Molecular Aggregation

Transcription

1 Molecular Aggregation Structure Analysis and Molecular Simulation of Crystals and Liquids ANGELO GAVEZZOTTI University of Milano OXFORD UNIVERSITY PRESS

2 Contents PART I FUNDAMENTALS 1 The molecule: structure, size and shape Atoms and bonds Classification concepts in many particle systems Structure Symmetry Order Enthalpy and entropy Must a molecule have a size? Mass and length dimensions Atomic radü Molecular volume and surface Size in terms of electron density Must a molecule have a shape? Historical portraits: a chemistry course in the early 1960's 24 2 Molecular vibrations and molecular force fields Vibrational modes and force constants Molecular mechanics Evolution of molecular force fields Appendix: an example of coordinate transformation Historical portraits: Got a force constant? 45 3 Quantum chemistry Some fundamentals of quantum mechanics Dynamic variables, wavefunctions, operators The Schrödinger equation and stationary states Linear momentum Angular momentum Spherical harmonics The harmonic oscillator The hydrogen atom and atomic orbitals Spin Many-electron systems Molecular orbitals: The Fock and Roothaan equations The variational principle Why do a molecular orbital calculation? 72

3 x CONTENTS 3.6 Approximate quantum chemical methods: NDO and EHT Evolution of quantum chemical calculations: Beyond Hartree Fock Configuration interaction and M011er Plesset perturbation methods Density functional theory (DFT) methods Other beyond-hartree Fock methods Ethylene in perspective Dimerization energies and basis set superposition error Historical portraits: early experiences in quantum chemistry 82 4 The physical nature and the computer simulation of the intermolecular potential Experimental facts and conceptual framework The representation of the molecular charge distribution and of the electric potential Full electron density Central multipoles Distributed multipoles Point charges Coulombic potential energy Polarization (electrostatic induction) energy Dispersion energy Pauli (exchange) repulsion energy Total energies versus partitioned energies Pairwise additivity Interpretation Intermolecular hydrogen bonding Simulation methods The intermolecular atom atom model for organic crystals Distributed multipole methods Other density-based methods Ad hoc or transferable? Force field fitting from ab initio calculations Crystal symmetry and X-ray diffraction A structural view of crystal symmetry: bottom-up crystallography Space group symmetry and its mathematical representation von Laue's idea, The structure factor Scattering by one or two charge points The atomic scattering factor 133

4 CONTENTS xi The molecular structure factor The structure factor for infinite periodic systems Miller indices and Bragg's law The electron density in a crystal The atomic prejudice Structure and X-ray diffraction: Some examples Historical portraits: Training of a crystallographer in the 1960s Periodic systems: Crystal orbitals and lattice dynamics The mathematical description of crystal periodicity Equivalent positions and systematic absences in diffraction patterns Reciprocal space, wave vector, Brillouin zone Bloch functions The electronic structure of solids The crystal orbital approach Band structures: Complicated but not difficult Comparison with experiment; electronic density of states Lattice dynamics and lattice vibrations Periodic vibrations in infinite crystals Comparison with experiment; measuring lattice-vibration frequencies Molecular structure and macroscopic properties: Calorimetry and thermodynamics Molecules and macroscopic bodies Energy The partition function: Molecules The partition function: Macroscopic systems Internal energy I: From statistics and quantum mechanics Internal energy II: From thermal and mechanical experiments Heat capacity Entropy Classical entropy Statistical entropy The calculation of entropy for chemical systems Free energy and chemical equilibrium Chemical potential Free energy Chemical potentials in practice Thermodynamic measurements 186

5 xii CONTENTS Heat capacity Melting enthalpies Sublimation enthalpies Derivatives Correlation studies in organic solids The Cambridge Structural Database (CSD) of organic crystals Structure correlation Retrieval of molecular and crystal structures from the CSD The SubHeat database The geometrical categorization of intermolecular bonding Space analysis of molecular packing modes Empty space versus filled space Close packing in crystals The calculation of intermolecular energies in crystals Lattice energies: Some basic concepts Convergence problems in lattice sums Sublimation entropies and vapor pressures of crystals General-purpose force fields for organic crystals Accuracy and reproducibility Correlation between molecular and crystal properties: Fact or fiction? Bivariate analysis Principal component analysis Acceptable crystal structures Historical portraits: Lattice energies and the phase problem in the old days The liquid state Proper liquids Molecular dynamics (MD) Equations of motion Temperature Pressure NPT and NVT simulations Performance and constraints in molecular dynamics simulations The Monte Carlo (MC) method Structural and dynamic descriptors for liquids Radial distribution functions Correlation functions Physicochemical properties of liquids from MD or MC simulations Enthalpy, heat capacity and density 243

6 CONTENTS xiii The Jorgensen school Crystal and liquid equations of state Polarizability and dielectric constants Free energy simulations A theme with variations Water Computers Bits and pieces Operating systems Computer programming Bugs and program checking and validation Reproducibility "Because it's there"? 262 PART II THE FRONTIER 11 Structure-property and structure activity relationships Fundamental research and applied technology The structure activity dogma Crystal dissolution Thermal properties Thermal expansion coefficients Heat capacity and heat transport Strain and stress, elastic and viscous properties Optical, electric and magnetic properties Color Optical properties and the polar axis Electric and magnetic properties Intermolecular bonding The decline of the intermolecular atom atom bond The Feynman Ehrenfest chemical bond More familiar models: distance energy analyses Full density models: the SCDS Pixel method Theory Coulombic energy Polarization energy Dispersion energy Repulsion energy Total energies and parameters The generation of crystal coordinates Pixel calculations: General features 310

7 xiv CONTENTS Pixel theory: Pros and cons Systematic application of the Pixel theory to intermolecular bonding A glossary of intermolecular recognition modes Interactions not involving hydrogen C H X interactions The 0 H X and N H- X hydrogen Bond n-interactions Crystal energies Directed bonds versus diffuse bonding Phase equilibria, phase changes, and mesophases: Analysis and simulation Things and molecules Basic thermodynamic functions Melting Solid liquid equilibrium and nucleation from the melt Vapor liquid and vapor solid equilibrium Glasses Liquid crystals Nucleation and growth from solution: Experiments Overview Light scattering, calorimetry Chemical spectroscopy X-ray scattering and diffraction Crystal growth and morphology Crystal faces, attachments energies, and morphology prediction Electron micrography and atomic force microscopy (AFM) Evolutionary molecular simulation Crystal polymorphism and crystal structure prediction A fundamental fact What are crystal polymorphs? The taxonomy of organic crystals Phenomenology of crystal polymorphism Crystal structure fingerprints: Detecting real polymorphism Analysis of crystal polymorphism by Pixel and quantum chemical calculations The construction of crystal structures by computer "Brate force" approach 384

8 CONTENTS xv The "Prom" sequential approach Molecular clusters with one symmetry Operator Combination of two or three symmetry operators The translation search: Sorting and ranking The Prom algorithm: Pros and cons Some examples of crystal structure generation Crystal structure prediction by computer The aims The tools Are crystal structures predictable? Epilogue: A theory of crystallization? Laws and theories Aggregation stages Oligomers Nanoparticles Mesoparticles Macroscopic crystals Thermodynarnics, kinetics, and symmetry The language of the theory 416 Index 419 Supplementary material OPiX, an open-code computer program package for crystal packing analysis, polymorph generation and prediction, and Pixel-SCDS calculation; manuals and source Codes Other open-source program Codes for the calculations described in the book The SubHeat database (see in Section 8.4) The polymorph database (see in Section 14.2) Details of calculations (lists of atomic coordinates, etc.) This material is available at the author's website: