Advances in chemical physics. Volume 160 / ‡c edited by Stuart A. Rice, Department of Chemistry and the James Franck Institute, the University of Chicago, Chicago, Illinois; Aaron R. Dinner, Department of Chemistry and The James Franck Institute, the Univ

The __Advances in Chemical Physics__ series provides the chemical physics field with a forum for critical, authoritative evaluations of advances in every area of the discipline. This volume explores the following topics: * Thermodynamic Perturbation Theory for Associating Molecules * Path Integrals and Effective Potentials in the Study of Monatomic Fluids at Equilibrium * Sponteneous Symmetry Breaking in Matter Induced by Degeneracies and Pseudogeneracies * Mean-Field Electrostatics Beyond the Point-Charge Description * First Passage Processes in Cellular Biology * Theoretical Modeling of Vibrational Spectra and Proton Tunneling in Hydroen-Bonded Systems Title Page 5 Copyright Page 6 Contents 9 Contributors List 11 Preface to the Series 13 Chapter 1 Thermodynamic Perturbation Theory for Associating Molecules 15 I. INTRODUCTION 15 II. A BRIEF INTRODUCTION TO CLUSTER EXPANSIONS 19 III. SINGLE ASSOCIATION SITE: BOND RENORMALIZATION 22 IV. SINGLE ASSOCIATION SITE: TWO-DENSITY APPROACH 24 A. The Monovalent Case 26 B. The Divalent Case 28 V. MULTIPLE ASSOCIATION SITES: MULTI-DENSITY APPROACH 35 VI. THE TWO-SITE AB CASE 42 A. Steric Hindrance in Chain Formation 43 B. Ring Formation 46 C. Bond Cooperativity 50 VII. SPHERICALLY SYMMETRIC AND DIRECTIONAL ASSOCIATION SITES 53 VIII. DENSITY FUNCTIONAL THEORY 56 IX. CONCLUDING REMARKS 58 Acknowledgments 58 REFERENCES 58 Chapter 2 PATH INTEGRALS AND EFFECTIVE POTENTIALS IN THE STUDY OF MONATOMIC FLUIDS AT EQUILIBRIUM 63 I. INTRODUCTION 64 II. THE PI APPROACH 68 A. The Quantum Partition Function 68 B. Convolutions and Sum Over Histories 70 C. The Finite-P Primitive Approximation for Boltzmann Statistics 72 D. Higher-Order Propagators 77 E. Pair Product Actions 80 F. Quantum Exchange 85 G. Simulation Techniques 88 III. SEMICLASSICAL APPROACHES 92 A. An Overview of the Main Methods 92 B. PI-based approaches 93 C. Semiclassical Approaches for Quantum Hard Spheres 100 IV. STRUCTURAL PROPERTIES 101 A. The Meaning of the Quantum Fluid Structures 101 B. Structures at the Pair Level (Diffraction Effects) 107 C. Direct Correlation Functions 122 D. Further Topics 129 V. THERMODYNAMIC PROPERTIES 139 VI. FLUID SYSTEMS 145 A. Simulation Studies 145 B. Some Numerical Results 150 VII. CONCLUDING REMARKS 165 REFERENCES 166 Chapter 3 SPONTANEOUS SYMMETRY BREAKING IN MATTER INDUCED BY DEGENERACIES AND PSEUDODEGENERACIES 173 I. INTRODUCTION. SYMMETRY BREAKING AND SPONTANEOUS SYMMETRY BREAKING (SSB) 174 II. DEFINITION OF SSB IN ATOMIC SYSTEMS AND MEANS OF ITS OBSERVATION 176 A. General 176 B. The Thermodynamic Limit. Correlation Between Degeneracy, SSB, Internal Energy, and Entropy 177 C. SSB in Finite-Size Atomic Systems 178 D. Role of Observation in the Definition of SSB 180 III. MECHANISMS OF SSB INDUCED BY DEGENERACY AND PSEUDODEGENERACY IN POLYATOMIC SYSTEMS 182 A. The Jahn–Teller Effect 182 B. SSB in Polyatomic Systems Induced by Degeneracy 184 C. SSB Induced by Pseudodegeneracy via the PJTE 189 D. SSB Induced by Hidden Degeneracy and Pseudodegeneracy 196 IV. THEOREM: DEGENERACY AND PSEUDODEGENERACY