Advances In Chemical Physics -- Contributors -- Preface to The Series -- Contents -- Recent Advances in Ultrafast X-ray Absorption Spectroscopy of Solutions -- I. Introduction -- II. Experimental Methods -- A. Steady-State XAS -- 1. Transmission and Fluorescence Detection Modes -- B. Time-Resolved XAS -- 1. General Setup -- 2. Interpretation of the Transient Signal -- C. Sources of Ultrafast X-ray Pulses and Data Acquisition -- 1. Picosecond XAS -- 2. Femtosecond XAS: The Slicing Scheme -- 3. Future Developments: X-FELs -- III. Theoretical Approaches for XAFS -- A. Structural Analysis: The EXAFS Region -- B. The Quasiparticle Approximation: Modeling the Near Edge -- 1. Green's Functions and Multiple Scattering Theory -- 2. Beyond Spherical Potentials -- C. Many-Body Effects -- 1. The Self-Energy Operator -- 2. Time-Dependent Density Functional Theory -- 3. Post-Hartree-Fock Methods -- D. Beyond Picosecond Temporal Resolution -- IV. Examples -- A. Photoinduced Hydrophobicity -- B. Spin-Crossover Molecular Systems -- C. Solvent Effects -- D. Intramolecular Charge Transfer -- V. Outlook -- Acknowledgments -- References -- Scaling Perspective on Intramolecular Vibrational Energy Flow: Analogies, Insights, and Challenges -- I. Introduction: Motivation and Historical Overview -- II. IVR: Analogy to Anderson Localization -- A. Introducing the IVR State Space -- B. Quantum Ergodicity Threshold -- 1. Ensemble of Hamiltonians: Probabilistic Approach to the Transition -- III. Scaling Theory of IVR -- A. State Space Predictions -- IV. Important Questions -- V. Classical-Quantum Correspondence and IVR -- A. State Space-Phase Space Correspondence -- B. Geometry of the Resonance Network: Arnold Web -- C. Computing the Arnold Web -- 1. Variational Approaches -- 2. Time-Frequency Analysis -- 3. "Coarse-Grained" Frequency Ratio Space.

D. Quantum State Space ↔ Classical Phase Space -- VI. Concluding Remarks -- Acknowledgments -- References -- Longest Relaxation Time of Relaxation Processes for Classical and Quantum Brownian Motion in a Potential: Escape Rate Theory Approach -- I. Introduction -- II. Escape Rate for Classical Brownian Motion -- A. Review of the Kramers' Results: Escape Rate from a Single Isolated Well -- 1. Kramers' Escape Rate Theory -- 2. Range of Validity of the IHD and VLD Formulas -- 3. Extension of Kramers' Theory to Many Dimensions in the IHD Limit -- 4. Langer's Treatment of the IHD Limit -- 5. Kramers' Formula as a Special Case of Langer's Formula -- B. Kramers' Turnover Problem -- 1. Green Function of the Energy-Action Diffusion Equation -- 2. Integral Equation for the Distribution Function in Energy-Action Variables -- 3. Kramers' VLD Result -- 4. Criticisms of the Ad Hoc Approach of Mel'nikov and Meshkov -- C. Applications of the Theory of Brownian Movement in a Potential and of the Kramers Theory -- D. Escape Rate for a Fixed Axis Rotator in a Double-Well Potential -- 1. Turnover Formula for the Escape Rate for Fixed Axis Rotation -- 2. Exact Matrix Continued Fraction Solution of the Langevin Equation -- 3. Comparison of Exact Matrix Solution with Approximate Analytical Formula -- E. Escape Rate for a Fixed Axis Rotator in an Asymmetrical Double-Well Potential -- 1. The Langevin Equation and Differential-Recurrence Equations for Statistical Moments -- 2. Turnover Formula for λ1 -- 3. The VHD and VLD Asymptotes for τ׀׀ -- 4. Comparison of the Exact Matrix Solution with Analytical Approximations -- F. Escape Rate for a Translational Brownian Particle in a Double-Well Potential -- 1. Langevin Equation Approach -- 2. Turnover Formula -- 3. Correlation Time in the VHD and VLD Limits -- 4. Comparison of the Exact and Approximate Approaches.

G. The Brownian Particle in a Tilted Periodic Potential -- 1. Applications of the Model of a Brownian Particle in a Tilted Periodic Potential -- 2. Turnover Equation -- 3. The Mean First Passage Time Asymptotes for the Decay Rate at Zero Tilt -- 4. Asymptotic Formula and Matrix Solution: Comparison of the Results -- H. Escape Rate Formulas for Superparamagnets -- III. Quantum Brownian Motion in a Potential -- A. Escape Rate for Quantum Brownian Motion -- 1. Escape Rate in the IHD Region -- 2. Quantum Transition State Theory -- 3. Transition Probability (Semiclassical Green Function) -- 4. Integral Equation and its Solution -- 5. Escape Rate in the Underdamped Quantum Region -- B. Translational Motion of a Quantum Brownian Particle in a Double-Well Potential -- 1. Master Equation in Phase Space and its Solution -- 2. Calculation of Observables -- 3. Mel'nikov's Turnover Formula for the Escape Rate -- 4. Comparison of the Numerical and Analytical Approaches -- C. Translational Motion of a Quantum Brownian Particle in a Periodic Potential -- 1. Solution of the Master Equation in Phase Space -- 2. Calculation of Observables -- 3. Mel'nikov's Turnover Equation -- 4. Comparison of Exact Matrix Solution with Approximate Analytical Formula -- IV. Conclusion -- Acknowledgment -- Appendix A: Wiener-Hopf Method -- Appendix B: Matrices and Vectors Involved in the Matrix Continued Fraction Solutions -- B.1. Fixed Axis Rotator in a Symmetrical Double-Well Potential -- B.2. Fixed Axis Rotator in an Asymmetrical Double-Well Potential -- B.3. Brownian Particle in a Tilted Periodic Potential -- B.4. Quantum Brownian Particle in a Double-Well Potential -- B.5. Quantum Brownian Particle in a Periodic Potential -- Appendix C: Evaluation of Averages in the Undamped Limit -- C.1. Fixed Axis Rotator in a Symmetrical Double-Well Potential.

