Isotope Effects in Chemistry And Biology

by Kohen; Amnon

• ISBN13: 9780824724498
• ISBN10: 0824724496
• Edition: 1st
• Format: Hardcover
• Copyright: 2005-11-01
• Publisher: CRC Press

Summary

The field of isotope effects has expanded exponentially in the last decade, and researchers are finding isotopes increasingly useful in their studies. Bringing literature on the subject up to date, Isotope Effects in Chemistry and Biology covers current principles, methods, and a broad range of applications of isotope effects in the physical, biological, and environmental sciences.The authors first explain how kinetic, equilibrium, and anharmonic isotope effects are used to measure the ratio of reaction rates, the ratio between isotopes in thermodynamic equilibrium, and the geometric changes between molecules. The volume describes basic theories, including gas phase, simple condensed phase, small molecule studies, and applications of the Bigeleisen-Mayer theory before covering how isotopes affect molecular geometries, chemical bond breaking, formation and chemical dynamics, and hydrogen transfer. It explores novel, mass-independent isotope effects and problems encountered in hydrogen transfer, tunneling, and exchange. Authors also discuss isotope effects in organic and organometallic reactions and complex enzyme reactions and a unique chapter explores water isotope effects under pressure.Written by internationally recognized researchers from 13 countries, some chapters summarize the perspective of a well-established subject while others review recent findings and on-going research that occasionally present controversial viewpoints using clear scientific arguments and discussion presented by all relevant authors. Isotope Effects in Chemistry and Biology brings together a wide scope of different perspectives and practical developments and applications into a comprehensive reference of isotope effects that reflect the most current state of the art.

Table of Contents

Chapter 1 Theoretical Basis of Isotope Effects from an Autobiographical Perspective	1	(40)
Jacob Bigeleisen
I. From Soddy—Fajans through Urey—Greiff	1	(2)
II. Equilibrium Systems — General	3	(1)
III. Equilibrium in Ideal Gases	4	(8)
A. Classical and Quantum Mechanical Systems	4	(1)
B. The Reduced Partition Function Ratio of an Ideal Gas	5	(3)
1. Numerical Calculation of the Reduced Partition Function Ratio	7	(1)
C. Corrections to the Bigeleisen—Mayer Equation	8	(4)
IV. Isotope Chemistry and Molecular Structure	12	(6)
A. The First Order Rules of Isotope Chemistry	12	(1)
B. Statistical Mechanical Perturbation Theory	13	(1)
C. Polynomial Expansions of the Reduced Partition Function Ratio	14	(4)
V. Kinetic Isotope Effects	18	(7)
VI. Condensed Matter Isotope Effects	25	(7)
Acknowledgments	32	(1)
References	33	(8)
Chapter 2 Enrichment of Isotopes	41	(48)
Takanobu Ishida and Yasuhiko Fujii
I. Overview	42	(2)
A. Separation Factor, Material Balance, and Cascade of Separation Stages	42	(2)
II. Enrichment Processes	44	(12)
A. Enrichment Processes Based on Steady State Phenomena of Reversible Processes	44	(9)
1. Distillation	50	(1)
2. Chemical Exchange	50	(3)
3. Gas Centrifugation	53	(1)
B. Enrichment Processes Based on Nonsteady State Phenomena of Reversible Processes	53	(1)
C. Enrichment Based on Irreversible Processes	53	(3)
1. Laser Isotope Separation	53	(1)
2. Gaseous Diffusion	54	(1)
3. Thermal Diffusion	55	(1)
4. Electrolysis	55	(1)
5. Electromagnetic Method: Calutron	56	(1)
III. Separation Cascade	56	(10)
A. Ideal Cascade: Thermodynamic Efficiency and No-Mixing	56	(2)
B. Product-End Refluxer	58	(3)
C. McCabe-Thiele Diagram for Square Cascade	61	(3)
1. Case of Total Reflux	63	(1)
2. Case of Minimum Reflux Ratio	63	(1)
D. Separative Capacity for Close-Separation, Ideal Cascade	64	(1)
E. HETP (Height Equivalent of Theoretical Plate)	65	(1)
IV. Startup of Isotope Enrichment Cascade	66	(1)
A. Time-Dependence of Enrichment Profile along the Length of Cascade during Startup	66	(1)
B. Rate of Attainment of Steady-State Profile vs. Holdups	67	(1)
V. Empirical Determination of HETP and Separation Factor a	67	(2)
A. By Use of Analytic Solution of Material Balance Equation under Transient Condition	67	(2)
B. From Graphical Solution of Material Balance Equation under the Condition of Zero Time-Dependence at All Stages	69	(1)
VI. Miscellaneous Other Considerations	69	(3)
A. Possible Needs of Chemical Waste Disposal	70	(1)
B. Possibility of Failure to Achieve a High Target Enrichment	70	(1)
C. Possible Explosion of Working Material	71	(1)
D. Consideration of Supply for the Feed	72	(1)
VII. Enrichment by Nonsteady State Phenomena Involving Reversible Process	72	(10)
A. Ion Exchange Isotope Separation	72	(2)
B. Chromatographic Isotope Separation	74	(1)
C. Nonsteady-State Enrichment	75	(3)
1. Enrichment Profile	75	(2)
2. HETP	77	(1)
D. Isotope Separation by Ion Exchange	78	(12)
1. Boron Isotope Separation	78	(1)
2. Nitrogen Isotope Separation	79	(2)
3. Uranium Isotope Separation	81	(1)
VIII. Concluding Remarks	82	(1)
Acknowledgments	83	(1)
References	83	(6)
Chapter 3 Comments on Selected Topics in Isotope Theoretical Chemistry	89	(30)
Max Wolfsberg
I. Introduction	89	(1)
II. Born—Oppenheimer Approximation and Molecular Vibrations/Potential Energy Surfaces	90	(10)
A. Born —Oppenheimer Oppenheimer Approximation	90	(1)
B. The Adiabatic Correction to the Born—Oppenheimer Approximation	91	(5)
C. Molecular Vibrations/Potential Energy Surfaces	96	(3)
1. General	96	(1)
2. The Determination of Harmonic Force Constants in Valence Coordinates	97	(1)
3. The Determination of Harmonic Force Constants in Cartesian Displacement Coordinates	98	(1)
D. Two Important Equalities for Harmonic Frequencies of Isotopomers	99	(1)
III. The Statistical Mechanics of Equilibrium Isotope Effects in the Gas Phase	100	(9)
A. Equilibrium Constants	100	(2)
B. Rate Constants	102	(2)
C. The Symmetry Number in Isotope Chemistry	104	(5)
IV. Numerical Calculations of Isotope Effects	109	(6)
