A TREATISE ON DIFFERENTIAL EQUATIONS AND FINITE DIFFERENCE METHODS
CONTENTS PRINCIPLES THE ORBITAL MODEL MATHEMATICAL METHODS DIRAC NOTATION NORMALIZATION ORTHOGONALITY SET OF ORTHONORMAL FUNCTIONS LINEAR INDEPENDENCE BASIS SET LINEAR OPERATORS SUM AND PRODUCT OF OPERATORS EIGENVALUE EQUATION HERMITIAN OPERATORS ANTI-HERMITIAN OPERATORS EXPANSION THEOREM FROM OPERATORS TO MATRICES PROPERTIES OF THE OPERATOR R TRANSFORMATIONS IN COORDINATE SPACE BASIC POSTULATES CORRESPONDENCE BETWEEN PHYSICAL OBSERVABLES AND HERMITIAN OPERATORS STATE FUNCTION AND AVERAGE VALUE OF OBSERVABLES TIME EVOLUTION OF THE STATE FUNCTION PHYSICAL INTERPRETATION OF THE BASIC PRINCIPLES MATRICES DE?NITIONS AND ELEMENTARY PROPERTIES PROPERTIES OF DETERMINANTS SPECIAL MATRICES THE MATRIX EIGENVALUE PROBLEM ATOMIC ORBITALS ATOMIC ORBITALS AS A BASIS FOR MOLECULAR CALCULATIONS HYDROGEN-LIKE ATOMIC ORBITALS CHOICE OF AN APPROPRIATE COORDINATE SYSTEM SOLUTION OF THE RADIAL EQUATION SOLUTION OF THE ANGULAR EQUATION SOME PROPERTIES OF THE HYDROGEN-LIKE ATOMIC ORBITALS REAL FORM OF THE ATOMIC ORBITALS SLATER-TYPE ORBITALS GAUSSIAN-TYPE ORBITALS SPHERICAL GAUSSIANS CARTESIAN GAUSSIANS THE VARIATION METHOD VARIATIONAL PRINCIPLES NONLINEAR PARAMETERS GROUND STATE OF THE HYDROGENIC SYSTEM THE FIRST EXCITED STATE OF SPHERICAL SYMMETRY OF THE HYDROGENIC SYSTEM THE FIRST EXCITED 2P STATE OF THE HYDROGENIC SYSTEM THE GROUND STATE OF THE HE-LIKE SYSTEM LINEAR PARAMETERS AND THE RITZ METHOD APPLICATIONS OF THE RITZ METHOD THE FIRST 1S2S EXCITED STATE OF THE HE-LIKE ATOM THE FIRST 1S2P STATE OF THE HE-LIKE ATOM SPIN THE ZEEMAN EFFECT THE PAULI EQUATIONS FOR ONE-ELECTRON SPIN THE DIRAC FORMULA FOR N-ELECTRON SPIN ANTISYMMETRY OF MANY-ELECTRON WAVEFUNCTIONS ANTISYMMETRY REQUIREMENT AND THE PAULI PRINCIPLE SLATER DETERMINANTS DISTRIBUTION FUNCTIONS ONE- AND TWO-ELECTRON DISTRIBUTION FUNCTIONS ELECTRON AND SPIN DENSITIES AVERAGE VALUES OF OPERATORS SELF-CONSISTENT-?ELD CALCULATIONS AND MODEL HAMILTONIANS ELEMENTS OF HARTREE–FOCK THEORY FOR CLOSED SHELLS THE FOCK–DIRAC DENSITY MATRIX ELECTRONIC ENERGY EXPRESSION ROOTHAAN FORMULATION OF THE LCAO–MO–SCF EQUATIONS MOLECULAR SELF-CONSISTENT-?ELD CALCULATIONS H€UCKEL THEORY ETHYLENE (N ¼ 2) THE ALLYL RADICAL (N ¼ 3) BUTADIENE (N ¼ 4) CYCLOBUTADIENE (N ¼ 4) HEXATRIENE (N ¼ 6) BENZENE (N ¼ 6) A MODEL FOR THE ONE-DIMENSIONAL CRYSTAL POST-HARTREE–FOCK METHODS CON?GURATION INTERACTION MULTICON?GURATION SELF-CONSISTENT-?ELD MØLLER–PLESSET THEORY THE MP2-R12 METHOD THE CC-R12 METHOD DENSITY FUNCTIONAL THEORY VALENCE BOND THEORY AND THE CHEMICAL BOND THE BORN–OPPENHEIMER APPROXIMATION MOLECULAR ORBITAL THEORY HEITLER–LONDON THEORY THE ORIGIN OF THE CHEMICAL BOND SCHEMATIZATION OF VALENCE BOND THEORY SCHEMATIZATION OF MOLECULAR ORBITAL THEORY ADVANTAGES OF THE VALENCE BOND METHOD DISADVANTAGES OF THE VALENCE BOND METHOD CONSTRUCTION OF VALENCE BOND STRUCTURES HYBRIDIZATION AND MOLECULAR STRUCTURE THE H2O MOLECULE PROPERTIES OF HYBRIDIZATION PAULING’S FORMULA FOR CONJUGATED AND AROMATIC HYDROCARBONS ETHYLENE (ONE P-BOND, N ¼ 1) CYCLOBUTADIENE (N ¼ 2) BUTADIENE (OPEN CHAIN, N ¼ 2) BENZENE (N ¼ 3) ELEMENTS OF RAYLEIGH–SCHROEDINGER PERTURBATION THEORY RAYLEIGH–SCHROEDINGER PERTURBATION EQUATIONS UP TO THIRD ORDER FIRST-ORDER THEORY SECOND-ORDER THEORY APPROXIMATE E2 CALCULATIONS: THE HYLLERAAS FUNCTIONAL LINEAR PSEUDOSTATES AND MOLECULAR PROPERTIES SINGLE PSEUDOSTATE N-TERM APPROXIMATION QUANTUM THEORY OF MAGNETIC SUSCEPTIBILITIES DIAMAGNETIC SUSCEPTIBILITIES PARAMAGNETIC SUSCEPTIBILITIES APPENDIX: EVALUATION OF M AND