ESSENTIALS OF COMPUTATIONAL CHEMISTRY: THEORIES AND MODELS

By P. NORAM

CONTENTS WHAT ARE THEORY, COMPUTATION, AND MODELING? DE?NITION OF TERMS QUANTUM MECHANICS COMPUTABLE QUANTITIES STRUCTURE POTENTIAL ENERGY SURFACES CHEMICAL PROPERTIES COST AND EF?CIENCY INTRINSIC VALUE HARDWARE AND SOFTWARE ALGORITHMS NOTE ON UNITS BIBLIOGRAPHY AND SUGGESTED ADDITIONAL READING REFERENCES MOLECULAR MECHANICS HISTORY AND FUNDAMENTAL ASSUMPTIONS POTENTIAL ENERGY FUNCTIONAL FORMS BOND STRETCHING VALENCE ANGLE BENDING TORSIONS VAN DER WAALS INTERACTIONS ELECTROSTATIC INTERACTIONS CROSS TERMS AND ADDITIONAL NON-BONDED TERMS PARAMETERIZATION STRATEGIES FORCE-?ELD ENERGIES AND THERMODYNAMICS GEOMETRY OPTIMIZATION OPTIMIZATION ALGORITHMS OPTIMIZATION ASPECTS SPECI?C TO FORCE FIELDS MENAGERIE OF MODERN FORCE FIELDS AVAILABLE FORCE FIELDS VALIDATION FORCE FIELDS AND DOCKING CASE STUDY: (2R?,4S?)-1-HYDROXY-2,4-DIMETHYLHEX-5-ENE SIMULATIONS OF MOLECULAR ENSEMBLES RELATIONSHIP BETWEEN MM OPTIMA AND REAL SYSTEMS PHASE SPACE AND TRAJECTORIES PROPERTIES AS ENSEMBLE AVERAGES PROPERTIES AS TIME AVERAGES OF TRAJECTORIES MOLECULAR DYNAMICS HARMONIC OSCILLATOR TRAJECTORIES NON-ANALYTICAL SYSTEMS PRACTICAL ISSUES IN PROPAGATION STOCHASTIC DYNAMICS MONTE CARLO MANIPULATION OF PHASE-SPACE INTEGRALS METROPOLIS SAMPLING ENSEMBLE AND DYNAMICAL PROPERTY EXAMPLES KEY DETAILS IN FORMALISM CUTOFFS AND BOUNDARY CONDITIONS POLARIZATION CONTROL OF SYSTEM VARIABLES SIMULATION CONVERGENCE THE MULTIPLE MINIMA PROBLEM FORCE FIELD PERFORMANCE IN SIMULATIONS CASE STUDY: SILICA SODALITE FOUNDATIONS OF MOLECULAR ORBITAL THEORY QUANTUM MECHANICS AND THE WAVE FUNCTION THE HAMILTONIAN OPERATOR GENERAL FEATURES THE VARIATIONAL PRINCIPLE THE BORN–OPPENHEIMER APPROXIMATION CONSTRUCTION OF TRIAL WAVE FUNCTIONS THE LCAO BASIS SET APPROACH THE SECULAR EQUATION H¨UCKEL THEORY FUNDAMENTAL PRINCIPLES APPLICATION TO THE ALLYL SYSTEM MANY-ELECTRON WAVE FUNCTIONS HARTREE-PRODUCT WAVE FUNCTIONS THE HARTREE HAMILTONIAN ELECTRON SPIN AND ANTISYMMETRY SLATER DETERMINANTS THE HARTREE-FOCK SELF-CONSISTENT FIELD METHOD SEMIEMPIRICAL IMPLEMENTATIONS OF MOLECULAR ORBITAL THEORY SEMIEMPIRICAL PHILOSOPHY CHEMICALLY VIRTUOUS APPROXIMATIONS ANALYTIC DERIVATIVES EXTENDED H¨UCKEL THEORY CNDO FORMALISM INDO FORMALISM INDO AND INDO/S BASIC NDDO FORMALISM MNDO GENERAL PERFORMANCE OVERVIEW OF BASIC NDDO MODELS ENERGETICS GEOMETRIES CHARGE DISTRIBUTIONS ONGOING DEVELOPMENTS IN SEMIEMPIRICAL MO THEORY USE OF SEMIEMPIRICAL PROPERTIES IN SAR D ORBITALS IN NDDO MODELS SRP MODELS LINEAR SCALING OTHER CHANGES IN FUNCTIONAL FORM CASE STUDY: ASYMMETRIC ALKYLATION OF BENZALDEHYDE AB INITIO IMPLEMENTATIONS OF HARTREE–FOCK MOLECULAR ORBITAL THEORY AB INITIO PHILOSOPHY BASIS SETS FUNCTIONAL FORMS CONTRACTED GAUSSIAN FUNCTIONS SINGLE-?, MULTIPLE-?, AND SPLIT-VALENCE POLARIZATION FUNCTIONS DIFFUSE FUNCTIONS THE HF LIMIT EFFECTIVE CORE POTENTIALS SOURCES KEY TECHNICAL AND PRACTICAL POINTS OF HARTREE–FOCK THEORY SCF CONVERGENCE SYMMETRY OPEN-SHELL SYSTEMS EF?CIENCY OF IMPLEMENTATION AND USE GENERAL PERFORMANCE OVERVIEW OF AB INITIO HF THEORY CASE STUDY: POLYMERIZATION OF 4-SUBSTITUTED AROMATIC ENYNES INCLUDING ELECTRON CORRELATION IN MOLECULAR ORBITAL THEORY DYNAMICAL VS NON-DYNAMICAL ELECTRON CORRELATION MULTICON?GURATION SELF-CONSISTENT FIELD THEORY CONCEPTUAL BASIS ACTIVE SPACE SPECI?CATION FULL CON?GURATION INTERACTION CON?GURATION INTERACTION SINGLE-DETERMINANT REFERENCE MULTIREFERENCE PERTURBATION THEORY GENERAL PRINCIPLES SINGLE-REFERENCE FIRST-ORDER PERTURBATION THEORY FOR SOME RELATIVISTIC EFFECTS COUPLED-CLUSTER THEORY PRACTICAL ISSUES IN APPLICATION BASIS SET CONVERGENCE SENSITIVITY TO REFERENCE WAVE FUNCTION PRICE/PERFORMANCE SUMMARY PARAMETERIZED METHODS SCALING CORRELATION ENERGIES EXTRAPOLATION MULTILEVEL METHODS CASE STUDY: ETHYLENEDIONE RADICAL ANION DENSITY FUNCTIONAL THEORY THEORETICAL MOTIVATION PHILOSOPHY EARLY APPROXIMATIONS RIGOROUS FOUNDATION THE HOHENBERG–KOHN EXISTENCE THEOREM THE HOHENBERG–KOHN VARIATIONAL THEOREM KOHN–SHAM SELF-CONSISTENT FIELD METHODOLOGY EXCHANGE-CORRELATION FUNCTIONALS LOCAL DENSITY APPROXIMATION DENSITY GRADIENT AND KINETIC ENERGY DENSITY CORRECTIONS ADIABATIC CONNECTION METHODS SEMIEMPIRICAL DFT ADVANTAGES AND DISADVANTAGES OF DFT COMPARED TO MO THEORY DENSITIES VS WAVE FUNCTIONS COMPUTATIONAL EF?CIENCY LIMITATIONS OF THE KS FORMALISM SYSTEMATIC IMPROVABILITY WORST-CASE SCENARIOS GENERAL PERFORMANCE OVERVIEW OF DFT CASE STUDY: TRANSITION-METAL CATALYZED CARBONYLATION OF METHANOL CHARGE DISTRIBUTION AND SPECTROSCOPIC PROPERTIES PROPERTIES RELATED TO CHARGE DISTRIBUTION ELECTRIC MULTIPOLE MOMENTS MOLECULAR ELECTROSTATIC POTENTIAL PARTIAL ATOMIC CHARGES TOTAL SPIN POLARIZABILITY AND HYPERPOLARIZABILITY ESR HYPER?NE COUPLING CONSTANTS IONIZATION POTENTIALS AND ELECTRON AF?NITIES SPECTROSCOPY OF NUCLEAR MOTION ROTATIONAL VIBRATIONAL NMR SPECTRAL PROPERTIES TECHNICAL ISSUES CHEMICAL SHIFTS AND SPIN–SPIN COUPLING CONSTANTS CASE STUDY: MATRIX ISOLATION OF PER?UORINATED P-BENZYNE THERMODYNAMIC PROPERTIES MICROSCOPIC–MACROSCOPIC CONNECTION ZERO-POINT VIBRATIONAL ENERGY ENSEMBLE PROPERTIES AND BASIC STATISTICAL MECHANICS IDEAL GAS ASSUMPTION SEPARABILITY OF ENERGY COMPONENTS MOLECULAR ELECTRONIC PARTITION FUNCTION MOLECULAR TRANSLATIONAL PARTITION FUNCTION MOLECULAR ROTATIONAL PARTITION FUNCTION MOLECULAR VIBRATIONAL PARTITION FUNCTION STANDARD-STATE HEATS AND FREE ENERGIES OF FORMATION