The Theories of Chemistry - 1st Edition - ISBN: 9780444514912, 9780080519043

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
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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.


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


  • 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

  • Thermodynamics of Disorder
  • Landau Theory
  • The Van der Waals Equation
    The Scaling Hypothesis
    Renormalization Group
    Chemical Reaction


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© Elsevier Science 2003
Elsevier Science
eBook ISBN:

About the Author

Jan C.A. Boeyens

Affiliations and Expertise

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