation in solutions 308
14.3.3 Directed practice 309
14.4 The activity of ions in solution 309
14.5 Debye–Hückel theory 310
14.5.1 Directed practice 311
14.5.2 Directed practice 311
14.6 Use of activities in equilibrium calculations 312
14.6.1 Acid–base equilibrium 312
14.6.2 Buffers 313
14.6.3 Solubility product 313
14.6.4 Directed practice 315
14.7 Charge transport 315
14.7.1 Directed practice 317
Exercises 318
Further reading 319
15 Electrochemistry: The chemistry of free charge exchange 320
15.1 Introduction to electrochemistry 321
15.1.1 Defining the terms of electrochemistry 321
15.1.2 Relating current flow to amount of substance reacted: Faraday’s law 323
15.1.3 The electrical double layer 324
15.2 The electrochemical potential 326
15.2.1 Why does an electron ‘hop’? 326
15.2.2 Relating the electrochemical potential to the chemical potential 329
15.3 Electrochemical cells 330
15.4 Potential difference of an electrochemical cell 332
15.4.1 The Nernst equation 333
15.4.2 Standard potentials 334
15.4.3 Measurement of the standard potential E°(Ag+/Ag) 334
15.4.4 Practical reference electrodes 337
15.5 Surface charge and potential 338
15.6 Relating work functions to the electrochemical series 339
15.7 Applications of standard potentials 341
15.7.1 Constructing a cell from a redox couple 341
15.7.2 Determining E? and ??????rG? for half-reactions 343
15.7.3 Determination of activity coefficients 343
15.7.4 Determination of equilibrium constants 344
15.7.5 Determination of thermodynamic functions 344
15.8 Biological oxidation and proton-coupled electron transfer 346
15.8.1 Biochemical standard electrode potential 347
15.8.2 Gibbs energy change in terminal respiratory cycle 347
15.8.3 Membrane potentials 348
Exercises 349
Endnotes 351
Further reading 352
16 Empirical chemical kinetics 353
16.1 What is chemical kinetics? 353
16.2 Rates of reaction and rate equations 355
16.2.1 Example 355
16.2.2 Directed practice 356
16.3 Elementary versus composite reactions 356
16.3.1 Example 357
16.4 Kinetics and thermodynamics 357
16.5 Kinetics of specific orders 358
16.5.1 First-order kinetics 358
16.5.2 Second-order kinetics 360
16.5.3 Pseudo-order kinetics 362
16.5.4 Zeroth-order kinetics 363
16.5.5 Summary of rate equations 364
16.6 Reaction rate determination 365
16.7 Methods of determining reaction order 366
16.7.1 Integration 366
16.7.2 Isolation 367
16.7.3 Differential method (method of initial rates) 367
16.7.4 Half-life 367
16.8 Reversible reactions and the connection of rate constants to equilibrium constants 368
16.8.1 Reversible reactions 368
16.8.2 Reversible reaction at equilibrium 369
16.9 Temperature dependence of rates and the rate constant 370
16.9.1 The Arrhenius equation 370
16.9.2 Non-Arrhenius behavior 373
16.10 Microscopic reversibility and detailed balance 373
16.11 Rate-determining step (RDS) 374
Exercises 375
Endnotes 379
Further reading 379
17 Reaction dynamics I: Mechanisms and rates 380
17.1 Linking empirical kinetics to reaction dynamics 380
17.2 Hard-sphere collision theory 381
17.2.1 Collision density 381
17.2.2 The energy requirement 382
17.2.3 The steric requirement 382
17.3 Activation energy and the transition state 384
17.4 Transition-state theory (TST) 386
17.4.1 Directed practice 388
17.5 Composite reactions and mechanisms 388
17.5.1 Types of steps 389
17.5.2 Steady-state approximation (SSA) 391
17.6 The rate of unimolecular reactions 392
17.7 Desorption kinetics 394
17.7.1 Directed practice 395
17.7.2 Directed practice 397
17.8 Langmuir (direct) adsorption 398
17.8.1 The Langmuir model of adsorption 398
