Molecular modelling for beginners

Presenting a concise, basic introduction to modelling and computational chemistry this text includes relevant introductory material to ensure greater accessibility to the subject. • Provides a comprehensive introduction to this evolving and developing field • Focuses on MM, MC, and MD with an entire chapter devoted to QSAR and Discovery Chemistry. • Includes many real chemical applications combined with worked problems and solutions provided in each chapter • Ensures that up-to-date treatment of a variety of chemical modeling techniques are introduced.Alan Hinchliffe is the author of Molecular Modelling for Beginners, published by Wiley. Molecular Modelling for Beginners......Page 3 Contents......Page 7 Preface......Page 15 List of Symbols......Page 19 1.1 Chemical Drawing......Page 21 1.2 Three-Dimensional Effects......Page 22 1.3 Optical Activity......Page 23 1.5 Modelling......Page 24 1.6 Molecular Structure Databases......Page 26 1.7 File Formats......Page 27 1.8 Three-Dimensional Displays......Page 28 1.9 Proteins......Page 30 2.1 Point Charges......Page 33 2.2 Coulomb’s Law......Page 35 2.3 Pairwise Additivity......Page 36 2.4 The Electric Field......Page 37 2.5 Work......Page 38 2.6 Charge Distributions......Page 40 2.7 The Mutual Potential Energy U......Page 41 2.8 Relationship Between Force and Mutual Potential Energy......Page 42 2.9 Electric Multipoles......Page 43 2.9.2 The electric second moment......Page 46 2.10 The Electrostatic Potential......Page 49 2.11 Polarization and Polarizability......Page 50 2.12 Dipole Polarizability......Page 51 2.13 Many-Body Forces......Page 53 3.1 The Pair Potential......Page 55 3.3 The Charge–Dipole Interaction......Page 57 3.4 The Dipole–Dipole Interaction......Page 59 3.6 The Induction Energy......Page 61 3.7 Dispersion Energy......Page 63 3.8 Repulsive Contributions......Page 64 3.10 Comparison with Experiment......Page 66 3.11 Improved Pair Potentials......Page 67 3.12 Site–Site Potentials......Page 68 4 Balls on Springs......Page 71 4.1 Vibrational Motion......Page 72 4.2 The Force Law......Page 75 4.3 A Simple Diatomic......Page 76 4.4 Three Problems......Page 77 4.5 The Morse Potential......Page 80 4.6 More Advanced Potentials......Page 81 5.1 More About Balls on Springs......Page 83 5.2 Larger Systems of Balls on Springs......Page 85 5.4 Molecular Mechanics......Page 87 5.4.1 Bond-stretching......Page 88 5.4.3 Dihedral motions......Page 89 5.4.4 Out-of-plane angle potential (inversion)......Page 90 5.4.5 Non-bonded interactions......Page 91 5.6.1 United atoms......Page 92 5.7 Modern Force Fields......Page 93 5.7.1 Variations on a theme......Page 94 5.8.2 MM1......Page 95 5.8.3 MM2 (improved hydrocarbon force field)......Page 96 5.8.4 AMBER......Page 97 5.8.6 R. A. Johnson......Page 98 6.1 Multiple Minima......Page 99 6.2 Saddle Points......Page 100 6.4 Finding Minima......Page 102 6.5 Multivariate Grid Search......Page 103 6.6 Derivative Methods......Page 104 6.7.1 Steepest descent......Page 105 6.7.2 Conjugate gradients......Page 106 6.8.1 Newton–Raphson......Page 107 6.8.3 Quasi-Newton–Raphson......Page 110 6.9 Choice of Method......Page 111 6.10 The Z Matrix......Page 112 6.11.1 Linear structures......Page 114 6.11.2 Cyclic structures......Page 115 6.12 The End of the Z Matrix......Page 117 6.13 Redundant Internal Coordinates......Page 119 7.1 Geometry Optimization......Page 121 7.2 Conformation Searches......Page 122 7.3 QSARs......Page 124 7.3.1 Atomic partial charges......Page 125 7.3.2 Polarizabilities......Page 127 7.3.3 Molecular volume and surface area......Page 129 7.3.4 log(P)......Page 130 8 Quick Guide to Statistical Thermodynamics......Page 133 8.1 The Ensemble......Page 134 8.2 The Internal Energy U(th)......Page 136 8.5 Equation of State and Pressure......Page 137 8.6 Phase Space......Page 138 8.7 The Configurational Integral......Page 