Chemical dynamics in condensed phases relaxation transfer and reactions in condensed molecular systems 1st edition by Abraham Nitzan ISBN 0191523879  9780191523878

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ISBN 10: 0191523879
ISBN 13: 9780191523878
Author: Abraham Nitzan

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. The first part of the book starts with a general review of basic mathematical and physical methods (Chapter 1) and a few introductory chapters on quantum dynamics (Chapter 2), interaction of radiation and matter (Chapter 3) and basic properties of solids (chapter 4) and liquids (Chapter 5). In the second part the text embarks on a broad coverage of the main methodological approaches. The central role of classical and quantum time correlation functions is emphasized in Chapter 6. The presentation of dynamical phenomena in complex systems as stochastic processes is discussed in Chapters 7 and 8. The basic theory of quantum relaxation phenomena is developed in Chapter 9, and carried on in Chapter 10 which introduces the density operator, its quantum evolution in Liouville space, and the concept of reduced equation of motions. The methodological part concludes with a discussion of linear response theory in Chapter 11, and of the spin-boson model in chapter 12. The third part of the book applies the methodologies introduced earlier to several fundamental processes that underlie much of the dynamical behaviour of condensed phase molecular systems. Vibrational relaxation and vibrational energy transfer (Chapter 13), Barrier crossing and diffusion controlled reactions (Chapter 14), solvation dynamics (Chapter 15), electron transfer in bulk solvents (Chapter 16) and at electrodes/electrolyte and metal/molecule/metal junctions (Chapter 17), and several processes pertaining to molecular spectroscopy in condensed phases (Chapter 18) are the main subjects discussed in this part.

Chemical dynamics in condensed phases relaxation transfer and reactions in condensed molecular systems 1st Table of contents:

PART I: BACKGROUND

1 Review of some mathematical and physical subjects

1.1 Mathematical background

1.2 Classical mechanics

1.3 Quantum mechanics

1.4 Thermodynamics and statistical mechanics

1.5 Physical observables as random variables

1.6 Electrostatics

2 Quantum dynamics using the time-dependent Schrödinger equation

2.1 Formal solutions

2.2 An example: The two-level system

2.3 Time-dependent Hamiltonians

2.4 A two-level system in a time-dependent field

2.5 A digression on nuclear potential surfaces

2.6 Expressing the time evolution in terms of the Green’s operator

2.7 Representations

2.8 Quantum dynamics of the free particles

2.9 Quantum dynamics of the harmonic oscillator

2.10 Tunneling

2A: Some operator identities

3 An Overview of Quantum Electrodynamics and Matter–Radiation Field Interaction

3.1 Introduction

3.2 The quantum radiation field

3A: The radiation field and its interaction with matter

4 Introduction to solids and their interfaces

4.1 Lattice periodicity

4.2 Lattice vibrations

4.3 Electronic structure of solids

4.4 The work function

4.5 Surface potential and screening

5 Introduction to liquids

5.1 Statistical mechanics of classical liquids

5.2 Time and ensemble average

5.3 Reduced configurational distribution functions

5.4 Observable implications of the pair correlation function

5.5 The potential of mean force and the reversible work theorem

5.6 The virial expansion—the second virial coefficient

PART II: METHODS

6 Time correlation functions

6.1 Stationary systems

6.2 Simple examples

6.3 Classical time correlation functions

6.4 Quantum time correlation functions

6.5 Harmonic reservoir

7 Introduction to stochastic processes

7.1 The nature of stochastic processes

7.2 Stochastic modeling of physical processes

7.3 The random walk problem

7.4 Some concepts from the general theory of stochastic processes

7.5 Harmonic analysis

7A: Moments of the Gaussian distribution

7B: Proof of Eqs (7.64) and (7.65)

