Principles of physical chemistry:
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
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Hoboken, NJ
Wiley
2009
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| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XLII, 1032 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 9780471965411 9780470089644 |
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| 100 | 1 | |a Kuhn, Hans |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Principles of physical chemistry |c by Hans Kuhn ; Horst-Dieter Försterling ; David H. Waldeck |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2009 | |
| 300 | |a XLII, 1032 S. |b Ill., graph. Darst. |e 1 CD-ROM (12 cm) | ||
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| 700 | 1 | |a Försterling, Horst-Dieter |d 1934- |e Verfasser |0 (DE-588)141908599 |4 aut | |
| 700 | 1 | |a Waldeck, David H. |e Verfasser |4 aut | |
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| adam_text | Titel: Principles of physical chemistry
Autor: Kuhn, Hans
Jahr: 2009
Contents
List of Foundations, xxiii
List of Justifications, xxix
Preface, xxxiii
Acknowledgments, xxxv
Authors Biography, xxxvii
List of Symbols, xxxix
Introduction, 1
1 Wave-Particle Duality, 3
1.1 Overview of Quantum Mechanics, 3
1.1.1 Historical Highlights, 3
1.1.2 An Approach to Quantum Mechanics, 4
1.2 Light, 5
1.2.1 Particle Nature of Light: Photoelectric Effect, 6
1.2.2 Wave Nature of Light: Diffraction, 7
1.2.3 Interpretation of the Experiments, 12
1.3 Electrons, 12
1.3.1 Particle Nature of Electrons, 13
1.3.2 Wave Nature of Electrons, 13
1.3.3 Interpretation of the Experiments, 15
1.3.4 Formal Similarity Between Electron and Photon, 16
1.4 Questions Arising about Wave-Particle Duality, 16
1.4.1 Single Event—Probability Statement; Collective
Behavior—Definite Statement, 16
1.4.2 Wave-Particle Duality and the Need to Abandon Familiär Ways of
Thinking, 18
1.5 Conclusion, 20
2 Essential Aspects ofStructure and Bonding, 21
2.1 Introduction, 21
2.2 Distinct Energy States, 22
2.2.1 Atomic Spectra, 22
2.2.2 Franck-Hertz Experiment, 23
2.3 Standing Waves, 24
2.3.1 Particle Between Parallel Walls, 25
2.3.2 Ill-Posed Questions, 29
233 Electron in a Cubic Box, 29
vii
viii CONTENTS
2.4 Ground-State H Atom, 30
2.4.1 Result of Rigorous Treatment (see Chapter 4), 30
2.4.2 Box Model for H Atom and the Variational Principle, 32
2.5 Ground-State H+, 36
2.5.1 Forming H* from an H Atom and a Proton, 36
2.5.2 Box Test Functions for H+, 37
2.6 Conclusion, 40
Reference, 41
3 Schrodinger Equation, 42
3.1 Introduction, 42
3.2 Wave Equation and Schrodinger Equation, 42
3.2.1 Wave Equation, 42
3.2.2 One-Dimensional Schrodinger Equation, 45
3.2.3 Three-Dimensional Schrodinger Equation, 53
3.3 Normalized Wavefunction: p = iff2, 57
3.3.1 One-Dimensional Box Function, 57
3.3.2 Three-Dimensional Box Function, 59
3.4 Orthogonality of the Wavefunctions, 60
3.4.1 Nondegenerate Wavefunctions, 60
3.4.2 Degenerate Wavefunctions, 61
3.4.3 Degeneracy Removed in an Electric Field, 62
3.5 Bohr Correspondence Principle and Generalized Form
of Quantum Mechanics, 63
3.5.1 Bohr Correspondence Principle, 64
3.5.2 popif of a Free Electron and Eigenvalue Equations, 65
3.5.3 Electron Moving on a Circle, 66
3.5.4 Degeneracy Removed by Magnetic Field, 68
3.5.5 Operator for Angular Momentum, 68
3.5.6 Operator ihd/dt and the Time-Dependent Schrodinger
Equation, 69
3.5.7 Relation Between Time-Independent and Time-Dependent
Schrodinger Equations, 70
3.5.8 Average Values of an Observable (also Called Expectation
Value), 71
3.5.9 Heisenberg Uncertainty Principle, 71
3.6 Summary of Postulates of Quantum Mechanics, 74
3.7 Conclusion, 75
References, 75
4 Hydrogen Atom, 76
4.1 Introduction, 76
4.2 Hydrogen Atom in the Ground State, 76
4.2.1 Wavefunction, 77
4.2.2 Energy, 78
4.2.3 Radial Probability Distribution of Electron, 79
CONTENTS ix
4.2.4 Most Probable Distance and Average Distance, 80
4.2.5 Average Potential Energy and Virial Theorem, 81
4.3 H Atom in Excited States, 82
4.3.1 Energies, 82
4.3.2 Wavefunctions, 83
4.3.3 Radial Probability Distribution Function and Average
Distance, 87
4.3.4 Emission Spectra, 88
4.3.5 Degeneracy of H-atom Orbitals Can Be Removed
by a Magnetic Field, 90
4.4 Conclusion, 92
5 Atoms and the Variational Principle, 93
5.1 Introduction, 93
5.2 Vanational Principle, 93
5.2.1 Introducing the Variational Principle, 93
5.2.2 Justification of the Variational Principle, 94
5.3 He Atom, 98
5.3.1 Ground State of He, 98
5.3.2 Indistinguishability of Electrons, 103
5.3.3 Excited States of He Described by the Product of One-Electron
Trial Functions (Orbitals), 103
5.4 Electron Spin and Pauli Exclusion Principle, 104
5.4.1 Energy Splitting in a Magnetic Field, Electron Paramagnetic
Resonance, 104
5.4.2 Spin Variables, 107
5.4.3 Antisymmetry Postulate (Pauli Exclusion Principle), 109
5.4.4 Singlet-Triplet Splitting: Magnetic Forces Negligible, 111
5.5 Many-Electron Atoms, 112
5.5.1 Atomic Number Z and lonization Energy, 112
5.5.2 Electronic Structure of the First Three Elements, 113
5.5.3 Aufbau Principle and the Periodic Table, 115
5.5.4 Periodic Properties of the Elements, 120
5.6 Spin-Orbit Interactions of Electrons in Atoms, 122
5.6.1 Angular Momentum and Vector Model of Atoms, 123
5.6.2 Atomic Term Symbols, 125
5.7 Conclusion, 127
References, 127
6 A Quantitative View of Chemical Bonding, 128
6.1 Introduction, 128
6.2 H^ Molecular Ion, 129
6.2.1 Electron Described by Exact Wavefunction, 129
6.2.2 Electron Density and the Chemical Bond, 131
6.2.3 Electron Described by the Linear Combination of Atomic
Orbitals (LCAO) Wavefunction, 133
x CONTENTS
6.2.4 Comparison of Box Model and LCAO Method, 136
6.2.5 Excited State of H : Bonding and Antibonding Orbitals, 138
6.3 H2: A Two-Electron System, 139
6.3.1 Rigorous Treatment, 139
6.3.2 Product of One-Electron Wavefunctions, 141
6.3.3 Indistinguishability of Electrons, 143
6.3.4 Pauli Exclusion Principle: Electronic Wavefunctions Must Be
Antisymmetric, 146
6.4 Tunneling, 148
6.4.1 Electron Oscillating Between Protons a and b, 148
6.4.2 Tunneling Barrier and Frequency of Oscillation, 148
6.4.3 Importance of Tunneling in Redox Chemistry, 148
6.5 Conclusions, 149
References, 149
7 Bonding Described by Electron Pairs and Molecular Orbitals, 150
7.1 Introduction, 150
7.2 Electron Pair Bonds, 150
7.2.1 Connectivity of Atoms in Three-Atom Molecules, 151
7.2.2 Geometries for Electron Pair Bonds, 154
7.2.3 Limitations of the Electron Pair Model, 160
7.3 Molecular Orbitals, 161
7.3.1 Homonuclear Diatomics, 161
7.3.2 Heteronuclear Diatomics, 167
7.3.3 Triatomics (H2O), 170
7.3.4 Polyatomics, 174
7.4 Polarity, Bond length, and Elasticity, 177
7.4.1 Polarity of Bonds and Electronegativity, 177
7.4.2 Covalent Radii and Van der Waals Radii, 179
7.4.3 Stretching, Bending, and Torsion of Bonds, 182
7.5 Conclusions, 188
References, 188
8 Molecules with n-Electron Systems, 189
8.1 Introduction, 189
8.2 Bonding Properties of 7t-Electrons, 190
8.2.1 a -Bonded Molecular Skeleton and tt -Electrons, 190
8.2.2 Overview of Models for it-Systems, 192
8.3 Free Electron Molecular Orbital (FEMO) Model, 194
8.3.1 Ethene, Butadiene, Amidinium 7i-Electron Chains, 194
8.3.2 Benzene: A Tt-Electron Ring, 195
8.3.3 Charge Density dQ/ds, 197
8.3.4 Branched Molecules, 200
8.4 Bondlength Consistent With Total it-Electron Density Method
(BCD), 203
8.5 Principles of Density Functional Theory (DFT), 209
8.6 HMO Model, 210
8.6.1 Wavefunctions and Energies, 210
CONTENTS xi
8.6.2 Application of the HMO Method to 7t-Electron Chains, 213
8.6.3 Bond Length and HMO Bond Order, 215
8.7 Resonance, 216
8.8 Conclusions, 218
References, 219
9 Absorption of Light, 220
9.1 Introduction, 220
9.2 Excitation of it-Electron Systems, 220
9.2.1 Basic Experimental Facts, 220
9.2.2 Absorption Maxima of Dyes, 226
9.2.3 Strength and Polarization of Absorption Bands, 231
9.2.4 Hetero-Atoms as Probes for Electron Distribution, 235
9.2.5 HOMO-LUMO Gap by Bond Alternation, 239
9.2.6 Cyclic jr-Systems, 242
9.2.7 Coupling of n-Electrons, 247
9.3 Optical Activity, 249
9.3.1 Rotatory Dispersion, 250
9.3.2 Ellipticity and Circular Dichroism, 251
9.3.3 Anisotropy Factor g for Model in Fig. 9.23, 254
9.3.4 Absolute Configuration of Chiral Molecules, 255
9.3.5 Circular Dichroism of Spirobisanthracene, 255
9.3.6 Circular Dichroism of Chiral Cyanine Dye, 258
9.4 Conclusions, 260
References, 260
10 Emission of Light, 261
10.1 Introduction, 261
10.2 Spontaneous Emission, 261
10.2.1 Fluorescence, 262
10.2.2 Phosphorescence and Triplet States, 267
10.2.3 Relative Energetics of Fluorescence, Phosphorescence,
and Absorption, 270
10.2.4 Quenching of Fluorescence, 272
10.2.5 Absorption from Excited States, 273
10.3 Stimulated Emission and Laser Action, 275
10.3.1 Inversion of Population, 276
10.3.2 Dye Laser Operation, 276
10.3.3 Excimer and Exciplex Laser, 279
10.4 Conclusions, 279
References, 279
11 Nuclei: Particle and Wave Properties, 280
11.1 Introduction, 280
11.2 Rotational Motion of Molecules, 281
11.2.1 Diatomic Quantum-Mechanical Rotator, 281
11.2.2 Polyatomic Molecules, 284
11.2.3 Rotational Spectra, 287
xii CONTENTS
11.3 Vibrational Motion of Molecules, 293
11.3.1 Classical Oscillator, 293
11.3.2 Quantum-Mechanical Harmonic Oscillator, 296
11.3.3 Vibrational-Rotational Spectra, 301
11.3.4 Quantum-Mechanical Anharmonic Oscillator, 310
11.4 Raman Spectra, 315
11.4.1 Rayleigh Scattering, 315
11.4.2 Raman Spectroscopy, 317
11.4.3 Rotational Raman Spectra of Heteronuclear Diatomic
Molecules, 318
11.4.4 Raman Spectra of Poly atomics, 322
11.5 Vibrational Structure of Electronic Spectra, 324
11.5.1 Franck-Condon Principle, 325
11.5.2 Photoelectron Spectroscopy, 328
11.5.3 Polyatomic Molecules, 331
11.6 Conclusion, 336
References, 336
12 Nuclear Spin, 337
12.1 Introduction, 337
12.2 Nuclear Spin: Fundamentals, 337
12.2.1 Spin of Protons in H2, 337
12.2.2 Antisymmetry of Total Wavefunction of a Molecule Including
Electrons and Nuclei, 338
12.2.3 Nuclei With Half-Integer Spin (Antisymmetric Total
Wavefunction) and Nuclei With Integral Spin
(Symmetric Total Wavefunction), 340
12.3 Nuclear Magnetic Resonance (NMR), 343
12.3.1 Fundamentals, 343
12.3.2 Chemical Shift, 345
12.3.3 Fine Structure of NMR Spectra, 347
12.3.4 NMR Spectroscopy for Determination of Protein Structures in
Solution, 349
12.3.5 Magnetic Resonance Imaging (MRI), 350
12.4 Conclusion, 350
References, 350
13 Solids and Intermolecular Forces, 351
13.1 Introduction, 351
13.2 Ionic Crystals, 352
13.2.1 Bond Energy of an Ion Pair, 352
13.2.2 Lattice Types, 354
13.3 Metals, 358
13.3.1 Free Electron Model for Conduction Electrons, 358
13.3.2 Cohesion Energy of Metals, 364
133.3 Quantum Wires and Nanostructure, 366
CONTENTS xlii
13.4 Semiconductors, 369
13.4.1 Soliton Conductors: Polyacetylene, 369
13.4.2 Silicon, 370
13.4.3 Semiconductor Bandgap, 371
