Molecular Excitation Dynamics and Relaxation: Quantum Theory and Spectroscopy

This work brings together quantum theory and spectroscopy to convey excitation processes to advanced students and specialists wishing to conduct research and understand the entire fi eld rather than just single aspects. Written by experienced authors and recognized authorities in the field, this text covers numerous applications and offers examples taken from different disciplines. As a result, spectroscopists, molecular physicists, physical chemists, and biophysicists will all fi nd this a must–have for their research. Also suitable as supplementary reading in graduate level courses. INDICE: Preface XI Part One Dynamics and Relaxation 1 1 Introduction 3 2 Overview of Classical Physics 5 2.1 Classical Mechanics 5 2.1.1 Concepts of Theoretical Mechanics: Action, Lagrangian, and Lagrange Equations 7 2.1.2 Hamilton Equations 9 2.1.3 Classical Harmonic Oscillator 11 2.2 Classical Electrodynamics 13 2.2.1 Electromagnetic Potentials and the Coulomb Gauge 14 2.2.2 Transverse and Longitudinal Fields 14 2.3 Radiation in Free Space 16 2.3.1 Lagrangian and Hamiltonian of the Free Radiation 16 2.3.2 Modes of the Electromagnetic Field 18 2.4 Light–Matter Interaction 20 2.4.1 Interaction Lagrangian and Correct Canonical Momentum 20 2.4.2 Hamiltonian of the Interacting Particle–Field System 22 2.4.3 Dipole Approximation 23 3 Stochastic Dynamics 27 3.1 Probability and Random Processes 27 3.2 Markov Processes 32 3.3 Master Equation for Stochastic Processes 33 3.3.1 Two–Level System 36 3.4 Fokker–Planck Equation and Diffusion Processes 37 3.5 Deterministic Processes 39 3.6 Diffusive Flow on a Parabolic Potential (a Harmonic Oscillator) 41 3.7 Partially Deterministic Process and the Monte Carlo Simulation of a Stochastic Process 44 3.8 Langevin Equation and Its Relation to the Fokker–Planck Equation 46 4 Quantum Mechanics 51 4.1 Quantum versus Classical 51 4.2 The Schrödinger Equation 53 4.3 Bra–ket Notation 56 4.4 Representations 57 4.4.1 Schrödinger Representation 57 4.4.2 Heisenberg Representation 59 4.4.3 Interaction Representation 60 4.5 Density Matrix 61 4.5.1 Definition 61 4.5.2 Pure versus Mixed States 63 4.5.3 Dynamics in the Liouville Space 65 4.6 Model Systems 66 4.6.1 Harmonic Oscillator 66 4.6.2 Quantum Well 70 4.6.3 Tunneling 71 4.6.4 Two–Level System 73 4.6.5 Periodic Structures and the Kronig–Penney Model 76 4.7 Perturbation Theory 81 4.7.1 Time–Independent Perturbation Theory 81 4.7.2 Time–Dependent Perturbation Theory 86 4.8 Einstein Coefficients 89 4.9 Second Quantization 91 4.9.1 Bosons and Fermions 93 4.9.2 Photons 94 4.9.3 Coherent States 96 5 Quantum States of Molecules and Aggregates 101 5.1 Potential Energy Surfaces, Adiabatic Approximation 101 5.2 Interaction between Molecules 106 5.3 Excitonically Coupled Dimer 107 5.4 Frenkel Excitons of Molecular Aggregates 112 5.5 Wannier–Mott Excitons 118 5.6 Charge–Transfer Excitons 121 5.7 Vibronic Interaction and Exciton Self–Trapping 124 5.8 Trapped Excitons 130 6 The Concept of Decoherence 133 6.1 Determinism in Quantum Evolution 133 6.2 Entanglement 136 6.3 Creating Entanglement by Interaction 137 6.4 Decoherence 139 