Elements of Quantum Chemistry

ISBN-13: 9781461339236 / Angielski / Miękka / 2013 / 462 str.

Rudolf Zahradnik; Rudolf Polak

Opis

The post-war generation of chemists learned to handle a blow pipe at the university as thoroughly as modern chemistry students learn to write computer programmes. Even after World War II the rule of three was considered to be sufficient mathematical knowledge for chemists and the short course of "higher mathematics" at technical universities was the test most feared by chemistry students. However, even then some en- visaged the theoretical derivation of information on the properties of molecules from knowledge of the bonding of the component atoms. During the last quarter of this century, amazing changes have occurred in chemistry, some of them almost incredible. Dirac's famous clairvoyant statement* has been partially realized. Incorporation of quantum mechanics into chemistry encountered numerous difficulties. After all, the reserve of experimental chemists is not surprising. For decades the hydrogen and helium atoms and the hydrogen molecule belonged among the systems most frequently investigated by theoreti- cians. Later these systems were supplemented by ethylene and benzene. The authors of this book can therefore recall with understanding the words of the late Professor Lukes: "Well, when they succeed in computing a molecule of some alkaloid by those methods of yours ... ." Unfortunately, the calculations on calycanin were not completed before his death. Now there is no need to convince even the members of the older generation of the usefulness of quantum chemistry for chemists. Even the most conservative were convinced after the introduction of the W ood- ward-Hoffmann rules.

Spis treści

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.