13.4.4 Semiconductor Quantum Dots, 372
13.5 Molecular Crystals and Intermolecular Forces, 374
13.5.1 Electrostatic Forces, the Dipole, 375
13.5.2 Hydrogen Bonds, 378
13.5.3 Induction Forces, 381
13.5.4 Dispersion Forces, 383
13.6 Conclusions, 386
References, 386
14 Thermal Motion of Molecules, 387
14.1 Introduction, 387
14.2 Kinetic Gas Theory and Temperature, 387
14.2.1 Thermal Motion and Pressure, 388
14.2.2 Avogadro s Law, 395
14.2.3 Thermal Equilibration and Heat, 397
14.2.4 Ideal Gas Law and the Definition of Absolute
Temperature, 397
14.2.5 Law of Partial Pressures, 401
14.3 Speed and Collisions of Gas Molecules, 402
14.3.1 Average Speed of Molecules in a Gas, 402
14.3.2 Mean Free Path and Number of Collisions, 405
14.3.3 Diffusion, 408
14.3.4 Viscosity Arising from Collisions of Molecules, 422
14.4 Thermal Motion in Liquids, 426
14.4.1 Collisions in Liquids, 426
14.4.2 Diffusion Coefficient D of a Liquid, 427
14.4.3 Viscosity of a Liquid, 428
14.4.4 Stokes-Einstein Equation, 429
14.5 Conclusions, 431
References, 431
15 Energy Distribution in Molecular Assemblies, 433
15.1 Introduction, 433
15.2 The Boltzmann Distribution Law, 434
15.2.1 System Consisting of Two Quantum States, 434
15.2.2 Systems Consisting of Many Quantum States, 436
15.2.3 Internal Energy U, 438
15.3 Electronic Energy, 439
15.4 Vibrational Energy, 440
15.4.1 Population Number Nn of a Harmonic Oscillator, 441
15.4.2 Internal Energy Uvn, of Diatomic Molecules, 444
15.4.3 Internal Energy Uvn, of Polyatomic Molecules, 446
xiv CONTENTS
15.5 Rotational Energy, 448
15.5.1 Population Number Nj of Rigid Rotator
(Heteronuclear Molecules), 449
15.5.2 Internal Energy UI0t of Rotation
(Heteronuclear Molecules), 451
15.5.3 Homonuclear Diatomic Molecules: Ortho- and
Para-H2, 453
15.6 Translational Energy, 455
15.6.1 Internal Energy [/trans of Translation According to Quantum
Mechanics, 455
15.6.2 Maxwell-Boltzmann Distribution of Speeds, 456
15.7 Characteristic Temperature, 462
15.8 Proving the Boltzmann Distribution for Distinguishable
Particles, 463
15.8.1 Distribution of N Particles Among Three Levels with Given
Internal Energy, 463
15.8.2 Rigorous Treatment, 468
15.9 Proving the Boltzmann Distribution for Indistinguishable Particles
(High Temperature), 469
15.9.1 Number of Available Quantum States, 469
15.9.2 Number of Representations and Boltzmann Law, 470
15.9.3 Calculating the Internal Energy U of an Ideal Atomic
Gas, 471
15.9.4 Relation Between 0 and T, 472
15.10 Energy Distribution of Fermions and Bosons Among Quantum
States, 472
15.11 Conclusions, 475
Reference, 475
16 Work w, Heat q, and Internal Energy U, 476
16.1 Introduction, 476
16.2 Thermodynamic Systems, 477
16.2.1 Defining System and Surroundings, 477
16.2.2 Defining Thermodynamic States, 477
16.2.3 Change of State, 480
16.3 Change of State at Constant Volume (Isochoric Process), 481
16.3.1 Change of Internal Energy A U and the Heat q, 482
16.3.2 Heat Capacity Cy: Definition, 484
16.3.3 Translational Contribution to Cy of a Gas, 485
16.3.4 Rotational and Vibrational Contributions to Cy
of a Gas, 486
16.3.5 Ortho- and Para-Hj: Fascinating Quantum Effects
on Cv, 488
16.3.6 Electronic Contribution to Cy (Cy,ei), 489
16.3.7 Heat Capacity and Characteristic Temperature, 490
16.3.8 Cv of Solids, 491
CONTENTS XV
16.4 Change of State at Constant Pressure (Isobaric Process), 494
16.4.1 Change of Internal Energy AU: Heat q and work w, 494
16.4.2 Enthalpy H and Heat Capacity Cp: Definition, 495
16.5 Heat Exchange and Chemical Reactions, 498
16.5.1 Reaction at Constant Volume: AU, 498
16.5.2 Reaction at Constant Pressure: AH, 501
16.5.3 Temperature Dependence of AU and AH, 502
16.5.4 Molar Enthalpies of Formation from Elements
AfH°, 505
16.5.5 Molar Enthalpy of Reaction Ar#°, 505
16.5.6 Bond Enthalpies and Bond Energies, 508
16.5.7 Enthalpies and Reaction Cycles, 509
16.6 Conclusions, 510
References, 511
17 Reversible Work w^y, Reversible Heat ^rev, and Entropy S, 512
17.1 Introduction, 512
17.2 Irreversible and Reversible Changes of State, 513
17.2.1 Irreversible Changes, 513
17.2.2 Reversible Changes, 513
17.3 Counting the Number of Representations of a Thermodynamic
State, Q, 523
17.3.1 Distribution Possibilities, 523
17.3.2 Number of Representations £2 of an Atomic Gas in a Given
Thermodynamic State, 526
17.4 The Entropy: S = k In ft, 529
17.4.1 Entropy of Subsystems, 529
17.4.2 Entropy of Atomic Gas: Sackur-Tetrode Equation, 530
17.5 Entropy Change AS, 533
17.5.1 Temperature Equilibration: Entropy Increase, 534
17.5.2 Mixing: Entropy Increase, 536
17.5.3 Entropy Cannot Decrease for an Isolated System, 537
17.5.4 Entropy Can Decrease in Closed Systems, 537
17.6 Heat and Entropy Change, 537
17.6.1 Heat and Entropy Change for an Ideal Gas, 538
17.6.2 Cyclic Processes (AS — 0) and Processes in Isolated Systems
(AS 0), 542
17.6.3 Heat and Entropy Change in Arbitrary Processes, 542
17.7 Thermodynamic Temperature Scale and Cooling, 543
17.7.1 Thermodynamic Temperature Scale, 543
17.7.2 How Low Can Temperature Go?, 547
17.8 Entropies of Substances, 547
17.8.1 Entropy of an Atomic Gas, 550
17.8.2 Entropy of Diatomic Gases, 553
17.8.3 Entropy of Polyatomic Gases, 555
17.8.4 Entropy of Different Substances, 557
xvi CONTENTS
17.9 Laws of Thermodynamics, 559
17.10 Conclusions, 561
References, 561
18 General Conditions for Spontaneity and its Application to Equilibria of Ideal
Gases and Dilute Solutions, 562
18.1 Introduction, 562
18.2 General Conditions for Spontaneity, 563
18.2.1 Helmholtz Energy A, 565
18.2.2 Gibbs Energy G, 566
18.3 AG and its Dependence on Temperature, 567
18.3.1 Molar Gibbs Energy of Formation from Elements
AfG°, 567
18.3.2 Molar Gibbs Energy of Reaction ArG°, 567
18.3.3 Temperature Dependence of AG°, 568
18.4 Pressure Dependence of AG in Ideal Gases, 570
18.4.1 Vapor Pressure (Clausius-Clapeyron Equation), 572
18.4.2 Chemical Evolution of a Gas, 574
18.5 AG and Chemical Equilibrium in Ideal Gases, 575
18.5.1 Formal Derivation of Mass Action Law, 575
18.5.2 Mass Action Law: A Direct Consequence of the Relation
Between Work and Heat, 578
18.5.3 Applying the Mass Action Law, 581
18.5.4 Temperature Dependence of Equilibrium Constant K, 584
18.5.5 Pressure Changes and Equilibrium, 588
18.5.6 Reactions Involving Gases and Immiscible Condensed
Species, 589
18.5.7 Equilibrium Constant from Molecular Properties, 590
18.6 AG and Equilibrium in Dilute Solution, 593
18.6.1 Osmotic Pressure and Concentration, 593
18.6.2 Depression of Vapor Pressure (Raoult s law), 596
18.6.3 Elevation of Boiling Point and Depression of Melting
Point, 600
18.6.4 Mass Action Law (Solutions of Neutral Particles), 602
18.6.5 Mass Action Law (Solutions of Charged Particles), 604
18.6.6 Gibbs Energy of Formation in Aqueous Solution, 604
18.6.7 Part of Reactants or Products in Condensed or Gaseous
State, 607
18.7 Conclusions, 608
References, 608
19 Formal Thermodynamics and its Application to Phase Equilibria, 609
19.1 Introduction, 609
19.2 Internal Energy, Enthalpy, Work, and Heat, 609
19.2.1 Work, 610
19.2.2 Heat, 611
CONTENTS xvii
19.2.3 Relating U and H to Measurable Quantities, 612
19.2.4 Maxwell Relations, 615
19.2.5 An Important Application: Calculating Cp — Cy, 615
19.3 Spontaneity and Free Energy, 617
19.3.1 Helmholtz Energy A, 618
19.3.2 Gibbs Energy G, 619
19.4 Phase Equilibria and Phase Transitions, 620
19.4.1 Solid-Liquid Equilibria, 622
19.4.2 Liquid-Gas and Solid-Gas Equilibria, 624
19.4.3 Phase Diagrams and Phase Rule, 626
19.5 Conclusions, 630
References, 630
20 Real Gases, 631
20.1 Introduction, 631
20.2 AG for Real Gases and the Fugacity, 631
20.3 Equations of State for Real Gases, 634
20.3.1 Hard Sphere Gas, 634
20.3.2 Van der Waals Equation, 637
20.3.3 Critical Point and Van der Waals Constants, 638
20.3.4 Virial Equation of State, 641
20.4 Change of State of Real Gases, 644
20.4.1 Adiabatic Expansion into Vacuum, 644
20.4.2 Joule-Thomson Effect, 646
20.5 Chemical Equilibria Involving Real Gases, 649
20.6 Conclusions, 651
References, 651
21 Real Solutions, 652
21.1 Introduction, 652
21.2 Partial Molar Quantities and Thermodynamics of Multicomponent
Systems, 652
21.2.1 Partial Molar Volume, 653
21.2.2 Chemical Potential, 654
21.2.3 Thermodynamic Relations, 655
21.3 Activities and Activity Coefficient for Real Solutions, 657
21.3.1 Activity from Vapor Pressure Above a Solution, 657
21.3.2 Activity from Osmotic Pressure, 659
21.4 Phase Transitions of Solutions, 661
21.4.1 Elevation of Boiling Point and Depression of Melting
Point, 661
21.4.2 Solutions with Two Volatile Components, 663
21.5 Mass Action Law For Reactions in Solution, 665
21.6 Electrolyte Solutions and the Debye-Hiickel Theory, 667
21.6.1 Debye-Hiickel Theory for Electrolytes, 667
21.7 Conclusions, 671
References, 671
xviii CONTENTS
22 Reaction Equilibria in Aqueous Solutions and Biosystems, 672
22.1 Introduction, 672
22.2 Proton Transfer Reactions: Dissociation of Weak Acids, 673
22.2.1 Henderson-Hasselbalch Equation, 673
22.2.2 Degree of Dissociation in Aqueous Solution, 675
22.2.3 Degree of Dissociation in a Buffer Solution, 676
22.2.4 Titration Curve of a Weak Acid, 677
22.3 Stepwise Proton Transfer, 678
22.3.1 Diprotic Acid, 678
22.3.2 Amino Acids, 681
22.4 Electron Transfer Reactions, 682
22.4.1 Electron Transfer from Metal to Proton: Dissolution of Metals
in Acid, 682
22.4.2 Electron Transfer from Metal 1 to Metal 2 Ion:
Coupled Redox Reactions, 684
22.4.3 Electron Transfer to Proton at pH 7: AG° , 685
22.4.4 Photoinduced Electron Transfer, 686
22.5 Electron Transfer Coupled with Proton Transfer, 688
22.6 Group Transfer Reactions in Biochemistry, 691
22.6.1 Group Transfer Potential, 692
22.6.2 Coupled Reactions in Biology, 692
22.7 Bioenergetics, 693
22.7.1 Synthesis of Glucose, 694
22.7.2 Combustion of Glucose, 695
22.7.3 Energy Balance of Formation and Degradation (Combustion)
of Glucose, 695
22.8 Conclusions, 696
References, 696
23 Chemical Reactions in Electrochemical Cells, 697
23.1 Introduction, 697
23.2 AG and Potential E of an Electrochemical Cell, 697
23.3 Simple Cells and Nernst Equation, 701
23.3.1 Metal/Metal Ions, 701
23.3.2 Gas Electrodes, 704
23.3.3 Nernst Equation and Standard Potential, 705
23.4 Standard Potential £° and Reference Electrodes, 707
23.4.1 Practical Determination of £°, 708
23.4.2 Absolute Electrode Potential, 709
23.5 Use of Electrochemical Cells for Thermodynamic
Measurements, 714
23.5.1 pH Electrodes, 714
23.5.2 Measurement of Mean Activity Coefficient y±, 716
23.53 Measurement of Equilibrium Constant, 718
23.5.4 Liquid-Liquid Junctions, 719
23.6 Applications of Electrochemical Cells, 721
23.6.1 Galvanic Cells: Batteries and Accumulators, 721
CONTENTS Xix
23.6.2 Fuel Cells, 724
23.6.3 Electrolysis and Electrosynthesis, 725
23.6.4 Overvoltage, 727
23.7 Conductivity of Electrolyte Solutions, 728
23.7.1 Mobility of Ions, 728
23.7.2 Generalization, 730