17.8.2 Nondissociative (molecular) adsorption 398
17.8.3 Dissociative adsorption 400
17.9 Precursor-mediated adsorption 400
17.10 Adsorption isotherms 401
17.11 Surmounting activation barriers 402
Exercises 406
Endnotes 409
Further reading 410
18 Reaction dynamics II: Catalysis, photochemistry and charge transfer 411
18.1 Catalysis 412
18.2 Heterogeneous catalysis 413
18.2.1 Surface reaction mechanisms 414
18.2.2 Examples of Langmuir–hinshelwood dynamics 416
18.2.3 Molecular chemisorption: The Blyholder model of CO chemisorption 418
18.2.4 Dissociative chemisorption of H2: The Nørskov model 420
18.2.5 Promoters and poisons 421
18.2.6 Directed practice 422
18.3 Acid–base catalysis 422
18.4 Enzyme catalysis 423
18.4.1 Directed practice 427
18.5 Chain reactions 427
18.5.1 Directed practice 428
18.5.2 Chain polymerization 428
18.5.3 Self-catalyzed step polymerization 429
18.6 Explosions 430
18.6.1 Explosive limits 430
18.7 Photochemical reactions 431
18.7.1 Kinetics of photochemical reactions 431
18.8 Charge transfer and electrochemical dynamics 435
18.8.1 Rates of electrochemical reactions 438
18.8.2 Inner-sphere mechanism 439
18.8.3 Outer-sphere mechanism: Marcus theory of electron transfer 440
18.8.4 Heterogeneous electron transfer 444
Exercises 448
Endnotes 451
Further reading 451
19 Developing quantum mechanical intuition 453
19.1 Classical electromagnetic waves 454
19.1.1 Characteristics of light 454
19.1.2 Superposition of waves 456
19.1.3 Double slit interference 460
19.1.4 Multiple-slit interference 461
19.1.5 ‘Diffraction’ in crystals 462
19.2 Classical mechanics to quantum mechanics 463
19.3 Necessity for an understanding of quantum mechanics 464
19.3.1 Black-body radiation 465
19.3.2 Photoelectric effect 466
19.3.3 Electron energy loss spectroscopy 468
19.4 Quantum nature of light 468
19.4.1 Example 468
19.5 Wave–particle duality 469
19.5.1 Photon linear momentum and the de broglie relation 469
19.5.2 Elementary quantum particles and composite quantum particles 472
19.6 The Bohr atom 473
19.6.1 Example 477
Exercises 478
Endnotes 480
Further reading 481
20 The quantum mechanical description of nature 482
20.1 What determines if a quantum description is necessary? 483
20.2 The postulates of quantum mechanics 483
20.3 Wavefunctions 484
20.3.1 Mathematical requirements 484
20.3.2 Born interpretation of the wavefunction 485
20.4 The Schrödinger equation 487
20.4.1 Directed practice 489
20.5 Operators and eigenvalues 489
20.5.1 Example 490
20.6 Solving the Schrödinger equation 491
20.6.1 Free particle in one dimension 491
20.6.2 Linear momentum of a free particle 493
20.6.3 Wavepackets 494
20.7 Expectation values 495
20.7.1 Example 496
20.7.2 Example 496
20.8 Orthonormality and superposition 497
20.8.1 Example 498
20.8.2 Example 498
20.8.3 Variational principle 499
20.9 Dirac notation 500
20.9.1 Example 501
20.9.2 Directed practice 501
20.10 Developing quantum intuition 501
20.10.1 The uncertainty principle 501
20.10.2 Directed practice 502
20.10.3 Position–momentum uncertainty relationship 503
20.10.4 Energy–time uncertainty relationship 503
20.10.5 Coordinate systems 503
20.10.6 Evaluation of brackets by inspection 505
Exercises 506
Endnotes 508
Further reading 508
21 Model quantum systems 509
21.1 Particle in a box 510
21.1.1 One-dimensional box 510
21.1.2 Three-dimensional box 512
21.1.3 Quantum confinement and the correspondence principle 513
21.2 Quantum tunneling 515
21.3 Vibrational motion 517
21.3.1 Directed practice 520
21.4 Angular momentum 520
21.4.1 The operators 520
21.4.2 Particle on a ring 523
