Chemical Dynamics in Condensed Phases: Relaxation, Transfer, and Reactions in Condensed Molecular Systems

by Abraham Nitzan

Overview

This text provides a uniform and consistent approach to diversified problems encountered in the study of dynamical processes in condensed phase molecular systems. Given the broad interdisciplinary aspect of this subject, the book focuses on three themes: coverage of needed background material, in-depth introduction of methodologies, and analysis of several key applications. The uniform approach and common language used in all discussions help to develop general understanding and insight on condensed phases chemical dynamics. The applications discussed are among the most fundamental processes that underlie physical, chemical, and biological phenomena in complex systems.

Product Details

ISBN-13:	9780198529798
Publisher:	Oxford University Press, USA
Publication date:	06/01/2006
Series:	Oxford Graduate Texts Series
Edition description:	New Edition
Pages:	744
Product dimensions:	9.60(w) x 6.80(h) x 1.80(d)

About the Author

Abraham Nitzan, Professor of Chemistry, Department of Chemistry, Tel Aviv University

Table of Contents

Part I	Background	1
1	Review of some mathematical and physical subjects	3
1.1	Mathematical background	3
1.2	Classical mechanics	18
1.3	Quantum mechanics	22
1.4	Thermodynamics and statistical mechanics	25
1.5	Physical observables as random variables	38
1.6	Electrostatics	45
2	Quantum dynamics using the time-dependent Schrodinger equation	57
2.1	Formal solutions	57
2.2	An example: The two-level system	59
2.3	Time-dependent Hamiltonians	63
2.4	A two-level system in a time-dependent field	66
2.5	A digression on nuclear potential surfaces	71
2.6	Expressing the time evolution in terms of the Green's operator	74
2.7	Representations	76
2.8	Quantum dynamics of the free particles	80
2.9	Quantum dynamics of the harmonic oscillator	89
2.10	Tunneling	101
2A	Some operator identities	109
3	An Overview of Quantum Electrodynamics and Matter-Radiation Field Interaction	112
3.1	Introduction	112
3.2	The quantum radiation field	114
3A	The radiation field and its interaction with matter	120
4	Introduction to solids and their interfaces	131
4.1	Lattice periodicity	131
4.2	Lattice vibrations	132
4.3	Electronic structure of solids	143
4.4	The work function	164
4.5	Surface potential and screening	167
5	Introduction to liquids	175
5.1	Statistical mechanics of classical liquids	176
5.2	Time and ensemble average	177
5.3	Reduced configurational distribution functions	179
5.4	Observable implications of the pair correlation function	182
5.5	The potential of mean force and the reversible work theorem	186
5.6	The virial expansion-the second virial coefficient	188
Part II	Methods	191
6	Time correlation functions	193
6.1	Stationary systems	193
6.2	Simple examples	195
6.3	Classical time correlation functions	201
6.4	Quantum time correlation functions	206
6.5	Harmonic reservoir	209
7	Introduction to stochastic processes	219
7.1	The nature of stochastic processes	219
7.2	Stochastic modeling of physical processes	223
7.3	The random walk problem	225
7.4	Some concepts from the general theory of stochastic processes	233
7.5	Harmonic analysis	242
7A	Moments of the Gaussian distribution	250
7B	Proof of Eqs (7.64) and (7.65)	251
7C	Cumulant expansions	252
7D	Proof of the Wiener-Khintchine theorem	253
8	Stochastic equations of motion	255
8.1	Introduction	255
8.2	The Langevin equation	259
8.3	Master equations	273
8.4	The Fokker-Planck equation	281
8.5	Passage time distributions and the mean first passage time	293
8A	Obtaining the Fokker-Planck equation from the Chapman-Kolmogorov equation	296
8B	Obtaining the Smoluchowski equation from the overdamped Langevin equation	299
8C	Derivation of the Fokker-Planck equation from the Langevin equation	301
9	Introduction to quantum relaxation processes	304
9.1	A simple quantum-mechanical model for relaxation	305
9.2	The origin of irreversibility	312
9.3	The effect of relaxation on absorption lineshapes	316
9.4	Relaxation of a quantum harmonic oscillator	322
9.5	Quantum mechanics of steady states	329
9A	Using projection operators	338
9B	Evaluation of the absorption lineshape for the model of Figs 9.2 and 9.3	341
9C	Resonance tunneling in three dimensions	342
10	Quantum mechanical density operator	347
10.1	The density operator and the quantum Liouville equation	348
10.2	An example: The time evolution of a two-level system in the density matrix formalism	356
10.3	Reduced descriptions	359
10.4	Time evolution equations for reduced density operators: The quantum master equation	368
10.5	The two-level system revisited	390
10A	Analogy of a coupled 2-level system to a spin 1/2 system in a magnetic field	395
11	Linear response theory	399
11.1	Classical linear response theory	400
11.2	Quantum linear response theory	404
11A	The Kubo identity	417
12	The Spin-Boson Model	419
12.1	Introduction	420
12.2	The model	421
12.3	The polaron transformation	424
12.4	Golden-rule transition rates	430
12.5	Transition between molecular electronic states	439
12.6	Beyond the golden rule	449
Part III	Applications	451
13	Vibrational energy relaxation	453
13.1	General observations	453
13.2	Construction of a model Hamiltonian	457
13.3	The vibrational relaxation rate	460
13.4	Evaluation of vibrational relaxation rates	464
13.5	Multi-phonon theory of vibrational relaxation	471
13.6	Effect of supporting modes	476
13.7	Numerical simulations of vibrational relaxation	478
13.8	Concluding remarks	481
14	Chemical reactions in condensed phases	483
14.1	Introduction	483
14.2	Unimolecular reactions	484
14.3	Transition state theory	489
14.4	Dynamical effects in barrier crossing-The Kramers model	499
14.5	Observations and extensions	512
14.6	Some experimental observations	520
14.7	Numerical simulation of barrier crossing	523
14.8	Diffusion-controlled reactions	527
14A	Solution of Eqs (14.62) and (14.63)	531
14B	Derivation of the energy Smoluchowski equation	533
15	Solvation dynamics	536
15.1	Dielectric solvation	537
15.2	Solvation in a continuum dielectric environment	539
15.3	Linear response theory of solvation	543
15.4	More aspects of solvation dynamics	546
15.5	Quantum solvation	549
16	Electron transfer processes	552
16.1	Introduction	552
16.2	A primitive model	555
16.3	Continuum dielectric theory of electron transfer processes	559
16.4	A molecular theory of the nonadiabatic electron transfer rate	570
16.5	Comparison with experimental results	574
16.6	Solvent-controlled electron transfer dynamics	577
16.7	A general expression for the dielectric reorganization energy	579
16.8	The Marcus parabolas	581
16.9	Harmonic field representation of dielectric response	582
16.10	The nonadiabatic coupling	588
16.11	The distance dependence of electron transfer rates	589
16.12	Bridge-mediated long-range electron transfer	591
16.13	Electron tranport by hopping	596
16.14	Proton transfer	600
16A	Derivation of the Mulliken-Hush formula	602
17	Electron transfer and transmission at molecule-metal and molecule-semiconductor interfaces	607
17.1	Electrochemical electron transfer	607
17.2	Molecular conduction	618
18	Spectroscopy	640
18.1	Introduction	641
18.2	Molecular spectroscopy in the dressed-state picture	643
18.3	Resonance Raman scattering	651
18.4	Resonance energy transfer	656
18.5	Thermal relaxation and dephasing	664
18.6	Probing inhomogeneous bands	682
18.7	Optical response functions	691
18A	Steady-state solution of Eqs (18.58): the Raman scattering flux	703
	Index	709

Editorial Reviews

"Beautifully and clearly written, describing mathematics in necessary detail without overloading the reader, and very neatly and concisely explaining physics of the described phenomena." — European Journal of Chemical Physics and Physical Chemistry

"This is an excellent book which is intended to be a text for a graduate course in condensed matter chemistry and physics. It is extremely well written from the pedagogic and literary points of view. I particularly enjoyed the extremely pertinent quotations from Lucretius at the beginning of each chapter." — Journal of Statistical Physics

"... an exceptionally timely book with a broad readership at the graduate level." — Gregory Voth, University of Utah

"... excellent without any doubt." — Peter Rossky, University of Texas, Austin

From the Publisher