23.7.3 Mobility of H+, 731
23.7.4 Ion Transport through Membranes, 732
23.8 Conclusions, 733
References, 733
24 Chemical Kinetics, 735
24.1 Introduction, 735
24.2 Collision Theory for Gas Reactions, 736
24.2.1 Counting the Number of Collisions, 736
24.2.2 Activation, 737
24.2.3 Steric Factor, 740
24.3 Rate Equation for Elementary Bimolecular Reactions, 740
24.3.1 Rate Constant and Frequency Factor for a Gas-Phase
Reaction, 740
24.3.2 Rate Constant and Frequency Factor for a Reaction
in Solution, 745
24.4 Rate Laws, 748
24.4.1 What is a Rate Law?, 749
24.4.2 Zero-Order Rate Law, 749
24.4.3 First-Order Rate Law, 750
24.4.4 Second-Order Rate Law, 752
24.5 Activation Energy and Frequency Factor, 755
24.5.1 Arrhenius Plot, 755
24.5.2 The Chemist s Rule of Thumb, 756
24.6 Combinations of Elementary Reactions, 756
24.6.1 Reactions Leading to Equilibrium, 756
24.6.2 Parallel Reactions, 759
24.6.3 Consecutive Reactions, 760
24.7 Complex Reactions, 761
24.7.1 Approximation Methods, 761
24.7.2 Lindemann-Hinshelwood Mechanism, 764
24.7.3 Chain Reactions, 767
24.7.4 Enzyme Reactions (Michaelis-Menten Mechanism), 769
24.7.5 Autocatalytic Reactions, 772
24.7.6 Bistability, 778
24.7.7 Oscillating Reactions, 780
24.7.8 Chemical Waves, 784
24.8 Experimental Methods, 786
24.8.1 Monitor Reaction Progress and Sampling, 786
24.8.2 How Methods, 787
24.8.3 Quenching Methods, 788
xx CONTENTS
24.8.4 Flash Photolysis, 789
24.8.5 Relaxation Method, 791
24.9 Conclusions, 794
References, 794
25 Transition States and Chemical Reactions, 795
25.1 Introduction, 795
25.2 Transition State in a Statistical View, 795
25.2.1 Transition State Theory for Bimolecular Reactions, 796
25.2.2 Transition State Theory for Unimolecular Reactions, 806
25.2.3 Applications of Transition State Theory, 808
25.3 Transition State in a Dynamical View, 813
25.3.1 State to State Reaction Rates, 813
25.3.2 Transition State Spectroscopy, 816
25.3.3 Rate Constant kt(E) from Reaction Cross-Sections, 817
25.3.4 Relation Between kT(E) and the Rate Constant kt(T), 819
25.4 Transition State Theory and Reactions in Solution, 820
25.4.1 Unimolecular Reactions and Frictional Coupling, 821
25.4.2 Dissociation Reactions, 823
25.4.3 Proton Transfer Reactions, 826
25.5 Conclusions, 827
References, 828
26 Macromolecules, 829
26.1 Introduction, 829
26.2 Random Coil, 829
26.2.1 A Chain of Statistical Chain Elements, 831
26.3 Measuring the Length of Statistical Chain Elements, 835
26.3.1 Light Scattering, 835
26.3.2 Hydrodynamics: Coil Approximated as a Sphere, 839
26.3.3 Hydrodynamics: Macroscopic Modeling, 842
26.4 Uncoiling a Coil and its Recoiling, 848
26.4.1 Unraveling Coil by Force Applied at Chain Ends, 848
26.4.2 Fully Unraveling a Coil in a Flowing Medium, 852
26.4.3 Partially Unraveling a Coil in a Flowing Medium, 854
26.4.4 Restoring Coil, 857
26.5 Proteins as Biopolymers, 859
26.6 Motion Through Entangled Polymer Chains, 861
26.6.1 Moving Random Coil by Winding Through Meshwork:
Gel Electrophoresis of DNA Fragments, 863
26.7 Rubber Elasticity, 865
26.8 Conclusion, 867
References, 867
27 Organized Molecular Assemblies, 869
27.1 Introduction, 869
27.2 Liquid Surfaces and Liquid/Liquid Interfaces, 869
27.2.1 Surface Tension and Interfacial Tension, 869
CONTENTS XXJ
27.2.2 Surface Active Molecules (Surfactants), 874
27.3 Films on Solid Surfaces, 880
27.3.1 Langmuir-Blodgett Films (LB Films), 880
27.3.2 Self-Assembled Monolayers (SAM), 881
27.3.3 Contact Angle, 882
27.4 Micelles, 883
27.4.1 Spherical Micelles: Critical Micelle Concentration, 885
27.4.2 Geometry of Packing, 891
27.5 Membranes, 892
27.5.1 Liposomes, 892
27.5.2 Soap lamella, 893
27.5.3 Black lipid membranes, 894
27.6 Biomembranes, 896
27.6.1 Lateral Diffusion, 896
27.6.2 Ion Transport Through a Membrane, 896
27.6.3 Transport of Small Protein Through a Membrane, 899
27.7 Liquid Crystals, 900
27.7.1 Optics Applications of Liquid Crystals, 902
27.8 Conclusions, 906
References, 906
28 Supramolecular Machines, 908
28.1 Introduction, 908
28.2 Idea of a Supramolecular Machine, 909
28.2.1 A Simple Energy Transduction Device, 909
28.2.2 Programmed Interlocking Molecules, 910
28.3 Manipulating Photon Motion, 913
28.3.1 Energy Transfer Between Dye Molecules: FRET, Ruler
in Nanometer Range; SNOM, 913
28.3.2 Functional Unit by Coupling Chromophores, 920
28.3.3 Dye Aggregate as Energy-Harvesting Device, 921
28.3.4 Solar Energy Harvesting in Biosystems, 926
28.3.5 Manipulating Luminescence Lifetime by Programming Echo
Radiation Field, 927
28.4 Manipulating Electron Motion, 930
28.4.1 Photoinduced Electron Transfer in Designed Monolayer
Assemblies, 930
28.4.2 Tunneling Current Through Monolayers, 932
28.4.3 Conduction Through Single Molecules, 935
28.4.4 Conjugated Molecular Tethers, 940
28.4.5 Electron Transfer in Proteins, 941
28.4.6 Solar Energy Conversion: The Electron Pump of Plants
and Bacteria, 943
28.4.7 Electron Transfer in Soft Medium, 947
28.4.8 Inverted Region of Electron Transfer Reactions, 949
28.4.9 Artificial Photoinduced Electron Pumping, 951
28.5 Manipulating Nuclear Motion, 952
28.5.1 Light-Induced Change of Monolayer Properties, 952
xxii CONTENTS
28.5.2 Mechanical Switching Devices, 954
28.5.3 Photoinduced Sequence of Amplification Steps: The Visual
System, 955
28.5.4 Solar Energy Conversion in Halobacteria, 956
28.5.5 Biomotors, 961
28.6 Conclusions, 969
References, 969
29 Origin of Life: Matter Carrying Information, 973
29.1 Introduction, 973
29.2 Investigation of Complex Systems, 974
29.2.1 Need for Simplifying Models, 974
29.2.2 Increasing Simplification with Increasing Stages
of Complexity, 974
29.3 Can Life Emerge by Physicochemical Processes?, 974
29.3.1 Bioevolution as a Process of Learning How to Survive
as a Species, 974
29.3.2 Model Case for the Learning Mechanism, 975
29.4 Modeling the Emergence of the Genetic Apparatus, 977
29.4.1 Basic Questions, 977
29.4.2 Evolution of the Universe and Evolution of Life: The Big Bang
and the Tiny Bang, 980
29.4.3 Paradigm of Present Attempt to Understand the Origin
of Life, 980
29.4.4 General Conditions for Life to Come into Being:
Periodicity in Time, Compartmentalization, and Structural
Diversity, 981
29.4.5 Definition of Life in the Present Context, 982
29.4.6 Modelling a Continuous Sequence of Physicochemical
Processes Leading to a Genetic Apparatus, 982
29.5 General Aspects of Life s Emergence and Evolution, 986
29.5.1 Information and Knowledge, 986
29.5.2 Processing Information, Genesis of Information
and Knowledge, and the Maxwell Demon, 986
29.5.3 Limits of Physicochemical Ways of Thinking, 990
29.6 Conclusions, 993
References, 993
Index, 995
List of Foundations
1 Chapter 1
2 Chapter 2
3 Chapter 3
3.1 Electron in a Potential Well of Finite Depth
3.1.1 Symmetric Solutions
3.1.2 Antisymmetric Solutions
3.1.3 Numerical Evaluation
3.2 Orthogonality
3.3 Uncertainty Principle
3.3.1 Uncertainty in the Momentum
3.3.2 Uncertainty in the Position
3.3.3 Uncertainty Product
3.3.4 Example: Gaussian Distribution of Momenta
4 Chapter 4
4.1 H Atom: Solution of the Schrodinger Equation
4.2 H Atom: Angular and Radial Wavefunctions
4.2.1 The Angular Solution
4.2.2 The Radial Solution
4.2.3 The Total Wavefunction
5 Chapter 5
5.1 Proof of Variational Principle
5.2 First Order Perturbation Theory
5.2.1 Example: Electron in a Potential Well
5.3 Perturbation Theory (Rigorous Treatment)
5.3.1 Example: Electron in a Potential Well
5.4 He-Atom: Repulsion Energy
5.5 The Self-Consistent Field approximation
5.6 Atomic Term Symbols
6 Chapter 6
6.1 H^ Ion: Exact Wavefunction and Energy
6.1.1 Energy
6.1.2 Wavefunction for the Equilibrium Distance
6.1.3 Virial Theorem for Molecules
6.2 Evaluation of LCAO Integrals in H^
6.3 Oscillation of Electron between Protons at Distance d (Tunneling)
6.3.1 Calculating E and £2 in H^ for Large Distance d
6.3.2 Calculating £2 — £1
6.3.3 Calculating the Time-Dependent Probability Density p
6.3.4 Period of Oscillation
6.3.5 Tunneling Probability
xxiii
xxiv LIST OF FOUNDATIONS
7 Chapter 7
7.1 LCAO-Treatment of Heteronuclear Diatomic Molecules
8 Chapter 8
8.1 Construction of V(s) in Figure 8.3
8.2 Free-Electron Model
8.2.1 Case 1: Symmetric Wavefunctions
8.2.2 Case 2: Antisymmetric Wavefunctions
8.2.3 Energies
8.2.4 Normalization
8.3 Free-Electron Model, Representation by Determinants
8.4 HMO Model
8.4.1 Finding the Minimum of e
8.4.2 Solving a system of N linear equations with constant
coefficients
8.4.3 Example: butadiene
8.4.4 Example: benzene
8.5 Fullerene
9 Chapter 9
9.1 Integrated Absorption: Classical Oscillator
9.1.1 Absorbed Power in a Radiation Beam and Absorption
Coefficient e
9.1.2 Calculating the Absorption Coefficient e Classically
9.1.3 Resonance Curve for e: Calculating Jband £ • du
9.1.4 Integrated Absorption Power
9.1.5 Derivation of Equation (9.4) for the Intensity /
9.2 Oscillator Strength: Quantum Mechanical Treatment
9.2.1 Quantum Mechanical Expression for /
9.3 Classical and Quantum Mechanical Description of Light
Absorption
9.3.1 Light Absorption Calculated from the Schrodinger
Equation
9.3.2 Power Absorbed by the Molecule
9.3.3 Classical Oscillator
9.3.4 Equivalence of Classical and Quantum Mechanical
Treatment
9.4 Coupling Transitions with Parallel Transition Moments
9.4.1 Replacing Quantum Mechanical System by Coupled Classical
Oscillators
9.4.2 Doubly Occupied Orbitals
9.5 Normal Modes of Coupled Oscillators
9.5.1 Resonance Frequencies of Two Coupled Oscillators
9.5.2 Oscillator Strength of Two Coupled Oscillators
9.5.3 Coupling Two Identical Oscillators
10 Chapter 10
10.1 Fluorescence Life Time
10.1.1 Antenna Equation of Hertz
10.1.2 Natural Lifetime
10.1.3 Lifetime and Line Width
LIST OF FOUNDATIONS xxv
10.2 Calculation of Repulsion Integrals
10.2.1 Deriving Equations for the Integrals
10.2.2 Numerical Integration
11 Chapter 11
11.1 Rotator: Solution of the Schrodinger Equation
11.1.1 Diatomics
11.1.2 Polyatomics
11.2 Quantum-Mechanical Treatment of the Harmonic Oscillator
11.2.1 Diatomics
11.2.2 Symmetric wavefunctions
11.2.3 Antisymmetric wavefunctions
11.3 Selection Rules for Rotation of Linear Molecules (Absorption
Spectra)
11.3.1 Transition Moment
11.3.2 Intensity Distribution of Absorption Lines
11.4 Centrifugal Effect on Energy of Diatomic Rotator
11.5 Selection Rules for Vibration (Absorption Spectra)
11.5.1 Diatomic Molecules
11.5.2 Polyatomic Molecules
11.6 Selection Rules for Rotation of Linear Molecules (Raman Spectra)
11.6.1 Transition Moment
11.6.2 Intensity of Raman Lines
11.7 Selection Rules for Vibration of Diatomic Molecules (Raman
Spectra)
12 Chapter 12
13 Chapter 13
13.1 Some Features of Crystal Structures and Lattices
13.2 Polarizability of a Conducting Sphere
14 Chapter 14
14.1 The Random Walk in Three Dimensions
14.2 Intermolecular Forces Affecting the Mean Free Path
14.3 Law of Hagen-Poiseuille
14.3.1 Flow in a Tube
14.3.2 Volume V of a Gas Flowing Through the Tube
14.3.3 Law of Hagen-Poiseuille for Liquids