139 8.8 The Virial of Clausius......Page 141 9 Molecular Dynamics......Page 143 9.1 The Radial Distribution Function......Page 144 9.2 Pair Correlation Functions......Page 147 9.3.2 The finite square well......Page 148 9.3.3 Lennardjonesium......Page 150 9.4 The Periodic Box......Page 151 9.5 Algorithms for Time Dependence......Page 153 9.5.2 The Verlet algorithm......Page 154 9.6 Molten Salts......Page 155 9.7 Liquid Water......Page 156 9.8 Different Types of Molecular Dynamics......Page 159 9.9 Uses in Conformational Studies......Page 160 10.1 Introduction......Page 163 10.2 MC Simulation of Rigid Molecules......Page 168 10.3 Flexible Molecules......Page 170 11.1 The Schrödinger Equation......Page 171 11.2 The Time-Independent Schrödinger Equation......Page 173 11.3.1 The one-dimensional infinite well......Page 174 11.4 The Correspondence Principle......Page 177 11.5 The Two-Dimensional Infinite Well......Page 178 11.6 The Three-Dimensional Infinite Well......Page 180 11.7 Two Non-Interacting Particles......Page 181 11.8 The Finite Well......Page 183 11.9 Unbound States......Page 184 11.10 Free Particles......Page 185 11.11 Vibrational Motion......Page 186 12 Quantum Gases......Page 191 12.1 Sharing Out the Energy......Page 192 12.2 Rayleigh Counting......Page 194 12.3 The Maxwell Boltzmann Distribution of Atomic Kinetic Energies......Page 196 12.4 Black Body Radiation......Page 197 12.5.1 The Drude model......Page 200 12.5.2 The Pauli treatment......Page 203 12.6 The Boltzmann Probability......Page 204 12.7 Indistinguishability......Page 208 12.8 Spin......Page 212 12.10 The Pauli Exclusion Principle......Page 214 12.11 Boltzmann’s Counting Rule......Page 215 13.1 Atomic Spectra......Page 217 13.1.1 Bohr’s theory......Page 218 13.3 The Infinite Nucleus Approximation......Page 220 13.4 Hartree’s Atomic Units......Page 221 13.5 Schrödinger Treatment of the H Atom......Page 222 13.6 The Radial Solutions......Page 224 13.7 The Atomic Orbitals......Page 226 13.7.1 l = 0 (s orbitals)......Page 227 13.7.2 The p orbitals......Page 230 13.7.3 The d orbitals......Page 231 13.8 The Stern–Gerlach Experiment......Page 232 13.9 Electron Spin......Page 235 13.10 Total Angular Momentum......Page 236 13.11 Dirac Theory of the Electron......Page 237 13.12 Measurement in the Quantum World......Page 239 14.1 One- and Two-Electron Operators......Page 241 14.2 The Many-Body Problem......Page 242 14.3 The Orbital Model......Page 243 14.4 Perturbation Theory......Page 245 14.5 The Variation Method......Page 247 14.6 The Linear Variation Method......Page 250 14.7 Slater Determinants......Page 253 14.8 The Slater–Condon–Shortley Rules......Page 255 14.9 The Hartree Model......Page 256 14.10 The Hartree–Fock Model......Page 258 14.11 Atomic Shielding Constants......Page 259 14.11.1 Zener’s wavefunctions......Page 260 14.11.2 Slater’s rules......Page 261 14.12 Koopmans’ Theorem......Page 262 15 Simple Molecules......Page 265 15.1 The Hydrogen Molecule Ion H(2)(+)......Page 266 15.2 The LCAO Model......Page 268 15.3 Elliptic Orbitals......Page 271 15.4 The Heitler–London Treatment of Dihydrogen......Page 272 15.5 The Dihydrogen MO Treatment......Page 274 15.7 Population Analysis......Page 276 15.7.1 Extension to many-electron systems......Page 278 16 The HF–LCAO Model......Page 281 16.1 Roothaan’s Landmark Paper......Page 282 16.3 The HF–LCAO Equations......Page 284 16.3.1 The HF–LCAO equations......Page 287 16.4 The Electronic Energy......Page 288 16.6 Open Shell Systems......Page 289 16.7 The Unrestricted Hartree–Fock Model......Page 291 16.8 Basis Sets......Page 293 16.8.1 Clementi and Raimondi......Page 294 16.8.2 Extension to second-row atoms......Page 295 16.9 Gaussian Orbitals......Page 296 16.9.1 STO/nG......Page 300 16.9.2 STO/4–31G......Page 302 16.9.4 Extended basis sets......Page 303 17 HF–LCAO Examples......Page 307 17.1 Output......Page 309 