A. "Early" Calculations	109	(1)
B. Isotope Effect Calculations Coupled with A Priori Calculation of Electronic Structures	110	(10)
1. Some General Considerations of Electronic Structure Calculations	110	(2)
2. The Program THERMISTP	112	(3)
References	115	(4)
Chapter 4 Condensed Matter Isotope Effects	119	(34)
W. Alexander Van Hook
I. Introduction	120	(1)
II. The Vapor Pressure Isotope Effect in Liquids and Solutions	120	(11)
A. Measurements on Separated Isotopes	120	(3)
1. The Vapor Phase	121	(1)
2. The Condensed Phase	122	(1)
3. The VPIE	123	(1)
B. Fractionation Factors	123	(1)
C. Relation of VPIE to Condensed Phase Molecular Properties and Vibrational Dynamics	124	(10)
1. Application to Polyatomics	125	(1)
2. What Happens When Molecules Condense? A Simplified Physical Picture	125	(2)
3. VPIEs in Monatomic and Polyatomic Systems. Approximate Vibrational Analysis	127	(1)
4. Monatomic Systems Continued. Accurate Calculations of VPIE	128	(1)
5. Polyatomic Systems in First Approximation: The Cell Model	129	(1)
6. Spectroscopic vs. Thermodynamic Precision	130	(1)
7. A Further Approximation. The AB Equation	130	(1)
III. Illustrations. Representative Effects, Especially H/D Effects	131	(3)
IV. Further Remarks on Connections with Spectroscopy	134	(2)
A. Anharmonicity	134	(1)
B. The Dielectric Effect	134	(6)
1. Example, VPIE of Carbon Disulfide	134	(2)
V. The Molar Volume Isotope Effect	136	(2)
VI. Excess Free Energies in Solutions of Isotopes. The Relation between VPIE, the Liquid Vapor Fractionation Factor, a, and RPFR	138	(1)
VII. Anharmonicity	139	(1)
VIII. Some Examples	140	(5)
A. Ethylene	140	(1)
B. Benzene	141	(1)
C. Water	142	(3)
IX. Solute and Solvent IEs in Polymer—Polymer and Polymer Solvent Mixtures	145	(3)
A. Demixing of Polymer—Polymer Isotopomer Solutions	145	(1)
B. Demixing in Polymer—Solvent Systems	145	(3)
X. Conclusion	148	(1)
References	148	(5)
Chapter 5 Anharmonicities, Isotopes, and IR and NMR Properties of Hydrogen-Bonded Complexes	153	(22)
Janet E. Del Bene
I. Introduction	153	(1)
II. Hydrogen Bond Types	154	(1)
A. Traditional	154	(1)
B. Ion-Pair	154	(1)
C. Proton-Shared	154	(1)
III. X–H Stretching Bands in the IR Spectra of Complexes with X–H–Y Hydrogen Bonds	154	(11)
A. Anharmonicity Effects	154	(4)
B. Matrix Effects	158	(4)
C. Deuterium Substitution Effects on Proton-Stretching Frequencies	162	(3)
IV. Two-Bond Spin–Spin Coupling Constants across Hydrogen Bonds	165	(6)
A. Anharmonicity and Field Effects	166	(4)
B. Isotopic Substitution Effects on Zero-Point Motion and Thermal Vibrational Averaging of Coupling Constants	170	(1)
V. Concluding Remarks	171	(1)
References	172	(3)
Chapter 6 Isotope Effects on Hydrogen-Bond Symmetrization in Ice and Strong Acids at High Pressure	175	(18)
Katsutoshi Aoki
I. Introduction	175	(2)
A. Hydrogen-Bond Symmetrization	175	(1)
B. Candidate Compounds and Promising Probe	176	(1)
II. Hydrogen-Bond Symmetrization in Ice	177	(6)
A. Crystal Structure	177	(1)
B. Infrared Absorption Study	178	(5)
1. Symmetrization in Ice VIII	179	(2)
2. Symmetrization in Ice VII	181	(1)
3. Phase Diagram and Isotope Effect	182	(1)
III. Hydrogen-Bond Symmetrization in Hydrogen Chloride	183	(7)
A. Crystal Structure	183	(2)
B. Raman Scattering Study	185	(9)
1. Symmetrization in HCl	185	(2)
2. Symmetrization in DCl	187	(2)
3. Isotope Effect on Stretching Vibration and Symmetrization	189	(1)
IV. Summary	190	(1)
References	191	(2)
Chapter 7 Hydrogen Bond Isotope Effects Studied by NMR	193	(38)
Hans-Heinrich Limbach, Gleb S. Denisov, and Nikolai S. Golubev
I. Introduction	193	(1)
II. Theoretical Section	194	(11)
A. The Crystallographic View of Hydrogen Bonded Systems	194	(2)
B. Origin of Hydrogen Bond Isotope Effects	196	(2)
1. Influence of the Hydron Potential	196	(1)
2. Effects of the Environment	197	(1)
C. Inclusion of Quantum Corrections in Hydrogen Bond Correlations	198	(4)
D. H/D Isotope Effects on NMR Parameters and Hydrogen Bond Geometries: The Point Approximation	202	(2)
E. H/D Isotopic Fractionation, Hydrogen Bond Geometries and NMR Parameters	204	(1)
III. Applications	205	(21)
A. H/D Isotope Effects in Strong NHN Hydrogen Bonds	205	(5)
B. H/D Isotope Effects in OHN Hydrogen Bonded Pyridine–Acid and Collidine–Acid Complexes	210	(7)
1. Low-Temperature NMR Spectroscopy of Pyridine–Acid Complexes Dissolved in Liquefied Freon Mixtures	210	(1)
2. Geometric Hydrogen Bond Correlations of OHN Hydrogen Bonded Complexes	211	(2)
3. H/D Isotope Effects on the NMR Parameters of Pyridine–Acid and Collidine–Acid Complexes	213	(4)
4. H/D Isotopic Fractionation and NMR Parameters of Pyridine–Acid Complexes	217	(1)
C. Temperature-Induced Solvent H/D Isotope Effects on NMR Chemical Shifts of FHN Hydrogen Bonds	217	(5)
D. H/D Isotope Effects on the NMR Parameters and Geometries of Coupled Hydrogen Bonds	222	(4)
IV. Conclusions	226	(1)
Acknowledgments	227	(1)
References	227	(4)
Chapter 8 Isotope Effects and Symmetry of Hydrogen Bonds in Solution: Single- and Double-Well Potential	231	(22)
Jonathan S. Lau and Charles L. Perrin
I. Introduction	232	(2)
A. Single- and Double-Well H-Bonds	232	(1)
B. Low-Barrier H-Bonds, Short, Strong H-Bonds, "Symmetric" H-Bonds	232	(2)
1. Resonance-Assisted H-Bonds, Charge-Assisted H-Bonds	233	(1)
2. Sterically Enforced H-Bonds	233	(1)
II. Computational Work	234	(2)
A. Energetic and Geometric Descriptions	234	(1)
B. Accounting for Solvation	235	(1)
III. Methods of Observation	236	(5)
A. Measurement of pKa	237	(1)
B. Fractionation Factors	237	(1)
C. NMR Chemical Shifts	238	(1)
D. NMR Coupling Constants	239	(1)
E. Infrared (IR)	240	(1)
F. X-Ray and Neutron Diffraction	240	(1)
IV. Current Work	241	(6)
A. Intramolecular Systems	241	(4)
1. Enol Tautomers of β-Dicarbonyls and Related Molecules	241	(1)
2. Proton Sponge	242	(1)
3. Dicarboxylic Acids	243	(1)
4. Schiff Bases	244	(1)
B. Intermolecular Systems	245	(14)
1. Pyridine-Acid Complexes	245	(1)
2. Enzymes	246	(1)
V. Conclusion	247	(1)
Acknowledgments	247	(1)
References	247	(6)