15 Chapter 15
15.1 Classical Derivation of the One-Dimensional Maxwell-Boltzmann
Distribution of Speeds
15.1.1 Calculation of Constant A
15.2 How to Find the Maximum of In a
15.3 Energy Distribution of Fermions and Boson
15.3.1 Fermions
15.3.2 Bosons
15.3.3 Classical Case ( boltzons )
15.3.4 Distribution Functions
15.4 Canonical and Microcanonical Ensembles
15.5 Internal Energy U as Sum of Contributions Uei, Uvn,, Urot, and
U trans
xxvi LIST OF FOUNDATIONS
16 Chapter 16
16.1 Deriving the Debye Function (Cy of Solids)
16.2 How to Calculate f£ ACfm ¦ AT
16.2.1 Hydrogen and Oxygen Gas Reaction, Temperature Range
298 K to 350 K
16.2.2 Hydrogen and Oxygen Gas Reaction, Temperature Range
298 K to 1500 K
16.2.3 Heating Limestone
17 Chapter 17
17.1 Number of Representations Q from Molecular Partition
Function Z
17.1.1 Distinguishable Particles
17.1.2 Indistinguishable Particles
17.2 Entropy of Homonuclear Diatomic Gases
18 Chapter 18
18.1 How to Calculate AGt2 from AGTl
18.2 Relationship between the Molecular Partition Function and the
Equilibrium Constant
18.3 Isotope Exchange Equilibrium
18.4 How to Determine A G° for Ions
19 Chapter 19
19.1 Some Formal Thermodynamic Relationships
19.1.1 First Order Relations (Maxwell Relations)
19.1.2 Combinations of First Order Relations
19.1.3 Second Order Relations
19.1.4 Change of Variables
19.1.5 Evaluation of Thermodynamic Functions by Measurable
Quantities
19.2 Molecular Perspective on Solid-Gas Equilibria
19.2.1 Solid Argon
19.2.2 Solid-Gas Equilibrium for Argon
19.2.3 Thermodynamics of Solids
19.3 Distinguishing Between Phases
20 Chapter 20
20.1 Virial Equation of State
20.1.1 Classical Partition Function
20.2 Joule-Thomson Coefficient and Inversion Temperature
21 Chapter 21
21.1 Activity Coefficient of Solute From Activity Coefficient of Solvent
21.2 Distribution of Ions in Solution
21.2.1 Charge Distribution between Two Plates
21.2.2 Charge Distribution Around an Ion
21.2.3 Poisson Equation
22 Chapter 22
22.1 Titration of Acetic Acid by NaOH
22.1.1 Effect of Increasing Volume
22.2 Two Coupled Chemical Equilibria
LIST OF FOUNDATIONS xxvii
22.2.1 Evaluation of concentrations q/2a Om- ar d ca2~
22.2.2 Titration curve
23 Chapter 23
24 Chapter 24
25 Chapter 25
25.1 Thermal Rate Constants
25.2 Derivation of the Kramers formula
26 Chapter 26
26.1 Light Scattering of Macromolecules
26.1.1 Polarizability a of Macromolecules in the Field of an Incident
Light Wave
26.1.2 Forward and Backward Light Scattering
26.2 Viscosity of Dilute Solutions of Polymers and Macroscopic
Models
26.2.1 The Dumbbell Model
26.2.2 Viscosity of a Dilute Solution of Dumbbells
26.2.3 Dumbbells and Rotational Form Factor Crot
26.2.4 Conclusion on Viscosity of Dilute Solutions of Random
Coils
26.3 Diffusion of a Random Coil in a Gel in the Absence of an Electric Field
and Force-Induced Motion
26.3.1 Time r to Leave the Cage. Diffusion Coefficient Di
26.3.2 Global Diffusion of Coil. Diffusion Coefficient D
26.3.3 Force-Induced Motion of Coil
26.4 Stretching a Chain
27 Chapter 27
21.1 Head-to-Head Repulsion Energy
27.2 Clausius-Mosotti Equation
27.2.1 Permanent Dipoles in Electric Field (Simplified Model)
27.2.2 Permanent Dipoles in Electric Field (Rigorous
Calculation)
27.2.3 Field Strength in a Liquid
28 Chapter 28
28.1 Energy Transfer
28.1.1 One Donor and One Acceptor in Distance r
28.1.2 Molecules in a Layer Plane
28.1.3 Relation Between r$ and do
28.1.4 Comparison of Absorbed Power in Far Field and Near
Field
28.2 Energy Transfer from Exciton to Acceptor
28.2.1 Case (a): Arrangement in Figure 28.14a
28.2.2 Case (b): Arrangement in Figure 28.14b
28.3 Radiation Echo Field
28.3.1 Excited Dye Molecule Without Mirror
28.3.2 Excited Dye Molecule in the Field F of a Mirror
28.3.3 Note 1: Lifetime of Oscillator
28.3.4 Note 2: Conversion of the Hertz Equation
28.4 Electron Transfer Between Tt-Electron Systems
xxviii LIST OF FOUNDATIONS
28.4.1 General Case
28.4.2 Rate of Electron Transfer
28.4.3 Evaluation of s
28.4.4 Evaluation of eeiectroniC
28.4.5 Evaluation of Rate Constant kr
28.5 Calculation of Ebarrier
28.6 Marcus Equation
28.7 Chloride Ion Pump and Sensory Receptor of Halobacteria
28.7.1 Chloride Ion Pump
28.7.2 Sensory Receptors
29 Chapter 29
29.1 Search for Logical Conditions Driving the Emergence of a Genetic
Translation Device
29.2 The Emergence of a Simple Genetic Apparatus Viewed as a
Supramolecular Engineering Problem. A Thought Experiment
29.2.1 A Short Template Marks the Beginning
29.2.2 Intricate Cycles of Temperature Drive Replication
29.2.3 Strand Evolution Requires Rare Replication Errors
29.2.4 Strand Lengthening-Colonization of Larger Porous
Regions
29.2.5 Strand Folding: Hairpins-Most Resistant Structure
29.2.6 Aggregation of Hairpins: an Error Filter
29.2.7 Assembler Strand Guides Hairpin Aggregation
29.2.8 A New Variety (a-Monomers) Appears: a-Oligomers Formed
by HA Device Enable Colonization of Larger Porous
Regions
29.2.9 Breakthrough of Translational Device
29.2.10 Breakthrough of an Integrative Translation Device
29.2.11 Computer Simulation of Thought Experiment
29.3 Attempts to Model the Origin of Life
29.3.1 The Earliest Phase
29.3.2 Breaking Symmetry: Chirality of Nucleotides and Its
Evolutionary Benefit
29.3.3 The Earliest HA-Device
29.3.4 The Reading Frame Requirement
29.3.5 Stage-by-Stage Evolution of the Code
29.4 Maxwell s Demon
29.5 Later Evolutionary Steps: Emergence of an Eye With Lens
List of Justifications
1 Chapter 1
1.1 Diffraction on a Double Slit
2 Chapter 2
2.1 Mean Distance 7
2.2 Mean Potential Energy V
2.3 Particle in a Box Trial Function for H Atom
3 Chapter 3
3.1 Energy and Momentum of Free Electron
3.2 Energy and Momentum
4 Chapter 4
4.1 Bohr Radius
4.2 Laplace Operator for the H Atom
4.3 Probability in the 2s State of the H Atom
4.4 Calculation of Average Distance 7 for the 2pz state of the H Atom
5 Chapter 5
5.1 Ground State Energy of H Atom by Variational Principle
5.2 Ground State Energy of He+
6 Chapter 6
6.1 Normalization Constant in Hj Wavefunction
6.2 Excited State of H+
6.3 Hamiltonian of the H2 Molecule Compared to the Hamiltonians of Two
H^ Ions
7 Chapter 7
7.1 Orthogonal Set of Hybrid Functions
7.2 Tetrahedral Hybrid Function
7.3 Stretching Force Constant of H^ Ion
7.4 Morse Function
7.4.1 Limit of Small Elongations
7.4.2 Inflection Point
7.4.3 Maximum Force
8 Chapter 8
8.1 Energies of Benzene for n — 3
8.2 Resonance of Hiickel (An + 2) Rings
8.3 HMO Model: Excited State of Ethene
9 Chapter 9
9.1 Interaction of Electron with Electric and Magnetic Field
9.2 Field Strength in a Molecule Compared to Field Strength of Light
Wave
9.3 Energy Shift in Azacyanines
9.4 Shift of Energy Levels by Bond Alternation
9.5 Transition Moment Mx for Phthalocyanine
xxix
xxx LIST OF J USTIFICAT1ONS
9.6 Light Absorption of Porphynn
9.7 Amsotropy Factor g in Section 9.3.3
9.7.1 Proof of Relation (9.15)
10 Chapter 10
10.1 Singlet-Triplet Transition
10.2 Non-Existence of He2
11 Chapter 11
11.1 Nonrigid Rotator
11.2 Oscillator: Box Wavefunctions
11.3 Classical Oscillator: Probability Density p(x)
11.4 Rotational-Vibrational Spectra: Spacing of Absorption Lines
12 ChapterU
12.1 Raman Spectrum of N2
12.2 Spacing of Raman Lines in O2 and CO2
13 Chapter 13
13.1 Cohesion Energy in Li Metal
13.2 Dipole and Induction Energies
13.2.1 Dipole Energy (Dipoles in Line)
13.2.2 Dipole Energy (Dipoles parallel)
13.2.3 Dipole Energy (Dipoles in Angle /J)
13.2.4 Dipole in the Field of a Point Charge
13.2.5 Electric Field Strength of Dipole
13.3 Polarizability of a Conducting Plate and of a Conducting Sphere
14 Chapter 14
14.1 Collision of Heavy Particle with Light Particle
15 Chapter 15
15.1 Rotational Energy of Symmetric Top Molecules
15.2 Molecular Partition Function Ztmns of Translation
15.3 Calculation of Normalization Constant
15.4 Constant in the Maxwell-Boltzmann Distribution
15.5 Mean Speed
15.6 Occupation Probability in Lowest Quantum State
15.7 Distinguishable Particles Occupying Degenerate Energy levels
16 Chapter 16
16.1 Heat Capacity: Electronic Contribution
16.2 Limits of Debye Function of Heat Capacity
17 Chapter 17
17.1 Temperature Scale
18 Chapter 18
18.1 Equilibrium Constant of H2 + D2 ^ 2HD Equilibrium
18.2 Depression of Melting point
19 Chapter 19
19.1 Derivation of Equation for (dH/dP)T
19.2 More Precise Calculation of AHtotai m
193 Calculation of Vapor Pressure
20 Chapter 20
20.1 Definition of Ideal Gas
LIST OF JUSTIFICATIONS xxxi
21 Chapter 21
21.1 Maxwell Relations
21.1.1 Derivation of Equation 21.21
21.1.2 Derivation of Equation 21.22
21.1.3 Derivation of Equation 21.23
21.2 Chemical Potential of Ideal Solution
21.3 Activity Coefficient of Solute from Activity Coefficient of Solvent
21.4 Boiling Point: Approximation for Small Temperature Difference
21.5 Depression of Freezing Point
22 Chapter 22
22.1 pH Change in Buffer Solutions
22.2 pH of Amino Acids
23 Chapter 23
23.1 Thermodynamic and Electrochemical Data
23.2 Gas Electrodes With Different Hydrogen Gas Pressures
24 Chapter 24
24.1 General Form of Second Order Reaction
24.2 Reactions Leading to Equilibrium
24.3 Different Reaction Orders in Both Reactions
24.4 Consecutive Reaction
24.5 Maximum Concentration of Intermediate
24.6 Consecutive Reaction: Special Case k 2 = £ ,
24.7 Autocatalytic Reaction
25 Chapter 25
25.1 Reduced Mass of Activated Complex
25.2 Isotope Effect on Reaction Rates
26 Chapter 26
26.1 Light Scattering: Backward Scattering
26.2 Light Scattering: Ratio /i35=//45°
26.3 Force Acting on Chain Ends
27 Chapter 27
21.1 Contact Angles in Figure 27.4
28 Chapter 28
28.1 Circular Dichroism and Structural Features of Chlorosomes
28.2 Electron Transfer: Tunneling Versus Thermal Activation
28.3 Proton Pump: Field of Charged Amino Acids at Chromophore
|
| adam_txt |
Titel: Principles of physical chemistry
Autor: Kuhn, Hans
Jahr: 2009
Contents
List of Foundations, xxiii
List of Justifications, xxix
Preface, xxxiii
Acknowledgments, xxxv
Authors Biography, xxxvii
List of Symbols, xxxix
Introduction, 1
1 Wave-Particle Duality, 3
1.1 Overview of Quantum Mechanics, 3
1.1.1 Historical Highlights, 3
1.1.2 An Approach to Quantum Mechanics, 4
1.2 Light, 5
1.2.1 Particle Nature of Light: Photoelectric Effect, 6
1.2.2 Wave Nature of Light: Diffraction, 7
1.2.3 Interpretation of the Experiments, 12
1.3 Electrons, 12
1.3.1 Particle Nature of Electrons, 13
1.3.2 Wave Nature of Electrons, 13
1.3.3 Interpretation of the Experiments, 15
1.3.4 Formal Similarity Between Electron and Photon, 16
1.4 Questions Arising about Wave-Particle Duality, 16
1.4.1 Single Event—Probability Statement; Collective
Behavior—Definite Statement, 16
1.4.2 Wave-Particle Duality and the Need to Abandon Familiär Ways of
Thinking, 18
1.5 Conclusion, 20
2 Essential Aspects ofStructure and Bonding, 21
2.1 Introduction, 21
2.2 Distinct Energy States, 22
2.2.1 Atomic Spectra, 22
2.2.2 Franck-Hertz Experiment, 23