AND REACTION DIRECT COMPUTATION PARAMETRIC IMPROVEMENT ISODESMIC EQUATIONS TECHNICAL CAVEATS SEMIEMPIRICAL HEATS OF FORMATION LOW-FREQUENCY MOTIONS EQUILIBRIUM POPULATIONS OVER MULTIPLE MINIMA STANDARD-STATE CONVERSIONS STANDARD-STATE FREE ENERGIES, EQUILIBRIUM CONSTANTS, AND CONCENTRATIONS CASE STUDY: HEAT OF FORMATION OF H2NOH IMPLICIT MODELS FOR CONDENSED PHASES CONDENSED-PHASE EFFECTS ON STRUCTURE AND REACTIVITY FREE ENERGY OF TRANSFER AND ITS PHYSICAL COMPONENTS SOLVATION AS IT AFFECTS POTENTIAL ENERGY SURFACES ELECTROSTATIC INTERACTIONS WITH A CONTINUUM THE POISSON EQUATION GENERALIZED BORN CONDUCTOR-LIKE SCREENING MODEL CONTINUUM MODELS FOR NON-ELECTROSTATIC INTERACTIONS SPECI?C COMPONENT MODELS ATOMIC SURFACE TENSIONS STRENGTHS AND WEAKNESSES OF CONTINUUM SOLVATION MODELS GENERAL PERFORMANCE FOR SOLVATION FREE ENERGIES PARTITIONING NON-ISOTROPIC MEDIA POTENTIALS OF MEAN FORCE AND SOLVENT STRUCTURE MOLECULAR DYNAMICS WITH IMPLICIT SOLVENT EQUILIBRIUM VS NON-EQUILIBRIUM SOLVATION CASE STUDY: AQUEOUS REDUCTIVE DECHLORINATION OF HEXACHLOROETHANE EXPLICIT MODELS FOR CONDENSED PHASES MOTIVATION COMPUTING FREE-ENERGY DIFFERENCES RAW DIFFERENCES FREE-ENERGY PERTURBATION SLOW GROWTH AND THERMODYNAMIC INTEGRATION FREE-ENERGY CYCLES POTENTIALS OF MEAN FORCE TECHNICAL ISSUES AND ERROR ANALYSIS OTHER THERMODYNAMIC PROPERTIES SOLVENT MODELS CLASSICAL MODELS QUANTAL MODELS RELATIVE MERITS OF EXPLICIT AND IMPLICIT SOLVENT MODELS ANALYSIS OF SOLVATION SHELL STRUCTURE AND ENERGETICS SPEED/EF?CIENCY NON-EQUILIBRIUM SOLVATION MIXED EXPLICIT/IMPLICIT MODELS CASE STUDY: BINDING OF BIOTIN ANALOGS TO AVIDIN HYBRID QUANTAL/CLASSICAL MODELS BOUNDARIES THROUGH SPACE UNPOLARIZED INTERACTIONS POLARIZED QM/UNPOLARIZED MM FULLY POLARIZED INTERACTIONS BOUNDARIES THROUGH BONDS LINEAR COMBINATIONS OF MODEL COMPOUNDS LINK ATOMS FROZEN ORBITALS EMPIRICAL VALENCE BOND METHODS FOLLOWING REACTION PATHS GENERALIZATION TO QM/MM CASE STUDY: CATALYTIC MECHANISM OF YEAST ENOLASE EXCITED ELECTRONIC STATES DETERMINANTAL/CON?GURATIONAL REPRESENTATION OF EXCITED STATES SINGLY EXCITED STATES SCF APPLICABILITY CI SINGLES RYDBERG STATES GENERAL EXCITED STATE METHODS HIGHER ROOTS IN MCSCF AND CI CALCULATIONS PROPAGATOR METHODS AND TIME-DEPENDENT DFT SUM AND PROJECTION METHODS TRANSITION PROBABILITIES SOLVATOCHROMISM ADIABATIC REACTION DYNAMICS REACTION KINETICS AND RATE CONSTANTS UNIMOLECULAR REACTIONS BIMOLECULAR REACTIONS REACTION PATHS AND TRANSITION STATES TRANSITION-STATE THEORY CANONICAL EQUATION VARIATIONAL TRANSITION-STATE THEORY QUANTUM EFFECTS ON THE RATE CONSTANT CONDENSED-PHASE DYNAMICS NON-ADIABATIC DYNAMICS GENERAL SURFACE CROSSINGS MARCUS THEORY CASE STUDY: ISOMERIZATION OF PROPYLENE OXIDE