Physical Chemistry

A rigorous course on physical chemistry — from quantum chemistry and molecular orbital theory through thermodynamics, chemical kinetics, statistical mechanics, electrochemistry, and spectroscopy — with full derivations, MathJax equations, and Python/Fortran simulations.

Course Overview

Physical chemistry bridges the gap between physics and chemistry, applying quantum mechanics, thermodynamics, and statistical mechanics to understand chemical systems at the molecular level. This course develops the mathematical foundations rigorously, deriving every key equation from first principles, following the tradition of Atkins, McQuarrie, Berry-Rice-Ross, and Levine.

What You Will Learn

● Quantum chemistry: hydrogen atom, molecular orbitals, Hartree-Fock, variational & perturbation methods
● Thermodynamics: equations of state, phase equilibria, chemical potential, mixtures
● Chemical kinetics: rate laws, Arrhenius theory, transition state theory, enzyme kinetics
● Statistical thermodynamics: partition functions, ensembles, fluctuation-dissipation
● Electrochemistry: Nernst equation, Butler-Volmer kinetics, transport
● Spectroscopy: rotational, vibrational, and electronic transitions

Central Equations

Schrödinger: $\hat{H}\psi = E\psi$

Gibbs Free Energy: $G = H - TS$

Arrhenius: $k = A e^{-E_a/(RT)}$

Partition Function: $q = \sum_i e^{-\epsilon_i/(k_BT)}$

Nernst: $E = E^\circ - \frac{RT}{nF}\ln Q$

Beer-Lambert: $A = \varepsilon c l$

Clausius-Clapeyron: $\frac{dP}{dT} = \frac{\Delta H_{vap}}{T\Delta V}$

Eyring: $k = \frac{k_BT}{h}e^{-\Delta G^\ddagger/(RT)}$

Part I: Quantum Chemistry

Hydrogen atom, molecular orbital theory, Hartree-Fock self-consistent field, variational method, perturbation theory.

Part II: Thermodynamics

Ideal and real gases, phase equilibria, chemical potential, Gibbs-Duhem, mixtures and colligative properties.

Part III: Chemical Kinetics

Reaction rate laws, Arrhenius & collision theory, transition state theory, Michaelis-Menten enzyme kinetics.

Part IV: Statistical Thermodynamics

Partition functions, molecular thermodynamics, canonical & grand canonical ensembles, fluctuations and response.

Part V: Electrochemistry

Electrochemical cells, Nernst equation, Butler-Volmer kinetics, ionic conductivity and transport.

Part VI: Spectroscopy

Rotational, vibrational, and electronic spectroscopy: selection rules, molecular structure determination, Franck-Condon principle.

Prerequisites & References

Prerequisites

• Multivariable calculus and linear algebra
• Introductory quantum mechanics
• Classical thermodynamics
• General chemistry
• Differential equations

Recommended Texts

• Atkins & de Paula, Physical Chemistry
• McQuarrie & Simon, Physical Chemistry: A Molecular Approach
• Levine, Physical Chemistry
• Berry, Rice & Ross, Physical Chemistry
• Engel & Reid, Physical Chemistry