Wolfsberg / Hook / Paneth Isotope Effects

in the Chemical, Geological, and Bio Sciences
1. Auflage 2009
ISBN: 978-90-481-2265-3
Verlag: Springer Netherlands
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 466 Seiten

As the title suggests, Isotope Effects in the Chemical, Geological and Bio Sciences deals with differences in the properties of isotopically substituted molecules, such as differences in the chemical and physical properties of water and the heavy waters. Since the various fields in which isotope effects are applied do not only share fundamental principles but also experimental techniques, this book includes a discussion of experimental apparatus and experimental techniques. Isotope Effects in the Chemical, Geological and Bio Sciences is an educational monograph addressed to graduate students and others undertaking isotope effect research. The fundamental principles needed to understand isotope effects are presented in appropriate detail. While it is true that these principles are more familiar to students of physical chemistry and some background in physical chemistry is recommended, the text provides enough detail to make the book an asset to students in organic and biochemistry, and geochemistry.

Autoren/Hrsg.

Wolfsberg, Max

Hook, W. Alexander van

Paneth, Piotr

Rebelo, Luís Paulo N.

Inhaltsverzeichnis

1;Isotope
Effects ;1
1.1;1 A Short History of Early Work on Isotopes;16
1.1.1;1.1 Introduction;16
1.1.2;1.2 From Dalton to the Discovery of Isotopes;17
1.1.2.1;1.2.1 The Periodic Table;18
1.1.3;1.3 From the Discovery of Isotopes through the Invention of the Mass Spectrograph by Aston;21
1.1.3.1;1.3.1 The Historic Papers of Soddy and Fajans in 1913 and the Work Leading up to These Papers;21
1.1.3.2;1.3.2 Further Elucidation of the Concepts of Elements and Isotopes Including Works of van den Broek, Moseley, Rutherford, Thomson, Aston and Lindemann;29
1.1.3.2.1;1.3.2.1 Van den Broek;29
1.1.3.2.2;1.3.2.2 Moseley;31
1.1.3.2.3;1.3.2.3 Thomson;33
1.1.3.2.4;1.3.2.4 Lindemann;34
1.1.3.2.5;1.3.2.5 Another Component of the Nucleus;35
1.1.3.2.6;1.3.2.6 Aston, the Mass Spectrograph, the Whole Number Rule;35
1.1.3.3;1.3.3 The Work of Harkins on the Whole Number Rule;36
1.1.3.4;1.3.4 Understanding the ``Modern'' Periodic Table;38
1.1.4;1.4 The 1920s and 1930s Through the Discovery of Deuterium;40
1.1.4.1;1.4.1 Early Work on Isotope Effects on Spectra;40
1.1.4.2;1.4.2 The Discovery of Isotopes of Carbon, Nitrogen, and Oxygen, and Hydrogen;45
1.1.4.3;1.4.3 Deuterium;46
1.1.5;1.5 A Brief Look at the Position of Theoretical and Experimental Developments at the Time of the Discovery of Deuterium;48
1.1.5.1;1.5.1 Quantum Theory;48
1.1.5.2;1.5.2 Thermodynamics and Statistical Mechanics;48
1.1.5.3;1.5.3 Instrumentation – The Mass Spectrometer;49
1.1.6;References;49
1.2;2 The Born–Oppenheimer Approximation: Potential Energy Surfaces;52
1.2.1;2.1 Introduction;52
1.2.2;2.2 The Quantum Mechanical Schrödinger Equation of the Molecule;52
1.2.3;2.3 The Separation of the Nuclear and Electronic Parts of the Schrödinger Equation;54