7C: Cumulant expansions

7D: Proof of the Wiener–Khintchine theorem

8 Stochastic equations of motion

8.1 Introduction

8.2 The Langevin equation

8.3 Master equations

8.4 The Fokker–Planck equation

8.5 Passage time distributions and the mean first passage time

8A: Obtaining the Fokker–Planck equation from the Chapman–Kolmogorov equation

8B: Obtaining the Smoluchowski equation from the overdamped Langevin equation

8C: Derivation of the Fokker–Planck equation from the Langevin equation

9 Introduction to quantum relaxation processes

9.1 A simple quantum-mechanical model for relaxation

9.2 The origin of irreversibility

9.3 The effect of relaxation on absorption lineshapes

9.4 Relaxation of a quantum harmonic oscillator

9.5 Quantum mechanics of steady states

9A: Using projection operators

9B: Evaluation of the absorption lineshape for the model of Figs 9.2 and 9.3

9C: Resonance tunneling in three dimensions

10 Quantum mechanical density operator

10.1 The density operator and the quantum Liouville equation

10.2 An example: The time evolution of a two-level system in the density matrix formalism

10.3 Reduced descriptions

10.4 Time evolution equations for reduced density operators: The quantum master equation

10.5 The two-level system revisited

10A: Analogy of a coupled 2-level system to a spin ½ system in a magnetic field

11 Linear response theory

11.1 Classical linear response theory

11.2 Quantum linear response theory

11A: The Kubo identity

12 The Spin–Boson Model

12.1 Introduction

12.2 The model

12.3 The polaron transformation

12.4 Golden-rule transition rates

12.5 Transition between molecular electronic states

12.6 Beyond the golden rule

PART III: APPLICATIONS

13 Vibrational energy relaxation

13.1 General observations

13.2 Construction of a model Hamiltonian

13.3 The vibrational relaxation rate

13.4 Evaluation of vibrational relaxation rates

13.5 Multi-phonon theory of vibrational relaxation

13.6 Effect of supporting modes

13.7 Numerical simulations of vibrational relaxation

13.8 Concluding remarks

14 Chemical reactions in condensed phases

14.1 Introduction

14.2 Unimolecular reactions

14.3 Transition state theory

14.4 Dynamical effects in barrier crossing—The Kramers model

14.5 Observations and extensions

14.6 Some experimental observations

14.7 Numerical simulation of barrier crossing

14.8 Diffusion-controlled reactions

14A: Solution of Eqs (14.62) and (14.63)

14B: Derivation of the energy Smoluchowski equation

15 Solvation dynamics

15.1 Dielectric solvation

15.2 Solvation in a continuum dielectric environment

15.3 Linear response theory of solvation

15.4 More aspects of solvation dynamics

15.5 Quantum solvation

16 Electron transfer processes

16.1 Introduction

16.2 A primitive model

16.3 Continuum dielectric theory of electron transfer processes

16.4 A molecular theory of the nonadiabatic electron transfer rate

16.5 Comparison with experimental results

16.6 Solvent-controlled electron transfer dynamics

16.7 A general expression for the dielectric reorganization energy

16.8 The Marcus parabolas

16.9 Harmonic field representation of dielectric response

16.10 The nonadiabatic coupling

16.11 The distance dependence of electron transfer rates

16.12 Bridge-mediated long-range electron transfer

16.13 Electron tranport by hopping

16.14 Proton transfer

16A: Derivation of the Mulliken–Hush formula

17 Electron transfer and transmission at molecule–metal and molecule–semiconductor interfaces

17.1 Electrochemical electron transfer

17.2 Molecular conduction

18 Spectroscopy

18.1 Introduction

18.2 Molecular spectroscopy in the dressed-state picture

18.3 Resonance Raman scattering

18.4 Resonance energy transfer

18.5 Thermal relaxation and dephasing

18.6 Probing inhomogeneous bands

18.7 Optical response functions

18A: Steady-state solution of Eqs (18.58): the Raman scattering flux

Index

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Tags: Abraham Nitzan, Chemical dynamics, condensed phases, condensed molecular