Chapter 9 NMR Studies of Isotope Effects of Compounds with Intramolecular Hydrogen Bonds	253	(28)
Poul Erik Hansen
I. Introduction and Outline	253	(2)
II. Definitions	255	(1)
III. Theory	255	(3)
IV. Experimental Conditions	258	(1)
V. Static Systems	259	(10)
A. Resonance-Assisted Hydrogen Bonded Systems	259	(3)
1. Transmission of Isotope Effects across Hydrogen Bonds	261	(1)
B. Non-RAHB Cases	262	(2)
C. Medium- and Long-Range Isotope Effects	264	(1)
D. Isotope Effects through Space	264	(1)
E. nΔ15N(D)	265	(1)
1. ¹Δ15N(D)	265	(1)
2. 5A.15N(D)	266	(1)
F. nΔ17O(D)	266	(1)
G. nΔYH(XH) (X,Y = O or N)	266	(1)
H. nΔ19F(XD)	267	(1)
I. nΔ¹³C(18O)	267	(1)
J. Primary Isotope Effects	267	(1)
K. Summary for Intrinsic Isotope Effects	268	(1)
1. RAHB Systems	268	(1)
2. Non-RAHB Systems	269	(1)
VI. Equilibrium Isotope Effects	269	(6)
A. General Findings	269	(4)
B. Long-Range Effects in Equilibrium Systems	273	(1)
C. Identifying Equilibrium Systems	274	(1)
VII. Calculations	275	(1)
References	275	(6)
Chapter 10 Vibrational Isotope Effects in Hydrogen Bonds	281	(24)
Zofia Mielke and Lucjan Sobczyk
I. Introduction	281	(4)
A. Classical and Quantum Mechanical Calculations of Force Field and Vibrational Spectra in the Harmonic Approximation	282	(2)
B. The Effect of Deuterium Substitution on the Vibrations Involving Hydrogen Motion	284	(1)
C. The Isotopic Substitution, the Potential Energy Distribution, and the Frequency Isotopic Ratio (ISR)	284	(1)
II. Sources of Anomalous H/D Isotope Effects in Hydrogen-Bonded Systems	285	(2)
III. The Hydrogen Bond Effect on Anharmonicity of Protonic Vibrations	287	(3)
IV. Potential Energy Functions for the Proton-Stretching Vibrations	290	(2)
V. The Shape of the Potential and Evolution of IR Spectra of Hydrogen-Bonded Systems	292	(2)
VI. Frequency Isotopic Ratio (ISR) and Its Correlation with Other Parameters of Hydrogen Bonds	294	(2)
VII. The Isotope Effect upon Other Spectroscopic Parameters of Hydrogen-Bonded Systems	296	(2)
VIII. Low-Barrier Hydrogen Bonds	298	(3)
References	301	(4)
Chapter 11 Isotope Selective Infrared Spectroscopy and Intramolecular Dynamics	305	(56)
Michael Hippler and Martin Quack
I. Introduction	306	(5)
A. Principles of Isotope Effects in Infrared Spectroscopy and Molecular Dynamics	306	(2)
B. Intramolecular Dynamics and Isotope Selective Spectroscopic Techniques: An Overview	308	(3)
II. Intramolecular Redistribution Processes: From High-Resolution Spectroscopy to Ultrafast Intramolecular Dynamics	311	(6)
A. Intramolecular Quantum Dynamics and Molecular Spectroscopy	311	(2)
B. Spectroscopic States and Intramolecular Dynamics: An Intuitive Perspective	313	(7)
1. General Aspects	313	(1)
2. An Example of Two-Level Dynamics	314	(2)
3. Coupling Many Levels in a Multistate Dynamics	316	(1)
III. The Experimental Approach to Infrared Spectroscopy with Mass and Isotope Selection (IRSIMS)	317	(3)
IV. Mass Selective Overtone Spectroscopy by Vibrationally Assisted Dissociation and Photofragment Ionization: OSVADPI	320	(9)
A. Mechanism of Vibrationally Assisted Dissociation and Photofragment Ionization	320	(3)
B. Isotopomer Selective Overtone Spectroscopy of the Nj = 42 CH Chromophore Absorption of CHCl3	323	(2)
C. Isotopomer Selective Overtone Spectroscopy of the Nj = 41 CH Chromophore Absorption of CHCl3: A Hierarchy of Time Scales and Isotope Effects in Intramolecular Vibrational Energy Redistribution (IVR)	325	(4)
V. Isotope Selective Overtone Spectroscopy by Resonantly Enhanced Two-Photon Ionization of Vibrationally Excited Molecules	329	(17)
A. Overview	330	(1)
B. Mechanism of Resonantly Enhanced Two-Photon Ionization of Vibrationally Excited Molecules	331	(3)
C. The N = 2 NH Chromophore Absorption of Aniline Isotopomers Near 6750 cm-¹: Isotope Effects and Vibrational Mode Specificity in IVR and Tunneling Processes	334	(4)
D. ¹³C Isotope Effects in the IVR of Vibrationally Excited Benzene	338	(8)
VI. Conclusions and Outlook	346	(2)
Acknowledgments	348	(1)
References	348	(13)
Chapter 12 Nonmass-Dependent Isotope Effects	361	(26)
Ralph E. Weston, Jr.
I. Introduction	361	(3)
II. Ozone Isotopologues	364	(8)
A. Laboratory Experiments	364	(3)
B. Atmospheric Ozone	367	(1)
C. Theoretical Explanations of the NMD Isotopic Fractionation in Ozone	368	(4)
III. Carbon Monoxide Isotopologues	372	(2)
A. Laboratory Experiments	372	(2)
B. Atmospheric Carbon Monoxide	374	(1)
IV. Carbon Dioxide Isotopologues	374	(2)
A. Laboratory Experiments	374	(1)
B. Atmospheric Carbon Dioxide	375	(1)
C. Theoretical Models for NMD Isotopic Fractionation in Carbon Dioxide	375	(1)
V. Nitrous Oxide Isotopologues	376	(1)
A. Laboratory Experiments	376	(1)
B. Atmospheric Nitrous Oxide	376	(1)
C. Theoretical Explanations and Modeling Calculations	376	(1)
VI. Oxygen and Sulfur Isotopic Fractionation in Terrestrial and Extraterrestrial Solids	377	(3)
A. Carbonates	377	(1)
B. Sulfates	378	(2)
1. Laboratory Experiments	378	(1)
2. Terrestrial Sulfates	379	(1)
3. Extraterrestrial Sulfur Compounds	379	(1)
C. Nitrate Aerosols	380	(1)
VII. Other Molecules	380	(1)
A. Hydrogen Peroxide Isotopologues	380	(1)
B. Atmospheric Oxygen Isotopologues	381	(1)
Acknowledgments	381	(1)
References	382	(5)
Chapter 13 Isotope Effects in the Atmosphere	387	(30)
Etienne Roth, René Létolle, C.M. Stevens, and François Robert
I. Introduction	388	(1)
II. Isotopes in Geochemical Cycles	389	(1)
III. Isotope Effects in the Water Cycle	390	(6)
A. The Reservoir Model	390	(1)
B. Exchange between Different Phases of Water	390	(1)
C. Vapor—Liquid Isotope Fractionation and the Study of Reservoirs	391	(1)
D. Water in Precipitation	392	(6)
1. The Isotope Composition of Rain	392	(1)
2. Migration Effects, Altitude Effects, Seasonal Effects, Reevaporation Effects	392	(1)
3. The Case of Hailstorms	393	(1)
a. Early Tenets of the Method	393	(1)
i. Experiments	393	(1)
ii. Results, Further Models, and Discussion	393	(2)
4. The δH-δ18O Relation in Precipitations	395	(1)
IV. Archives of Atmospheric Isotopic Effects Retained by Ice Caps	396	(2)
V. Isotopic Effects on Atmospheric Carbon in the Carbon Cycle	398	(4)