1.2.3.1;2.3.1 Solutions of the Electronic Schrödinger Equation for Molecules;55
1.2.3.2;2.3.2 Nuclear Motion;57
1.2.3.3;2.3.3 Corrections;57
1.2.3.4;2.3.4 Substituent Effects, Isotope Effects, and the First Law of Isotopics;57
1.2.3.5;2.3.5 Separation of Internal and External Degrees of Freedom;58
1.2.4;2.4 The Adiabatic Correction;59
1.2.4.1;2.4.1 An Example;60
1.2.4.2;2.4.2 Adiabatic BO Corrections for Hydrogenic Atoms;62
1.2.4.3;2.4.3 Muonium (Mu);65
1.2.5;2.5 Numerical Calculations of Eelec(S);66
1.2.5.1;2.5.1 Historical Development;66
1.2.5.2;2.5.2 Present Day Approaches;67
1.2.6;References/Suggestions for Further Reading;68
1.3;3 Molecular Vibrations;70
1.3.1;3.1 Introduction;70
1.3.1.1;3.1.1 Vibrations in Diatomic Molecules;70
1.3.1.2;3.1.2 Extension to Polyatomics;73
1.3.1.2.1;3.1.2.1 Degrees of Freedom;73
1.3.1.2.2;3.1.2.2 Coordinate Systems;73
1.3.1.2.3;3.1.2.3 Vibrations of Water Isotopomers;74
1.3.1.3;3.1.3 Remarks;75
1.3.2;3.2 Discussion of Two Types of Coordinate Systems;75
1.3.3;3.3 Calculations in Cartesian Coordinates;77
1.3.3.1;3.3.1 Separation of Translation and Rotation from Vibration;82
1.3.4;3.4 Calculations Employing Valence (Internal) Coordinates;83
1.3.5;3.5 Two Important Rules for Harmonic Vibrational Frequencies;85
1.3.5.1;3.5.1 The Teller–Redlich Product Rule;85
1.3.5.2;3.5.2 The Sum Rule;86
1.3.6;3.A1 Appendix: Matrix Operations;86
1.3.6.1;3.A1.1 Some Definitions;86
1.3.6.2;3.A1.2 Matrix Diagonalization;87
1.3.7;3.A2 An Equality for Use in the Derivation of the Teller–Redlich Product Rule;90
1.3.8;Reading List;91
1.4;4 Isotope Effects on Equilibrium Constants of Chemical Reactions; Transition State Theory of Isotope Effects;92
1.4.1;4.1 Introduction;92
1.4.2;4.2 Brief Review of the Laws of Thermodynamics;92
1.4.2.1;4.2.1 The First Law;92
1.4.2.2;4.2.2 The Second Law;93
1.4.2.3;4.2.3 The Third Law;94
1.4.3;4.3 The Free Energies and the Concept of Equilibrium;95
1.4.3.1;4.3.1 The Helmholtz Free Energy;95
1.4.3.2;4.3.2 The Gibbs Free Energy;96
1.4.3.3;4.3.3 Relations Involving A, A, G and G;96
1.4.4;4.4 Application to Ideal Gases at Equilibrium;99
1.4.4.1;4.4.1 Remarks, Nonideality, Condensed Phases;100
1.4.5;4.5 Statistical Mechanics of Ideal Gases and Isotope Effects;101
1.4.5.1;4.5.1 General Remarks;101
1.4.5.2;4.5.2 Equilibrium Constants and Partition Functions;103
1.4.6;4.6 Evaluation of Partition Functions, q, and Isotope Effects on Partition Functions, qheavy/qlight for Ideal Gases;104
1.4.6.1;4.6.1 The Rigid Rotor Harmonic Oscillator Approximation;104
1.4.6.1.1;4.6.1.1 Degrees of Freedom;105
1.4.6.2;4.6.2 Considerations of Level Spacing;106
1.4.6.3;4.6.3 The Energy Zero;107
1.4.6.4;4.6.4 Bigeleisen and Mayer; The Reduced Isotopic Partition Function Ratio;108
1.4.6.5;4.6.5 Limiting Values for the Isotope Effects;111
1.4.6.5.1;4.6.5.1 The High Temperature Limit;111
1.4.6.5.2;4.6.5.2 The Low Temperature Limit: The ZPE Approximation;111
1.4.7;4.7 The High Temperature Limit: Generalization, (No Classical) Isotope Effects on Chemical Equilibrium;112
1.4.7.1;4.7.1 Further Remarks, RRHO Ideal Gas;116