21.4.3 Particle on a sphere 524
21.4.4 Spin 527
21.4.5 Spin in a magnetic field 528
21.4.6 Directed practice 530
Exercises 531
Endnotes 533
Further reading 533
22 Atomic structure 534
22.1 The hydrogen atom 535
22.1.1 Set up hamiltonian and solve Schrödinger equation 535
22.2 How do you make it better? The Dirac equation 538
22.2.1 Directed practice 540
22.3 Atomic orbitals 540
22.3.1 Comparing representations 540
22.3.2 Shells and subshells 541
22.3.3 Shapes of orbitals 542
22.3.4 Directed practice 544
22.4 Many-electron atoms 544
22.4.1 Set up the hamiltonian 544
22.4.2 The central field model 545
22.4.3 Pauli exclusion and Aufbau principles 546
22.4.4 Directed practice 546
22.5 Ground and excited states of He 548
22.5.1 Ground state 548
22.5.2 Excited states 548
22.5.3 He atom wavefunctions 548
22.6 Slater–Condon theory for approximating atomic energy levels 550
22.6.1 Directed practice 553
22.6.2 Directed practice 553
22.7 Electron configurations 553
22.7.1 Rydberg series 555
Exercises 556
Endnotes 558
Further reading 558
23 Introduction to spectroscopy and atomic spectroscopy 559
23.1 Fundamentals of spectroscopy 560
23.1.1 Terminology 560
23.1.2 Lineshape and linewidth 561
23.1.3 Types of spectroscopy 563
23.2 Time-dependent perturbation theory and spectral transitions 564
23.2.1 Einstein transition probabilities 566
23.3 The Beer–Lambert law 567
23.3.1 Transmittance and absorbance 567
23.3.2 Relating absorption coefficient, Einstein coefficients and transition dipole moment 568
23.4 Electronic spectra of atoms 570
23.4.1 Transition dipole moment 570
23.4.2 Hydrogenic atoms 570
23.4.3 Multi-electron atoms 571
23.5 Spin–orbit coupling 571
23.5.1 Total angular momentum 574
23.6 Russell–Saunders (LS) coupling 574
23.6.1 Total orbital angular momentum 575
23.6.2 Spin multiplicity 577
23.6.3 Total angular momentum 577
23.6.4 Russell–Saunders coupling term and level symbols 578
23.6.5 Hund’s rules 578
23.7 jj-coupling 579
23.7.1 Example of jj-coupling 579
23.8 Selection rules for atomic spectroscopy 580
23.8.1 Hydrogenic atoms 580
23.8.2 Multi-electron atoms 580
23.9 Photoelectron spectroscopy 581
23.9.1 X-ray photoelectron spectroscopy (XPS) 582
23.9.2 Auger electron spectroscopy (AES) 584
Exercises 586
Endnotes 589
Further reading 589
24 Molecular bonding and structure 590
24.1 Born–Oppenheimer approximation 591
24.2 Valence bond theory 593
24.2.1 Homonuclear diatomic molecules 593
24.2.2 Polyatomic molecules 595
24.3 Molecular orbital theory 596
24.4 The hydrogen molecular ion H+2 597
24.4.1 Directed practice 598
24.4.2 Molecular orbitals from linear combinations of atomic orbitals (LCAO-MO) 598
24.5 Solving the H2 Schrödinger equation 600
24.5.1 Directed practice 602
24.6 Homonuclear diatomic molecules 605
24.6.1 Directed practice 608
24.7 Heteronuclear diatomic molecules 608
24.7.1 Directed practice 610
24.8 The variational principle in molecular orbital calculations 611
24.9 Polyatomic molecules: The Hückel approximation 613
24.9.1 Applying Hückel molecular orbital theory to allyl C3H3 614
24.10 Density functional theory (DFT) 617
Exercises 618
Endnotes 621
Further reading 621
25 Molecular spectroscopy and excited-state dynamics: Diatomics 622
25.1 Introduction to molecular spectroscopy 623
25.2 Pure rotational spectra of molecules 624
25.2.1 Diatomic molecules 624
25.2.2 Polyatomic molecules 628
25.3 Rovibrational spectra of molecules 629
25.3.1 Diatomic molecules 629
25.3.2 P, Q, and R branches 631
25.3.3 Anharmonicity and the morse oscillator 631
25.3.4 Vibrations of polyatomic molecules 633
25.4 Raman spectroscopy 634