A. Isotopes of Atmospheric Methane	398	(2)
1. Sources	399	(1)
2. Discussion	399	(1)
3. Removal Processes	399	(1)
4. Atmospheric 14CH4	400	(1)
5. Atmospheric δD	400	(1)
B. Isotopes of Atmospheric Carbon Monoxide	400	(2)
1. Sources and Sinks	400	(1)
2. Atmospheric Concentration and Isotopic Composition	401	(1)
3. Summary	401	(1)
C. Isotopes of Atmospheric Carbon Dioxide	402	(1)
VI. Isotope Effects of Atmospheric Nitrogen	402	(1)
VII. Isotope Effects of Atmospheric Oxygen	403	(1)
A. Air Oxygen	403	(1)
B. Ozone	403	(1)
C. Nitrous Oxide	403	(1)
D. Atmospheric Sulfates	403	(1)
VIII. Isotope Effects of Atmospheric Sulfur	403	(4)
A. Introduction	404	(1)
B. Turnover and Inventory	405	(1)
C. Nature, Isotopic Composition, and Atmospheric Chemistry of Sulfur	405	(2)
D. Effects during Removal of Sulfur from the Atmosphere	407	(3)
1. Archean Isotope Atmospheric Chemistry of Sulphur and Nonmass-Dependent Isotope Effect	407	(1)
IX. Isotope Effects on Zinc and Lead in the Atmosphere	407	(1)
X. Deuterium Enrichments in the Organic Molecules of the Interstellar Medium	407	(3)
XI. Constraints in Using Deltas, Capital Deltas, and Reference Samples	410	(1)
A. Possible Evolution of Measurements of Isotope Effects	411	(1)
Acknowledgments	411	(1)
References	411	(6)
Chapter 14 Isotope Effects for Exotic Nuclei	417	(16)
Olle Matsson
I. Introduction	417	(1)
II. Isotope Effects with Short-Lived Radionuclides	418	(1)
A. Fluorine Kinetic Isotope Effects	418	(1)
B. Carbon Kinetic Isotope Effects	418	(1)
III. Synthesis of Compounds Labelled with Short-Lived Radionuclides	419	(1)
A. Labelling with ¹¹C	419	(1)
B. Labelling with 18F	419	(1)
IV. Kinetic Methods — A Combination of Liquid Chromatography and Liquid Scintillation	420	(1)
V. Determination of Rate-Limiting Steps	421	(2)
A. Using Leaving Group F KIEs — Nucleophilic Aromatic Substitution	421	(1)
1. The Effect of Solvent on the Rate-Limiting Step	422	(1)
2. The Effect of Steric Hindrance on the Rate-Limiting Step	422	(1)
B. Concerted or Stepwise Reaction? The Use of F KIEs and Double Labelling for a Base-Promoted Elimination	422	(1)
VI. Probing Transition-State Structure — Nucleophilic Aliphatic Substitution	423	(3)
A. Relative Carbon KIEs	423	(1)
B. Labelled Central atom: Probing Steric Effects	424	(1)
C. Labelled Nucleophile	425	(10)
1. The Effect of Substitution in the Substrate	425	(1)
2. The Effect of Substitution in the Leaving Group	426	(1)
VII. The Determination of Secondary Deuterium KIEs by the Aid of Radioactive Carbon	426	(1)
VIII. Secondary Carbon KIE in a Proton-Transfer Reaction	427	(1)
IX. Carbon Isotope Effects for Enzyme-Catalysed Reactions	428	(1)
Acknowledgments	428	(1)
References	428	(5)
Chapter 15 Muonium — An Ultra-Light Isotope of Hydrogen	433	(18)
Emil Roduner
I. Physical Properties and the Chemical Nature of Mu in Comparison with H and D	434	(1)
II. Chemically Bound Mu States: Structural Isotope Effects of Vibrating Species	435	(6)
A. Zero-Point Energy and Anharmonicity Effects	435	(1)
B. Isotope Effects in Vibrationally Averaged Bond Lengths and Bond Angles	436	(1)
C. Isotope Effects in Equilibrium Conformations	437	(2)
D. Isotope Effects in Hyperfine Interactions of Free Radicals	439	(1)
E. The Validity of the Born–Oppenheimer Approximation	439	(2)
III. Kinetic Isotope Effects: The Competing Effects of Zero-Point Energy and Tunneling	441	(5)
A. The Mu Reaction with Molecular Hydrogen: The Dominance of Zero-Point Energy	441	(1)
B. Mu Addition to Benzene: Evidence of Tunneling	442	(1)
C. Mu Addition to Dioxygen: Cross-Over of Isotope Effects	443	(1)
D. Mu Transfer: A World Record of a Kinetic Isotope Effect	444	(1)
E. A Reaction Proceeding over a Solvent-Induced Barrier: A Dynamic Solvent Effect	445	(1)
IV. Mass Effect on Diffusion	446	(1)
A. Coherent and Incoherent Tunneling of Mu Diffusion in Crystals	446	(1)
B. Diffusion of Mu in Liquid Water	447	(1)
V. Concluding Remarks	447	(1)
References	448	(3)
Chapter 16 The Kinetic Isotope Effect in the Photo-Dissociation Reaction of Excited-State Acids in Aqueous Solutions	451	(14)
Ehud Pines
I. Introduction	451	(1)
II. General Kinetic Models for Acid–Base Reactions in Solutions	452	(4)
A. The Two-State Proton-Transfer Reaction Model (The Eigen–Weller Model)	452	(2)
B. Free-Energy Correlations of the Proton (Deuteron) Transfer Rates	454	(1)
C. The Isotope Effect in a Series of Similar Reactions	455	(1)
III. The Isotope Effect in the Equilibrium Constant of Photoacids	456	(3)
IV. The KIE in Photoacid Dissociation	459	(3)
V. Concluding Remarks on the KIE in Photoacid (Phenol-Type) Dissociation	462	(1)
References	462	(3)
Chapter 17 The Role of an Internal-Return Mechanism on Measured Isotope Effects	465	(10)
Heinz F. Koch
I. The Internal-Return Mechanism for Hydron-Transfer Reactions	466	(2)
II. The Internal-Return Mechanism for Alkoxide-Promoted E2 Dehydrohalogenations	468	(2)
III. Chlorine Isotope Effects vs. the Element Effect	470	(1)
IV. Hydron Transfer from Alcohols to Carbanions	471	(1)
V. Conclusions	472	(1)
References	472	(3)
Chapter 18 Vibrationally Enhanced Tunneling and Kinetic Isotope Effects in Enzymatic Reactions	475	(24)
Steven D. Schwartz
I. Introduction	475	(1)
II. Theoretical Approaches to the Study of Chemical Dynamics in Complex Systems	476	(3)
III. Promoting Vibrations and the Dynamics of Hydrogen Transfer	479	(3)
A. Promoting Vibrations and the Symmetry of Coupling	479	(1)
B. Promoting Vibrations — Corner Cutting and the Masking of KIEs	480	(2)
IV. Enzymatic Hydrogen Transfer and KIEs	482	(9)
A. Alcohol Dehydrogenase	482	(5)
B. Lactate Dehydrogenase	487	(4)
V. Hydrogen Transfer Coupled to Electron Transfer — Kinetic Trends in the Presence of a Promoting Vibration	491	(4)
VI. Conclusions	495	(1)
Acknowledgments	495	(1)
References	495	(4)
Chapter 19 Kinetic Isotope Effects for Proton-Coupled Electron Transfer Reactions	499	(22)
Sharon Hammes-Schiffer
I. Introduction	499	(1)
II. Theory and Methods	500	(6)
A. Electron Transfer Theory	500	(1)
B. Proton Transfer Theory	501	(1)