ARE THE ONLY SOURCE OF SSB IN ATOMIC SYSTEMS 201 V. DEGENERACY-INDUCED SSB IN INTERATOMIC AND INTERMOLECULAR INTERACTIONS 204 VI. SSB IN GAS–LIQUID AND LIQUID–SOLID TRANSITIONS AS DRIVEN BY DEGENERACIES 206 A. Degeneracy-Induced Gas–Liquid Transition 206 B. Degeneracy-Induced Liquid–Solid Transition 207 VII. LOCALLY TRIGGERED SSB INDUCING SOLID-STATE PHASE TRANSITIONS 208 VIII. SSB IN ELEMENTARY PARTICLE PHYSICS AS RELATED TO DEGENERACIES 213 IX. GENERALIZATION: NATURE TENDS TO AVOID DEGENERACIES BY MEANS OF SSB 215 REFERENCES 218 Chapter 4 MEAN FIELD ELECTROSTATICS BEYOND THE POINT CHARGE DESCRIPTION 223 I. INTRODUCTION 223 II. THE MEAN FIELD APPROXIMATION 225 III. POINT-ION WITH A STRUCTURE 227 A. The Standard PB Equation 227 B. Dipolar PB Equation 229 C. Langevin PB Equation 233 D. Charged Point Dipoles 236 E. Polarizable PB Equation 237 IV. FINITE-SPREAD PB EQUATION 243 A. Spherical Distribution w(|r-r|) 244 B. Needle Ions: The Case for Non-Spherical w(r-r¢) 252 C. Dumbbell Ions 254 V. SHORT-RANGE NON-ELECTROSTATIC INTERACTIONS 255 A. The Mean Field Implementation 256 B. Short-Range Interactions beyond the Mean Field 260 C. Local Schemes 266 VI. CONCLUSION 271 ACKNOWLEDGMENT 272 REFERENCES 273 Chapter 5 FIRST-PASSAGE PROCESSES IN CELLULAR BIOLOGY 275 I. INTRODUCTION AND CONTEXT 275 II. FRAMEWORK 277 A. Stochastic Processes 277 B. Time Evolution Equation(s) for the System 278 C. Backward Evolution Equations 281 D. First Passage (FP) Processes 283 III. APPLICATIONS 290 A. Channel Transport 290 B. Receptor Binding and Adhesion 301 C. Single-Cell Growth and Division 304 IV. CONCLUDING REMARKS 314 ACKNOWLEDGMENTS 315 REFERENCES 315 Chapter 6 THEORETICAL MODELING OF VIBRATIONAL SPECTRA AND PROTON TUNNELING IN HYDROGEN‐BONDED SYSTEMS 321 I. INTRODUCTION 321 II. MODEL OF IR SPECTRA OF HYDROGEN-BONDED SYSTEMS 323 III. THEORETICAL SIMULATION OF EXPERIMENTAL SPECTRA OF HYDROGEN‐BONDED SYSTEMS 327 A. 1-Methylthymine Crystal 327 B. 1-Methyluracil Crystal 330 C. β-Oxalic Acid Crystal 330 D. Salicylic Acid Crystal 333 E. Imidazole Crystal 335 F. Acetic and Benzoic Acid Dimers 336 G. Summary 339 IV. MODELING OF O-H/O-D STRETCHING BANDS OF VIBRATIONAL SPECTRA OF ICES AND AQUEOUS SOLUTIONS 340 V. PROTON TUNNELING IN SYMMETRICAL DOUBLE-WELL POTENTIAL IN THE EXCITED ELECTRONIC STATE 344 VI. SELECTED OTHER PROBLEMS 346 VII. CONCLUSIONS 350 ACKNOWLEDGMENTS 351 REFERENCES 351 Index 357 Supplemental Images 363 EULA 371 The Advances In Chemical Physics Series Provides The Chemical Physics Field With A Forum For Critical, Authoritative Evaluations Of Advances In Every Area Of The Discipline.- This Is The Only Series Of Volumes Available That Presents The Cutting Edge Of Research In Chemical Physics.- Includes Contributions From Experts In This Field Of Research.- Contains A Representative Cross-section Of Research That Questions Established Thinking On Chemical Solutions- Structured With An Editorial Framework That Makes The Book An Excellent Supplement To An Advanced Graduate Class In Physical Chemistry Or Chemical Physics. Title Page ; Copyright Page ; Contents ; Contributors To Volume 161 ; Preface To The Series ; Chapter 1 Structural Analysis By X-ray Intensity Angular Cross Correlations ; I. Introduction ; Ii. Theory ; A. Scattering From A Disordered System Of Reproducible Particles ; B. 2d Disordered Systems ; 1. Dilute Systems ; 2. Dense Systems ; C. 3d Disordered Systems ; D. Two- And Three-point Angular Ccfs And Their Fourier Decomposition ; 1. General Definitions ; 2. Analysis Of Disordered Systems By Angular Ccfs ; Iii. Applications ; A. Single-particle Structure Recovery From Fxs. 1. 