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

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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.
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Editorial Reviews

From the Publisher

"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

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Product Details

  • ISBN-13: 9780198529798
  • Publisher: Oxford University Press, USA
  • Publication date: 6/1/2006
  • Series: Oxford Graduate Texts Series
  • Edition description: New Edition
  • Pages: 744
  • Sales rank: 569,109
  • Product dimensions: 9.60 (w) x 6.80 (h) x 1.80 (d)

Meet the Author

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

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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
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