Molecules in Physics, Chemistry, and Biology

Mathematical Molecular Physics.- The Mathematical Definition of a Molecule and Molecular Structure.- 1. Dedication.- 2. Some Aspects of the Historical Development of the Concepts of Atoms, Molecules, and Quanta.- 3. Some Aspects of the Historical Development of Modern Quantum Mechanics and of Quantum Chemistry in Particular.- 4. Some Aspects of the Various Levels of Mathematics Involved: The Abstract Hilbert Space.- 5. On the Axioms of Quantum Theory.- 6. Some Comments about Strict and Rigorous Mathematical Proofs.- 7. Some Mathematical Tools Useful in the Quantum Theory of Atoms and Molecules.- 8. Some Properties of the Coulombic Hamiltonian.- 9. The Mathematical Definition of a Molecule.- Acknowledgement.- References.- From Geometrical Molecules to Topological Molecules: A Quantum Mechanical View.- 1. Localization, Quantization and Continuity.- 2. Wave Packet Topology.- 3. The Topology of Nuclear Configurations.- 4. Epilogue.- References.- Relativistic Molecular Physics.- Ab-Initio Relativistic Quantum Chemistry.- 1. Introduction.- 2. Relati vistic Theory for Many-Electron Systems.- 3. Relativistic Self Consistent Field Theory for Molecules.- 4. Ab-initio Fully Relativistic Calculations for Diatomics.- 5. Ab-initio Dirac—Hartree—Fock—Roothaan (DHFR) Calculations for Heavy-Atom Polyatomics.- 6. Miscellaneous Applications of the RIP Program.- 7. Conclusion and Future Prospects.- Acknowledgements.- References.- Space-Curvature Effects in Atomic and Molecular-Structure Calculations.- 1. Introduction.- 2. The One-Electron Schrödinger Equation.- 3. Multipolar Expansion of the Bielectronic Repulsion Potential.- 4. The Dirac Equation and Fine Structure Energies.- 5. The Hyperfine Structure Interactions and Parameters.- 6. The Zeeman and Stark Effects.- 7. Conclusion.- Appendix A: The Dirac—Coulomb Equation in a Space of Constant Curvature.- Appendix B: The Maxwell Equations in a Space of Constant Curvature.- References.- Molecules in Space.- Organic and Exotic Molecules in Space.- 1. Introduction.- 2. Observational Methods.- 3. Distribution and Abundance of As trophy sical Molecules.- 4. Detection and Identification of “Non Terrestrial” Species.- 5. Organic Interstellar Molecules.- Acknowledgement.- References.- Molecular Processes in the Interstellar Medium.- 1. Astrophysical Background.- 2. Gas Phase Formation Processes.- 3. Examples of the Necessary Interplay Between Interstellar and Molecular Studies.- 4. Conclusion.- References.- Small Molecular Structures.- Electric and Magnetic Properties for the Ground and Excited States of Molecular Hydrogen.- 1. Introduction.- 2. Basic Theory of the Hydrogen Molecule.- 3. A Molecule in an External Electric Field.- 4. A Molecule in an External Magnetic Field.- 5. Conclusions.- Acknowledgements.- References.- Photoionization Dynamics of Diatomic Molecules.- 1. Introduction.- 2. Shape Resonances.- 3. Autoionization Resonances.- 4. Conclusion.- References.- Low-Energy Electron-Molecule Dynamics.- 1. Introduction.- 2. Diatomic Molecules.- 3. Polyatomic Molecules.- 4. Conclusion.- References.- Small Naked Homonuclear Clusters of Transition Metal Atoms.- 1. Introduction.- 2. Generation and Detection.- 3. Theoretical Methods.- 4. Dimers.- 5. Trimers.- 6. Concluding Remarks.- References.- Nonrigid and Large Systems.- Understanding the Structure and Spectra of Non-Rigid Molecules.- 1. Introduction.- 2. The Treatment of Non-Rigid Triatomic Molecules.- 3. Some Results for Triatomic Systems.- 4. Conclusions.- References.- Effective Vibration-Rotation Hamiltonian of a Molecule with a Large-Amplitude Internal Motion.- 1. Introduction.- 2. Applications to Vibration-Rotation Spectroscopy.- 3. The Hamiltonian of Nitromethane.- References.- Ultrafast Dynamics of Diphenyl Polyenes: Experiment, Theory and Models of Conformational Motion Properties.- 1. Introduction.- 2. Experimental Conditions.- 3. Experimental Results.- 4. A Conformational Motion Model.- 5. Conclusion.- References.- Laser-Line Narrowing and Laser-Excited Shpol’skii Effect of Impurity Spectra of Polynuclear Aromatic Hydrocarbon Solids.- 1. Introduction.- 2. Experimental.- 3. Results and Discussion.- Acknowledgements.- References.- Molecular Interactions.