2.3 Standing Waves, 24
2.3.1 Particle Between Parallel Walls, 25
2.3.2 Ill-Posed Questions, 29
233 Electron in a Cubic Box, 29
vii
viii CONTENTS
2.4 Ground-State H Atom, 30
2.4.1 Result of Rigorous Treatment (see Chapter 4), 30
2.4.2 Box Model for H Atom and the Variational Principle, 32
2.5 Ground-State H+, 36
2.5.1 Forming H* from an H Atom and a Proton, 36
2.5.2 Box Test Functions for H+, 37
2.6 Conclusion, 40
Reference, 41
3 Schrodinger Equation, 42
3.1 Introduction, 42
3.2 Wave Equation and Schrodinger Equation, 42
3.2.1 Wave Equation, 42
3.2.2 One-Dimensional Schrodinger Equation, 45
3.2.3 Three-Dimensional Schrodinger Equation, 53
3.3 Normalized Wavefunction: p = iff2, 57
3.3.1 One-Dimensional Box Function, 57
3.3.2 Three-Dimensional Box Function, 59
3.4 Orthogonality of the Wavefunctions, 60
3.4.1 Nondegenerate Wavefunctions, 60
3.4.2 Degenerate Wavefunctions, 61
3.4.3 Degeneracy Removed in an Electric Field, 62
3.5 Bohr Correspondence Principle and Generalized Form
of Quantum Mechanics, 63
3.5.1 Bohr Correspondence Principle, 64
3.5.2 popif of a Free Electron and Eigenvalue Equations, 65
3.5.3 Electron Moving on a Circle, 66
3.5.4 Degeneracy Removed by Magnetic Field, 68
3.5.5 Operator for Angular Momentum, 68
3.5.6 Operator ihd/dt and the Time-Dependent Schrodinger
Equation, 69
3.5.7 Relation Between Time-Independent and Time-Dependent
Schrodinger Equations, 70
3.5.8 Average Values of an Observable (also Called Expectation
Value), 71
3.5.9 Heisenberg Uncertainty Principle, 71
3.6 Summary of Postulates of Quantum Mechanics, 74
3.7 Conclusion, 75
References, 75
4 Hydrogen Atom, 76
4.1 Introduction, 76
4.2 Hydrogen Atom in the Ground State, 76
4.2.1 Wavefunction, 77
4.2.2 Energy, 78
4.2.3 Radial Probability Distribution of Electron, 79
CONTENTS ix
4.2.4 Most Probable Distance and Average Distance, 80
4.2.5 Average Potential Energy and Virial Theorem, 81
4.3 H Atom in Excited States, 82
4.3.1 Energies, 82
4.3.2 Wavefunctions, 83
4.3.3 Radial Probability Distribution Function and Average
Distance, 87
4.3.4 Emission Spectra, 88
4.3.5 Degeneracy of H-atom Orbitals Can Be Removed
by a Magnetic Field, 90
4.4 Conclusion, 92
5 Atoms and the Variational Principle, 93
5.1 Introduction, 93
5.2 Vanational Principle, 93
5.2.1 Introducing the Variational Principle, 93
5.2.2 Justification of the Variational Principle, 94
5.3 He Atom, 98
5.3.1 Ground State of He, 98
5.3.2 Indistinguishability of Electrons, 103
5.3.3 Excited States of He Described by the Product of One-Electron
Trial Functions (Orbitals), 103
5.4 Electron Spin and Pauli Exclusion Principle, 104
5.4.1 Energy Splitting in a Magnetic Field, Electron Paramagnetic
Resonance, 104
5.4.2 Spin Variables, 107
5.4.3 Antisymmetry Postulate (Pauli Exclusion Principle), 109
5.4.4 Singlet-Triplet Splitting: Magnetic Forces Negligible, 111
5.5 Many-Electron Atoms, 112
5.5.1 Atomic Number Z and lonization Energy, 112
5.5.2 Electronic Structure of the First Three Elements, 113
5.5.3 Aufbau Principle and the Periodic Table, 115
5.5.4 Periodic Properties of the Elements, 120
5.6 Spin-Orbit Interactions of Electrons in Atoms, 122
5.6.1 Angular Momentum and Vector Model of Atoms, 123
5.6.2 Atomic Term Symbols, 125
5.7 Conclusion, 127
References, 127
6 A Quantitative View of Chemical Bonding, 128
6.1 Introduction, 128
6.2 H^ Molecular Ion, 129
6.2.1 Electron Described by Exact Wavefunction, 129
6.2.2 Electron Density and the Chemical Bond, 131
6.2.3 Electron Described by the Linear Combination of Atomic
Orbitals (LCAO) Wavefunction, 133
x CONTENTS
6.2.4 Comparison of Box Model and LCAO Method, 136
6.2.5 Excited State of H\: Bonding and Antibonding Orbitals, 138
6.3 H2: A Two-Electron System, 139
6.3.1 Rigorous Treatment, 139
6.3.2 Product of One-Electron Wavefunctions, 141
6.3.3 Indistinguishability of Electrons, 143
6.3.4 Pauli Exclusion Principle: Electronic Wavefunctions Must Be
Antisymmetric, 146
6.4 Tunneling, 148
6.4.1 Electron Oscillating Between Protons a and b, 148
6.4.2 Tunneling Barrier and Frequency of Oscillation, 148
6.4.3 Importance of Tunneling in Redox Chemistry, 148
6.5 Conclusions, 149
References, 149
7 Bonding Described by Electron Pairs and Molecular Orbitals, 150
7.1 Introduction, 150
7.2 Electron Pair Bonds, 150
7.2.1 Connectivity of Atoms in Three-Atom Molecules, 151
7.2.2 Geometries for Electron Pair Bonds, 154
7.2.3 Limitations of the Electron Pair Model, 160
7.3 Molecular Orbitals, 161
7.3.1 Homonuclear Diatomics, 161
7.3.2 Heteronuclear Diatomics, 167
7.3.3 Triatomics (H2O), 170
7.3.4 Polyatomics, 174
7.4 Polarity, Bond length, and Elasticity, 177
7.4.1 Polarity of Bonds and Electronegativity, 177
7.4.2 Covalent Radii and Van der Waals Radii, 179
7.4.3 Stretching, Bending, and Torsion of Bonds, 182
7.5 Conclusions, 188
References, 188
8 Molecules with n-Electron Systems, 189
8.1 Introduction, 189
8.2 Bonding Properties of 7t-Electrons, 190
8.2.1 a -Bonded Molecular Skeleton and tt -Electrons, 190
8.2.2 Overview of Models for it-Systems, 192
8.3 Free Electron Molecular Orbital (FEMO) Model, 194
8.3.1 Ethene, Butadiene, Amidinium 7i-Electron Chains, 194
8.3.2 Benzene: A Tt-Electron Ring, 195
8.3.3 Charge Density dQ/ds, 197
8.3.4 Branched Molecules, 200
8.4 Bondlength Consistent With Total it-Electron Density Method
(BCD), 203
8.5 Principles of Density Functional Theory (DFT), 209
8.6 HMO Model, 210
8.6.1 Wavefunctions and Energies, 210
CONTENTS xi
8.6.2 Application of the HMO Method to 7t-Electron Chains, 213
8.6.3 Bond Length and HMO Bond Order, 215
8.7 Resonance, 216
8.8 Conclusions, 218
References, 219
9 Absorption of Light, 220
9.1 Introduction, 220
9.2 Excitation of it-Electron Systems, 220
9.2.1 Basic Experimental Facts, 220
9.2.2 Absorption Maxima of Dyes, 226
9.2.3 Strength and Polarization of Absorption Bands, 231
9.2.4 Hetero-Atoms as Probes for Electron Distribution, 235
9.2.5 HOMO-LUMO Gap by Bond Alternation, 239
9.2.6 Cyclic jr-Systems, 242
9.2.7 Coupling of n-Electrons, 247
9.3 Optical Activity, 249
9.3.1 Rotatory Dispersion, 250
9.3.2 Ellipticity and Circular Dichroism, 251
9.3.3 Anisotropy Factor g for Model in Fig. 9.23, 254
9.3.4 Absolute Configuration of Chiral Molecules, 255
9.3.5 Circular Dichroism of Spirobisanthracene, 255
9.3.6 Circular Dichroism of Chiral Cyanine Dye, 258
9.4 Conclusions, 260
References, 260
10 Emission of Light, 261
10.1 Introduction, 261
10.2 Spontaneous Emission, 261
10.2.1 Fluorescence, 262
10.2.2 Phosphorescence and Triplet States, 267
10.2.3 Relative Energetics of Fluorescence, Phosphorescence,
and Absorption, 270
10.2.4 Quenching of Fluorescence, 272
10.2.5 Absorption from Excited States, 273
10.3 Stimulated Emission and Laser Action, 275
10.3.1 Inversion of Population, 276
10.3.2 Dye Laser Operation, 276
10.3.3 Excimer and Exciplex Laser, 279
10.4 Conclusions, 279
References, 279
11 Nuclei: Particle and Wave Properties, 280
11.1 Introduction, 280
11.2 Rotational Motion of Molecules, 281
11.2.1 Diatomic Quantum-Mechanical Rotator, 281
11.2.2 Polyatomic Molecules, 284
11.2.3 Rotational Spectra, 287
xii CONTENTS
11.3 Vibrational Motion of Molecules, 293
11.3.1 Classical Oscillator, 293
11.3.2 Quantum-Mechanical Harmonic Oscillator, 296
11.3.3 Vibrational-Rotational Spectra, 301
11.3.4 Quantum-Mechanical Anharmonic Oscillator, 310
11.4 Raman Spectra, 315
11.4.1 Rayleigh Scattering, 315
11.4.2 Raman Spectroscopy, 317
11.4.3 Rotational Raman Spectra of Heteronuclear Diatomic
Molecules, 318
11.4.4 Raman Spectra of Poly atomics, 322
11.5 Vibrational Structure of Electronic Spectra, 324
11.5.1 Franck-Condon Principle, 325
11.5.2 Photoelectron Spectroscopy, 328
11.5.3 Polyatomic Molecules, 331
11.6 Conclusion, 336
References, 336
12 Nuclear Spin, 337
12.1 Introduction, 337
12.2 Nuclear Spin: Fundamentals, 337
12.2.1 Spin of Protons in H2, 337
12.2.2 Antisymmetry of Total Wavefunction of a Molecule Including
Electrons and Nuclei, 338
12.2.3 Nuclei With Half-Integer Spin (Antisymmetric Total
Wavefunction) and Nuclei With Integral Spin
(Symmetric Total Wavefunction), 340
12.3 Nuclear Magnetic Resonance (NMR), 343
12.3.1 Fundamentals, 343
12.3.2 Chemical Shift, 345
12.3.3 Fine Structure of NMR Spectra, 347
12.3.4 NMR Spectroscopy for Determination of Protein Structures in
Solution, 349
12.3.5 Magnetic Resonance Imaging (MRI), 350
12.4 Conclusion, 350
References, 350
13 Solids and Intermolecular Forces, 351
13.1 Introduction, 351
13.2 Ionic Crystals, 352
13.2.1 Bond Energy of an Ion Pair, 352
13.2.2 Lattice Types, 354
13.3 Metals, 358
13.3.1 Free Electron Model for Conduction Electrons, 358
13.3.2 Cohesion Energy of Metals, 364
133.3 Quantum Wires and Nanostructure, 366
CONTENTS xlii
13.4 Semiconductors, 369
13.4.1 Soliton Conductors: Polyacetylene, 369
13.4.2 Silicon, 370
13.4.3 Semiconductor Bandgap, 371
13.4.4 Semiconductor Quantum Dots, 372
13.5 Molecular Crystals and Intermolecular Forces, 374
13.5.1 Electrostatic Forces, the Dipole, 375
13.5.2 Hydrogen Bonds, 378
13.5.3 Induction Forces, 381
13.5.4 Dispersion Forces, 383
13.6 Conclusions, 386
References, 386
14 Thermal Motion of Molecules, 387
14.1 Introduction, 387
14.2 Kinetic Gas Theory and Temperature, 387
14.2.1 Thermal Motion and Pressure, 388
14.2.2 Avogadro's Law, 395
14.2.3 Thermal Equilibration and Heat, 397
14.2.4 Ideal Gas Law and the Definition of Absolute
Temperature, 397
14.2.5 Law of Partial Pressures, 401
14.3 Speed and Collisions of Gas Molecules, 402
14.3.1 Average Speed of Molecules in a Gas, 402
14.3.2 Mean Free Path and Number of Collisions, 405
14.3.3 Diffusion, 408
14.3.4 Viscosity Arising from Collisions of Molecules, 422
14.4 Thermal Motion in Liquids, 426
14.4.1 Collisions in Liquids, 426
14.4.2 Diffusion Coefficient D of a Liquid, 427
14.4.3 Viscosity of a Liquid, 428
14.4.4 Stokes-Einstein Equation, 429
14.5 Conclusions, 431
References, 431
15 Energy Distribution in Molecular Assemblies, 433
15.1 Introduction, 433
15.2 The Boltzmann Distribution Law, 434
15.2.1 System Consisting of Two Quantum States, 434
15.2.2 Systems Consisting of Many Quantum States, 436
15.2.3 Internal Energy U, 438
15.3 Electronic Energy, 439
15.4 Vibrational Energy, 440
15.4.1 Population Number Nn of a Harmonic Oscillator, 441
15.4.2 Internal Energy Uvn, of Diatomic Molecules, 444
15.4.3 Internal Energy Uvn, of Polyatomic Molecules, 446
xiv CONTENTS
15.5 Rotational Energy, 448
15.5.1 Population Number Nj of Rigid Rotator
(Heteronuclear Molecules), 449
15.5.2 Internal Energy UI0t of Rotation
(Heteronuclear Molecules), 451
15.5.3 Homonuclear Diatomic Molecules: Ortho- and
Para-H2, 453
15.6 Translational Energy, 455
15.6.1 Internal Energy [/trans of Translation According to Quantum
Mechanics, 455
15.6.2 Maxwell-Boltzmann Distribution of Speeds, 456
15.7 Characteristic Temperature, 462
15.8 Proving the Boltzmann Distribution for Distinguishable
Particles, 463
15.8.1 Distribution of N Particles Among Three Levels with Given
Internal Energy, 463
15.8.2 Rigorous Treatment, 468
15.9 Proving the Boltzmann Distribution for Indistinguishable Particles
(High Temperature), 469
15.9.1 Number of Available Quantum States, 469
15.9.2 Number of Representations and Boltzmann Law, 470
15.9.3 Calculating the Internal Energy U of an Ideal Atomic
Gas, 471
15.9.4 Relation Between 0 and T, 472
15.10 Energy Distribution of Fermions and Bosons Among Quantum
States, 472
15.11 Conclusions, 475
Reference, 475
16 Work w, Heat q, and Internal Energy U, 476
16.1 Introduction, 476
16.2 Thermodynamic Systems, 477
16.2.1 Defining System and Surroundings, 477
16.2.2 Defining Thermodynamic States, 477
16.2.3 Change of State, 480
16.3 Change of State at Constant Volume (Isochoric Process), 481
16.3.1 Change of Internal Energy A U and the Heat q, 482
16.3.2 Heat Capacity Cy: Definition, 484
16.3.3 Translational Contribution to Cy of a Gas, 485
16.3.4 Rotational and Vibrational Contributions to Cy
of a Gas, 486
16.3.5 Ortho- and Para-Hj: Fascinating Quantum Effects
on Cv, 488
16.3.6 Electronic Contribution to Cy (Cy,ei), 489
16.3.7 Heat Capacity and Characteristic Temperature, 490
16.3.8 Cv of Solids, 491
CONTENTS XV
16.4 Change of State at Constant Pressure (Isobaric Process), 494
16.4.1 Change of Internal Energy AU: Heat q and work w, 494
16.4.2 Enthalpy H and Heat Capacity Cp: Definition, 495
16.5 Heat Exchange and Chemical Reactions, 498
16.5.1 Reaction at Constant Volume: AU, 498
16.5.2 Reaction at Constant Pressure: AH, 501
16.5.3 Temperature Dependence of AU and AH, 502
16.5.4 Molar Enthalpies of Formation from Elements
AfH°, 505
16.5.5 Molar Enthalpy of Reaction Ar#°, 505
16.5.6 Bond Enthalpies and Bond Energies, 508
16.5.7 Enthalpies and Reaction Cycles, 509
16.6 Conclusions, 510
References, 511
17 Reversible Work w^y, Reversible Heat ^rev, and Entropy S, 512
17.1 Introduction, 512
17.2 Irreversible and Reversible Changes of State, 513
17.2.1 Irreversible Changes, 513
17.2.2 Reversible Changes, 513
17.3 Counting the Number of Representations of a Thermodynamic
State, Q, 523
17.3.1 Distribution Possibilities, 523
17.3.2 Number of Representations £2 of an Atomic Gas in a Given
Thermodynamic State, 526
17.4 The Entropy: S = k In ft, 529
17.4.1 Entropy of Subsystems, 529
17.4.2 Entropy of Atomic Gas: Sackur-Tetrode Equation, 530
17.5 Entropy Change AS, 533
17.5.1 Temperature Equilibration: Entropy Increase, 534
17.5.2 Mixing: Entropy Increase, 536
17.5.3 Entropy Cannot Decrease for an Isolated System, 537
17.5.4 Entropy Can Decrease in Closed Systems, 537
17.6 Heat and Entropy Change, 537
17.6.1 Heat and Entropy Change for an Ideal Gas, 538
17.6.2 Cyclic Processes (AS — 0) and Processes in Isolated Systems
(AS 0), 542
17.6.3 Heat and Entropy Change in Arbitrary Processes, 542
17.7 Thermodynamic Temperature Scale and Cooling, 543
17.7.1 Thermodynamic Temperature Scale, 543
17.7.2 How Low Can Temperature Go?, 547
17.8 Entropies of Substances, 547
17.8.1 Entropy of an Atomic Gas, 550
17.8.2 Entropy of Diatomic Gases, 553
17.8.3 Entropy of Polyatomic Gases, 555
17.8.4 Entropy of Different Substances, 557
xvi CONTENTS
17.9 Laws of Thermodynamics, 559
17.10 Conclusions, 561
References, 561
18 General Conditions for Spontaneity and its Application to Equilibria of Ideal
Gases and Dilute Solutions, 562
18.1 Introduction, 562
18.2 General Conditions for Spontaneity, 563
18.2.1 Helmholtz Energy A, 565
18.2.2 Gibbs Energy G, 566
18.3 AG and its Dependence on Temperature, 567
18.3.1 Molar Gibbs Energy of Formation from Elements
AfG°, 567
18.3.2 Molar Gibbs Energy of Reaction ArG°, 567
18.3.3 Temperature Dependence of AG°, 568
18.4 Pressure Dependence of AG in Ideal Gases, 570
18.4.1 Vapor Pressure (Clausius-Clapeyron Equation), 572
18.4.2 Chemical Evolution of a Gas, 574
18.5 AG and Chemical Equilibrium in Ideal Gases, 575
18.5.1 Formal Derivation of Mass Action Law, 575
18.5.2 Mass Action Law: A Direct Consequence of the Relation
Between Work and Heat, 578
18.5.3 Applying the Mass Action Law, 581
18.5.4 Temperature Dependence of Equilibrium Constant K, 584
18.5.5 Pressure Changes and Equilibrium, 588
18.5.6 Reactions Involving Gases and Immiscible Condensed
Species, 589
18.5.7 Equilibrium Constant from Molecular Properties, 590
18.6 AG and Equilibrium in Dilute Solution, 593
18.6.1 Osmotic Pressure and Concentration, 593
18.6.2 Depression of Vapor Pressure (Raoult's law), 596
18.6.3 Elevation of Boiling Point and Depression of Melting
Point, 600
18.6.4 Mass Action Law (Solutions of Neutral Particles), 602
18.6.5 Mass Action Law (Solutions of Charged Particles), 604
18.6.6 Gibbs Energy of Formation in Aqueous Solution, 604
18.6.7 Part of Reactants or Products in Condensed or Gaseous
State, 607
18.7 Conclusions, 608
References, 608
19 Formal Thermodynamics and its Application to Phase Equilibria, 609
19.1 Introduction, 609
19.2 Internal Energy, Enthalpy, Work, and Heat, 609
19.2.1 Work, 610
19.2.2 Heat, 611
CONTENTS xvii
19.2.3 Relating U and H to Measurable Quantities, 612
19.2.4 Maxwell Relations, 615
19.2.5 An Important Application: Calculating Cp — Cy, 615
19.3 Spontaneity and Free Energy, 617
19.3.1 Helmholtz Energy A, 618
19.3.2 Gibbs Energy G, 619
19.4 Phase Equilibria and Phase Transitions, 620
19.4.1 Solid-Liquid Equilibria, 622
19.4.2 Liquid-Gas and Solid-Gas Equilibria, 624
19.4.3 Phase Diagrams and Phase Rule, 626
19.5 Conclusions, 630
References, 630
20 Real Gases, 631
20.1 Introduction, 631
20.2 AG for Real Gases and the Fugacity, 631
20.3 Equations of State for Real Gases, 634
20.3.1 Hard Sphere Gas, 634
20.3.2 Van der Waals Equation, 637
20.3.3 Critical Point and Van der Waals Constants, 638
20.3.4 Virial Equation of State, 641
20.4 Change of State of Real Gases, 644
20.4.1 Adiabatic Expansion into Vacuum, 644
20.4.2 Joule-Thomson Effect, 646
20.5 Chemical Equilibria Involving Real Gases, 649
20.6 Conclusions, 651
References, 651
21 Real Solutions, 652
21.1 Introduction, 652
21.2 Partial Molar Quantities and Thermodynamics of Multicomponent
Systems, 652
21.2.1 Partial Molar Volume, 653
21.2.2 Chemical Potential, 654
21.2.3 Thermodynamic Relations, 655
21.3 Activities and Activity Coefficient for Real Solutions, 657
21.3.1 Activity from Vapor Pressure Above a Solution, 657
21.3.2 Activity from Osmotic Pressure, 659
21.4 Phase Transitions of Solutions, 661
21.4.1 Elevation of Boiling Point and Depression of Melting
Point, 661
21.4.2 Solutions with Two Volatile Components, 663
21.5 Mass Action Law For Reactions in Solution, 665
21.6 Electrolyte Solutions and the Debye-Hiickel Theory, 667
21.6.1 Debye-Hiickel Theory for Electrolytes, 667
21.7 Conclusions, 671
References, 671
xviii CONTENTS
22 Reaction Equilibria in Aqueous Solutions and Biosystems, 672
22.1 Introduction, 672
22.2 Proton Transfer Reactions: Dissociation of Weak Acids, 673
22.2.1 Henderson-Hasselbalch Equation, 673
22.2.2 Degree of Dissociation in Aqueous Solution, 675
22.2.3 Degree of Dissociation in a Buffer Solution, 676
22.2.4 Titration Curve of a Weak Acid, 677
22.3 Stepwise Proton Transfer, 678
22.3.1 Diprotic Acid, 678
22.3.2 Amino Acids, 681
22.4 Electron Transfer Reactions, 682
22.4.1 Electron Transfer from Metal to Proton: Dissolution of Metals
in Acid, 682
22.4.2 Electron Transfer from Metal 1 to Metal 2 Ion:
Coupled Redox Reactions, 684
22.4.3 Electron Transfer to Proton at pH 7: AG°', 685
22.4.4 Photoinduced Electron Transfer, 686
22.5 Electron Transfer Coupled with Proton Transfer, 688
22.6 Group Transfer Reactions in Biochemistry, 691
22.6.1 Group Transfer Potential, 692
22.6.2 Coupled Reactions in Biology, 692
22.7 Bioenergetics, 693
22.7.1 Synthesis of Glucose, 694
22.7.2 Combustion of Glucose, 695
22.7.3 Energy Balance of Formation and Degradation (Combustion)
of Glucose, 695
22.8 Conclusions, 696
References, 696
23 Chemical Reactions in Electrochemical Cells, 697
23.1 Introduction, 697
23.2 AG and Potential E of an Electrochemical Cell, 697
23.3 Simple Cells and Nernst Equation, 701
23.3.1 Metal/Metal Ions, 701
23.3.2 Gas Electrodes, 704
23.3.3 Nernst Equation and Standard Potential, 705
23.4 Standard Potential £° and Reference Electrodes, 707
23.4.1 Practical Determination of £°, 708
23.4.2 Absolute Electrode Potential, 709
23.5 Use of Electrochemical Cells for Thermodynamic
Measurements, 714
23.5.1 pH Electrodes, 714
23.5.2 Measurement of Mean Activity Coefficient y±, 716
23.53 Measurement of Equilibrium Constant, 718
23.5.4 Liquid-Liquid Junctions, 719
23.6 Applications of Electrochemical Cells, 721
23.6.1 Galvanic Cells: Batteries and Accumulators, 721
CONTENTS Xix
23.6.2 Fuel Cells, 724
23.6.3 Electrolysis and Electrosynthesis, 725
23.6.4 Overvoltage, 727
23.7 Conductivity of Electrolyte Solutions, 728
23.7.1 Mobility of Ions, 728
23.7.2 Generalization, 730
23.7.3 Mobility of H+, 731
23.7.4 Ion Transport through Membranes, 732
23.8 Conclusions, 733
References, 733
24 Chemical Kinetics, 735
24.1 Introduction, 735
24.2 Collision Theory for Gas Reactions, 736
24.2.1 Counting the Number of Collisions, 736
24.2.2 Activation, 737
24.2.3 Steric Factor, 740
24.3 Rate Equation for Elementary Bimolecular Reactions, 740
24.3.1 Rate Constant and Frequency Factor for a Gas-Phase
Reaction, 740
24.3.2 Rate Constant and Frequency Factor for a Reaction
in Solution, 745
24.4 Rate Laws, 748
24.4.1 What is a Rate Law?, 749
24.4.2 Zero-Order Rate Law, 749
24.4.3 First-Order Rate Law, 750
24.4.4 Second-Order Rate Law, 752
24.5 Activation Energy and Frequency Factor, 755
24.5.1 Arrhenius Plot, 755
24.5.2 The Chemist's Rule of Thumb, 756
24.6 Combinations of Elementary Reactions, 756
24.6.1 Reactions Leading to Equilibrium, 756
24.6.2 Parallel Reactions, 759
24.6.3 Consecutive Reactions, 760
24.7 Complex Reactions, 761
24.7.1 Approximation Methods, 761
24.7.2 Lindemann-Hinshelwood Mechanism, 764
24.7.3 Chain Reactions, 767
24.7.4 Enzyme Reactions (Michaelis-Menten Mechanism), 769
24.7.5 Autocatalytic Reactions, 772
24.7.6 Bistability, 778
24.7.7 Oscillating Reactions, 780
24.7.8 Chemical Waves, 784
24.8 Experimental Methods, 786
24.8.1 Monitor Reaction Progress and Sampling, 786
24.8.2 How Methods, 787
24.8.3 Quenching Methods, 788
xx CONTENTS
24.8.4 Flash Photolysis, 789
24.8.5 Relaxation Method, 791
24.9 Conclusions, 794
References, 794
25 Transition States and Chemical Reactions, 795
25.1 Introduction, 795
25.2 Transition State in a Statistical View, 795
25.2.1 Transition State Theory for Bimolecular Reactions, 796
25.2.2 Transition State Theory for Unimolecular Reactions, 806
25.2.3 Applications of Transition State Theory, 808
25.3 Transition State in a Dynamical View, 813
25.3.1 State to State Reaction Rates, 813
25.3.2 Transition State Spectroscopy, 816
25.3.3 Rate Constant kt(E) from Reaction Cross-Sections, 817
25.3.4 Relation Between kT(E) and the Rate Constant kt(T), 819
25.4 Transition State Theory and Reactions in Solution, 820
25.4.1 Unimolecular Reactions and Frictional Coupling, 821
