THE MODIFICATION OF CNDO-INDO PROGRAM & ITS APPLICATION TO STUDY OF SUBSTITUENTS ON ELECTRON DENSITIES OF ACETYLENES & ETHYLENES

By CHARLES GONZALEZ

CONTENTS I LECTURES BASIC QUANTUM MECHANICS OPERATORS IN QUANTUM MECHANICS EIGENFUNCTIONS AND EIGENVALUES COMMUTATORS CONSTRUCTION OF OPERATORS POSTULATES OF QUANTUM MECHANICS POSTULATES SEPARATION OF THE SCHR¨ODINGER EQUATION HYDROGEN ATOM ANGULAR MOMENTUM OPERATORS DE?NITIONS RADIAL FUNCTION OF HYDROGEN ATOM BASIC MATHEMATICAL REVIEW LINEAR ALGEBRA VECTOR SPACES OPERATORS MATRICES DETERMINANTS DIRAC NOTATION CHANGE OF BASIS EIGENVALUE PROBLEM FUNCTIONS OF MATRICES PERTURBATION THEORY DERIVATION ENERGY CORRECTIONS CORRECTIONS ?(1) N AND E(2) N SUMMARY THE VARIATION METHOD THE VARIATION PRINCIPLE LINEAR VARIATIONS MOLECULAR HAMILTONIAN TIME-INDEPENDENT NON-RELATIVISTIC SCHR¨ODINGER EQUATION BORN–OPPENHEIMER APPROXIMATION PART I PART II PART III STATIONARY POINTS INTERNAL COORDINATES Z-MATRIX TWO-ELECTRON SYSTEMS AND SPIN HELIUM ATOM: GROUND STATE BASICS ORBITAL MODEL FORMAL SEPARATION VARIATIONAL CALCULATIONS OVERVIEW OF GROUND STATE ENERGIES ELECTRON SPIN ELECTRONS ARE INDISTINGUISHABLE PAULI PRINCIPLE HARTREE–FOCK APPROXIMATION SLATER-DETERMINANT ENERGY EXPECTATION VALUE FOR SLATER DETERMINANTS UNITARY TRANSFORMATION OF SPIN ORBITALS HARTREE–FOCK METHOD SOLUTION OF THE HARTREE-FOCK EQUATIONS ORBITAL ENERGIES AND KOOPMANS’ THEOREM BRILLOUIN’S THEOREM MOLECULAR ORBITAL THEORY LCAO-ANSATZ ROOTHAAN-HALL EQUATIONS UNRESTRICTED OPEN-SHELL HARTREE–FOCK SPIN CONTAMINATION POPLE–NESBET EQUATIONS CORRELATION ENERGY MATRIXELEMENTS CON?GURATION INTERACTION METHOD (CI) DYNAMICAL AND NON-DYNAMICAL ELECTRON CORRELATION COUPLED CLUSTER APPROACHES SIZE CONSISTENCY COUPLED CLUSTER METHODS APPROXIMATE COUPLED CLUSTER METHODS ACCURACY IN COUPLED CLUSTER CALCULATIONS MØLLER–PLESSET PERTURBATION THEORY ELECTRON CORRELATION WITH PERTURBATION THEORY CONVERGENCE OF MP SERIES THE DISSOCIATION PROBLEM 10 DENSITY FUNCTIONAL THEORY: PART I 10 1 BASICS 10 1 1 HOHENBERG–KOHN THEOREMS 10 1 2 KOHN–SHAM THEORY 11 DENSITY FUNCTIONAL THEORY: PART II 11 1 EXCHANGE AND CORRELATION ENERGY 11 1 1 DENSITY OPERATORS 11 1 2 ELECTRON-ELECTRON INTERACTION 11 1 3 ONE-DETERMINANT WAVE FUNCTIONS 11 1 4 EXCHANGE AND CORRELATION ENERGY IN THE KOHN–SHAM METHOD 12 DENSITY FUNCTIONAL THEORY: PART III LOCAL DENSITY APPROXIMATION 12 2 GRADIENT CORRECTIONS 12 2 1 EXCHANGE FUNCTIONAL OF BECKE (1988) 12 2 2 CORRELATION FUNCTIONALS OF PERDEW ET AL 12 2 3 LEE-YANG-PARR (LYP) CORRELATION FUNCTIONAL (1988) HYBRID FUNCTIONALS 12 4 BASIS SETS 12 5 MODEL CALCULATIONS 12 6 COULOMB ENERGY 12 6 1 RESOLUTION OF IDENTITY METHOD 12 6 2 LOCAL EXPANSION OF DENSITY 12 7 NUMERICAL INTEGRATION 12 7 1 VORONOI POLYHEDRA 12 7 2 RADIAL INTEGRATION 12 7 3 ANGULAR INTEGRATION 13 MOLECULAR PROPERTIES 13 1 WAVEFUNCTION ANALYSIS 13 1 1 BASISFUNCTION BASED POPULATION ANALYSIS 13 1 2 ELECTROSTATIC POTENTIAL DERIVED CHARGES 13 1 3 DENSITY BASED CHARGES 13 2 RESPONSE PROPERTIES 13 2 1 DERIVATIVE TECHNIQUES 14 NMR CHEMICAL SHIELDING 14 1 GENERAL 14 2 CHEMICAL SHIFTS 14 3 LINEAR RESPONSE FOR HARTREE–FOCK 14 3 1 CALCULATION OF RESPONSE ORBITALS