Molecular Interactions

David A. Micha, PhD, is a Professor of Chemistry and Physics at the University of Florida, presently Adjunct and Emeritus, with continuing research activity. His many research interests include molecular interactions and kinetics, and quantum molecular dynamics involving energy transfer, electron transfer, light emission, reactions in gas phase collisions, and also at solid surfaces. His work has been recognized with awards from the Alfred P. Sloan Foundation and the Dreyfus Foundation, and with an Alexander von Humboldt Senior Scientist Award. Dr. Micha has been the organizer of several Pan-American Workshops and is a co-organizer of the "Sanibel Symposium on Theory and Computation for the Molecular and Materials Sciences" at the University of Florida.

• Preface xi1 Fundamental Concepts 11.1 Molecular Interactions in Nature 21.2 Potential Energies for Molecular Interactions 41.2.1 The Concept of a Molecular Potential Energy 41.2.2 Theoretical Classification of Interaction Potentials 61.2.2.1 Small Distances 71.2.2.2 Intermediate Distances 81.2.2.3 Large Distances 81.2.2.4 Very Large Distances 81.3 Quantal Treatment and Examples of Molecular Interactions 91.4 Long-Range Interactions and Electrical Properties of Molecules 211.4.1 Electric Dipole of Molecules 211.4.2 Electric Polarizabilities of Molecules 221.4.3 Interaction Potentials from Multipoles 231.5 Thermodynamic Averages and Intermolecular Forces 241.5.1 Properties and Free Energies 241.5.2 Polarization in Condensed Matter 251.5.3 Pair Distributions and Potential of Mean-Force 261.6 Molecular Dynamics and Intermolecular Forces 271.6.1 Collisional Cross Sections 271.6.2 Spectroscopy of van der Waals Complexes and of Condensed Matter 281.7 Experimental Determination and Applications of Interaction Potential Energies 291.7.1 Thermodynamics Properties 301.7.2 Spectroscopy and Diffraction Properties 301.7.3 Molecular Beam and Energy Deposition Properties 301.7.4 Applications of Intermolecular Forces 31References 312 Molecular Properties 352.1 Electric Multipoles of Molecules 352.1.1 Potential Energy of a Distribution of Charges 352.1.2 Cartesian Multipoles 362.1.3 Spherical Multipoles 372.1.4 Charge Distributions for an Extended System 382.2 Energy of a Molecule in an Electric Field 402.2.1 Quantal Perturbation Treatment 402.2.2 Static Polarizabilities 412.3 Dynamical Polarizabilities 432.3.1 General Perturbation 432.3.2 Periodic Perturbation Field 472.4 Susceptibility of an Extended Molecule 492.5 Changes of Reference Frame 522.6 Multipole Integrals from Symmetry 542.7 Approximations and Bounds for Polarizabilities 572.7.1 Physical Models 572.7.2 Closure Approximation and Sum Rules 582.7.3 Upper and Lower Bounds 59References 603 Quantitative Treatment of Intermolecular Forces 633.1 Long Range Interaction Energies from Perturbation Theory 643.1.1 Interactions in the Ground Electronic States 643.1.2 Interactions in Excited Electronic States and in Resonance 683.2 Long Range Interaction Energies from Permanent and Induced Multipoles 683.2.1 Molecular Electrostatic Potentials 683.2.2 The Interaction Potential Energy at Large Distances 703.2.3 Electrostatic, Induction, and Dispersion Forces 733.2.4 Interacting Atoms and Molecules from Spherical Components of Multipoles 753.2.5 Interactions from Charge Densities and their Fourier Components 763.3 Atom–Atom, Atom–Molecule, and Molecule–Molecule Long-Range Interactions 783.3.1 Example of Li++Ne 783.3.2 Interaction of Oriented Molecular Multipoles 793.3.3 Example of Li++HF 803.4 Calculation of Dispersion Energies 813.4.1 Dispersion Energies from Molecular Polarizabilities 813.4.2 Combination Rules 823.4.3 Upper and Lower Bounds 833.4.4 Variational Calculation of Perturbation Terms 863.5 Electron Exchange and Penetration Effects at Reduced Distances 873.5.1 Quantitative Treatment with Electronic Density Functionals 873.5.2 Electronic Rearrangement and Polarization 933.5.3 Treatments of Electronic Exchange and Charge Transfer 983.6 Spin-orbit Couplings and Retardation Effects 1023.7 Interactions in Three-Body and Many-Body Systems 1033.7.1 Three-Body Systems 1033.7.2 Many-Body Systems 106References 1074 Model Potential Functions 1114.1 Many-Atom Structures 1114.2 Atom–Atom Potentials 1144.2.1 Standard Models and Their Relations 1144.2.2 Combination Rules 1164.2.3 Very Short-Range Potentials 1174.2.4 Local Parametrization of Potentials 1174.3 Atom–Molecule and Molecule–Molecule Potentials 1194.3.1 Dependences on Orientation Angles 1194.3.2 Potentials as Functionals of Variable Parameters 1244.3.3 Hydrogen Bonding 1244.3.4 Systems with Additive Anisotropic Pair-Interactions 1254.3.5 Bond Rearrangements 1254.4 Interactions in Extended (Many-Atom) Systems 1274.4.1 Interaction Energies in Crystals 1274.4.2 Interaction Energies in Liquids 1314.5 Interaction Energies in a Liquid Solution and in Physisorption 1354.5.1 Potential Energy of a Solute in a Liquid Solution 1354.5.2 Potential Energies of Atoms and Molecules Adsorbed at Solid Surfaces 1394.6 