C. Proton-Coupled Electron Transfer Theory	502	(3)
D. Methodological Developments	505	(1)
III. Applications to Chemical and Biological Systems	506	(8)
A. PCET in Solution	506	(2)
B. Enzyme Reactions	508	(4)
C. Role of Motion in Enzyme Reactions	512	(2)
IV. Summary and Conclusions	514	(1)
Acknowledgments	515	(1)
References	515	(6)
Chapter 20 Kinetic Isotope Effects in Multiple Proton Transfer	521	(28)
Zorka Smedarchina, Willem Siebrand, and Antonio Fernández-Ramos
I. Introduction	521	(2)
II. Theoretical Methods	523	(6)
A. Transition State Theory	523	(1)
B. Tunneling Preliminaries	524	(2)
C. Approximate Instanton Method	526	(2)
D. Isotope Effects	528	(1)
E. Comparison of AIM with Other Methods	528	(1)
III. Stepwise Transfer	529	(6)
A. Example: Porphine	529	(1)
B. Isotope Effects	530	(2)
C. Temperature Effects	532	(1)
D. Applications	533	(2)
IV. Concerted Transfer	535	(8)
A. Example: Acetic Acid—Methanol Complex	535	(2)
B. Hydrogen Bonded Dimers and Complexes	537	(1)
C. Water Wires	537	(5)
D. The Proton Inventory Problem	542	(1)
V. Conclusions	543	(1)
Acknowledgments	544	(1)
References	544	(5)
Chapter 21 Interpretation of Primary Kinetic Isotope Effects for Adiabatic and Nonadiabatic Proton-Transfer Reactions in a Polar Environment	549	(30)
Philip M. Kiefer and James T. Hynes
I. Introduction	549	(4)
II. Adiabatic Proton Transfer	553	(9)
A. Adiabatic Proton-Transfer Free-Energy Relationship	553	(5)
1. General Adiabatic Proton-Transfer Picture	553	(2)
2. Adiabatic Proton-Transfer Free-Energy Relationship	555	(2)
3. Further Analysis of the Intrinsic Barrier. Mass Scaling	557	(1)
B. Adiabatic Proton-Transfer KIEs	558	(3)
1. KIE Arrhenius Behavior	559	(1)
2. KIE Magnitude and Variation with Reaction Asymmetry	559	(1)
3. Swain–Schaad Relationship	560	(1)
C. Further Discussion of Nontunneling KIEs	561	(1)
III. Nonadiabatic 'Tunneling' Proton Transfer	562	(10)
A. General Nonadiabatic Proton-Transfer Perspective and Rate Constant	562	(5)
B. Nonadiabatic Proton-Transfer KIEs	567	(17)
1. KIE Magnitude and Variation with Reaction Asymmetry	567	(1)
2. Temperature Behavior	568	(3)
3. Swain–Schaad Relationship	571	(1)
IV. Concluding Remarks	572	(1)
Acknowledgments	573	(1)
References	573	(6)
Chapter 22 Variational Transition-State Theory and Multidimensional Tunneling for Simple and Complex Reactions in the Gas Phase, Solids, Liquids, and Enzymes	579	(42)
Donald G. Truhlar
I. Introduction	580	(3)
II. Previous Reviews	583	(1)
III. Validation Against Accurate Quantum Mechanical Dynamics	583	(1)
IV. Theory	584	(16)
A. Gas Phase	584	(6)
B. Reactions in the Solid State and at Solid Surfaces	590	(1)
C. Reaction in Liquids	591	(8)
1. Solute–Solvent Separation	591	(1)
2. Reaction Coordinates and Nonequilibrium Solvation	592	(2)
3. VTST/MT Methods for Condensed-Phase Reactions	594	(1)
a. Implicit Bath	594	(1)
b. Reduced-Dimensionality Bath	595	(1)
c. Explicit Bath	596	(3)
D. Reactions in Enzymes	599	(1)
V. Applications to KIEs	600	(5)
A. Gas Phase	600	(3)
B. KIEs in Liquid Phase	603	(1)
C. Enzymes	603	(2)
VI. Software	605	(1)
VII. Concluding Remarks	605	(1)
Acknowledgments	606	(1)
Glossary	606	(1)
References	607	(14)
Chapter 23 Computer Simulations of Isotope Effects in Enzyme Catalysis	621	(24)
Arieh Warshel, Mats H.M. Olsson, and Jordi Villà-Freixa
I. Introduction	621	(2)
II. Methods for Simulations of Chemical Processes in Enzymes	623	(3)
A. QM/MM Molecular Orbital Methods	624	(1)
B. EVB as a Reliable QM/MM Method	625	(1)
III. Simulating Nuclear Quantum Mechanical Effects in Condensed Phase	626	(4)
A. The Dispersed Polaron (Spin Boson) Model	626	(1)
B. Quantized Classical Path Simulations	627	(3)
IV. Simulations of the KIE and Nuclear Quantum Mechanical Effects in Enzymatic Reactions	630	(5)
A. Systematic Studies of Hydride Transfer in Solutions	630	(1)
B. Simulating NQM Effects in LDH by a Microscopically Based Quasiharmonic Model and a QCP Treatment	630	(1)
C. Nuclear Quantum Mechanical Effects in Carbonic Anhydrase	631	(1)
D. Nuclear Quantum Mechanical Effects in Alcohol Dehydrogenase	632	(2)
E. Lipoxygenase and the Large Tunneling Limit	634	(1)
V. What is the Catalytic Contribution from Nuclear Quantum Mechanical Effects?	635	(1)
VI. What Can and What Cannot be Learned from Simulations of Isotope Effects?	636	(3)
A. The Use of Vibronic Models in Studies of Isotope Effects	636	(1)
B. Using Calculated and Observed Isotope Effects as a Tool for Validating Single Only Simulations of NQM and Determining the Catalytic Contributions of NQM Effects	637	(1)
C. Determining the Concertedness of Enzymatic Reactions by the KIE	638	(1)
D. Dynamical Effects and Promoting Modes	638	(1)
VII. Concluding Remarks	639	(1)
Acknowledgments	640	(1)
References	640	(5)
Chapter 24 Oxygen-18 Isotope Effects as a Probe of Enzymatic Activation of Molecular Oxygen	645	(26)
Justine P. Roth and Judith P. Klinman
I. Introduction	645	(1)
II. Instrumentation	646	(2)
III. Equilibrium Isotope Effects	648	(2)
IV. Applications	650	(15)
A. Glucose Oxidase	650	(3)
B. Tyrosine Hydroxylase	653	(2)
C. Soybean Lipoxygenase	655	(2)
D. Methane Monooxygenase	657	(1)
E. Cytochrome P-450	658	(2)
F. Dopamine β-Monooxygenase and Peptidylglycine α-Hydroxylating Monooxygenase	660	(2)
G. Copper Amine Oxidases	662	(3)
V. Overview and Perspectives for the Future	665	(1)
References	666	(5)
Chapter 25 Solution and Computational Studies of Kinetic Isotope Effects in Flavoprotein and Quinoprotein Catalyzed Substrate Oxidations as Probes of Enzymic Hydrogen Tunneling and Mechanism	671	(20)
Jaswir Basran, Laura Masgrau, Michael J. Sutcliffe, and Nigel S. Scrutton
I. Enzymic H-Tunneling and Kinetic Isotope Effects	671	(2)
A. Stopped-Flow Methods to Access the Half-Reactions of Flavoenzymes and Quinoproteins	672	(1)
II. Interpreting Temperature Dependence of Isotope Effects in Terms of H-Tunneling	673	(2)
III. H-Tunneling in Flavoenzymes PETN Reductase and MR	675	(3)
IV. H-Tunneling in TTQ-Dependent MADH and AADH	678	(1)
V. Computational Studies of Substrate Oxidation in TTQ-Dependent Amine Dehydrogenases	679	(3)
