Geschäftskunden Kundenprogramme
Vor Ort
Merkzettel Warenkorb
Produktbild: Molecular Kinetics in Condensed Phases

Molecular Kinetics in Condensed Phases Theory, Simulation, and Analysis

Fr. 143.00

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

18.02.2020

Verlag

John Wiley & Sons

Seitenzahl

288

Maße (L/B/H)

23.3/15.6/2.2 cm

Gewicht

567 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-119-17677-0

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

18.02.2020

Verlag

John Wiley & Sons

Seitenzahl

288

Maße (L/B/H)

23.3/15.6/2.2 cm

Gewicht

567 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-119-17677-0

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

Kundinnen und Kunden meinen

0 Bewertungen

Informationen zu Bewertungen

Zur Abgabe einer Bewertung ist eine Anmeldung im Konto notwendig. Die Authentizität der Bewertungen wird von uns nicht überprüft. Wir behalten uns vor, Bewertungstexte, die unseren Richtlinien widersprechen, entsprechend zu kürzen oder zu löschen.

Die Bewertungen sind nach Format, Anzahl Sterne und Datum sortiert.

Verfassen Sie die erste Bewertung zu diesem Artikel

Helfen Sie anderen Kund*innen durch Ihre Meinung

Kundinnen und Kunden meinen

0 Bewertungen filtern
Die Leseprobe wird geladen.
  • Produktbild: Molecular Kinetics in Condensed Phases

  • Acknowledgments xiii

    Introduction: Historical Background and Recent Developments that Motivate this Book xv