17.2 Visualization......Page 313 17.3 Properties......Page 314 17.3.1 The electrostatic potential......Page 315 17.4.1 The Hellmann–Feynman Theorem......Page 317 17.4.2 Energy minimization......Page 318 17.5 Vibrational Analysis......Page 320 17.6 Thermodynamic Properties......Page 323 17.6.1 The ideal monatomic gas......Page 324 17.6.3 q(rot)......Page 326 17.6.4 q(vib)......Page 327 17.7 Back to L-phenylanine......Page 328 17.8 Excited States......Page 329 17.9 Consequences of the Brillouin Theorem......Page 333 17.10 Electric Field Gradients......Page 335 18.1 Hückel p-Electron Theory......Page 339 18.2 Extended Hückel Theory......Page 342 18.2.1 Roald Hoffman......Page 343 18.3 Pariser, Parr and Pople......Page 344 18.4 Zero Differential Overlap......Page 345 18.5 Which Basis Functions Are They?......Page 347 18.7 Complete Neglect of Differential Overlap......Page 348 18.8 CNDO/2......Page 349 18.10 Intermediate Neglect of Differential Overlap......Page 350 18.12 The Modified INDO Family......Page 351 18.12.1 MINDO/3......Page 352 18.15 PM3......Page 353 18.18 Effective Core Potentials......Page 354 19.1 Electron Density Functions......Page 357 19.2 Configuration Interaction......Page 359 19.3 The Coupled Cluster Method......Page 360 19.4 Møller–Plesset Perturbation Theory......Page 361 19.5 Multiconfiguration SCF......Page 366 20 Density Functional Theory and the Kohn–Sham LCAO Equations......Page 367 20.1 The Thomas–Fermi and Xa Models......Page 368 20.2 The Hohenberg–Kohn Theorems......Page 370 20.3 The Kohn–Sham (KS–LCAO) Equations......Page 372 20.4 Numerical Integration (Quadrature)......Page 373 20.5 Practical Details......Page 374 20.6 Custom and Hybrid Functionals......Page 375 20.7 An Example......Page 376 20.8 Applications......Page 378 21.1 Modelling Polymers......Page 381 21.2 The End-to-End Distance......Page 383 21.3 Early Models of Polymer Structure......Page 384 21.3.2 The freely rotating chain......Page 386 21.4.1 G1 theory......Page 387 21.4.3 G3 theory......Page 389 21.5 Transition States......Page 390 21.6 Dealing with the Solvent......Page 392 21.7 Langevin Dynamics......Page 393 21.8 The Solvent Box......Page 395 21.9 ONIOM or Hybrid Models......Page 396 A.1 Scalars and Vectors......Page 399 A.2.1 Vector addition and scalar multiplication......Page 400 A.2.3 Cartesian components of a vector......Page 401 A.2.4 Vector products......Page 402 A.4 Vector Calculus......Page 404 A.4.1 Differentiation of fields......Page 405 A.4.2 The gradient......Page 406 A.4.3 Volume integrals of scalar fields......Page 407 A.4.4 Line integrals......Page 408 A.5 Determinants......Page 409 A.5.1 Properties of determinants......Page 410 A.6.1 The transpose of a matrix......Page 411 A.6.3 Algebra of matrices......Page 412 A.6.5 Matrix eigenvalues and eigenvectors......Page 413 A.7 Angular Momentum......Page 414 A.8 Linear Operators......Page 416 A.9 Angular Momentum Operators......Page 419 References......Page 423 Index......Page 427 "Molecular Modelling for Beginners is a self contained introduction to modelling and computational chemistry. Assuming only a basic knowledge of physical chemistry, physics and mathematics, relevant introductory material is provided to ensure greater accessibility to this exciting subject. Carefully structured, the text begins by presenting the fundamental theories that are based on classical mechanics, classical electrostatics and statistical thermodynamics. The focus is on Molecular Mechanics, Monte Carlo and Molecular Dynamics. Emphasis is given to discovery chemistry and QSAR, and the text successfully combines essential theory with relevant applications and examples designed to encourage student understanding." "This text will appeal to those students taking undergraduate courses in chemistry, biochemistry and materials science who want to explore the latest techniques of molecular modelling."--Jacket