1.4.8;4.8 The First Quantum Correction;117
1.4.8.1;4.8.1 Application to an Equilibrium;119
1.4.8.2;4.8.2 Polynomial Expansions of (s2/s1)f: Orthogonal Polynomial Methods;120
1.4.9;4.9 Symmetry Numbers;121
1.4.9.1;4.9.1 Symmetry Numbers; Diatomic Molecules;121
1.4.9.2;4.9.2 Symmetry Numbers Continued, Comments,Polyatomics;125
1.4.9.3;4.9.3 The Determination of Relative Symmetry Numbers for Isotopomers;127
1.4.9.4;4.9.4 More Comments, Symmetry Numbers Do Not Lead to Isotope Enrichment;128
1.4.10;4.10 Further Remarks on Temperature Dependence of (s/s)f: Limiting Forms: An Example;130
1.4.11;4.11 Transition State Theory of Isotope Effects;132
1.4.11.1;4.11.1 Fundamentals of Transition State Theory;132
1.4.11.2;4.11.2 Introduction of the Partition Functions;136
1.4.11.2.1;4.11.2.1 Further Details: The MMIEXCZPE Formalism;139
1.4.11.3;4.11.3 Comments;141
1.4.11.3.1;4.11.3.1 The Wigner Correction;141
1.4.11.3.2;4.11.3.2 The High Temperature Limit;141
1.4.11.3.3;4.11.3.3 Remarks;142
1.4.12;4.12 The Development of Modern Methods to Calculate Reduced Isotopic Partition Function Ratios;142
1.4.12.1;4.12.1 The Calculation of (s/s)f for Normal Molecular Species;143
1.4.13;4.13 Corrections to the Bigeleisen–Mayer Equation: The Nuclear Field Shift Effect;145
1.4.14;4.A1 Appendix: The Connection Between the Equilibrium Constant, Its Isotope Effects, and Pressure or Concentration Ratios: Corrections for Nonideality;147
1.4.15;4.A2 Corrections to the Rigid Rotor Harmonic Oscillator Approximation in the Calculation of Equilibrium Constants;149
1.4.15.1;4.A2.1 Corrections to RRHO: Diatomic Molecules;149
1.4.16;Reading List;151
1.5;5 Condensed Phase Isotope Effects: Isotope Effects in Non-ideal Gases;153
1.5.1;5.1 Introduction;153
1.5.2;5.2 Thermodynamic Formalism;153
1.5.2.1;5.2.1 The Vapor Phase Reference;154
1.5.2.2;5.2.2 The Condensed Phase;155
1.5.2.3;5.2.3 The Vapor Pressure Isotope Effect, Separated Isotopes;155
1.5.2.3.1;5.2.3.1 The Corrective Terms: Simplification of Equation 5.10;156
1.5.2.4;5.2.4 Fractionation Factors;156
1.5.3;5.3 Reprise: Remarks Concerning the Partition Functions: The Relation of VPIE to Condensed Phase Molecular Properties and Vibrational Dynamics;158
1.5.3.1;5.3.1 Application to Polyatomics;158
1.5.3.2;5.3.2 What Happens When Molecules Interact or Condense? A Simplified Physical Picture;159
1.5.4;5.4 VPIE's in Monatomic and Polyatomic Systems: Approximate Vibrational Analysis;161
1.5.4.1;5.4.1 Dispersion Forces, Frequency Shifts on Condensation, and the VPIE;163
1.5.4.2;5.4.2 Polyatomic Systems in Approximation: The Cell Model;164
1.5.4.2.1;5.4.2.1 Remarks on Spectroscopic and Thermodynamic Precision;164
1.5.4.3;5.4.3 A Further Approximation: The AB Equation;165
1.5.5;5.5 Non-ideal Gases: Virial Coefficient Isotope Effects (VCIE);166
1.5.6;5.6 Further Discussion of VPIE's;168
1.5.6.1;5.6.1 Representative Effects, Especially H/D Effects and Solvent Dependence;168
1.5.6.2;5.6.2 Interpretation of VPIE Using Model Calculations: Preliminary Remarks;171
1.5.6.3;5.6.3 Anharmonic Corrections;171
1.5.6.3.1;5.6.3.1 Lattice Anharmonicity and the Pseudo-harmonic Approximation;171
1.5.6.3.2;5.6.3.2 Anharmonicity: Internal Modes, Effect of Zero Point Anharmonicity;172
1.5.6.4;5.6.4 Corrections for the Dielectric Effect;174
1.5.6.4.1;5.6.4.1 Example, VPIE of Carbon Disulfide;175
1.5.7;5.7 Some Examples;176
1.5.7.1;5.7.1 Example #1: Monatomic Systems Reconsidered: Accurate Calculations;176
1.5.7.2;5.7.2 Example #2: VPIE's of Ethylene Isotopomers;177
1.5.7.3;5.7.3 Example #3: VPIE's of Benzene Isotopomers; Excess Pressures of Isotopomer Solutions;179
1.5.7.4;5.7.4 Example #4: Water;180
1.5.8;5.8 Excess Free Energies in Solutions of Isotopes: Connections Between VPIE, the Liquid Vapor Fractionation Factor, , and RPFR;184
1.5.8.1;5.8.1 Excess Free Energies and Demixing in Isotopomer Solutions, Further Discussion;186
1.5.9;5.9 The Isotope Effect on TCR for the Superconducting/ Resistive Transition in Metals;187
1.5.10;5.10 Isotope Effects on Solubility;188
1.5.10.1;5.10.1 Liquid–Liquid Equilibria: Two Component Systems;188
1.5.10.2;5.10.2 Small Molecule Solutions Including Aqueous Systems;189
1.5.10.3;5.10.3 IE's on Solubility of Gases in Liquids, Chromatographic IE's;191
1.5.10.4;5.10.4 Solubility of Ionic Solids in H2O/D2O;193
1.5.11;Further Reading;194
1.6;6 Kinetic Isotope Effects Continued: Variational Transition State Theory and Tunneling;195
1.6.1;6.1 Introduction: Transition State Theory, Variational Transition State Theory, and Tunneling;195
1.6.1.1;6.1.1 Transition State Theory;195
1.6.2;6.2 The Basics of Variational Transition State Theory and How It Differs from Conventional Transition State Theory;196
1.6.2.1;6.2.1 The Dividing Surface for the Reaction;196
1.6.2.2;6.2.2 The Minimum Energy Path;199
1.6.2.3;6.2.3 Classical Trajectory Calculations;199
1.6.2.4;6.2.4 The Differences Between TST and VTST;200
1.6.2.5;6.2.5 Locating Dividing Surfaces;201
1.6.2.6;6.2.6 Quantum Mechanical VTST;201
1.6.2.7;6.2.7 Isotope Effects, Comments;202
1.6.3;6.3 Tunneling;203
1.6.3.1;6.3.1 Tunneling in TST;203
1.6.3.1.1;6.3.1.1 Tunneling on Potentials of Arbitrary Shape;206
1.6.3.2;6.3.2 Tunneling in VTST;206
1.6.3.2.1;6.3.2.1 Jacobi Coordinates: The Skew Angle in Three Center Collinear Reactions;206
1.6.3.2.2;6.3.2.2 The Skew Angle: Transformation Between the (rAB, rBC)and (x, y) Coordinates;209
1.6.3.3;6.3.3 Tunneling in Three Center Collinear Reactions;210
1.6.4;6.4 Tests of Variational Transition State Theory(Including Tunneling);213
1.6.4.1;6.4.1 Collinear Three Center Reactions;213
1.6.5;Further Reading;215
1.7;7 Instrumentation and Experimental Techniques;217
1.7.1;7.1 Experimental Determination of Kinetic Isotope Effects;217
1.7.1.1;7.1.1 The Non-competitive or ``Direct'' Method;217
1.7.1.1.1;7.1.1.1 Mixing Studies and Non-competitive KIE's;219
1.7.1.1.2;7.1.1.2 Comment;219
1.7.1.2;7.1.2 Simultaneous Non-competitive Measurements;220
1.7.1.3;7.1.3 KIE's of Enzyme Catalyzed Reactions by Isotope Perturbation;221
1.7.1.4;7.1.4 Competitive Measurements of KIE's;222
1.7.1.4.1;7.1.4.1 Double Labeling;222
1.7.1.4.2;7.1.4.2 Competitive Studies with Single Labeling;223
