# The Theories of Chemistry

## 1st Edition

**Authors:**Jan C.A. Boeyens

**eBook ISBN:**9780080519043

**Imprint:**Elsevier Science

**Published Date:**24th November 2003

**Page Count:**570

## Description

Theories of Chemistry reviews the theories that underpin chemistry, but yet are not traditionally recognized as such, being normally considered as part of physics. Based on the argument that the needs of chemistry are distinctive, a mathematical structure of topics such as quantum mechanics, relativity theory, thermodynamics and statistical mechanics, suiting the needs of chemistry, is outlined. The subject matter is arranged in a sequence that reveals the foundations of chemistry. Starting from the mathematical basis, the sequence runs through the general concepts (mechanics and wave formalism) and the elementary building blocks, to molecules and macrosystems.

The book is the product of the author's reading of original literature rather than of standard texts. It differs from what is conventionally emphasized because of the different approach that it argues for the recognition of chemistry as an emergent discipline, ultimately based on the properties and structure of space and time. Hence the emphasis on otherwise unexpected topics such as quaternions, lie groups, polarized light, compressed atoms, rydberg atoms, solitons, molecular hydrogen, and phase transitions, amongst others. The topic is the understanding of chemistry from first principles.

The book is self-contained and can be used without reference to other sources.

## Key Features

- All chemisty theories are covered in this one volume.
- The book is self-contained and can be used without reference to other sources.
- Many topics, routinely referred to in advanced chemistry texts, without making them accessible to the non-specialist, are brought together.

## Readership

Theoretical and physical chemists. Physisists. Students and researchers at university and institutional libraries. Private scientists.

## Table of Contents

**Basic Mathematics**
Elementary Vector Algebra

- Vectors
- Sum of Vectors
- Scalar Product
- Three-dimensional Vectors
- Vector Product
- Three-vector products
- Complex Numbers
- N-dimensional Vectors
- Quaternions

Determinants and Matrices - Matrix Operations
- Inverse of a Matrix
- Linear Homogeneous Equations
- Linear Transformations
- Direct Sums and Products

Vector Fields- The Gradient
- The Laplacian
- The Divergence
- The Curl
- Orthogonal Curvilinear Coordinates
- Tensor Analysis Differential Equations
- Series Solution of Differential Equations
- Separation of Variables
- Special Functions

**Group Theory**

The Multiplication Table

Conjugate Elements and Classes

Homomorphis
Some examples of symmetry groups

- Cayley's theorem

Field and Space - Unitary Space
- Hilbert Space
- The Eigenvalue Problem

Representation of Groups - Equivalent representations
- Reducible Representations
- Orthogonality
- Orthogonal Relationships
- Direct Product Representations

Continuous Groups (Lie Groups) - Representations of a Lie group
- Important Lie Groups
- Homomorphism of SU(2) with O(3)

**Particles and Waves**
Review of Classical Dynamics

Hamilton's Principle

- Lagrangian Density
- The Hamiltonian Function

Hamilton-Jacobi Theory

Potential Theory

Wave Motion - Harmonic Waves
- Fourier Series
- Fourier Transforms
- Wave Packets
- Solitons
- The Eikonal Equation

**Space and Time**
The Electromagnetic Field

- Units
- The Maxwell Equations
- Electromagnetic Potentials
- Electromagnetic Waves

Special Relativity - The Lorentz Transformation
- Physical Interpretation of Special Relativity

General Relativity

Gauge Fields - The Higgs Field

The Arrow of Time

**Quantum Theory**

Basic Concepts

- Polarized Light: A familiar example of quantum behaviour
- Electron Spin
- Quantum States
- Observables
- Mean Values
- Eigenvectors
- Incompatibility
- Matrix Mechanics
- Quantum Particles
- Stationary States

Wave Mechanics - The Hydrogen Atom

Relativistic Wave Equations - Dirac's Equation

Angular Momentum and Spin - Measurement of Angular Momentum
- General Theory
- Schroedinger's Equation and Spin
- Addition of Angular Momenta
- Exclusion Principle

Quantum Mechanics of the Photon - The Quantized Field
- Energy
- Momentum
- Polarization
- Spherical Waves

**Quantum Chemistry**

Quantum Aspects of General Chemistry

- The Equipartition Principle

Molecular Spectroscopy - The Raman effect
- Electronic spectra
- Spin Resonance Spectroscopy
- Optical Rotation Spectroscopy
- Moessbauer Spectroscopy
- Symmetry Aspects
- Spectroscopic selection rules

Free-Particle Models - Particle in a Sphere
- Electron Gas
- Potential Barriers
- The Tunnel Effect
- The Nearly-free electron model
- Delocalized Chemical Systems

**Atoms and Molecules**

Many-particle Systems

- Two-body Systems
- Particles with spin

Approximation Methods - Time-dependant Perturbation
- The Variational Method

Atomic Structure - Many-electron Atoms
- Compressed Atoms

Molecular Systems - The Born-Oppenheimer Approximation
- The H2+ Molecule
- The Hydrogen Molecule
- Polyatomic Molecules
- The LCAO-MO-SCF Method
- Hueckel Molecular-Orbital (HMO) Theory
- The Extended Hueckel Method
- Density Functional Theory
- Molecular Geometry

**Macrosystems**

Thermodynamics

- Theoretical Formulation
- Equilibrium Thermodynamics
- Thermodynamic Potentials
- Irreversible Thermodynamics

Mechanics of Macrosystems - Classical Systems
- Statistical Mechanics
- Equilibrium Systems
- Statistics and Thermodynamics

Quantum Statistics

The Quantum Formalism

The Density Matrix

Macroscopic Variables Axioms of the Theory

Symmetry Considerations The Microcanonical Ensemble

The canonical ensemble

The grand canonical ensemble Generalized Ensembles

Non-equilibrium Statistical Mechanics - The fluctuation-dissipation theorem
- Chemical Reaction

**Chemical Change**

Phase Change

Disorder

- Thermodynamics of Disorder
- Landau Theory
- The Van der Waals Equation

The Scaling Hypothesis

Renormalization Group

Chemical Reaction

## Details

- No. of pages:
- 570

- Language:
- English

- Copyright:
- © Elsevier Science 2003

- Published:
- 24th November 2003

- Imprint:
- Elsevier Science

- eBook ISBN:
- 9780080519043

## About the Author

### Jan C.A. Boeyens

### Affiliations and Expertise

Department of Chemistry, University of Pretoria, Pretoria, South Africa