VI. H-Tunneling in Flavoprotein Amine Dehydrogenases: TSOX and Engineering Gated Motion in TMADH	682	(3)
VII. Concluding Remarks	685	(1)
Acknowledgments	685	(1)
References	685	(6)
Chapter 26 Proton Transfer and Proton Conductivity in Condensed Matter Environment	691	(34)
Alexander M. Kuznetsov and Jens Ulstrup
I. Introduction	691	(2)
II. Mechanisms of Elementary Proton Transfer between Molecular Fragments	693	(9)
A. Basic PT Model at Fixed Donor/Acceptor Distance	693	(2)
B. The Born–Oppenheimer Approximation and Potential Free-Energy Surfaces	695	(1)
C. Totally Diabatic Proton Transfer	696	(1)
D. Partially Adiabatic Proton Transfer	697	(1)
E. Totally Adiabatic Proton Transfer	698	(1)
F. General Expressions for the Tunnel Transmission Coefficient and Transition Probability. The Environmental Medium Dynamics	698	(2)
G. Fluctuations of the Interreactant Distance and Gated Proton Transfer	700	(1)
H. Free Energy Relations and Kinetic Isotope Effects	701	(1)
III. Proton Transfer in Hydrogen-Bonded Systems	702	(8)
A. Hydrogen Bonds with Double-Well Proton Potentials	703	(2)
B. Excess Aqueous Proton Conductivity and Proton Transfer	705	(4)
1. Proton Hops between Two Water Molecules	706	(1)
2. Short-Range Proton Transfer via Adjacent Zundel Complexes	706	(1)
3. Long-Range Proton Transfer via Remote Zundel Complexes	707	(2)
B. Proton Transfer in Single-Well Proton Potentials	709	(1)
IV. Electron-Coupled Proton Transfer	710	(10)
A. Mechanisms of Dynamic and Step-Wise Coupling	711	(3)
B. A View on Coherent Two-Proton Transfer in Zundel Complexes	714	(1)
C. Models and Mechanisms of Electron-Coupled Proton Transfer (ECPT)	715	(5)
1. Diabatic States	716	(2)
2. Mechanisms of Transitions and Rate Constants	718	(2)
D. Synchronous Electron and Proton Transfer	720	(1)
V. Concluding Remarks	720	(2)
Acknowledgments	722	(1)
References	722	(3)
Chapter 27 Mechanisms of CH-Bond Cleavage Catalyzed by Enzymes	725	(18)
Willem Siebrand and Zorka Smedarchina
I. Introduction	725	(2)
II. Observations	727	(3)
A. Rate Constants	727	(1)
B. kinetic Isotope Effects	728	(1)
C. Temperature Dependence	728	(1)
D. Systems without Proteins	729	(1)
III. Theoretical Models	730	(5)
A. Two-Oscillator Models	730	(1)
B. Golden Rule Treatment	731	(3)
C. Semiclassical Instanton Approach	734	(1)
D. Model Parameters	734	(1)
IV. Applications	735	(3)
A. Coenzyme B12	735	(1)
B. Lipoxygenase	736	(1)
C. Primary Amine Dehydrogenases	737	(1)
D. Dicopper Complexes	738	(1)
V. Discussion	738	(1)
Acknowledgments	739	(1)
References	739	(4)
Chapter 28 Kinetic Isotope Effects as Probes for Hydrogen Tunneling in Enzyme Catalysis	743	(22)
Amnon Kohen
I. Introduction	744	(1)
A. Enzyme Catalysis	744	(1)
B. The Chemical Step: Contributions of Quantum Mechanical Tunneling, Equilibrium Fluctuations, and Dynamics	744	(1)
II. Kinetic Isotope Effects as Probes of the Chemical Step	745	(8)
A. Semiclassical Relationship of Reaction Rates of H, D, and T	746	(1)
B. Primary (1°) Swain—Schaad Relationship	746	(2)
1. Intrinsic 1° KIE	746	(2)
2. Experimental Examples Using Intrinsic 1° KIE	748	(1)
a. Peptidylglycine α-Hydroxylating Monooxygenase	748	(1)
b. Thymidylate Synthase	748	(1)
c. Dihydrofolate Reductase	748	(1)
C. Secondary (2°) Swain—Schaad Relationship	748	(5)
1. Mixed Labeling Experiments as Probes for Tunneling and 1°-2° Coupled Motion	749	(1)
2. Upper Semiclassical Limit for 2° Swain—Schaad Relationship	750	(1)
a. Zero-Point Energy and Reduced Mass Considerations	750	(1)
b. Vibrational Analysis	751	(1)
c. Effect of Kinetic Complexity	751	(1)
d. The New Effective Upper Limit	752	(1)
3. Experimental Examples Using 2° Swain—Schaad Exponents	753	(1)
a. Horse Liver Alcohol Dehydrogenase	753	(1)
b. Thermophilic ADH from Bacillus stearothermophilus (ADH-hT)	753	(1)
III. Temperature Dependence of KIEs	753	(4)
A. Temperature Dependence of Reaction Rates and KIEs	753	(1)
B. KIEs on Arrhenius Activation Factors	754	(1)
C. Experimental Examples Using Isotope Effects on Arrhenius Activation Factors	755	(2)
1. Soybean Lipoxygenase-1	755	(1)
2. Thermophilic ADH (ADH-hT)	756	(1)
IV. Theoretical Approaches	757	(2)
A. Phenomenological "Marcus-Like" Models	757	(1)
B. QM/MM Models and Simulations	758	(1)
V. Comparison to Studies of Nonenzymatic Reactions	759	(1)
VI. Conclusions	760	(1)
References	760	(5)
Chapter 29 Hydrogen Bonds, Transition-State Stabilization, and Enzyme Catalysis	765	(28)
Richard L. Schowen
I. The Problem of Enzyme Catalysis	766	(5)
A. Magnitudes of Catalytic Accelerations by Enzymes	766	(1)
B. Transition-State Stabilization and Catalysis	767	(1)
C. H-Bonds as a Means of Transition-State Stabilization	768	(2)
D. Beyond the Transition-State Theory of Catalysis	770	(1)
II. Structure and Strength of H-Bonds	771	(4)
A. The Concept of H-Bond Strength	771	(1)
B. Categorization of H-Bonds	772	(1)
C. Some Probes of Hydrogen Bonds	772	(3)
1. NMR Approaches	773	(1)
2. Theoretical Studies of H-Bonds	773	(1)
3. Thermochemical, Spectroscopic, and Structural Approaches	774	(1)
III. Isotope Effects in Hydrogen Bonding	775	(2)
A. Simple H-Bonds	775	(1)
B. Unusual H-Bonds	776	(1)
C. Primary Catalytic H-Bonds	776	(1)
D. Secondary Catalytic H-Bonds	777	(1)
IV. Issues in H-Bonding and Enzyme Catalysis	777	(11)
A. Cautionary Notes on Mutations at H-Bonding Sites in Enzymes	777	(4)
1. H-Bonds in the Orientation of Ligands for Optimal Catalysis	777	(2)
2. The Catalytic Triad of Serine Hydrolases	779	(2)
B. Primary Catalytic H-Bonds	781	(1)
C. Secondary Catalytic H-Bonds	781	(6)
1. The Catalytic Triad of Serine Hydrolases	781	(4)
2. The Oxyanion Hole of Serine Hydrolases	785	(2)
D. Conformational Changes Signaled by Proton Inventories	787	(1)
V. Summary	788	(1)
References	789	(4)
Chapter 30 Substrate and pH Dependence of Isotope Effects in Enzyme Catalyzed Reactions	793	(18)
William E. Karsten and Paul F. Cook
I. Introduction	794	(1)
A. Nomenclature	794	(1)
B. Types of Isotope Effects	794	(1)
II. Enzyme-Catalyzed vs. Nonenzymatic Reactions	794	(2)
