The Atom-Atom Potential Method

The history of physics furnishes many examples of how a simple semiem­ pirical method, essentially based on intuitive considerations, may prove to be much more successful than a rigorous theoretical approach. A pertinent example is the method of atom-atom potentials, which treats the intermolec­ ular interactions between polyatomic molecules in terms of pairwise inter­ actions between their constituent atoms. Despite a few conceptual short­ comings, the method provides a fairly reliable practical means of handling, on a microscopic level, a wide range of problems that arise in the solid-state physics and chemistry of organic compounds. This monograph is an attempt to generalize the experience gained in the past twenty years in interpreting the static and dynamic properties of organic molecular solids in terms of atom-atom potentials. It embraces nearly all aspects of the application of the method, including an evaluation of cohesive energies, equilibrium crystal structures, phonon spectra, ther­ modynamic functions, and crystal defects. Many related topics such as the effect of the crystal field on molecular conformation, the determination of crystal structures from raw diffraction data, and the problem of polymor­ phic transitions are also discussed. We believe that this book will be of use to researchers in solid-state physics, chemistry, crystallography, physical chemistry, and polymer chem­ istry. It also gives us an opportunity to acknowledge our indebtedness to those who sent us published as well as unpublished information and sugges­ tions, including A.T. Amos, E.L. Bokhenkov, H. Bonadeo, R.K. Boyd, C.P.

Inhalt

1. Introduction.- 2. Non-Empirical Calculations of Intermolecular Forces Between Organic Molecules.- 2.1 The Supermolecule Method.- 2.1.1 Molecular Orbital Theory.- 2.1.2 MO Treatment of the Interaction Energy.- 2.1.3 Application to Organic Systems.- 2.1.4 Valence Bond Method.- 2.2 Perturbation Methods and Simplified Equations for the Interaction Energy.- 2.2.1 Exchange Perturbation Theories.- 2.2.2 Electrostatic Energy.- 2.2.3 Polarization Energy.- 2.2.4 Exchange Energy.- 3. The Atom-Atom Potential Method.- 3.1 General Remarks.- 3.2 Formulation of the Atom-Atom Method.- 3.3 Determination of Atom-Atom Potentials from Crystal Data.- 3.3.1 Fitting Procedures.- 3.3.2 Hydrocarbons.- 3.3.3 Atom-Atom Potentials for Interactions Involving Sulfur, Selenium, Oxygen and Nitrogen Atoms.- 3.3.4 Halogenated Hydrocarbons.- 3.3.5 Amides and Carboxylic Acids.- 3.4 The Use of Molecular Data in Deriving the Parameters of Potentials.- 3.5 Ab Initio Atom-Atom Potentials.- 3.6 Semiempirical Atom-Atom Potentials.- 4. Lattice Statics.- 4.1 The Lattice at Equilibrium.- 4.2 Determination of Equilibrium Crystal Configurations Using a Symmetry-Constrained Model.- 4.2.1 Equilibrium Conditions.- 4.2.2 The Lattice Energy and Its Derivatives.- 4.2.3 Minimization Techniques.- 4.2.4 Convergence Properties of the Lattice Energy.- 4.3 The Use of Atom-Atom Potentials in Predicting Stable Crystal Configurations.- 4.4 The Influence of Crystal Forces on the Molecular Conformation.- 4.5 The Atom-Atom Potential Method as an Aid in Determining Crystal Structures.- 4.5.1 Determination of Crystal Structure from Unit-Cell Dimensions.- 4.5.2 Atom-Atom Potentials in Interpreting Single Crystal Diffraction Data.- 4.5.3 The Case of Non-Rigid Molecule.- 4.5.4 Inclusion Compounds.- 4.6 Polymeric Crystals.- 4.6.1 Chain Conformation and Symmetry Constraints.- 4.6.2 Variable Virtual Bond Method.- 4.6.3 Application to Cellulose.- 5. Lattice Dynamics.- 5.1 General Theory.- 5.2 The Taddei-Califano Formalism and the Rigid-Molecule Approximation.- 5.3 Calculation of Force Constants Using the Atom-Atom Potential Method.- 5.4 Symmetry Properties of Force Constants.- 5.5 Experimental Tests.- 5.6 Numerical Results.- 5.6.1 Benzene.- 5.6.2 Naphthalene.- 5.6.3 Anthracene.- 5.6.4 Hexamethylenetetramine.- 5.6.5 ?-p-Dichlorobenzene.- 5.6.6 Pyrazine.- 5.6.7 Concluding Remarks.- 6. Thermodynamics.- 6.1 Quasi-Harmonic Approximation.- 6.2 Cell Model.- 6.3 Comparison of the Cell Model and the Quasi-Harmonic Approximation with Computer Experiments.- 6.4 Extension of the Cell Model to Organic Molecular Crystals.- 6.4.1 Basic Formulas.- 6.4.2 Evaluation of Six-Fold Integrals.- 6.4.3 Numerical Results. Comparison with Experiment and Quasi-Harmonic Approximation.- 6.5 Calculations of Polymorphic Transitions.- 6.5.1 Temperature-Induced Transitions in p-Dichlorobenzene and, 2, 4, 5-Tetrachlorobenzene 322.- 6.5.2 Pressure-Induced Transition in Benzene.- 6.5.3 Plastic-Phase Transition in Adamantane.- 7. Imperfect Crystals.- 7.1 Point Defects.- 7.1.1 Microscopic Model.- 7.1.2 Vacancies.- 7.1.3 Orientational Defects.- 7.1.4 Conformational Defects.- 7.1.5 Substitutional Impurities.- 7.2 Linear Faults.- 7.3 Planar Faults.- 7.3.1 Surface.- 7.3.2 Stacking Faults.- 7.4 Volume Defects.- References.