1.7.1.4.3;7.1.4.3 Approximations to Equations 7.17 and 7.18;224
1.7.1.5;7.1.5 Error Analysis;226
1.7.2;7.2 Mass Spectrometry and Isotope Ratio Mass Spectrometry;229
1.7.2.1;7.2.1 Whole Molecule Mass Spectrometry;229
1.7.2.2;7.2.2 Isotope-Ratio Mass Spectrometry;233
1.7.2.2.1;7.2.2.1 Sample Preparation;236
1.7.2.2.2;7.2.2.2 Remote Labeling for IRMS of Oxygen and Nitrogen IE's;237
1.7.2.2.3;7.2.2.3 Cavity Ring-Down Spectroscopy;238
1.7.3;7.3 NMR Measurements of Isotope Effects: Isotope Effects on NMR Spectra;239
1.7.3.1;7.3.1 Isotope Labeling in NMR Investigations of Molecular Structure;239
1.7.3.2;7.3.2 Rovibrational NMR Isotope Effects;240
1.7.3.2.1;7.3.2.1 NMR Studies of Fast Exchange IE's;245
1.7.3.3;7.3.3 NMR as an Analytical Tool: NMR Measurements of Carbon IE's;245
1.7.4;7.4 Radioisotopes;247
1.7.4.1;7.4.1 Errors;247
1.7.5;7.5 Equilibrium Isotope Effects;248
1.7.5.1;7.5.1 Fractionation Measurements;248
1.7.5.2;7.5.2 Studies Using Separated Isotopes;249
1.7.5.2.1;7.5.2.1 Vapor Pressure Isotope Effects;249
1.7.5.2.2;7.5.2.2 PVT Isotope Effects for Liquids, Vapors, and VPIE at LV Equilibrium;251
1.7.5.3;7.5.3 Liquid–Vapor Isotope Fractionation Measurements;252
1.7.5.4;7.5.4 Isotope Effects on Liquid–Liquid Equilibria;252
1.7.5.4.1;7.5.4.1 Demixing of Polymer Blends;254
1.7.6;7.6 H/D Isotope Effects and Small Angle Neutron Scattering;256
1.7.7;Further Reading;258
1.8;8 Isotope Separation;259
1.8.1;8.1 Introduction;259
1.8.2;8.2 Theory of Cascades: Terminology;261
1.8.2.1;8.2.1 Gaseous Diffusion of UF6;262
1.8.2.2;8.2.2 Types of Separations: Cascades;263
1.8.2.2.1;8.2.2.1 Simple and Countercurrent Cascades;263
1.8.2.2.2;8.2.2.2 The Ideal Cascade;265
1.8.2.2.3;8.2.2.3 Equilibrium Time;267
1.8.2.3;8.2.3 Further Discussion of Gaseous Diffusion: Separative Work;268
1.8.3;8.3 Practical Isotope Separation: Some Examples;269
1.8.3.1;8.3.1 Electromagnetic Separation;270
1.8.3.1.1;8.3.1.1 The Plasma Separation Process;272
1.8.3.2;8.3.2 Thermal Diffusion of Gases;273
1.8.3.3;8.3.3 Large Scale Separations and Energy Demands;275
1.8.3.4;8.3.4 Centrifuge Based Separations;278
1.8.3.5;8.3.5 Aerodynamic Isotope Separation;281
1.8.4;8.4 Distillation and Exchange Distillation: The Large Scale Production of Deuterium;281
1.8.4.1;8.4.1 An Aside: Monothermal Isotope Exchange with Chemical Reflux; 15N Enrichment;283
1.8.4.2;8.4.2 Dual Temperature Exchange: The GS Process for Deuterium Enrichment;284
1.8.4.3;8.4.3 Other Exchange Reactions for Deuterium Enrichment;286
1.8.4.4;8.4.4 Distillation;286
1.8.4.5;8.4.5 Specific Examples, Isotope Separation by Distillation;288
1.8.4.5.1;8.4.5.1 Hydrogen;289
1.8.4.5.2;8.4.5.2 Carbon Monoxide;289
1.8.4.5.3;8.4.5.3 Isotope Enrichment by Distillation of Nitrous Oxide or Water;290
1.8.4.6;8.4.6 Exchange Distillation: 10B Enrichment;290
1.8.4.7;8.4.7 Liquid–Liquid Exchange: Lithium Enrichment;291
1.8.5;8.5 Chromatography;291
1.8.5.1;8.5.1 Gas Chromatography;292
1.8.5.2;8.5.2 Redox Ion Exchange Chromatography;294
1.8.6;8.6 Photochemical and Laser Isotope Separation;296
1.8.6.1;8.6.1 Outline of a Laser Isotope Separation Scheme;296
