MOLECULAR ENERGY METHODS
CONTENTS PART I FOUNDATIONS OF QUANTUM MECHANICS SOURCES EXPERIMENTAL ORIGINS AND OLD QUANTUM THEORY CLASSICAL–MECHANICAL DESCRIPTION AND A NEED FOR ITS REVISION IN GENERALIZED MECHANICS IMPLICATIONS FROM THE PARTICLE DIFFRACTION EXPERIMENT PARTICLE SPIN BIRTH OF MODERN QUANTUM MECHANICS REFERENCES MATHEMATICAL APPARATUS 2 1 GEOMETRICAL ANALOGIES 2 2 DIRAC’S VECTOR NOTATION AND DELTA FUNCTION 2 3 LINEAR OPERATORS AND THEIR ADJOINTS 2 4 BASIS SET REPRESENTATIONS OF VECTORS AND OPERATORS 2 5 EIGENVALUE PROBLEM OF LINEAR HERMITIAN OPERATORS 2 6 POSITION AND MOMENTUM REPRESENTATIONS 2 7 ENERGY REPRESENTATION AND UNITARY TRANSFORMATIONS 2 8 FUNCTIONAL DERIVATIVES BASIC CONCEPTS AND AXIOMS 3 1 N-ELECTRON WAVE FUNCTIONS AND THEIR PROBABILISTIC INTERPRETATION 3 2 SUPERPOSITION PRINCIPLE, EXPECTATION VALUES, AND INDISTINGUISHABILITY OF IDENTICAL PARTICLES 3 3 RESULTS OF PHYSICAL MEASUREMENTS 3 3 1 CLASSICAL OBSERVABLES IN POSITION AND MOMENTUM REPRESENTATIONS 3 3 2 POSSIBLE OUTCOMES OF A SINGLE MEASUREMENT 3 3 3 EXPECTATION VALUE OF REPEATED MEASUREMENTS AND HEISENBERG UNCERTAINTY PRINCIPLE 3 3 4 ENSEMBLE AVERAGES IN MIXED STATES 3 4 ANGULAR MOMENTUM AND SPIN OPERATORS 3 5 PICTURES OF TIME EVOLUTION 3 6 SCHRO¨DINGER PICTURE: DYNAMICS OF WAVE FUNCTIONS AND DENSITY OPERATORS 3 6 1 ENERGY REPRESENTATION AND STATIONARY STATES 3 6 2 TIME DEPENDENCE OF EXPECTATION VALUES AND EHRENFEST PRINCIPLE 3 6 3 PROBABILITY CURRENT AND CONTINUITY EQUATION 3 7 HEISENBERG AND INTERACTION PICTURES OF QUANTUM DYNAMICS HYDROGEN-LIKE ATOM 4 1 SEPARATION OF HAMILTONIAN AND CENTER-OF-MASS MOTION 4 2 FREE MOTION IN SPHERICAL COORDINATES 4 3 EIGENFUNCTIONS OF ANGULAR MOMENTUM OPERATORS 4 4 RADIAL EIGENFUNCTIONS AND ENERGY LEVELS 4 5 ORBITAL DEGENERACY AND ELECTRON DISTRIBUTION 4 6 ATOMIC UNITS PART II THEORIES OF ELECTRONIC STRUCTURE APPROXIMATING MOLECULAR SCHRO¨DINGER EQUATION 5 1 RUDIMENTS OF PERTURBATIONAL AND VARIATIONAL APPROACHES 5 1 1 PERTURBATION THEORY 5 1 2 VARIATIONAL METHOD 5 2 ADIABATIC SEPARATION OF ELECTRONIC AND NUCLEAR MOTIONS 5 3 ORBITAL APPROXIMATION OF ELECTRONIC WAVE FUNCTIONS 5 4 MATRIX ELEMENTS OF ELECTRONIC HAMILTONIAN IN ORBITAL APPROXIMATION 5 5 EXAMPLE: HELIUM ATOM 5 5 1 PERTURBATION APPROXIMATION 5 5 2 VARIATIONAL ESTIMATES 5 6 IDEA OF A PSEUDOPOTENTIAL WAVE FUNCTION METHODS 6 1 SELF-CONSISTENT FIELD THEORIES 6 1 1 HARTREE METHOD 6 1 2 HARTREE–FOCK THEORY 6 1 3 TRANSITION-STATE CONCEPT 6 1 4 ANALYTICAL REALIZATION OF HALL AND ROOTHAAN 6 1 5 LOCAL PSEUDOPOTENTIAL 6 2 BEYOND HF THEORY: ELECTRON COULOMB CORRELATION 6 2 1 ERRORS IN SCF MO CALCULATIONS 6 2 2 STATIC AND DYNAMIC CORRELATION 6 2 3 CORRELATION HOLES 6 3 CON?GURATION INTERACTION TECHNIQUES 6 3 1 SPECIAL VARIANTS OF LIMITED CI 6 3 2 PERTURBATIONAL THEORY OF MØLLER