A. Physical vs. Chemical Steps	794	(1)
B. Commitment Factors	795	(1)
C. Substrate Stickiness	795	(1)
III. Substrate Dependence of Isotope Effects	796	(6)
A. Sequential Mechanisms	796	(4)
1. Ordered Mechanisms (k5, k6, k7, and k8 = 0)	797	(1)
a. Formate Dehydrogenase	797	(1)
b. Mannitol Dehydrogenase	798	(1)
2. Random Mechanisms (All Rate Constants of Mechanism 3 Apply)	798	(1)
a. NAD-Malic Enzyme	799	(1)
b. Ketopantoate Reductase	799	(1)
B. Ping Pong Kinetic Mechanisms	800	(1)
1. Dihydroorotate Dehydrogenase	801	(1)
2. p-Cresol Methylhydroxylase	801	(1)
C. Substrate Dependence of Isotope Effects in Terreactant and Higher Order Mechanisms	801	(1)
1. NAD-Malic Enzyme	802	(1)
2. Alanine Dehydrogenase	802	(1)
IV. pH Dependence of Isotope Effects	802	(5)
A. Proton Transfer and Chemistry are Concerted	802	(4)
1. Random Addition of Proton and Substrate to Enzyme	803	(1)
a. NADP-Malic Enzyme	804	(1)
b. Nitroalkane Oxidase	804	(1)
2. Dead-End Protonation of Enzyme	804	(1)
a. NAD-Malic Enzyme	805	(1)
3. Dead-End Protonation of Enzyme and the Enzyme-Reactant Complex	805	(1)
a. Ketpantoate Reductase	805	(1)
4. Dead-End Formation of a Protonated Enzyme-Reactant Complex	806	(1)
B. Proton Transfer and Chemistry not Concerted	806	(6)
1. Equine Liver Alcohol Dehydrogenase	807	(1)
V. Closing Remarks	807	(1)
References	808	(3)
Chapter 31 Catalysis by Alcohol Dehydrogenases	811	(26)
Bryce V. Plapp
I. Introduction	811	(1)
II. Mechanism and Structure of Alcohol Dehydrogenases	812	(2)
A. Kinetic Mechanism from Isotope Effects	812	(1)
B. Structural Studies of Ternary Complexes	813	(1)
III. Transient Kinetics and Simulation of Complete Mechanisms	814	(2)
IV. Unmasking Chemistry for Mechanistic Studies	816	(6)
A. Poor Substrates and Chemical Modification	816	(1)
B. Site-Directed Mutagenesis	816	(2)
C. Isotope Effects and Altered Rate Constants	818	(4)
V. Dynamics of Hydrogen Transfer	822	(5)
A. Tunneling Detected by Comparison of H/D/T Isotope Effects	822	(1)
B. Temperature Dependence and Isotope Effects	822	(3)
C. Pressure and Isotope Effects	825	(1)
D. Protein Motions and Computational Studies	826	(1)
VI. Solvent (D2O) Isotope Effects and Proton Transfer	827	(1)
A. Steady-State Kinetic Studies	827	(1)
B. Transient Kinetic Studies and a Low-Barrier Hydrogen Bond	827	(1)
VII. Future Studies	828	(2)
Acknowledgments	830	(1)
References	830	(7)
Chapter 32 Effects of High Hydrostatic Pressure on Isotope Effects	837	(10)
Dexter B. Northrop
I. Introduction	837	(1)
II. Theory	837	(4)
III. Experimental Examples	841	(3)
A. Hydrogen Tunneling	841	(1)
B. Yeast Alcohol Dehydrogenase	842	(2)
C. Yeast Formate Dehydrogenase	844	(1)
IV. Conclusion	844	(1)
References	844	(3)
Chapter 33 Solvent Hydrogen Isotope Effects in Catalysis by Carbonic Anhydrase: Proton Transfer through Intervening Water Molecules	847	(14)
David N. Silverman and Ileana Elder
I. Introduction	847	(3)
A. Catalytic Mechanism	848	(1)
B. Structure	849	(1)
C. Relevance of Ordered Water in Crystal Structures of Carbonic Anhydrase	850	(1)
II. Isotope Effects on First Stage of Catalysis — The Hydration of CO2	850	(1)
III. Solvent Hydrogen Isotope Effects on the Proton Transfer Steps	850	(7)
A. Intramolecular Proton Transfer in Catalysis by Carbonic Anhydrase	850	(6)
1. Proton inventory	850	(1)
2. Interpreting the Isotope Effects	851	(1)
3. Theorists View of Isotope Effects in Catalysis by Carbonic Anhydrase	851	(1)
4. Use of 18O Exchange	852	(1)
5. Marcus Rate Theory Allows Enhanced Interpretation of Proton-Transfer Rates	853	(1)
6. Marcus Plot for Intramolecular Proton Transfer	854	(1)
7. Marcus Plot for Solvent Hydrogen Isotope Effects	855	(1)
B. Intermolecular Proton Transfer in Catalysis by Carbonic Anhydrase	856	(10)
1. Marcus Plot for Solvent Hydrogen Isotope Effects	856	(1)
2. The Marcus Formalism Extended to the β and γ Classes	857	(1)
VI. Conclusions	857	(1)
References	857	(4)
Chapter 34 Isotope Effects from Partitioning of Intermediates in Enzyme-Catalyzed Hydroxylation Reactions	861	(14)
Paul F. Fitzpatrick
I. Introduction	861	(1)
II. Theory	862	(4)
III. Examples	866	(5)
A. Cytochrome P450	866	(2)
B. The Aromatic Amino Acid Hydroxylases	868	(2)
C. Dopamine β-Monooxygenase	870	(1)
IV. Conclusion	871	(1)
References	871	(4)
Chapter 35 Chlorine Kinetic Isotope Effects on Biological Systems	875	(18)
Piotr Paneth
I. Introduction	875	(3)
A. Dehalogenation — Environmental Perspective	875	(1)
B. Chlorine Kinetic Isotope Effects	876	(1)
C. Calculations of Chlorine KIEs	876	(1)
D. Chlorine Isotopic Ratio Measurements	877	(1)
II. Chlorine Isotopic Fractionation in Microbial Processes	878	(10)
A. Chlorine KIEs on Microbial Degradation of Chlorinated Compounds	878	(1)
1. Reduction of Perchlorate	878	(1)
2. Reduction of Chlorinated Aliphatic Hydrocarbons	879	(1)
B. Chlorine KIEs on Reactions Catalyzed by Dehalogenases	879	(7)
1. Haloalkane Dehalogenases	880	(3)
2. DL-2-Haloacid Dehalogenase	883	(2)
3. Fluoroacetate Dehalogenase	885	(1)
4. 4-Chlorobenzoil-CoA Dehalogenase	885	(1)
C. Chlorine KIEs on Enzymatic Halogenation	886	(2)
III. Future Perspectives	888	(1)
Acknowledgments	888	(1)
References	888	(5)
Chapter 36 Nucleophile Isotope Effects	893	(22)
Vernon E. Anderson, Adam G. Cassano, and Michael E. Harris
I. Nucleophilic Activation and Reaction Mechanisms	893	(2)
II. 18O Isotope Effects	895	(13)
A. Activation of Water and Associated Equilibrium Isotope Effects	895	(4)
1. Desolvation and H-Bonding	895	(3)
2. Equilibrium Isotope Effects on Hydroxide Formation	898	(1)
3. Isotope Effects on Coordination of Water by Metal Ions	898	(1)
B. Kinetic Effects on Reactions	899	(9)
1. Experimental and Theoretical Considerations	899	(2)
2. Nucleophilic Attack on Electrophilic sp2 Carbon	901	(2)
3. Attack on Carbon–Oxygen Double Bonds, Addition to Carbonyl Compounds	903	(1)
a. Hydrolysis of Formic Acid Derivatives	903	(1)
b. Carboxypeptidase Catalyzed Amide and Ester Hydrolysis	905	(1)
4. Hydrolysis of Phosphate Esters	905	(2)
5. 18knuc Effect on Hexokinase	907	(1)
III. 15N Isotope Effects	908	(2)
