A CHEMIST'S GUIDE TO DENSITY FUNCTIONAL THEORY

By V. HISIK

CONTENTS PART A THE DEFINITION OF THE MODEL ELEMENTARY QUANTUM CHEMISTRY THE SCHRÖDINGER EQUATION THE VARIATIONAL PRINCIPLE THE HARTREE-FOCK APPROXIMATION THE RESTRICTED AND UNRESTRICTED HARTREE-FOCK MODELS ELECTRON CORRELATION ELECTRON DENSITY AND HOLE FUNCTIONS THE ELECTRON DENSITY THE PAIR DENSITY FERMI AND COULOMB HOLES THE FERMI HOLE THE COULOMB HOLE THE ELECTRON DENSITY AS BASIC VARIABLE: EARLY ATTEMPTS DOES IT MAKE SENSE? THE THOMAS-FERMI MODEL SLATER’S APPROXIMATION OF HARTREE-FOCK EXCHANGE THE HOHENBERG-KOHN THEOREMS THE FIRST HOHENBERG-KOHN THEOREM: PROOF OF EXISTENCE THE SECOND HOHENBERG-KOHN THEOREM: VARIATIONAL PRINCIPLE THE CONSTRAINED-SEARCH APPROACH DO WE KNOW THE GROUND STATE WAVE FUNCTION IN DENSITY FUNCTIONAL THEORY? DISCUSSION THE KOHN-SHAM APPROACH ORBITALS AND THE NON-INTERACTING REFERENCE SYSTEM THE KOHN-SHAM EQUATIONS THE KOHN-SHAM POTENTIAL IS LOCAL THE EXCHANGE-CORRELATION ENERGY IN THE KOHN-SHAM AND HARTREE-FOCK SCHEMES DO THE KOHN-SHAM ORBITALS MEAN ANYTHING? IS THE KOHN-SHAM APPROACH A SINGLE DETERMINANT METHOD? THE UNRESTRICTED KOHN-SHAM FORMALISM ON DEGENERACY, ENSEMBLES AND OTHER ODDITIES EXCITED STATES AND THE MULTIPLET PROBLEM THE QUEST FOR APPROXIMATE EXCHANGE-CORRELATION FUNCTIONALS IS THERE A SYSTEMATIC STRATEGY? THE ADIABATIC CONNECTION FROM HOLES TO FUNCTIONALS THE LOCAL DENSITY AND LOCAL SPIN-DENSITY APPROXIMATIONS THE GENERALIZED GRADIENT APPROXIMATION HYBRID FUNCTIONALS SELF-INTERACTION ASYMPTOTIC BEHAVIOR OF EXCHANGE-CORRELATION POTENTIALS THE BASIC MACHINERY OF DENSITY FUNCTIONAL PROGRAMS INTRODUCTION OF A BASIS: THE LCAO ANSATZ IN THE KOHN-SHAM EQUATIONS BASIS SETS THE CALCULATION OF THE COULOMB TERM NUMERICAL QUADRATURE TECHNIQUES TO HANDLE THE EXCHANGE-CORRELATION POTENTIAL GRID-FREE TECHNIQUES TO HANDLE THE EXCHANGE-CORRELATION POTENTIAL TOWARDS LINEAR SCALING KOHN-SHAM THEORY PART B THE PERFORMANCE OF THE MODEL MOLECULAR STRUCTURES AND VIBRATIONAL FREQUENCIES MOLECULAR STRUCTURES MOLECULAR STRUCTURES OF COVALENTLY BOUND MAIN GROUP ELEMENTS MOLECULAR STRUCTURES OF TRANSITION METAL COMPLEXES VIBRATIONAL FREQUENCIES VIBRATIONAL FREQUENCIES OF MAIN GROUP COMPOUNDS VIBRATIONAL FREQUENCIES OF TRANSITION METAL COMPLEXES RELATIVE ENERGIES AND THERMOCHEMISTRY ATOMIZATION ENERGIES ATOMIC ENERGIES BOND STRENGTHS IN TRANSITION METAL COMPLEXES IONIZATION ENERGIES ELECTRON AFFINITIES ELECTRONIC EXCITATION ENERGIES AND THE SINGLET/TRIPLET SPLITTING IN CARBENES ELECTRIC PROPERTIES POPULATION ANALYSIS DIPOLE MOMENTS POLARIZABILITIES HYPERPOLARIZABILITES INFRARED AND RAMAN INTENSITIES MAGNETIC PROPERTIES THEORETICAL BACKGROUND NMR CHEMICAL SHIFTS NMR NUCLEAR SPIN-SPIN COUPLING CONSTANTS ESR G-TENSORS HYPERFINE COUPLING CONSTANTS SUMMARY HYDROGEN BONDS AND WEAKLY BOUND SYSTEMS THE WATER DIMER – A WORKED EXAMPLE LARGER WATER CLUSTERS OTHER HYDROGEN BONDED SYSTEMS THE DISPERSION ENERGY PROBLEM CHEMICAL REACTIVITY: EXPLORATION OF POTENTIAL ENERGY SURFACES FIRST EXAMPLE: PERICYCLIC REACTIONS ELECTROCYCLIC RING OPENING OF CYCLOBUTENE CYCLOADDITION OF ETHYLENE TO BUTADIENE SECOND EXAMPLE: THE SN2 REACTION AT SATURATED CARBON THIRD EXAMPLE: PROTON TRANSFER AND HYDROGEN ABSTRACTION REACTIONS PROTON TRANSFER IN MALONALDEHYDE ENOL A HYDROGEN ABSTRACTION REACTION FOURTH EXAMPLE: H2 ACTIVATION BY FEO+ IN THE GAS PHASE