1.8.6.2;8.6.2 LIS of Deuterium;299
1.8.6.3;8.6.3 LIS for Uranium;299
1.8.6.3.1;8.6.3.1 AVLIS;299
1.8.6.3.2;8.6.3.2 LIS for UF6 (SILEX);300
1.8.7;8.7 Other Isotope Separation Processes;300
1.8.8;Further Reading;301
1.9;9 Isotope Effects in Nature: Geochemical and Environmental Studies;302
1.9.1;9.1 Introduction;302
1.9.2;9.2 Notation and Standards;303
1.9.2.1;9.2.1 The Delta, , Notation;303
1.9.2.2;9.2.2 Standards;303
1.9.2.3;9.2.3 Conversion from One Standard to Another;305
1.9.2.4;9.2.4 Remarks, Experimental Technique;305
1.9.3;9.3 Geochemical Temperature Scales;306
1.9.4;9.4 Isotope Hydrology; Rayleigh Fractionation;309
1.9.4.1;9.4.1 Fractionation in Hydrology; the Meteoric Water Line;311
1.9.4.2;9.4.2 Ice Cores;311
1.9.4.3;9.4.3 Clay Cores: 13C Enrichment in Paleo-Organics;314
1.9.5;9.5 Three Isotope Plots of Terrestrial and Extraterrestrial Samples;315
1.9.6;9.6 Isotope Fractionation by Living or Once Living Organisms;315
1.9.6.1;9.6.1 ``We Are What We Eat, a Few per Mil'';316
1.9.6.2;9.6.2 Isotope Fractionation and Dendrochronology of Bristlecone Pines;318
1.9.6.3;9.6.3 18O as a Probe for Storm Patterns;319
1.9.7;9.7 Coal, Petroleum and Natural Gas;320
1.9.8;9.8 Further Examples, Food Authentication;321
1.9.8.1;9.8.1 Food Authentication;321
1.9.8.1.1;9.8.1.1 Fruit and Vegetable Juice;321
1.9.8.1.2;9.8.1.2 Wines;321
1.9.8.1.3;9.8.1.3 Alcohols, Acetic Acid (Vinegar);322
1.9.8.1.4;9.8.1.4 Honey, Maple Syrup;322
1.9.8.2;9.8.2 Athletic `Doping';323
1.9.9;9.9 Stable Isotopes as Tracers in Biological, Agricultural, Nutritional and Medical Research;323
1.9.10;Suggestions for Further Reading;323
1.10;10 Kinetic Isotope Effects on Chemical Reactions;325
1.10.1;10.1 Introduction;325
1.10.2;10.2 KIE's on the ``Simplest'' Chemical Reaction (Hydrogen Atom + Diatomic Hydrogen);325
1.10.3;10.3 The Reaction Between Methane and Hydroxyl Radical;330
1.10.4;10.4 Further Discussion, Heavy Atom Isotope Effects, Secondary Isotope Effects;331
1.10.4.1;10.4.1 -2 Isotope Effects;332
1.10.4.2;10.4.2 -2 Isotope Effects;334
1.10.4.3;10.4.3 Steric Arguments and , …2 Isotope Effects;335
1.10.4.4;10.4.4 Comment;336
1.10.5;10.5 Relative Values for Deuterium and Tritium Isotope Effects: The Swain–Schaad Relation;337
1.10.6;10.6 Alternative Reaction Paths, SN2 and E2: Condensed and Vapor Phase Studies;339
1.10.7;10.7 KIE's as Probes of Transition State Structure;341
1.10.7.1;10.7.1 SN2 Reactions for CN- Attack on Substituted Benzyl Chlorides;342
1.10.7.2;10.7.2 Reaction of Substituted Anilines with Methyl Iodide;343
1.10.7.3;10.7.3 More on KIE's in Menshutkin Reactions;344
1.10.7.4;10.7.4 Decarboxylation Reactions;346
1.10.7.5;10.7.5 Bond Order Dependence of the KIE;347
1.10.7.6;10.7.6 Mechanism of the Diels–Alder Reaction;348
1.10.8;10.8 Remarks;351
1.10.8.1;10.8.1 Protocol of Harmonic TST Calculations of Kinetic Isotope Effects;351
1.10.8.2;10.8.2 The TST/VTST Interface;352
1.10.9;Reading List;353
1.11;11 Enzymes; Aqueous Solvent IE'S;355
1.11.1;11.1 Introduction;355
1.11.2;11.2 Some Simple Enzyme Kinetics;356