25.4.2 Dissociation Reactions, 823
25.4.3 Proton Transfer Reactions, 826
25.5 Conclusions, 827
References, 828
26 Macromolecules, 829
26.1 Introduction, 829
26.2 Random Coil, 829
26.2.1 A Chain of Statistical Chain Elements, 831
26.3 Measuring the Length of Statistical Chain Elements, 835
26.3.1 Light Scattering, 835
26.3.2 Hydrodynamics: Coil Approximated as a Sphere, 839
26.3.3 Hydrodynamics: Macroscopic Modeling, 842
26.4 Uncoiling a Coil and its Recoiling, 848
26.4.1 Unraveling Coil by Force Applied at Chain Ends, 848
26.4.2 Fully Unraveling a Coil in a Flowing Medium, 852
26.4.3 Partially Unraveling a Coil in a Flowing Medium, 854
26.4.4 Restoring Coil, 857
26.5 Proteins as Biopolymers, 859
26.6 Motion Through Entangled Polymer Chains, 861
26.6.1 Moving Random Coil by Winding Through Meshwork:
Gel Electrophoresis of DNA Fragments, 863
26.7 Rubber Elasticity, 865
26.8 Conclusion, 867
References, 867
27 Organized Molecular Assemblies, 869
27.1 Introduction, 869
27.2 Liquid Surfaces and Liquid/Liquid Interfaces, 869
27.2.1 Surface Tension and Interfacial Tension, 869
CONTENTS XXJ
27.2.2 Surface Active Molecules (Surfactants), 874
27.3 Films on Solid Surfaces, 880
27.3.1 Langmuir-Blodgett Films (LB Films), 880
27.3.2 Self-Assembled Monolayers (SAM), 881
27.3.3 Contact Angle, 882
27.4 Micelles, 883
27.4.1 Spherical Micelles: Critical Micelle Concentration, 885
27.4.2 Geometry of Packing, 891
27.5 Membranes, 892
27.5.1 Liposomes, 892
27.5.2 Soap lamella, 893
27.5.3 Black lipid membranes, 894
27.6 Biomembranes, 896
27.6.1 Lateral Diffusion, 896
27.6.2 Ion Transport Through a Membrane, 896
27.6.3 Transport of Small Protein Through a Membrane, 899
27.7 Liquid Crystals, 900
27.7.1 Optics Applications of Liquid Crystals, 902
27.8 Conclusions, 906
References, 906
28 Supramolecular Machines, 908
28.1 Introduction, 908
28.2 Idea of a Supramolecular Machine, 909
28.2.1 A Simple Energy Transduction Device, 909
28.2.2 Programmed Interlocking Molecules, 910
28.3 Manipulating Photon Motion, 913
28.3.1 Energy Transfer Between Dye Molecules: FRET, Ruler
in Nanometer Range; SNOM, 913
28.3.2 Functional Unit by Coupling Chromophores, 920
28.3.3 Dye Aggregate as Energy-Harvesting Device, 921
28.3.4 Solar Energy Harvesting in Biosystems, 926
28.3.5 Manipulating Luminescence Lifetime by Programming Echo
Radiation Field, 927
28.4 Manipulating Electron Motion, 930
28.4.1 Photoinduced Electron Transfer in Designed Monolayer
Assemblies, 930
28.4.2 Tunneling Current Through Monolayers, 932
28.4.3 Conduction Through Single Molecules, 935
28.4.4 Conjugated Molecular Tethers, 940
28.4.5 Electron Transfer in Proteins, 941
28.4.6 Solar Energy Conversion: The Electron Pump of Plants
and Bacteria, 943
28.4.7 Electron Transfer in Soft Medium, 947
28.4.8 Inverted Region of Electron Transfer Reactions, 949
28.4.9 Artificial Photoinduced Electron Pumping, 951
28.5 Manipulating Nuclear Motion, 952
28.5.1 Light-Induced Change of Monolayer Properties, 952
xxii CONTENTS
28.5.2 Mechanical Switching Devices, 954
28.5.3 Photoinduced Sequence of Amplification Steps: The Visual
System, 955
28.5.4 Solar Energy Conversion in Halobacteria, 956
28.5.5 Biomotors, 961
28.6 Conclusions, 969
References, 969
29 Origin of Life: Matter Carrying Information, 973
29.1 Introduction, 973
29.2 Investigation of Complex Systems, 974
29.2.1 Need for Simplifying Models, 974
29.2.2 Increasing Simplification with Increasing Stages
of Complexity, 974
29.3 Can Life Emerge by Physicochemical Processes?, 974
29.3.1 Bioevolution as a Process of Learning How to Survive
as a Species, 974
29.3.2 Model Case for the Learning Mechanism, 975
29.4 Modeling the Emergence of the Genetic Apparatus, 977
29.4.1 Basic Questions, 977
29.4.2 Evolution of the Universe and Evolution of Life: The Big Bang
and the Tiny Bang, 980
29.4.3 Paradigm of Present Attempt to Understand the Origin
of Life, 980
29.4.4 General Conditions for Life to Come into Being:
Periodicity in Time, Compartmentalization, and Structural
Diversity, 981
29.4.5 Definition of Life in the Present Context, 982
29.4.6 Modelling a Continuous Sequence of Physicochemical
Processes Leading to a Genetic Apparatus, 982
29.5 General Aspects of Life's Emergence and Evolution, 986
29.5.1 Information and Knowledge, 986
29.5.2 Processing Information, Genesis of Information
and Knowledge, and the Maxwell Demon, 986
29.5.3 Limits of Physicochemical Ways of Thinking, 990
29.6 Conclusions, 993
References, 993
Index, 995
List of Foundations
1 Chapter 1
2 Chapter 2
3 Chapter 3
3.1 Electron in a Potential Well of Finite Depth
3.1.1 Symmetric Solutions
3.1.2 Antisymmetric Solutions
3.1.3 Numerical Evaluation
3.2 Orthogonality
3.3 Uncertainty Principle
3.3.1 Uncertainty in the Momentum
3.3.2 Uncertainty in the Position
3.3.3 Uncertainty Product
3.3.4 Example: Gaussian Distribution of Momenta
4 Chapter 4
4.1 H Atom: Solution of the Schrodinger Equation
4.2 H Atom: Angular and Radial Wavefunctions
4.2.1 The Angular Solution
4.2.2 The Radial Solution
4.2.3 The Total Wavefunction
5 Chapter 5
5.1 Proof of Variational Principle
5.2 First Order Perturbation Theory
5.2.1 Example: Electron in a Potential Well
5.3 Perturbation Theory (Rigorous Treatment)
5.3.1 Example: Electron in a Potential Well
5.4 He-Atom: Repulsion Energy
5.5 The Self-Consistent Field approximation
5.6 Atomic Term Symbols
6 Chapter 6
6.1 H^ Ion: Exact Wavefunction and Energy
6.1.1 Energy
6.1.2 Wavefunction for the Equilibrium Distance
6.1.3 Virial Theorem for Molecules
6.2 Evaluation of LCAO Integrals in H^
6.3 Oscillation of Electron between Protons at Distance d (Tunneling)
6.3.1 Calculating E\ and £2 in H^ for Large Distance d
6.3.2 Calculating £2 — £1
6.3.3 Calculating the Time-Dependent Probability Density p
6.3.4 Period of Oscillation
6.3.5 Tunneling Probability
xxiii
xxiv LIST OF FOUNDATIONS
7 Chapter 7
7.1 LCAO-Treatment of Heteronuclear Diatomic Molecules
8 Chapter 8
8.1 Construction of V(s) in Figure 8.3
8.2 Free-Electron Model
8.2.1 Case 1: Symmetric Wavefunctions
8.2.2 Case 2: Antisymmetric Wavefunctions
8.2.3 Energies
8.2.4 Normalization
8.3 Free-Electron Model, Representation by Determinants
8.4 HMO Model
8.4.1 Finding the Minimum of e
8.4.2 Solving a system of N linear equations with constant
coefficients
8.4.3 Example: butadiene
8.4.4 Example: benzene
8.5 Fullerene
9 Chapter 9
9.1 Integrated Absorption: Classical Oscillator
9.1.1 Absorbed Power in a Radiation Beam and Absorption
Coefficient e
9.1.2 Calculating the Absorption Coefficient e Classically
9.1.3 Resonance Curve for e: Calculating Jband £ • du
9.1.4 Integrated Absorption Power
9.1.5 Derivation of Equation (9.4) for the Intensity /
9.2 Oscillator Strength: Quantum Mechanical Treatment
9.2.1 Quantum Mechanical Expression for /
9.3 Classical and Quantum Mechanical Description of Light
Absorption
9.3.1 Light Absorption Calculated from the Schrodinger
Equation
9.3.2 Power Absorbed by the Molecule
9.3.3 Classical Oscillator
9.3.4 Equivalence of Classical and Quantum Mechanical
Treatment
9.4 Coupling Transitions with Parallel Transition Moments
9.4.1 Replacing Quantum Mechanical System by Coupled Classical
Oscillators
9.4.2 Doubly Occupied Orbitals
9.5 Normal Modes of Coupled Oscillators
9.5.1 Resonance Frequencies of Two Coupled Oscillators
9.5.2 Oscillator Strength of Two Coupled Oscillators
9.5.3 Coupling Two Identical Oscillators
10 Chapter 10
10.1 Fluorescence Life Time
10.1.1 Antenna Equation of Hertz
10.1.2 Natural Lifetime
10.1.3 Lifetime and Line Width
LIST OF FOUNDATIONS xxv
10.2 Calculation of Repulsion Integrals
10.2.1 Deriving Equations for the Integrals
10.2.2 Numerical Integration
11 Chapter 11
11.1 Rotator: Solution of the Schrodinger Equation
11.1.1 Diatomics
11.1.2 Polyatomics
11.2 Quantum-Mechanical Treatment of the Harmonic Oscillator
11.2.1 Diatomics
11.2.2 Symmetric wavefunctions
11.2.3 Antisymmetric wavefunctions
11.3 Selection Rules for Rotation of Linear Molecules (Absorption
Spectra)
11.3.1 Transition Moment
11.3.2 Intensity Distribution of Absorption Lines
11.4 Centrifugal Effect on Energy of Diatomic Rotator
11.5 Selection Rules for Vibration (Absorption Spectra)
11.5.1 Diatomic Molecules
11.5.2 Polyatomic Molecules
11.6 Selection Rules for Rotation of Linear Molecules (Raman Spectra)
11.6.1 Transition Moment
11.6.2 Intensity of Raman Lines
11.7 Selection Rules for Vibration of Diatomic Molecules (Raman
Spectra)
12 Chapter 12
13 Chapter 13
13.1 Some Features of Crystal Structures and Lattices
13.2 Polarizability of a Conducting Sphere
14 Chapter 14
14.1 The Random Walk in Three Dimensions
14.2 Intermolecular Forces Affecting the Mean Free Path
14.3 Law of Hagen-Poiseuille
14.3.1 Flow in a Tube
14.3.2 Volume V of a Gas Flowing Through the Tube
14.3.3 Law of Hagen-Poiseuille for Liquids
15 Chapter 15
15.1 Classical Derivation of the One-Dimensional Maxwell-Boltzmann
Distribution of Speeds
15.1.1 Calculation of Constant A
15.2 How to Find the Maximum of In a
15.3 Energy Distribution of Fermions and Boson
15.3.1 Fermions
15.3.2 Bosons
15.3.3 Classical Case ("boltzons")
15.3.4 Distribution Functions
15.4 Canonical and Microcanonical Ensembles
15.5 Internal Energy U as Sum of Contributions Uei, Uvn,, Urot, and
U trans
xxvi LIST OF FOUNDATIONS
16 Chapter 16
16.1 Deriving the Debye Function (Cy of Solids)
16.2 How to Calculate f£ ACfm ¦ AT
16.2.1 Hydrogen and Oxygen Gas Reaction, Temperature Range
298 K to 350 K
16.2.2 Hydrogen and Oxygen Gas Reaction, Temperature Range
298 K to 1500 K
16.2.3 Heating Limestone
17 Chapter 17
17.1 Number of Representations Q from Molecular Partition
Function Z
17.1.1 Distinguishable Particles
17.1.2 Indistinguishable Particles
17.2 Entropy of Homonuclear Diatomic Gases
18 Chapter 18
18.1 How to Calculate AGt2 from AGTl
18.2 Relationship between the Molecular Partition Function and the
Equilibrium Constant
18.3 Isotope Exchange Equilibrium
18.4 How to Determine A G° for Ions
19 Chapter 19
19.1 Some Formal Thermodynamic Relationships
19.1.1 First Order Relations (Maxwell Relations)
19.1.2 Combinations of First Order Relations
19.1.3 Second Order Relations
19.1.4 Change of Variables
19.1.5 Evaluation of Thermodynamic Functions by Measurable
Quantities
19.2 Molecular Perspective on Solid-Gas Equilibria
19.2.1 Solid Argon
19.2.2 Solid-Gas Equilibrium for Argon
19.2.3 Thermodynamics of Solids
19.3 Distinguishing Between Phases
20 Chapter 20
20.1 Virial Equation of State
20.1.1 Classical Partition Function
20.2 Joule-Thomson Coefficient and Inversion Temperature
21 Chapter 21
21.1 Activity Coefficient of Solute From Activity Coefficient of Solvent
21.2 Distribution of Ions in Solution
21.2.1 Charge Distribution between Two Plates
21.2.2 Charge Distribution Around an Ion
21.2.3 Poisson Equation
22 Chapter 22
22.1 Titration of Acetic Acid by NaOH
22.1.1 Effect of Increasing Volume
22.2 Two Coupled Chemical Equilibria
