1. Introduction.- 2. A brief comment on the development of the theory of the chemical bond.- 3. The time-independent Schrödinger equation.- 3.1 Introduction of the equation.- 3.2 Formulation of the Schrödinger equation for simple systems.- 3.2.1 A particle in a one-dimensional potential box.- 3.2.2 The harmonic oscillator.- 3.2.3 The hydrogen atom.- 3.2.4 The hydrogen molecular ion, H2+.- 3.3 Examples of the solution of the Schrödinger equation.- 3.3.1 The free particle.- 3.3.2 A particle in a potential box; the solution and its consequences.- 3.3.3 The harmonic oscillator.- 3.3.4 The rigid rotator.- 3.3.5 The hydrogen atom.- References.- 4. Mathematics and logic of quantum mechanics.- 4.1 Linear operators and their properties.- 4.2 Axiomatic foundation of quantum mechanics.- 4.3 Consequences of the axiomatic system.- 4.4 Constants of motion. The Pauli principle.- 4.5 Matrix representation of operators and operations with matrices.- 4.6 Approximate solution of the Schrödinger equation: variation and perturbation methods.- References.- 5. Basic approximations in the theory of the chemical bond.- 5.1 Introductory comments.- 5.2 Neglecting of non-electrostatic interactions.- 5.3 The Born-Oppenheimer and adiabatic approximations.- 5.4 The method of configuration interaction.- 5.5 The independent electron model (one-electron approximation).- 5.6 The method of molecular orbitals as linear combinations of atomic orbitals.- References.- 6. Symmetry in quantum chemistry.- 6.1 Introduction.- 6.2 Symmetry transformations of the Hamiltonian.- 6.3 The principal symmetry groups and their notation.- 6.4 Matrix representation of symmetry groups.- 6.5 Selection rules for matrix elements.- 6.6 Symmetry and hybrid orbitals.- 6.7 Spin and spatial symmetry of many-electron systems.- 6.8 Perturbation treatment for symmetrical systems.- References.- 7. Atomic orbitals (AO) and molecular orbitals (MO).- 7.1 The significance of hydrogen type orbitals; atomic orbitals.- 7.2 Hybridization.- 7.3 Molecular orbitals.- References.- 8. Many-electron atoms.- 8.1 The one-electron approximation and the periodic system of the elements.- 8.2 The total angular momentum.- References.- 9. Diatomic molecules.- 9.1 Introductory comments; the hydrogen molecular ion, H2+.- 9.2 The H2 molecule.- 9.3 Calculation of the molecular integrals.- 9.4 General diatomic molecules and correlation diagrams.- References.- 10. Calculation methods in the theory of the chemical bond.- 10.1 Introductory remarks.- 10.2 All-valence electron MO-LCAO methods.- 10.2.1 Methods explicitly considering electron repulsion.- 10.2.2 Methods using an effective Hamiltonian.- 10.3 ?-Electron theory.- 10.3.1 ? —?-Electron separation.- 10.3.2 The Pople version of the SCF method for ?-electron systems.- 10.3.3 The Pariser-Parr method of limited configuration interaction.- 10.3.4 A survey of semiempirical ?-electron methods.- 10.3.5 Very simple ?-electron version of the MO method.- 10.3.6 Perturbation methods within the framework of the simple MO method.- 10.4 The FE-MO method.- 10.5 Valence bond theory (VB method).- 10.6 The crystal field and ligand field theories.- 10.6.1 Introductory comments.- 10.6.2 The electrostatic model (crystal field).- 10.6.3 Ligand field theory.- References.- 11. Use of the solution to the Schrödinger equation.- 11.1 Quantities related to the molecular energy (the total electron energy, ionization potential, electron affinity, excitation energy).- 11.2 Quantities derived from the wave function.- 11.2.1 Introductory comments.- 11.2.2 Density matrix.- 11.2.3 Localized orbitals.- 11.2.4 Electron distribution in molecules.- 11.2.5 Dipole moment.- 11.2.6 Nodal planes of molecular orbitals: the Woodward-Hoffmann rules.- References.- 12. Examples of the study of polyatomic molecules.- 12.1 Introductory comments.- 12.2 Inorganic compounds.- 12.3 Organic compounds.- 12.4 Examples of systems studied in biochemistry.- References.- 13. Molecular spectroscopy.- 13.1 Phenomenological description.- 13.1.1 Introductory comments.- 13.1.2 Units and the spectral regions.- 13.1.3 Absorption and emission spectra, the population of excited states.- 13.2 Excitation within a single electronic level.- 13.2.1 Introductory comments on radiofrequency spectroscopy.- 13.2.2 Nuclear quadrupole resonance (NQR).- 13.2.3 The elementary theory of magnetic resonance.- 13.2.4 Nuclear magnetic resonance (NMR).- 13.2.5 Electron spin resonance (ESR).- 13.2.6 Pure rotational spectra.- 13.2.7 Vibrational spectroscopy.- 13.2.8 Raman spectroscopy.- 13.3 Excitation within the framework of several electronic levels.- 13.3.1 Absorption spectra in the ultraviolet and visible regions.- 13.3.2 Luminescence phenomena (fluorescence, phosphorescence).- 13.3.3 Photochemistry.- References.- 14. Magnetic properties of molecules.- References.- 15. Thermochemical properties and molecular stability.- 15.1 Heats of formation and atomization.- 15.2 Delocalization energies of conjugated compounds.- 15.3 Stabilization of coordination compounds.- Reference.- 16. Chemical reactivity.- 16.1 Introductory comments.- 16.2 Empirical approach.- 16.3 Theoretical approach.- 16.3.1 Qualitative considerations.- 16.3.2 Quantitative considerations. Calculations of absolute values of equilibrium and rate constants.- 16.4 Calculations of relative equilibrium and rate constants.- 16.5 Compromise approach: the quantum chemical treatment.- 16.5.1 Reactions of conjugated compounds.- 16.5.2 Substitution reactions of complexes of the transition elements.- References.- 17. Weak interactions.- 17.1 Introduction.- 17.2 van der Waals interaction between a pair of linear oscillators.- 17.3 Various means of calculating intermolecular interaction energies.- 17.4 Application of weak interactions from the point of view of physical chemistry.- References.
