# The Theories of Chemistry

**By**

- Jan C.A. Boeyens, Department of Chemistry, University of Pretoria, Pretoria, South Africa

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.

View full description### Audience

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

### Book information

- Published: November 2003
- Imprint: ELSEVIER
- ISBN: 978-0-444-51491-2

### 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 HomomorphisSome 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