C.2. Fixed Axis Rotator in an Asymmetrical Double-Well Potential -- C.3. Brownian Particle in a Double-Well Potential -- C.4. Brownian Particle in a Periodic Potential -- Appendix D: Escape Rate in the IHD Limit -- Appendix E: Justification of Semiclassical Representation of Matrix Elements -- References -- Local Fluctuations in Solution: Theory and Applications -- I. Introduction -- II. Outline, Notation, and General Remarks -- III. Thermodynamic Background -- IV. Statistical Thermodynamics Background -- V. A General Fluctuation Theory of Solutions -- A. Theory -- B. Inversion of FT -- VI. Fluctuations in Terms of Molecular Distribution Functions -- VII. Limiting Expressions for the Fluctuating Quantities -- VIII. Application to Binary Mixtures -- A. Bulk Thermodynamic Properties in Terms of Local Fluctuating Quantities -- B. Local Fluctuating Quantities in Terms of Bulk Thermodynamic Properties -- C. Fluctuation Theory Analysis of Experimental Data -- D. Osmotic Systems -- E. Cosolvent Effects on Surface Tension -- F. Force Fields for Molecular Simulation -- IX. Ternary Mixtures -- A. Bulk Thermodynamic Properties in Terms of Local Fluctuating Quantities -- B. Local Fluctuating Quantities in Terms of Bulk Thermodynamic Properties -- C. Equilibrium Dialysis -- D. Cosolvent Effects on Solute Solubility -- X. Particle Number and Energy Distributions in Solution -- XI. Molecular Association and Conformational Equilibria -- A. General Background -- B. First Derivatives of the Equilibrium Constant -- C. Second Derivatives of the Equilibrium Constant -- D. The Infinitely Dilute Solute Case -- XII. The Effects of Temperature, Pressure, and Composition on Local Fluctuations -- XIII. Analysis of Computer Simulation Data -- XIV. Pseudochemical Potentials, Volumes, and Enthalpies -- XV. Ideal Solutions -- XVI. Electrolyte Solutions.

XVII. Summary and Future Directions -- Acknowledgments -- References -- The Macroscopic Effects of Microscopic Heterogeneity in Cell Signaling -- I. Molecular Structures Modulate Cellular Responses -- A. Membrane Heterogeneity: Signal Modulation at Its Entry Point -- B. Clusters and Scaffolds: Competing Effects on Mean Responses -- C. Macromolecules: The Effect of Dimensionality -- II. Spatiotemporal Correlations Modulate Responses Even in Homogeneous Systems -- A. Rapid Rebinding -- B. Renormalization: Integrating Out the Rebinding -- C. Beyond Renormalization: When Rebinding Causes New Behavior -- D. When Rebinding Can Be Integrated Out and When It Cannot -- E. Macromolecular Crowding and Anomalous Diffusion -- III. Outlook -- Acknowledgments -- References -- Ab Initio Methodology for Pseudospin Hamiltonians of Anisotropic Magnetic Complexes -- I. Introduction -- A. Spin or Pseudospin? -- B. Scope and Organization of the Review -- II. Effective, Spin, and Pseudospin Hamiltonians in the Limiting Cases -- A. Transition Metal Complexes: S-Pseudospin -- 1. Pseudospin Description -- B. Lanthanide Complexes: J-Pseudospin -- C. Highly Symmetrical Complexes: -Pseudospin -- III. General Properties of Pseudospin Wave Functions -- IV. Basic Pseudospins -- A. The Pseudospin S = 1/2 -- 1. The Sign of the Main Values of the g Tensor -- 2. Assignment of Pseudospin Eigenfunctions Using Point Group Symmetry -- 3. Origin of the Negative Main Values of the g Tensor -- B. The Pseudospin S = 1 -- 1. Assignment of Pseudospin Eigenfunctions Using Point Group Symmetry -- 2. Derivation of the ZFS Pseudospin Hamiltonian -- C. The Pseudospin S = 3/2 -- V. Irreducible Tensor Description of Pseudospin Hamiltonians -- A. General Form of Pseudospin Hamiltonians -- 1. Zeeman g Tensors for Arbitrary Pseudospins -- 2. ZFS D Tensors for Arbitrary Pseudospins -- 3. Symmetry Aspects.

B. Approximate Definition of Pseudospin.