AND PLESSET 6 3 3 DENSITY MATRICES AND NATURAL ORBITALS 6 4 ELECTRON PAIR THEORIES 6 4 1 ELECTRON PAIRS ON STRONGLY ORTHOGONAL GEMINALS 6 4 2 INDEPENDENT ELECTRON PAIR APPROXIMATION 6 4 3 COUPLED ELECTRON PAIR APPROXIMATIONS 6 5 SECOND-QUANTIZATION REPRESENTATION 6 5 1 FOCK SPACE AND CREATION/ANNIHILATION OPERATORS 6 5 2 CLUSTER EXPANSION OF ELECTRONIC STATES 6 5 3 COUPLED CLUSTER METHOD 6 6 ELEMENTS OF VALENCE BOND APPROACH 6 6 1 ORIGINS OF VB THEORY 6 6 2 BOND ENERGIES AND IONIC STRUCTURES 6 6 3 COMPARISON WITH MO THEORY AND AO EXPANSION THEOREM 6 6 4 SEMILOCALIZED AO AND EXTENSION TO POLYATOMIC SYSTEMS 6 6 5 AB INITIO VB CALCULATIONS DENSITY FUNCTIONAL THEORY 7 1 HOHENBERG–KOHN THEORY 7 1 1 FIRST HK THEOREM 7 1 2 SECOND HK THEOREM 7 1 3 RE?NEMENTS 7 1 4 FINITE TEMPERATURE AND OPEN SYSTEM EXTENSIONS 7 2 FUNCTIONALS FROM THE UNIFORM SCALING OF THE ELECTRON DENSITY 7 3 KOHN–SHAM THEORY 7 3 1 ORBITAL APPROXIMATION AND ENERGY EXPRESSION 7 3 2 ADIABATIC CONNECTION 7 3 3 KOHN–SHAM–MERMIN THEORY 7 3 4 DONOR–ACCEPTOR COMPLEXES 7 3 5 ZERO-TEMPERATURE LIMIT 7 3 6 PHYSICAL INTERPRETATION OF KS EIGENVALUES 7 3 7 CHEMICAL REACTIVITY CONCEPTS 7 4 LOCAL DENSITY AND GRADIENT APPROXIMATIONS ORBITAL-DEPENDENT FUNCTIONALS 7 5 1 OPTIMIZED POTENTIAL METHOD 7 5 2 DENSITY-FUNCTIONAL PERTURBATION THEORY 7 5 3 AB INITIO DFT RUDIMENTS OF ENSEMBLE THEORY FOR EXCITED STATES DENSITY-MATRIX FUNCTIONAL THEORY WEAK MOLECULAR INTERACTIONS IN DFT TIME-DEPENDENT DFT 7 9 1 EXTENSIONS OF HK THEOREMS INTO TIME DOMAIN 7 9 2 LINEAR-RESPONSE FUNCTIONS 7 9 3 EXCITATION ENERGIES 7 9 4 VAN DER WAALS INTERACTIONS REVISITED 7 10 CONCLUSION PART III INSIGHTS FROM INFORMATION THEORY ELEMENTS OF INFORMATION THEORY INTRODUCTION SHANNON AND FISHER MEASURES OF INFORMATION ENTROPY DE?CIENCY DEPENDENT PROBABILITY DISTRIBUTIONS INFORMATION PROPAGATION IN COMMUNICATION SYSTEMS SEVERAL PROBABILITY SCHEMES VARIATIONAL PRINCIPLES SCHRO¨DINGER EQUATIONS FROM INFORMATION PRINCIPLES FISHER-INFORMATION DENSITY AND ITS CURRENT CONTINUITY EQUATIONS AND INFORMATION SOURCE PHYSICAL INFORMATION PRINCIPLES GENERATING SCHRO¨DINGER EQUATIONS INFORMATION PRINCIPLE FOR ADIABATIC APPROXIMATION KOHN–SHAM EQUATIONS FROM INFORMATION RULE ELECTRON DENSITY AS CARRIER OF INFORMATION 10 1 LOCAL ENTROPY-DE?CIENCY (SURPRISAL) ANALYSIS 10 2 DISPLACEMENTS IN ENTROPY DENSITY 10 3 ILLUSTRATIVE APPLICATION TO PROPELLANES 10 4 NONADDITIVE INFORMATION MEASURES 10 5 ELECTRON LOCALIZATION FUNCTION 10 6 CONTRA-GRADIENCE CRITERION FOR LOCATING BONDING REGIONS IN MOLECULES 10 7 ILLUSTRATIVE APPLICATIONS OF CG PROBE BONDED ATOMS FROM INFORMATION THEORY CHEMICAL CONCEPTS STOCKHOLDER ATOMS IN MOLECULES INFORMATION THEORETIC JUSTI?CATION REPRESENTATIVE INFORMATION DENSITIES CHARGE SENSITIVITIES OF STOCKHOLDER AIM ORBITAL COMMUNICATION