1.11.2.1;11.2.1 Introduction: The Michaelis–Menten Mechanism;356
1.11.2.2;11.2.2 The Incorporation of Product Binding;359
1.11.2.3;11.2.3 A Simpler Notation;361
1.11.2.4;11.2.4 The Intrinsic IE, Commitments, and Partitioning Factor;362
1.11.3;11.3 More Complicated Enzyme Reactions;363
1.11.3.1;11.3.1 Reversible Reaction at the Active Site;363
1.11.3.2;11.3.2 Ordered Sequential Reactions;364
1.11.3.3;11.3.3 Random Binding;366
1.11.3.4;11.3.4 Comments;366
1.11.3.5;11.3.5 Multiple Isotope Effects;367
1.11.3.6;11.3.6 Multiple Isotope Effects, Different Steps;368
1.11.3.7;11.3.7 Reversible Competitive Inhibitors;369
1.11.4;11.4 Aqueous Solvent Equilibrium and Kinetic Isotope Effects;370
1.11.4.1;11.4.1 H2O/D2O Solvent Effects on pH (pD) and pKa;370
1.11.4.1.1;11.4.1.1 An Important Consequence;371
1.11.4.2;11.4.2 Monoprotic Acid/Base Equilibria in Mixed Solvents;372
1.11.4.2.1;11.4.2.1 Extension to Dissociation of Polyprotic Acids;374
1.11.4.3;11.4.3 Kinetic Isotope Effects in Mixed Solvents;374
1.11.5;11.5 Examples, Enzyme Catalysis;377
1.11.5.1;11.5.1 Decarboxylation KIE's;377
1.11.5.1.1;11.5.1.1 Enzyme Catalysed Conversion of l-Malate to Pyruvate;377
1.11.5.2;11.5.2 Glucose-6-Phosphate Dehydrogenase;378
1.11.5.3;11.5.3 Concentration Dependence of KIE; Phosphoenolpyruvate Carboxylase;380
1.11.5.4;11.5.4 Other Factors Influencing Commitment;383
1.11.6;11.6 Solvent Kinetic Isotope Effects in Enzyme Reactions (See Also Section 11.4);384
1.11.6.1;11.6.1 Examples;385
1.11.6.2;11.6.2 Coupled Motion;387
1.11.7;11.7 Tunneling (See Also Section 11.8);388
1.11.7.1;11.7.1 Tunneling in Alcohol Dehydrogenases;388
1.11.7.2;11.7.2 Hydrogen Atom Transfer in Methylmalonyl-CoA Mutase;389
1.11.8;11.8 Modeling Isotope Effects on Enzyme-Catalyzed Reactions;391
1.11.8.1;11.8.1 Examples of VTST QM/MM Calculations for Enzyme Reactions;392
1.11.8.1.1;11.8.1.1 Quantum Mechanical Dynamical Effects for an Enzyme Catalyzed Proton Transfer Reaction;392
1.11.8.1.2;11.8.1.2 Hydrogen Radical Transfer Catalyzed by a Coenzyme B12-Dependent Mutase;395
1.11.8.2;11.8.2 QM/MM for Haloalkane Dehalogenase: TST Calculations;397
1.11.8.3;11.8.3 Comment;400
1.11.9;Reading List;400
1.12;12 Isotope Effects on Dipole Moments, Polarizability, NMR Shielding, and Molar Volume;401
1.12.1;12.1 Introduction;401
1.12.1.1;12.1.1 Dipole Moments, Polarizabilites and Hyperpolarizabilities;401
1.12.2;12.2 Dipole Moments and Their Isotope Effects;405
1.12.2.1;12.2.1 Experimental Methods;405
1.12.2.2;12.2.2 The IE on 0, Discussion;406
1.12.2.3;12.2.3 Dipole Moments for Diatomic Isotopomers;408
1.12.2.4;12.2.4 Theoretical Approaches;410
1.12.3;12.3 Induced Moments, Polarizability Isotope Effects;410
1.12.3.1;12.3.1 The Polarizability;410
1.12.3.2;12.3.2 Frequency Dependence;410
1.12.3.3;12.3.3 Experimental Methods, Results, Discussion;412
1.12.4;12.4 Isotope Effects on NMR Shielding;415
1.12.4.1;12.4.1 Introduction;415
1.12.4.2;12.4.2 Application of the Rovibrational Theory;415
1.12.4.2.1;12.4.2.1 H/D Isotope Effects on [13C] NMR of Methane;417
1.12.4.2.2;12.4.2.2 Larger and More Complicated Molecules;417