Interaction Energies in Large Molecules and in Chemisorption 1434.6.1 Interaction Energies Among Molecular Fragments 1434.6.2 Potential Energy Surfaces and Force Fields in Large Molecules 1454.6.3 Potential Energy Functions of Global Variables Parametrized with Machine Learning Procedures 148References 1525 Intermolecular States 1575.1 Molecular Energies for Fixed Nuclear Positions 1585.1.1 Reference Frames 1585.1.2 Energy Density Functionals for Fixed Nuclei 1605.1.3 Physical Contributions to the Energy Density Functional 1625.2 General Properties of Potentials 1635.2.1 The Electrostatic Force Theorem 1635.2.2 Electrostatic Forces from Approximate Wavefunctions 1645.2.3 The Example of Hydrogenic Molecules 1655.2.4 The Virial Theorem 1665.2.5 Integral Form of the Virial Theorem 1685.3 Molecular States for Moving Nuclei 1695.3.1 Expansion in an Electronic Basis Set 1695.3.2 Matrix Equations for Nuclear Amplitudes in Electronic States 1705.3.3 The Flux Function and Conservation of Probability 1725.4 Electronic Representations 1725.4.1 The Adiabatic Representation 1725.4.2 Hamiltonian and Momentum Couplings from Approximate Adiabatic Wavefunctions 1735.4.3 Nonadiabatic Representations 1745.4.4 The Two-state Case 1755.4.5 The Fixed-nuclei, Adiabatic, and Condon Approximations 1765.5 Electronic Rearrangement for Changing Conformations 1805.5.1 Construction of Molecular Electronic States from Atomic States: Multistate Cases 1805.5.2 The Noncrossing Rule 1815.5.3 Crossings in Several Dimensions: Conical Intersections and Seams 1845.5.4 The Geometrical Phase and Generalizations 189References 1926 Many-Electron Treatments 1956.1 Many-Electron States 1956.1.1 Electronic Exchange and Charge Transfer 1956.1.2 Many-Electron Descriptions and Limitations 1986.1.3 Properties and Electronic Density Matrices 2036.1.4 Orbital Basis Sets 2056.2 Supermolecule Methods 2096.2.1 The Configuration Interaction Procedure for Molecular Potential Energies 2096.2.2 Perturbation Expansions 2156.2.3 Coupled-Cluster Expansions 2186.3 Many-Atom Methods 2226.3.1 The Generalized Valence-Bond Method 2226.3.2 Symmetry-Adapted Perturbation Theory 2256.4 The Density Functional Approach to Intermolecular Forces 2286.4.1 Functionals for Interacting Closed- and Open-Shell Molecules 2286.4.2 Electronic Exchange and Correlation from the Adiabatic-Connection Relation 2326.4.3 Issues with DFT, and the Alternative Optimized Effective Potential Approach 2386.5 Spin-Orbit Couplings and Relativistic Effects in Molecular Interactions 2436.5.1 Spin-Orbit Couplings 2436.5.2 Spin-Orbit Effects on Interaction Energies 245References 2477 Interactions Between Two Many-Atom Systems 2557.1 Long-range Interactions of Large Molecules 2557.1.1 Interactions from Charge Density Operators 2557.1.2 Electrostatic, Induction, and Dispersion Interactions 2587.1.3 Population Analyses of Charge and Polarization Densities 2607.1.4 Long-range Interactions from Dynamical Susceptibilities 2627.2 Energetics of a Large Molecule in a Medium 2657.2.1 Solute–Solvent Interactions 2657.2.2 Solvation Energetics for Short Solute–Solvent Distances 2687.2.3 Embedding of a Molecular Fragment and the QM/MM Treatment 2707.3 Energies from Partitioned Charge Densities 2727.3.1 Partitioning of Electronic Densities 2727.3.2 Expansions of Electronic Density Operators 2747.3.3 Expansion in a Basis Set of Localized Functions 2777.3.4 Expansion in a Basis Set of Plane Waves 2797.4 Models of Hydrocarbon Chains and of Excited Dielectrics 2817.4.1 Two Interacting Saturated Hydrocarbon Compounds: Chains and Cyclic Structures 2817.4.2 Two Interacting Conjugated Hydrocarbon Chains 2847.4.3 Electronic Excitations in Condensed Matter 2897.5 Density Functional Treatments for All Ranges 2917.5.1 Dispersion-Corrected Density Functional Treatments 2917.5.2 Long-range Interactions from Nonlocal Functionals 2947.5.3 Embedding of Atomic Groups with DFT 2977.6 Artificial Intelligence Learning Methods for Many-Atom Interaction Energies 300References 3038 Interaction of Molecules with Surfaces 3098.1 Interaction of a Molecule with a Solid Surface 3098.1.1 Interaction Potential Energies at Surfaces 3098.1.2 Electronic States at Surfaces 3148.1.3 Electronic Susceptibilities at Surfaces 3198.1.4 Electronic Susceptibilities for Metals and Semiconductors 3218.2 Interactions with a Dielectric Surface 3248.2.1 Long-range Interactions 3248.2.2 Short and Intermediate Ranges 3298.3 Continuum Models 3328.3.1 Summations Over Lattice Cell Units 3328.3.2 Surface Electric Dipole Layers 3338.3.3 Adsorbate Monolayers 3358.4 Nonbonding Interactions at a Metal Surface 3378.4.1 Electronic Energies for Varying Molecule–Surface Distances 3378.4.2 Potential Energy Functions and Physisorption Energies 3418.4.3 Embedding Models for Physisorption 3478.5 Chemisorption 3498.5.1 Models of Chemisorption 3498.5.2 Charge Transfer at a Metal Surface 3548.5.3 Dissociation and Reactions at a Metal Surface from Density Functionals 3598.6 Interactions with Biomolecular Surfaces 363References 367Index 373