THEORY OF THE CHEMICAL BOND MOLECULAR COMMUNICATION SYSTEMS INFORMATION CHANNELS IN ATOMIC ORBITAL RESOLUTION ENTROPY/INFORMATION DESCRIPTORS OF BOND COMPONENTS TWO-ORBITAL MODEL OF CHEMICAL BOND ADDITIVE AND NONADDITIVE COMPONENTS OF INFORMATION CHANNELS QUANTUM CONDITIONING OF ORBITAL SUBSPACES AND CONDITIONAL AO EVENTS FLEXIBLE INPUT APPROACH LOCALIZED BONDS IN DIATOMIC FRAGMENTS MANY-ORBITAL EFFECTS 12 10 THROUGH-SPACE AND THROUGH-BRIDGE BOND COMPONENTS 12 10 1 BOND PROJECTIONS AND DENSITY MATRIX 12 10 2 THROUGH-SPACE AND THROUGH-BRIDGE BOND ORDERS 12 10 3 CONDITIONAL PROBABILITIES FOR INFORMATION PROPAGATION 12 10 4 ILLUSTRATIVE APPLICATION TO P-ELECTRON SYSTEMS IN BENZENE AND BUTADIENE 12 10 5 INDIRECT ORBITAL COMMUNICATIONS 12 10 6 QUALITATIVE MODEL OF BONDS IN PROPELLANES 12 11 AMPLITUDE CHANNELS AND INTERFERENCE OF ORBITAL COMMUNICATIONS 12 11 1 PROBABILITY SCATTERING STATES AND STATIONARY COMMUNICATION MODES 12 11 2 CASCADE PROBABILITY SCATTERINGS AND THEIR INTERFERENCE 12 11 3 IMPLICIT DEPENDENCY ORIGINS OF THROUGH-BRIDGE INTERACTIONS 12 12 CONCLUSION PART IV CHEMICAL CONCEPTS FOR MOLECULAR STRUCTURE AND REACTIVITY ALTERNATIVE PERSPECTIVES IN CHEMICAL THEORIES 13 1 SURVEY OF REACTIVITY PHENOMENA AND NEED FOR CONCEPTUAL APPROACHES 13 2 CHEMICAL UNDERSTANDING OF MOLECULAR PROCESSES 13 3 HORIZONTAL AND VERTICAL DISPLACEMENTS OF MOLECULAR ELECTRONIC STRUCTURE 13 4 CONSTRAINED EQUILIBRIA IN MOLECULAR SUBSYSTEMS AND CHARGE SENSITIVITIES OF REACTANTS 13 5 TRANSFORMATIONS OF PERTURBATIONS INTO RESPONSES 13 6 ILLUSTRATIVE DESCRIPTION OF BIMOLECULAR REACTIVE SYSTEMS 13 6 1 EQUILIBRIA AND CHARGE SENSITIVITIES OF REACTANTS 13 6 2 IN SITU QUANTITIES IN DONOR–ACCEPTOR SYSTEMS 13 6 3 IMPLICATIONS OF EQUILIBRIUM AND STABILITY CRITERIA COUPLING BETWEEN ELECTRONIC AND GEOMETRICAL STRUCTURES 14 1 ELECTRONIC–GEOMETRIC REPRESENTATIONS OF MOLECULAR STATES 14 2 PERTURBATION–RESPONSE RELATIONS IN GEOMETRIC REPRESENTATIONS 14 3 DESCRIPTORS OF ELECTRONIC–GEOMETRIC INTERACTION 14 4 COMPLIANCE FORMALISM AND MINIMUM-ENERGY COORDINATES 14 5 ILLUSTRATIVE APPLICATION TO CONFORMATIONAL CHANGES 14 6 USE OF COMPLIANT CONSTANTS AS REACTIVITY INDICES 14 7 MODELING COUPLINGS IN COLLINEAR ATOM–DIATOM COLLISIONS 14 7 1 DERIVATIVE DESCRIPTORS OF COLLINEAR REACTIVE SYSTEM 14 7 2 MODELING ELECTRONIC AND NUCLEAR FUKUI FUNCTIONS 14 7 3 SENSITIVITIES FOR COLLECTIVE CHARGE DISPLACEMENTS 14 7 4 COUPLINGS ALONG THE MINIMUM-ENERGY PATH 14 8 CONCLUSION QUALITATIVE APPROACHES TO REACTIVITY PHENOMENA 15 1 INTRODUCTION 15 2 INFORMATION PROBES OF ELEMENTARY REACTION MECHANISMS 15 3 CHEMICAL REACTIVITY INDICES 15 4 INTERNAL AND EXTERNAL EIGENVALUE PROBLEMS 15 5 COMPLEMENTARY DECOUPLING SCHEMES OF MOLECULAR HARDNESS TENSOR 15 6 HARDNESS/SOFTNESS PRINCIPLES IN CHEMISTRY 15 7 CONCLUSION