LIST OF FOUNDATIONS xxvii
22.2.1 Evaluation of concentrations q/2a Om- ar d 'ca2~
22.2.2 Titration curve
23 Chapter 23
24 Chapter 24
25 Chapter 25
25.1 Thermal Rate Constants
25.2 Derivation of the Kramers formula
26 Chapter 26
26.1 Light Scattering of Macromolecules
26.1.1 Polarizability a of Macromolecules in the Field of an Incident
Light Wave
26.1.2 Forward and Backward Light Scattering
26.2 Viscosity of Dilute Solutions of Polymers and Macroscopic
Models
26.2.1 The Dumbbell Model
26.2.2 Viscosity of a Dilute Solution of Dumbbells
26.2.3 Dumbbells and Rotational Form Factor Crot
26.2.4 Conclusion on Viscosity of Dilute Solutions of Random
Coils
26.3 Diffusion of a Random Coil in a Gel in the Absence of an Electric Field
and Force-Induced Motion
26.3.1 Time r to Leave the Cage. Diffusion Coefficient Di
26.3.2 Global Diffusion of Coil. Diffusion Coefficient D
26.3.3 Force-Induced Motion of Coil
26.4 Stretching a Chain
27 Chapter 27
21.1 Head-to-Head Repulsion Energy
27.2 Clausius-Mosotti Equation
27.2.1 Permanent Dipoles in Electric Field (Simplified Model)
27.2.2 Permanent Dipoles in Electric Field (Rigorous
Calculation)
27.2.3 Field Strength in a Liquid
28 Chapter 28
28.1 Energy Transfer
28.1.1 One Donor and One Acceptor in Distance r
28.1.2 Molecules in a Layer Plane
28.1.3 Relation Between r$ and do
28.1.4 Comparison of Absorbed Power in Far Field and Near
Field
28.2 Energy Transfer from Exciton to Acceptor
28.2.1 Case (a): Arrangement in Figure 28.14a
28.2.2 Case (b): Arrangement in Figure 28.14b
28.3 Radiation Echo Field
28.3.1 Excited Dye Molecule Without Mirror
28.3.2 Excited Dye Molecule in the Field F of a Mirror
28.3.3 Note 1: Lifetime of Oscillator
28.3.4 Note 2: Conversion of the Hertz Equation
28.4 Electron Transfer Between Tt-Electron Systems
xxviii LIST OF FOUNDATIONS
28.4.1 General Case
28.4.2 Rate of Electron Transfer
28.4.3 Evaluation of s
28.4.4 Evaluation of eeiectroniC
28.4.5 Evaluation of Rate Constant kr
28.5 Calculation of Ebarrier
28.6 Marcus Equation
28.7 Chloride Ion Pump and Sensory Receptor of Halobacteria
28.7.1 Chloride Ion Pump
28.7.2 Sensory Receptors
29 Chapter 29
29.1 Search for Logical Conditions Driving the Emergence of a Genetic
Translation Device
29.2 The Emergence of a Simple Genetic Apparatus Viewed as a
Supramolecular Engineering Problem. A Thought Experiment
29.2.1 A Short Template Marks the Beginning
29.2.2 Intricate Cycles of Temperature Drive Replication
29.2.3 Strand Evolution Requires Rare Replication Errors
29.2.4 Strand Lengthening-Colonization of Larger Porous
Regions
29.2.5 Strand Folding: Hairpins-Most Resistant Structure
29.2.6 Aggregation of Hairpins: an Error Filter
29.2.7 Assembler Strand Guides Hairpin Aggregation
29.2.8 A New Variety (a-Monomers) Appears: a-Oligomers Formed
by HA Device Enable Colonization of Larger Porous
Regions
29.2.9 Breakthrough of Translational Device
29.2.10 Breakthrough of an Integrative Translation Device
29.2.11 Computer Simulation of Thought Experiment
29.3 Attempts to Model the Origin of Life
29.3.1 The Earliest Phase
29.3.2 Breaking Symmetry: Chirality of Nucleotides and Its
Evolutionary Benefit
29.3.3 The Earliest HA-Device
29.3.4 The Reading Frame Requirement
29.3.5 Stage-by-Stage Evolution of the Code
29.4 Maxwell's Demon
29.5 Later Evolutionary Steps: Emergence of an Eye With Lens
List of Justifications
1 Chapter 1
1.1 Diffraction on a Double Slit
2 Chapter 2
2.1 Mean Distance 7
2.2 Mean Potential Energy V
2.3 Particle in a Box Trial Function for H Atom
3 Chapter 3
3.1 Energy and Momentum of Free Electron
3.2 Energy and Momentum
4 Chapter 4
4.1 Bohr Radius
4.2 Laplace Operator for the H Atom
4.3 Probability in the 2s State of the H Atom
4.4 Calculation of Average Distance 7 for the 2pz state of the H Atom
5 Chapter 5
5.1 Ground State Energy of H Atom by Variational Principle
5.2 Ground State Energy of He+
6 Chapter 6
6.1 Normalization Constant in Hj Wavefunction
6.2 Excited State of H+
6.3 Hamiltonian of the H2 Molecule Compared to the Hamiltonians of Two
H^ Ions
7 Chapter 7
7.1 Orthogonal Set of Hybrid Functions
7.2 Tetrahedral Hybrid Function
7.3 Stretching Force Constant of H^ Ion
7.4 Morse Function
7.4.1 Limit of Small Elongations
7.4.2 Inflection Point
7.4.3 Maximum Force
8 Chapter 8
8.1 Energies of Benzene for n — 3
8.2 Resonance of Hiickel (An + 2) Rings
8.3 HMO Model: Excited State of Ethene
9 Chapter 9
9.1 Interaction of Electron with Electric and Magnetic Field
9.2 Field Strength in a Molecule Compared to Field Strength of Light
Wave
9.3 Energy Shift in Azacyanines
9.4 Shift of Energy Levels by Bond Alternation
9.5 Transition Moment Mx for Phthalocyanine
xxix
xxx LIST OF J USTIFICAT1ONS
9.6 Light Absorption of Porphynn
9.7 Amsotropy Factor g in Section 9.3.3
9.7.1 Proof of Relation (9.15)
10 Chapter 10
10.1 Singlet-Triplet Transition
10.2 Non-Existence of He2
11 Chapter 11
11.1 Nonrigid Rotator
11.2 Oscillator: Box Wavefunctions
11.3 Classical Oscillator: Probability Density p(x)
11.4 Rotational-Vibrational Spectra: Spacing of Absorption Lines
12 ChapterU
12.1 Raman Spectrum of N2
12.2 Spacing of Raman Lines in O2 and CO2
13 Chapter 13
13.1 Cohesion Energy in Li Metal
13.2 Dipole and Induction Energies
13.2.1 Dipole Energy (Dipoles in Line)
13.2.2 Dipole Energy (Dipoles parallel)
13.2.3 Dipole Energy (Dipoles in Angle /J)
13.2.4 Dipole in the Field of a Point Charge
13.2.5 Electric Field Strength of Dipole
13.3 Polarizability of a Conducting Plate and of a Conducting Sphere
14 Chapter 14
14.1 Collision of Heavy Particle with Light Particle
15 Chapter 15
15.1 Rotational Energy of Symmetric Top Molecules
15.2 Molecular Partition Function Ztmns of Translation
15.3 Calculation of Normalization Constant
15.4 Constant in the Maxwell-Boltzmann Distribution
15.5 Mean Speed
15.6 Occupation Probability in Lowest Quantum State
15.7 Distinguishable Particles Occupying Degenerate Energy levels
16 Chapter 16
16.1 Heat Capacity: Electronic Contribution
16.2 Limits of Debye Function of Heat Capacity
17 Chapter 17
17.1 Temperature Scale
18 Chapter 18
18.1 Equilibrium Constant of H2 + D2 ^ 2HD Equilibrium
18.2 Depression of Melting point
19 Chapter 19
19.1 Derivation of Equation for (dH/dP)T
19.2 More Precise Calculation of AHtotai m
193 Calculation of Vapor Pressure
20 Chapter 20
20.1 Definition of Ideal Gas
LIST OF JUSTIFICATIONS xxxi
21 Chapter 21
21.1 Maxwell Relations
21.1.1 Derivation of Equation 21.21
21.1.2 Derivation of Equation 21.22
21.1.3 Derivation of Equation 21.23
21.2 Chemical Potential of Ideal Solution
21.3 Activity Coefficient of Solute from Activity Coefficient of Solvent
21.4 Boiling Point: Approximation for Small Temperature Difference
21.5 Depression of Freezing Point
22 Chapter 22
22.1 pH Change in Buffer Solutions
22.2 pH of Amino Acids
23 Chapter 23
23.1 Thermodynamic and Electrochemical Data
23.2 Gas Electrodes With Different Hydrogen Gas Pressures
24 Chapter 24
24.1 General Form of Second Order Reaction
24.2 Reactions Leading to Equilibrium
24.3 Different Reaction Orders in Both Reactions
24.4 Consecutive Reaction
24.5 Maximum Concentration of Intermediate
24.6 Consecutive Reaction: Special Case k'2 = £',
24.7 Autocatalytic Reaction
25 Chapter 25
25.1 Reduced Mass of Activated Complex
25.2 Isotope Effect on Reaction Rates
26 Chapter 26
26.1 Light Scattering: Backward Scattering
26.2 Light Scattering: Ratio /i35=//45°
26.3 Force Acting on Chain Ends
27 Chapter 27
21.1 Contact Angles in Figure 27.4
28 Chapter 28
28.1 Circular Dichroism and Structural Features of Chlorosomes
28.2 Electron Transfer: Tunneling Versus Thermal Activation
28.3 Proton Pump: Field of Charged Amino Acids at Chromophore |
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| author | Kuhn, Hans Försterling, Horst-Dieter 1934- Waldeck, David H. |
| author_GND | (DE-588)141908599 |
| author_facet | Kuhn, Hans Försterling, Horst-Dieter 1934- Waldeck, David H. |
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| classification_tum | CHE 100f |
| ctrlnum | (OCoLC)213466575 (DE-599)BVBBV023425646 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 541 - Physical chemistry |
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| dewey-search | 541 |
| dewey-sort | 3541 |
| dewey-tens | 540 - Chemistry and allied sciences |
| discipline | Chemie / Pharmazie Physik Chemie |
| discipline_str_mv | Chemie / Pharmazie Physik Chemie |
| edition | 2. ed. |
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| index_date | 2024-07-02T21:32:43Z |
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| lccn | 2008012231 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016608009 |
| oclc_num | 213466575 |
| open_access_boolean | |
| owner | DE-20 DE-19 DE-BY-UBM DE-634 DE-29T DE-91G DE-BY-TUM DE-11 DE-355 DE-BY-UBR DE-188 |
| owner_facet | DE-20 DE-19 DE-BY-UBM DE-634 DE-29T DE-91G DE-BY-TUM DE-11 DE-355 DE-BY-UBR DE-188 |
| physical | XLII, 1032 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Wiley |
| record_format | marc |
| spelling | Kuhn, Hans Verfasser aut Principles of physical chemistry by Hans Kuhn ; Horst-Dieter Försterling ; David H. Waldeck 2. ed. Hoboken, NJ Wiley 2009 XLII, 1032 S. Ill., graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Chemistry, Physical and theoretical Physikalische Chemie (DE-588)4045959-7 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Physikalische Chemie (DE-588)4045959-7 s DE-604 Försterling, Horst-Dieter 1934- Verfasser (DE-588)141908599 aut Waldeck, David H. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016608009&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kuhn, Hans Försterling, Horst-Dieter 1934- Waldeck, David H. Principles of physical chemistry Chemistry, Physical and theoretical Physikalische Chemie (DE-588)4045959-7 gnd |
| subject_GND | (DE-588)4045959-7 (DE-588)4123623-3 |
| title | Principles of physical chemistry |
| title_auth | Principles of physical chemistry |
| title_exact_search | Principles of physical chemistry |
| title_exact_search_txtP | Principles of physical chemistry |
| title_full | Principles of physical chemistry by Hans Kuhn ; Horst-Dieter Försterling ; David H. Waldeck |
| title_fullStr | Principles of physical chemistry by Hans Kuhn ; Horst-Dieter Försterling ; David H. Waldeck |
| title_full_unstemmed | Principles of physical chemistry by Hans Kuhn ; Horst-Dieter Försterling ; David H. Waldeck |
| title_short | Principles of physical chemistry |
| title_sort | principles of physical chemistry |
| topic | Chemistry, Physical and theoretical Physikalische Chemie (DE-588)4045959-7 gnd |
| topic_facet | Chemistry, Physical and theoretical Physikalische Chemie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016608009&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kuhnhans principlesofphysicalchemistry AT forsterlinghorstdieter principlesofphysicalchemistry AT waldeckdavidh principlesofphysicalchemistry |