A. Equilibrium Isotope Effects on Protonation and N–C Bond Formation	908	(1)
B. Kinetic Isotope Effects on Nucleophilic Attack at sp³ Carbon	908	(1)
C. Kinetic Isotope Effects on Enzyme Catalyzed Nucleophilic Attack at sp² Carbons	909	(1)
IV. Prospectus	910	(1)
Acknowledgments	911	(1)
References	911	(4)
Chapter 37 Enzyme Mechanisms from Isotope Effects	915	(16)
W. Wallace Cleland
I. Isotope Effect Theory	915	(10)
A. Notation	916	(1)
B. Measurement of Isotope Effects	916	(5)
1. Direct Comparison	916	(1)
2. Internal Competition	917	(1)
a. The Remote Label Method — Stable Isotopes	918	(1)
b. The Remote Label Method — Radioactive Isotopes	920	(1)
3. Equilibrium Perturbation	920	(1)
C. Equation for the Isotope Effect	921	(2)
D. Determination of Intrinsic Isotope Effects	923	(2)
1. Northrop's Method	923	(1)
2. Multiple Isotope Effect Method	924	(1)
II. Examples of Mechanistic Analysis	925	(3)
A. Aspartate Transcarbamoylase	925	(1)
B. Malic Enzyme	926	(1)
C. Oxalate Decarboxylase	927	(1)
D. Chorismate Mutase	927	(1)
E. L-Ribulose-5-P 4-Epimerase	928	(1)
F. Other Enzymes	928	(1)
References	928	(3)
Chapter 38 Catalysis and Regulation in the Soluble Methane Monooxygenase System: Applications of Isotopes and Isotope Effects	931	(24)
John D. Lipscomb
I. Introduction	931	(1)
II. sMMO Components	932	(1)
III. sMMO Catalytic Cycle	933	(3)
IV. Kinetic Solvent Isotope Effect used to Probe Proton Donors	936	(2)
V. The Mechanism of Q Reaction with Substrates	938	(4)
VI. Arrhenius Plots for the Reactions of Reaction Cycle Intermediates	942	(1)
VII. The Effects of MMOB	943	(2)
VIII. A Test of the Molecular-Sieve Model using KIE Studies	945	(1)
IX. A Tunneling Reaction	946	(1)
X. New Insight into the Mechanism of C–H Bond Cleavage	947	(2)
Acknowledgments	949	(1)
References	949	(6)
Chapter 39 Secondary Isotope Effects	955	(20)
Alvan C. Hengge
I. Theory and Nomenclature	955	(1)
II. Origins of Secondary Isotope Effects	956	(5)
A. Secondary Isotope Effects Resulting from Hybridization Changes	956	(3)
B. Secondary Isotope Effects on Acidities	959	(1)
C. Steric Secondary Isotope Effects	960	(1)
III. Secondary Isotope Effects in Particular Reactions	961	(14)
A. Acyl Transfer	961	(3)
B. Glycosyl Transfer	964	(1)
C. N-Ribosyl Hydrolases and Transferases	965	(1)
D. Phosphoryl Transfer	966	(2)
E. Methyl Transfer	968	(1)
F. Hydride Transfer	969	(1)
G. Peptidyl Prolyl Cis–Trans Isomerase	969	(6)
References	975	(1)
Chapter 40 Isotope Effects in the Characterization of Low Barrier Hydrogen Bonds	975	(20)
Perry A. Frey
I. Introduction	975	(2)
II. Zero-Point Energy Effects and Hydrogen Bonds	977	(5)
A. Classification of Hydrogen Bond Types	977	(1)
B. NMR Chemical Shifts of Strong Hydrogen Bonds	978	(1)
C. Isotope Effects on Physical Parameters	979	(2)
1. Isotope Effects on Vibrational Frequencies	979	(1)
2. Isotope Effects on Chemical Shifts of LBHBs	980	(1)
3. D/H Fractionation Factors	981	(1)
D. Strengths of Hydrogen Bonds	981	(1)
III. Low-Barrier Hydrogen Bonds in Enzymes	982	(5)
A. Serine Proteases	982	(3)
B. Cholinesterases	985	(1)
C. Δ5-3-Ketosteroid Isomerase	986	(1)
IV. Role of Low-Barrier Hydrogen Bonds in the Actions of Enzymes	987	(3)
A. Serine Proteases and Esterases	987	(3)
B. Δ5-3-Ketosteroid Isomerase	990	(1)
C. Other Enzymes	990	(1)
Acknowledgments	990	(1)
References	990	(5)
Chapter 41 Theory and Practice of Solvent Isotope Effects	995	(24)
Daniel M. Quinn
I. Introduction	995	(1)
II. Origins of Solvent Isotope Effects	996	(2)
A. Equilibrium Solvent Isotope Effects	996	(1)
B. Kinetic Isotope Effects	997	(1)
III. The Kresge—Gross—Butler Equation	998	(6)
A. Derivation	998	(2)
B. The Proton Inventory Technique	1000	(4)
1. Proton Inventories of Elementary Steps	1000	(1)
2. Effects of Reactant State Fractionation	1001	(1)
3. Proton Inventories of Multistep Enzyme Reactions	1002	(2)
IV. Fractionation Factors	1004	(2)
A. Reactant State Fractionation Factors of Common Functional Groups	1004	(1)
B. Transition State Fractionation Factors	1005	(1)
V. Practical Considerations	1006	(2)
VI. Examples	1008	(8)
A. Nonenzymic Reactions	1008	(1)
B. Enzymatic Reactions	1009	(12)
1. Serine Proteases	1009	(3)
2. Acetylcholinesterase	1012	(2)
3. Carbonic Anhydrase	1014	(1)
4. Tyrosine Hydroxylase	1015	(1)
VII. Conclusions	1016	(1)
References	1016	(3)
Chapter 42 Enzymatic Binding Isotope Effects and the Interaction of Glucose with Hexokinase	1019	(36)
Brett E. Lewis and Vern L. Schramm
I. Introduction	1020	(1)
II. History of Enzymatic Binding Isotope Effects	1020	(1)
III. Contributions of Binding and Prebinding Steps to Isotope Effects in Enzymology	1021	(11)
A. BIE and ME	1022	(4)
1. Expressions of D(kcat/Km) and T(kcat/Km)	1022	(2)
2. Expressions of Dkcat	1024	(2)
B. Prebinding Isomeric Isotope Effects and KIE	1026	(4)
1. Effect on Competitive (kcat/Km) KIE Measurements	1026	(1)
a. Regimes I—III	1027	(1)
b. Regimes IV—VI	1027	(1)
c. Regimes VII—IX	1028	(1)
2. Effect on Noncompetitive Dkcat Measurements	1029	(1)
3. Curtin—Hammet Principle	1029	(1)
C. Prebinding Isotope Effects and BIE	1030	(2)
D. Conclusions	1032	(1)
1. Transition State Studies	1032	(1)
2. Determination of Rate-Limiting Steps and Tunneling	1032	(1)
IV. Physical Basis for Binding and Kinetic Isotope Effects	1032	(14)
A. Frequency Changes due to Reaction and Heavy-Atom Labeling	1033	(4)
1. Heavy Atom Labeling	1033	(1)
2. High-Frequency CH Bond Stretch: Equilibrium Isotope Effects	1034	(1)
3. Lower-Frequency CN Bond Stretch: Equilibrium Isotope Effects	1035	(1)
4. When Does MMI Count?	1036	(1)
5. When Does EXC Count?	1036	(1)
B. Alteration in Force Constants	1037	(8)
1. How Many Modes Actually Matter?	1038	(1)
2. Isotope Effects from Altering Mode Coupling Partners	1039	(3)
3. Sterics and Hyperconjugation	1042	(3)
C. Summary	1045	(1)
V. Example: Glucose and Brain Hexokinase	1046	(3)
A. Methods	1046	(1)
B. The Binary Complex	1047	(1)
C. The Ternary Complex	1048	(1)
VI. Applications for BIE	1049	(1)
VII. Conclusion	1049	(1)
Acknowledgments	1050	(1)
References	1050	(5)
Index	1055