6.5 Preferred States 144 6.6 Decoherence in Quantum Random Walk 147 6.7 Quantum Mechanical Measurement 149 6.8 Born Rule 153 6.9 Everett or Relative State Interpretation of Quantum Mechanics 154 6.10 Consequences of Decoherence for Transfer and Relaxation Phenomena 156 7 Statistical Physics 161 7.1 Concepts of Classical Thermodynamics 161 7.2 Microstates, Statistics, and Entropy 165 7.3 Ensembles 167 7.3.1 Microcanonical Ensemble 167 7.3.2 Canonical Ensemble 169 7.3.3 Grand Canonical Ensemble 170 7.4 Canonical Ensemble of Classical Harmonic Oscillators 172 7.5 Quantum Statistics 173 7.6 Canonical Ensemble of Quantum Harmonic Oscillators 174 7.7 Symmetry Properties of Many–ParticleWavefunctions 176 7.7.1 Bose–Einstein Statistics 178 7.7.2 Pauli–Dirac Statistics 180 7.8 Dynamic Properties of an Oscillator at Equilibrium Temperature 181 7.9 Simulation of Stochastic Noise from a Known Correlation Function 186 8 An Oscillator Coupled to a Harmonic Bath 189 8.1 Dissipative Oscillator 189 8.2 Motion of the Classical Oscillator 190 8.3 Quantum Bath 194 8.4 Quantum Harmonic Oscillator and the Bath: Density Matrix Description 196 8.5 Diagonal Fluctuations 201 8.6 Fluctuations of a Displaced Oscillator 203 9 Projection Operator Approach to Open Quantum Systems 209 9.1 Liouville Formalism 210 9.2 Reduced Density Matrix of Open Systems 212 9.3 Projection (Super)operators 213 9.4 Nakajima–Zwanzig Identity 214 9.5 Convolutionless Identity 216 9.6 Relation between the Projector Equations in Low–Order Perturbation Theory 218 9.7 Projection Operator Technique with State Vectors 219 10 Path Integral Technique in Dissipative Dynamics 223 10.1 General Path Integral 223 10.1.1 Free Particle 228 10.1.2 Classical Brownian Motion 229 10.2 Imaginary–Time Path Integrals 231 10.3 Real–Time Path Integrals and the Feynman–Vernon Action 233 10.4 Quantum Stochastic Process: The Stochastic Schrödinger Equation 238 10.5 Coherent–State Path Integral 240 10.6 Stochastic Liouville Equation 243 11 Perturbative Approach to Exciton Relaxation in Molecular Aggregates 245 11.1 Quantum Master Equation 246 11.2 Second–Order Quantum Master Equation 247 11.3 Relaxation Equations from the Projection Operator Technique 252 11.4 Relaxation of Excitons 254 11.5 Modified Redfield Theory 256 11.6 Förster Energy Transfer Rates 258 11.7 Lindblad Equation Approach to Coherent Exciton Transport 259 11.8 Hierarchical Equations of Motion for Excitons 263 11.9 Weak Interchromophore Coupling Limit 265 11.10 Modeling of Exciton Dynamics in an Excitonic Dimer 268 11.11 Coherent versus Dissipative Dynamics: Relevance for Primary Processes in Photosynthesis 273 Part Two Spectroscopy 275 12 Introduction 277 13 Semiclassical Response Theory 279 13.1 Perturbation Expansion of Polarization: Response Functions 280 13.2 First Order Polarization 284 13.2.1 Response Function and Susceptibility 284 13.2.2 Macroscopic Refraction Index and Absorption Coefficient 286 13.3 Nonlinear Polarization and Spectroscopic Signals 288 13.3.1 N–wave Mixing 288 13.3.2 Pump Probe 290 13.3.3 Heterodyne Detection 293 14 Microscopic Theory of Linear Absorption and Fluorescence 295 14.1 A Model of a Two–State System 295 14.2 Energy Gap