It was just over ten years ago, at Aspeniisgarden near Gothenburg, Sweden, that Pro- fessor Alexandr Sergeevich Davydov presented his soliton theory for the storage and transport of biological energy in protein to scientists from Europe, North America and Japan. Since then, his ideas have been vigorously studied and investigated throughout the world. Many feel that Davydov's theory is an important contribution to biomolecu- lar dynamics, but others caution that neglected dispersive effects may destroy the energy localization that arises ill his theory. It was to discuss these differences of opinion that we organized a NATO Advanced Research Workshop on "Self-trapping of Vibrational Energy in Protein" from July 30 to August 5, 1989 at Hanstholm, Denmark. In addition to substantial financial support from the Special Programme on "Chaos; Order and Patterns" of the NATO Scientific Affairs Division, we received it generous grant from the Danish Natural Science Research Council. We also acknowledge invalu- able assistance provided by the interdepartmental center of nonlinear studies ("MIDIT" is the Danish acronym) as well as the Laboratory of Applied Mathematical Physics, both at the Technical University of Denmark. It is a particular pleasure to thank Lise Gudmandsen and Dorthe Th[cent]gersen for many forms of assistance before, during, and after the workshop.

Table of Contents:
Section I: Low Temperature Theory.- 1. Solitons in Biology and Possible Role of Bisolitons in High-Tc Superconductivity.- 2. Quantum-Mechanical Derivation of the Davydov Equations for Multi-Quanta States.- 3. A Classical and Quantum Theory of Dynamical Self-Trapping in Nonlinear Systems and its Implication to Energy Transfer in Biological Systems.- 4. Vibron Solitons: A Semiclassical Approach.- 5. When Is A Soliton?.- 6. Quantum Monte Carlo Simulations of the Davydov Model.- 7. Quantum Effects on the Davydov Soliton.- 8. Davydov Ansatz and Proper Solutions of Schrödinger Equation for Fröhlich Hamiltonian.- 9. Unitary Transformation and “Decoupling” of Excitons and Phonons in ACN.- 10. Soliton Generation in Infinite and Half-Infinite Molecular Chains.- 11. Soliton Dynamics in the Eilbeck-Lomdahl-Scott Model for Hydrogen-Bonded Polypeptides.- 12. Influence of Davydov Splitting on Solitons in Alpha-Helix.- 13. Interaction of an Extra Electron with Optical Phonons in Long Molecular Chains and Ionic Crystals.- 14. Self-Trapping in a Molecular Chain with Substrate Potential.- Section II: Exciton-Phonon Coupling.- 15. On the Calculations of the Exciton-Phonon Coupling Parameters in the Theory of Davydov Solitons.- 16. Quantum Chemical Calculations of Molecular Parameters Defining Davydov Soliton Dynamics in Polypeptides.- 17. On Ab Initio Estimations of the Nonlinearity Parameters in the Davydov Model.- Section III: Temperature Stability.- 18. The Quantum Theory of Solitons with Thermal Vibration Taken into Account.- 19. Davydov Solitons at 300 Kelvin: The Final Search.- 20. Influence of Heat Bath and Disorder on Davydov Solitons.- 21. Perturbation Estimate of the Lifetime of the Davydov Soliton at 300K.- 22. The Temperature Dependence of Exciton-Phonon Coupling in theContext of Davydov’s Model; The Dynamic Damping of Soliton.- 23. Temperature Effects on the Davydov Soliton.- 24. Thermal Stability of the Davydov Soliton.- Section IV: Experimental Results.- 25. The Amide-I Band in Acetanilide: Physical Properties and Biological Suggestions.- 26. Incoherent Neutron Scattering and Infra-Red Measurements in Acetanilide and Derivatives.- 27. Spectroscopy of the Amide-I Modes of Acetanilide.- 28. Biomolecular Dynamics Studied by Vibrational Spectroscopy.- 29. Molecular Crystals and Localized Vibrational States.- 30. Search for Remote Transfer of Vibrational Energy in Proteins.- Section V: Related Topics.- 31. Davydov’s Soliton and Fröhlich’s Condensation: Is There a Connection?.- 32. The Soliton and Bisoliton Input into the Elastic Scattering of Slow Neutrons.- 33. Dissociation of Davydov Solitons by Electromagnetic Waves.- 34. Vibrational Properties and Energy Transport in Acetanilide by Molecular Dynamics.- 35. On the Possible Role of Phonon-Modulated Tunneling in Excimer Formation.- 36. Excimers in Molecular Crystals: The Relaxation of a Nonlinear Oscillator.- 37. The Nonresonant DST Equation as a Model for McClare’s Excimer.- Section VI: The Discrete Self-Trapping Equation.- 38. Introduction to the Discrete Self-Trapping Equation.- 39. Energy Localization in Small Biomolecules.- 40. Local Modes and Degenerate Perturbation Theory.- 41. Quantum and Classical Descriptions of Chaos in the DST Equation.- 42. Eigenvalue Statistics and Eigenstate Wigner Functions for the Discrete Self-Trapping Equation.- 43. The Discrete Nonlinear Schroedinger Equation: Nonadiabatic Effects, Finite Temperature Consequences, and Experimental Manifestations.- Participants.- Workshop Photograph.