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Chemistry 407: Statistical Mechanics in Chemistry

Course Level: 
Fourth Year
Academic Year: 
2017/2018

0. Review (Thermodynamics, Quantum Mechanics, Classical Mechanics, Math)

I. Fundamentals of equilibrium statistical mechanics (postulates, ensemble, probability distribution)

II. Ensembles 

II.1 Microcanonical ensemble, partition function, and thermodynamic properties

II.2 Canonical ensemble, partition function, and thermodynamic properties

II.3 Grand canonical ensemble, partition function, and thermodynamic properties

III. Statistics

III.1 Independence

III.2 Distinguishable, indistinguishable particles

III.3 Boltzmann statistics

III.4 Fermi-Dirac and Bose-Einstein statistics

IV. “Perfect Boltzmann” gas       
V. Atoms and molecules in the classical limit (Boltzmann statistics) and thermodynamic properties

V.1 Atoms

V.2 Molecules

VI. Chemical equilibrium

VI.1 Energy zero

VI.2 Equilibrium constant

Examples

VII. Ideal Fermi-Dirac gas

VII.1 Weakly degenerate FD gas

VII.2 Strongly degenerate FD gas - Conduction electrons in metals

VIII. Ideal Bose-Einstein gas

VIII.1 Weakly degenerate BE gas

VIII.2 Strongly degenerate BE gas – Bose Einstein Condensation

VIII.3 Photon gas

VIII.4 Phonon gas

IX. Classical statistical mechanics

IX.1 Phase space and classical mechanical partition function

IX.2 Gas of structureless particles

X. Classical statistical mechanics of fluids (imperfect gases and liquids)

X.1 Interaction potentials

X.2 Structural properties

XI. Analytical Methods and Computer Simulations

XI.1 Analytical methods

XI.2 Monte Carlo and Molecular Dynamics Methods

XI.3 Example: Phase Diagrams from Grand Canonical Monte Carlo calculations

XII. Time dependence