    1 The Langevin Equation and Stochastic Processes 1

    1.1 General Framework 1

    1.2 The Ornstein-Uhlenbeck (OU) Process 5

    1.3 The Overdamped Limit 8

    1.4 The Overdamped Harmonic Oscillator: An Ornstein-Uhlenbeck process 11

    1.5 Differential Form and Discretization 12

    1.5.1 Euler-Maruyama Discretization (EMD) and Itô Processes 15

    1.5.2 Stratonovich Discretization (SD) 17

    1.6 Relation Between Itô and Stratonovich Integrals 19

    1.7 Space Varying Diffusion Constant 21

    1.8 Itô vs Stratonovich 23

    1.9 Detailed Balance 23

    1.10 Memory Kernel 25

    1.11 The Many Particle Case 26

    References 26

    2 The Fokker-Planck Equation 29

    2.1 The Chapman-Kolmogorov Equation 29

    2.2 The Overdamped Case 30

    2.2.1 Derivation of the Smoluchowski (Fokker-Planck) Equation using the Chapman-Kolmogorov Equation 30

    2.2.2 Alternative Derivation of the Smoluchowski (Fokker-Planck) Equation 33

    2.2.3 The Adjoint (or Reverse or Backward) Fokker-Planck Equation 34

    2.3 The Underdamped Case 34

    2.4 The Free Case 35

    2.4.1 Overdamped Case 35

    2.4.2 Underdamped Case 36

    2.5 Averages and Observables 37

    References 39

    3 The Schrödinger Representation 41

    3.1 The Schrödinger Equation 41

    3.2 Spectral Representation 43

    3.3 Ground State and Convergence to the Boltzmann Distribution 44

    References 47

    4 Discrete Systems: The Master Equation and Kinetic Monte Carlo 49

    4.1 The Master Equation 49

    4.1.1 Discrete-Time Markov Chains 49

    4.1.2 Continuous-Time Markov Chains, Markov Processes 51

    4.2 Detailed Balance 53

    4.2.1 Final State Only 54

    4.2.2 Initial State Only 54

    4.2.3 Initial and Final State 55

    4.2.4 Metropolis Scheme 55

    4.2.5 Symmetrization 55

    4.3 Kinetic Monte Carlo (KMC) 58

    References 61

    5 Path Integrals 63

    5.1 The Itô Path Integral 63

    5.2 The Stratonovich Path Integral 66

    References 67

    6 Barrier Crossing 69

    6.1 First Passage Time and Transition Rate 69

    6.1.1 Average Mean First Passage Time 71

    6.1.2 Distribution of First Passage Time 73

    6.1.3 The Free Particle Case 74

    6.1.4 Conservative Force 75

    6.2 Kramers Transition Time: Average and Distribution 77

    6.2.1 Kramers Derivation 78

    6.2.2 Mean First Passage Time Derivation 80

    6.3 Transition Path Time: Average and Distribution 81

    6.3.1 Transition Path Time Distribution 82

    6.3.2 Mean Transition Path Time 84

    References 86

    7 Sampling Transition Paths 89

    7.1 Dominant Paths and Instantons 92

    7.1.1 Saddle-Point Method 92

    7.1.2 The Euler-Lagrange Equation: Dominant Paths 92

    7.1.3 Steepest Descent Method 96

    7.1.4 Gradient Descent Method 97

    7.2 Path Sampling 98

    7.2.1 Metropolis Scheme 98

    7.2.2 Langevin Scheme 99

    7.3 Bridge and Conditioning 99

    7.3.1 Free Particle 102

    7.3.2 The Ornstein-Uhlenbeck Bridge 102

    7.3.3 Exact Diagonalization 104

    7.3.4 Cumulant Expansion 105

    References 111

    Appendix A: Gaussian Variables 111

    Appendix B 113

    8 The Rate of Conformational Change: Definition and Computation 117

    8.1 First-order Chemical Kinetics 117

    8.2 Rate Coefficients from Microscopic Dynamics 119

    8.2.1 Validity of First Order Kinetics 120

    8.2.2 Mapping Continuous Trajectories onto Discrete Kinetics and Computing Exact Rates 123

    8.2.3 Computing the Rate More Efficiently 126

    8.2.4 Transmission Coefficient and Variational Transition State Theory 128

    8.2.5 Harmonic Transition-State Theory 129

    References 131

    9 Zwanzig-Caldeiga-Leggett Model for Low-Dimensional Dynamics 133

    9.1 Low-Dimensional Models of Reaction Dynamics From a Microscopic Hamiltonian 133

    9.2 Statistical Properties of the Noise and the Fluctuation-dissipation Theorem 137

    9.2.1 Ensemble Approach 138

    9.2.2 Single-Trajectory Approach 139

    9.3 Time-Reversibility of the Langevin Equation 142

    References 145

    10 Escape from a Potential Well in the Case of Dynamics Obeying the Generalized Langevin Equation: General Solution Based on the Zwanzig-Caldeira-Leggett Hamiltonian 147

    10.1 Derivation of the Escape Rate 147

    10.2 The Limit of Kramers Theory 150

    10.3 Significance of Memory Effects 152

    10.4 Applications of the Kramers Theory to Chemical Kinetics in Condensed Phases, Particularly in Biomolecular Systems 153

    10.5 A Comment on the Use of the Term "Free Energy" in Application to Chemical Kinetics and Equilibrium 155

    References 156

    11 Diffusive Dynamics on a Multidimensional Energy Landscape 157

    11.1 Generalized Langevin Equation with Exponential Memory can be Derived from a 2D Markov Model 157

    11.2 Theory of Multidimensional Barrier Crossing 161

    11.3 Breakdown of the Langer Theory in the Case of Anisotropic Diffusion: the Berezhkovskii-Zitserman Case 167

    References 171

    12 Quantum Effects in Chemical Kinetics 173

    12.1 When is a Quantum Mechanical Description Necessary? 173

    12.2 How Do the Laws of Quantum Mechanics Affect the Observed Transition Rates? 174

    12.3 Semiclassical Approximation and the Deep Tunneling Regime 177

    12.4 Path Integrals, Ring-Polymer Quantum Transition-State Theory, Instantons and Centroids 184

    References 191

    13 Computer Simulations of Molecular Kinetics: Foundation 193

    13.1 Computer Simulations: Statement of Goals 193

    13.2 The Empirical Energy 195

    13.3 Molecular States 197

    13.4 Mean First Passage Time 199

    13.5 Coarse Variables 199

    13.6 Equilibrium, Stable, and Metastable States 200

    References 202

    14 The Master Equation as a Model for Transitions Between Macrostates 203

    References 211

    15 Direct Calculation of Rate Coefficients with Computer Simulations 213

    15.1 Computer Simulations of Trajectories 213

    15.2 Calculating Rate with Trajectories 219

    References 221

    16 A Simple Numerical Example of Rate Calculations 223

    References 231

    17 Rare Events and Reaction Coordinates 233

    References 240

    18 Celling 241

    References 252

    19 An Example of the Use of Cells: Alanine Dipeptide 255

    References 257

    Index 259