2d Structure Determination 2. 3d Structure Determination ; B. Correlations In Disordered And Partially Ordered Phases ; 1. Local Structure Of Colloidal Systems ; 2. Bo Order In Liquid Crystals ; 3. Structural Inhomogeneities In Semicrystalline Polymers ; 4. Short-range And Medium-range Order In Metallic Glasses ; 5. Emergent Rotational Symmetries And Domain Memory In Magnetic Multilayers ; Iv. Conclusions And Outlook ; Acknowledgments ; References ; Chapter 2 Spin Relaxation In Phase Space ; I. Introduction. Ii. Density Matrix And Phase Space Formulations Of Relaxation Phenomena In Spin Systems A. Density Matrix Formulation Of Spin Relaxation And Resonance ; 1. General Equations ; 2. Collision Kernel In The Markovian Approximation ; 3. Time-dependent Hamiltonian ; 4. Method Of Statistical Moments ; B. Quasiprobability Distribution Functions For Particles ; 1. The Wigner Distribution Function For Particles ; 2. Application To Transition-state Theory ; 3. Application To Quantum Brownian Motion ; C. Quasiprobability Distribution Functions For Spins ; 1. Spin Phase-space Distribution Functions. 2. Weyl Symbols Of Some Spin Operators 3. Master Equation And Statistical Moment Equations For Spin Relaxation In Phase Space ; D. Equilibrium Phase Space Distribution Functions For Spins ; 1. Spins In A Uniform External Field ; 2. Uniaxial Nanomagnet In An External Field ; 3. Uniaxial Nanomagnet In A Transverse Field ; 4. Biaxial Anisotropy ; 5. Cubic Anisotropy ; 6. Tst Reversal Time ; 7. Switching Field Curves ; 8. Discussion ; Iii. Master Equation In Phase Space For Axially Symmetric Systems ; A. Master Equation For A Uniaxial Nanomagnet Subjected To A Dc Magnetic Field. 1. Explicit Form Of The Master Equation 2. Differential Recurrence Relations For The Statistical Moments ; B. Spin Relaxation In A Dc Magnetic Field ; 1. Basic Equations ; 2. Quantum Analog Of The Magnetic Langevin Equation ; 3. Exact Solution Of The Master Equation For Longitudinal Relaxation ; 4. Nonlinear Longitudinal Relaxation Time ; 5. Linear Response ; 6. Single-mode Approximation ; C. Longitudinal Relaxation Of Uniaxial Nanomagnets ; 1. Calculation Of The Observables ; 2. Analytic Equations For The Characteristic Relaxation Timesand Dynamic Susceptibility. Edited By Stuart A. Rice, Aaron R. Dinner. Includes Bibliographical References And Indexes. Mode Of Access: World Wide Web. The Advances in Chemical Physics series provides the chemical physics field with a forum for critical, authoritative evaluations of advances in every area of the discipline. This volume explores the following topics: Thermodynamic Perturbation Theory for Associating Molecules Path Integrals and Effective Potentials in the Study of Monatomic Fluids at Equillibrium Sponteneous Symmetry Breaking in Matter Induced by Degeneracies and Pseudogeneracies MeanField Electrostatics Beyond the PointCharge Description First Passage Processes in Cellular Biology Theoretical Modeling of Vibrational Spectra and Proton Tunneling in HydroenBonded Systems