25.4.1 Directed practice 636
25.4.2 Directed practice 636
25.5 Electronic spectra of molecules 637
25.5.1 Born–Oppenheimer meets Franck–Condon 637
25.5.2 Rovibrational structure of electronic transitions 638
25.5.3 State designations for linear molecules 638
25.5.4 Selection rules 640
25.6 Excited-state population dynamics 642
25.6.1 Radiative decay (photon emission) 642
25.6.2 Nonradiative relaxationnon-radiative relaxation 642
25.6.3 Photodissociation and pre-dissociation 644
25.6.4 Quenching and quantum yield 646
25.7 Electron collisions with molecules 648
25.7.1 Directed practice 648
Exercises 649
Endnotes 652
Further reading 653
26 Polyatomic molecules and group theory 654
26.1 Absorption and emission by polyatomics 655
26.2 Electronic and vibronic selection rules 657
26.3 Molecular symmetry 661
26.3.1 Rotation – n-fold axis of symmetry, Cn 661
26.3.2 Reflection – plane of symmetry, ?????? 664
26.3.3 Center of inversion, i 665
26.3.4 Rotation–reflection axis of symmetry, Sn 665
26.3.5 Identity element of symmetry, E 665
26.4 Point groups 665
26.5 Character tables 667
26.6 Dipole moments 670
26.6.1 Directed practice 672
26.7 Rovibrational spectroscopy of polyatomic molecules 672
26.7.1 Vibrational structure of polyatomics 672
26.7.2 Rotational structure of polyatomics 675
26.8 Excited-state dynamics 676
26.8.1 Radiative transitions 678
26.8.2 Nonradiative transitions 681
26.8.3 Quenching 682
Exercises 685
Endnotes 687
Further reading 687
27 Light–matter interactions: Lasers, laser spectroscopy, and photodynamics 688
27.1 Lasers 689
27.1.1 Directed practice 693
27.2 Harmonic generation (SHG and SFG) 693
27.2.1 Directed practice 695
27.3 Multiphoton absorption spectroscopy 695
27.3.1 Laser-induced fluorescence (LIF) 697
27.3.2 Stimulated emission pumping 699
27.3.3 Superresolution fluorescence microscopy 700
27.3.4 Resonance-enhanced multiphoton ionization (REMPI) 701
27.3.5 Multiphoton photoelectron spectroscopy (MPPE) 702
27.4 Cavity ring-down spectroscopy 702
27.5 Femtochemistry 705
27.5.1 Following molecular dynamics in real time 705
27.5.2 Coherent control 708
27.6 Beyond perturbation theory limit: High harmonic generation 708
27.7 Attosecond physics 710
27.7.1 Directed practice 710
27.8 Photosynthesis 711
27.9 Color and vision 714
27.9.1 Transition metal impurities and charge transfer 714
27.9.2 Color centers 715
27.9.3 Color perception 716
Exercises 717
Endnotes 718
Further reading 719
APPENDIX 1 Basic calculus and trigonometry 720
Characteristics of derivatives 720
Integrals 721
Mathematical relations 721
Trigonometry 722
Further reading 722
APPENDIX 2 The method of undetermined multipliers 723
APPENDIX 3 Stirling’s theorem 725
APPENDIX 4 Density of states of a particle in a box 726
APPENDIX 5 Black-body radiation: Treating radiation as a photon gas 728
APPENDIX 6 Definitions of symbols used in quantum mechanics and quantum chemistry 730
APPENDIX 7 Character tables 732
APPENDIX 8 Periodic behavior 734
APPENDIX 9 Thermodynamic parameters 737
Index 739
frontcover 747
backcover 748

Produkt-Details

• Erscheint lt. Verlag: 7.9.2016
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Chemie ► Physikalische Chemie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik
• Schlagworte: Analytical Chemistry • Analytische Chemie • Chemie • Chemistry • detection • equation manipulation • intermolecular interactions • Materials properties • Materials Science • Materialwissenschaften • Physical Chemistry • Physikalische Chemie • Quantenphysik • synthesis
• ISBN-10: 1-118-75121-3 / 1118751213
• ISBN-13: 978-1-118-75121-3 / 9781118751213