Operator 296 14.3 Cumulant Expansion of the First Order Response 297 14.4 Equation of Motion for Optical Coherence 299 14.5 Lifetime Broadening 300 14.6 Inhomogeneous Broadening in Linear Response 305 14.7 Spontaneous Emission 306 14.8 Fluorescence Line–Narrowing 309 14.9 Fluorescence Excitation Spectrum 311 15 Four–Wave Mixing Spectroscopy 315 15.1 Nonlinear Response of Multilevel Systems 315 15.1.1 Two– and Three–Band Molecules 316 15.1.2 Liouville Space Pathways 319 15.1.3 Third Order Polarization in the Rotating Wave Approximation 322 15.1.4 Third Order Polarization in Impulsive Limit 327 15.2 Multilevel System in Contact with the Bath 329 15.2.1 Energy Fluctuations of the General Multilevel System 330 15.2.2 Off–Diagonal Fluctuations and Energy Relaxation 332 15.2.3 Fluctuations in a Coupled Multichromophore System 333 15.2.4 Inter–Band Fluctuations: Relaxation to the Electronic Ground State 335 15.2.5 Energetic Disorder in Four–Wave Mixing 338 15.2.6 Random Orientations of Molecules 339 15.3 Application of the Response Functions to Simple FWMExperiments 342 15.3.1 Photon Echo Peakshift: Learning About System–Bath Interactions 342 15.3.2 Revisiting Pump–Probe 346 15.3.3 Time–Resolved Fluorescence 348 16 Coherent Two–Dimensional Spectroscopy 351 16.1 Two–Dimensional Representation of the Response Functions 351 16.2 Molecular System with Few Excited States 358 16.2.1 Two–State System 358 16.2.2 Damped Vibronic System – Two–Level Molecule 359 16.3 Electronic Dimer 364 16.4 Dimer of Three–Level Chromophores – Vibrational Dimer 372 16.5 Interferences of the 2D Signals: General Discussion Based on an ElectronicDimer 375 16.6 Vibrational vs. Electronic Coherences in 2D Spectrum of Molecular Systems 379 17 Two Dimensional Spectroscopy Applications for Photosynthetic Excitons 383 17.1 Photosynthetic Molecular Aggregates 383 17.1.1 Fenna–Matthews–Olson Complex 384 17.1.2 LH2 Aggregate of Bacterial Complexes 385 17.1.3 Photosystem I (PS–I) 386 17.1.4 Photosystem II (PS–II) 388 17.2 Simulations of 2D Spectroscopy of Photosynthetic Aggregates 389 17.2.1 Energy Relaxation in FMO Aggregate 389 17.2.2 Energy Relaxation Pathways in PS–I 393 17.2.3 Quantum Transport in PS–II Reaction Center 399 18 Single Molecule Spectroscopy 403 18.1 Historical Overview 403 18.2 How Photosynthetic Proteins Switch 405 18.3 Dichotomous Exciton Model 410 Appendix 415 A.1 Elements of the Field Theory 415 A.2 Characteristic Function and Cumulants 417 A.3 Weyl Formula 419 A.4 Thermodynamic Potentials and the Partition Function 420 A.5 Fourier Transformation 421 A.6 Born Rule 423 A.7 Green’s Function of a Harmonic Oscillator 424 A.8 Cumulant Expansion in Quantum Mechanics 425 A.8.1 Application to the Double Slit Experiment 427 A.8.2 Application to Linear Optical Response 428 A.8.3 Application to Third Order Nonlinear Response 429 A.9 Matching the Heterodyned FWM Signal with the Pump–Probe 430 A.10 Response Functions of an Excitonic System with Diagonal and Off–Diagonal Fluctuations in the Secular Limit 431 References 437 Index 447

• ISBN: 978-3-527-41008-8
• Editorial: Wiley VCH
• Encuadernacion: Cartoné
• Páginas: 470
• Fecha Publicación: 07/08/2013
• Nº Volúmenes: 1
• Idioma: Inglés