Book contents
- Quantum Mechanics in Nanoscience and Engineering
- Additional material
- Quantum Mechanics in Nanoscience and Engineering
- Copyright page
- Contents
- Preface: Who Can Benefit from Reading This Book?
- 1 Motivation
- 2 The State of a System
- 3 Observables and Operators
- 4 The Schrödinger Equation
- 5 Energy Quantization
- 6 Wave Function Penetration, Tunneling, and Quantum Wells
- 7 The Continuous Spectrum and Scattering States
- 8 Mechanical Vibrations and the Harmonic Oscillator Model
- 9 Two-Body Rotation and Angular Momentum
- 10 The Hydrogen-Like Atom
- 11 The Postulates of Quantum Mechanics
- 12 Approximation Methods
- 13 Many-Electron Systems
- 14 Many-Atom Systems
- 15 Quantum Dynamics
- 16 Incoherent States
- 17 Quantum Rate Processes
- 18 Thermal Rates in a Bosonic Environment
- 19 Open Quantum Systems
- 20 Open Many-Fermion Systems
- Index
- References
14 - Many-Atom Systems
Published online by Cambridge University Press: 11 May 2023
- Quantum Mechanics in Nanoscience and Engineering
- Additional material
- Quantum Mechanics in Nanoscience and Engineering
- Copyright page
- Contents
- Preface: Who Can Benefit from Reading This Book?
- 1 Motivation
- 2 The State of a System
- 3 Observables and Operators
- 4 The Schrödinger Equation
- 5 Energy Quantization
- 6 Wave Function Penetration, Tunneling, and Quantum Wells
- 7 The Continuous Spectrum and Scattering States
- 8 Mechanical Vibrations and the Harmonic Oscillator Model
- 9 Two-Body Rotation and Angular Momentum
- 10 The Hydrogen-Like Atom
- 11 The Postulates of Quantum Mechanics
- 12 Approximation Methods
- 13 Many-Electron Systems
- 14 Many-Atom Systems
- 15 Quantum Dynamics
- 16 Incoherent States
- 17 Quantum Rate Processes
- 18 Thermal Rates in a Bosonic Environment
- 19 Open Quantum Systems
- 20 Open Many-Fermion Systems
- Index
- References
Summary
The theory of chemical bond formation in molecules and extended crystals is outlined. We start from the Born–Oppenheimer approximation, which associates the forces experienced by nuclei to the quantum electronic state. The Schrödinger equation for diatomic molecules reveals the formation of stable molecules when electrons are occupying “bonding” molecular orbitals. These are linear combinations of atomic orbitals (LCAO), in which the nuclei “share” electrons that effectively mask the electrostatic repulsion between them. The formation of effective LCAOs relies on compatibility in symmetry and energy of the underlying atomic orbitals. This is ubiquitously found in covalently bounded molecules, including conjugated polyatomic molecules. In the absence of effective LCAO, ionic bonds can be formed by charge transfer between atomic orbitals. In periodic lattices, effective LCAOs result in broad energy bands, which increase electrical conductivity. Conductor-to-insulator transition in response to the type of LCAO in the underlying material is demonstrated for a model system.
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- Quantum Mechanics in Nanoscience and Engineering , pp. 237 - 285Publisher: Cambridge University PressPrint publication year: 2023