1.12.5;12.5 Molar Volume Isotope Effects;418
1.12.5.1;12.5.1 The Bartell Mechanical Model for MVIE;420
1.12.5.2;12.5.2 Hydrogen Bonded Liquids;421
1.12.5.3;12.5.3 Limitations of the Mechanical Model, the Temperature Dependence;423
1.12.6;Reading List;424
1.13;13 Reduced Equations of State: Critical Property Isotope Effects;425
1.13.1;13.1 Introduction, Corresponding States;425
1.13.1.1;13.1.1 Equations of State, Corresponding States;425
1.13.2;13.2 Reference Systems; Critical Property Data for Some Isotopomer Pairs;426
1.13.2.1;13.2.1 The PVT Surface for Isotopomer Pairs;426
1.13.2.2;13.2.2 IE's of Reference Pairs;429
1.13.2.3;13.2.3 PVT Isotope Effects and the Modified Van der Waals Equation;430
1.13.2.4;13.2.4 Reference Systems, Isotope Effects;430
1.13.3;13.3 Critical Property Isotope Effects;431
1.13.3.1;13.3.1 Experimental Data;431
1.13.3.2;13.3.2 Correlations Between Critical Property and Vapor Pressure IE's: ln(Tc/Tc) and ln(P/P);432
1.13.3.3;13.3.3 Uncertainties in Critical Property IE's;433
1.13.4;13.4 CS Calculations for Some Isotopomer Pairs;434
1.13.4.1;13.4.1 The Lighter Pairs;434
1.13.4.1.1;13.4.1.1 3He/4He;434
1.13.4.1.2;13.4.1.2 Hydrogen;434
1.13.4.2;13.4.2 VdW1 Parameters for Heavier Pairs;436
1.13.4.2.1;13.4.2.1 Water;436
1.13.4.2.2;13.4.2.2 Methane;436
1.13.5;13.5 Remarks;436
1.13.6;Further Reading;438
1.14;14 Isotope Effects in Unimolecular Processes: ``Mass Independent'' Isotope Fractionation and the Ozone Problem;439
1.14.1;14.1 Introduction: Isotope Effects in Unimolecular Reactions;439
1.14.2;14.2 The RRKM Mechanism for Unimolecular Gas Phase Reactions;440
1.14.2.1;14.2.1 The Expression for k1(E,dE)/k2;443
1.14.2.2;14.2.2 Discussion of ka(E);443
1.14.2.2.1;14.2.2.1 Classification of Molecular Energy Levels;444
1.14.2.3;14.2.3 The Expression for ka(E);445
1.14.2.4;14.2.4 The Pressure Dependence of the Rate Constant kuni;447
1.14.2.4.1;14.2.4.1 The High Pressure Rate Constant ([M] );447
1.14.2.4.2;14.2.4.2 The Low Pressure Rate Constant ([M] 0);448
1.14.2.5;14.2.5 Experimental Measurements of Isotope Effects in Unimolecular Reactions and the RRKM theory;448
1.14.2.6;14.2.6 Thermal Activation: Inverse 2-D-KIE's at Low Pressure;449
1.14.2.6.1;14.2.6.1 Gas Phase Isomerization of Methyl Isocyanide;449
1.14.2.6.2;14.2.6.2 Gas Phase Isomerization of Cyclopropane;451
1.14.2.6.3;14.2.6.3 Model Calculation of a 2--Deuterium KIE on C–C Bond Rupture;452
1.14.2.7;14.2.7 Primary Isotope Effects;453
1.14.3;14.3 17O and 18O Enrichment in Terrestrial and Extraterrestrial Samples: ``Mass Independent'' Isotope Fractionation and the Ozone Problem;454
1.14.3.1;14.3.1 Introduction;454
1.14.3.2;14.3.2 Oxygen Isotope Fractionation in Earth, Moon, and Meteorite Samples;455
1.14.3.3;14.3.3 Mass Independent Isotope Fractionation in the Laboratory, the Stratosphere,and the Troposphere;456
1.14.3.4;14.3.4 MIF's for Ozone from Natural Abundance and Enriched Starting Materials;458
1.14.4;14.4 Theory of Mass Independent Isotope Fractionation of Ozone;460
1.14.4.1;14.4.1 Comment;462
1.14.5;Further Reading;462
1.15;Author Index;464
1.16;Subject Index;469