- Molecular Charge Distributions and Response Functions: Multipolar and Penetration Terms; Application to the Theory of Intermolecular Interactions.- 1. Theoretical Background: Exchange Perturbation Treatments for Intermolecular Interactions.- 2. Electrostatic (1st-Order) Term: Charge Distributions and their Multicenter Multipolar Representations.- 3. Induction and Dispersion (2nd-Order) Terms: Response Functions.- 4. Conclusion.- References.- Towards Classification and Analytical Description of Molecular Interactions Including Quantum-Mechanical Many-Body Effects.- 1. Introduction: Scope of the Present Survey.- 2. Theoretical Background: Perturbative Approach to the Studies of Intermolecular Forces. The Role of Many-Body Effects.- 3. Molecular Properties Occurring in the Spherical Tensor Theory of Long-Range Interactions Between N Molecules.- 4. Contributions to the Interaction Energy in a System of N Molecules Arising from Perturbation Theory: Classification and Physical Interpretation.- 5. Mathematical Expressions for the First-, Second- and Third-Order Interaction Energies Resulting from the Quantum-Mechanical Perturbative Analysis of Long-Range Forces Between N Molecules.- 6. Towards an Analytical Description of Long-Range Molecular Interactions Including Quantum-Mechanical Many-Body Effects. The Use of Spherical Tensor Formalism and Racah—Wigner Algebra.- 7. Spherical Tensor Theory of Long-Range Molecular Interactions Including Quantum-Mechanical Many-Body Effects: Discussion of Results.- 8. Connection of E(2)disp?, ?; 2E(3)disp?, ?; ? 3E(3)disp?, ?Q; 2E(3)disp?, ?Q; 3 and E(3)disp?, ?Q; 2 with Electrical Properties of Interacting Molecules.- 9. Isotropic Interactions Within the Formalism of Spherical Tensors.- 10. Reduction of General Intermolecular Energy Expressions by Point Symmetries of Interacting Molecules.- Acknowledgements.- Appendix: Fundamental Information About Spherical Tensors and Mathematical Methods of Angular Momentum Theory.- References.- A Reappraisal of the Hydrogen Bonding Interaction Obtained by Com bining Energy Decomposition Analyses and Counterpoise Corrections.- 1. Introduction.- 2. The Interpretation of the H-Bond. The Motivation of the Present Report.- 3. Analysis of the Non-Covalent Interactions. Decomposition of the Interaction Energy.- 4. The Use of the Energy Decomposition in the Interpretation of the Hydrogen Bonding.- 5. The Use of Chemical Groups in the Interpretation of Hydrogen Bonding.- 6. Counterpoise Corrections to the Basis Set Superposition Error.- 7. A Test Case: The Effect of CP Corrections on ?Eeq and Req.- 8. A Test Case: Interpretation of the Hydrogen Bonding Using CP Corrected Energy Components.- 9. Conclusions.- Acknowledgements.- References.- Theoretical Approaches to Crystals.- Ab-Initio Potential Functions for Crystals and Ab-Initio Crystal Orbitals.- 1. Introduction.- 2. Methodology.- 3. Results and Discussion.- 4. Conclusions.- Acknowledgements.- References.- Molecular-Orbital Approach to Crystal-Field Theory for Transition Elements in Solids.- 1. Introduction.- 2. From Lanthanides to d-Transition Elements.- 3. The Crystal Field in the Atomic Spectroscopy Scheme.- 4. Extracting Crystal-Field Parameters from Paramagnetic Data.- 5. Simulating Crystal-Field Parameters from Structural Data.- References.- Lutetium Bisphthalocyanine: The First Molecular Semiconductor.- 1. Introduction.- 2. Definition of Molecular Materials.- 3. Conduction in Molecular Materials.- 4. Bands and Localized Models of Conduction.- 5. Definition of a Molecular Semiconductor.- 6. Lutetium Bisphthalocyanine: The First Molecular Semiconductor.- 7. Molecular Material Based Junctions.- 8. Conclusion.- Acknowledgements.- References.- From Quantum Chemistry to Organic Optical Signal Processing: A Computer-Aided Molecular Engineering Approach.- 1. Introduction.- 2. The Concept of an “Optimized” Material in Quadratic Nonlinear Optics.- 3. Quantum Theory of (Hyper)Polarizabilities in Molecules and Oligomers.- 4. Molecular and Crystal Engineering of Organic Materials.- 5. Conclusions.- Acknowledgements.- References.- Electronic Structure and the Classification of Materials.- 1. Introduction.- 2. The Electronic Structure of Molecules.- 3. Quantum Mechanics for Materials.- 4. Localization.- 5. Canonical Electronic-Structure Types.- Acknowledgements.- References.