Statistical Thermodynamics and Free Energy Computation

Welcome! These are the lecture notes on “Statistical Thermodynamics and Free Energy Computation” by Michael von Domaros. This web book is a living document and subject to constant change. Please do not print or save until the end of the lecture.

Summary

Many chemical processes happen at constant temperatures—their spontaneity and equilibrium must hence be judged using free energies (Helmholtz, Gibbs, Landau). But how can these thermodynamic potentials be computed from the energies resulting from conventional quantum chemical calculations? In this lecture, we introduce the field of statistical thermodynamics, which establishes this connection, as well as as several modern methods to compute free energies in gas phases and condensed matter.

After a short review of the most important theoretical concepts of traditional thermodynamics, we introduce the concept of an ensemble and a modern definition of entropy, based on information theory. We then apply our newly acquired knowledge to typical quantum mechanical model systems, establishing the foundation for the rigid-rotor/harmonic oscillator (RRHO) approximation of polyatomic gases and its improvements. We conclude this lecture with a discussion of computer simulation techniques and enhanced sapling methods used to estimate free energies in condensed phases.

Literature

Physical Chemistry

• J. D. Simon, D. A. McQuarrie (2023). Physical chemistry : A molecular approach.

Legendre Transforms

• R. K. P. Zia, E. F. Redish, S. R. McKay, Making sense of the Legendre transform.

Statistical Mechanics

• D. Chandler, D. Wu (1987). Introduction to Modern Statistical Mechanics.

• R. H. Swendsen. An Introduction to Statistical Mechanics and Thermodynamics.

Entropy

• H. E. Lieb, J. Yngvason (2002). The Mathematical Structure of the Second Law of Thermodynamics.

• A. Ben-Naim (2017). Entropy, Shannon’s Measure of Information and Boltzmann’s H-Theorem.

• A. Ben-Naim (2019). Entropy and Information Theory: Uses and Misuses.

Information Theory

• C. E. Shannon (1948). A mathematical theory of communication.

• E. T. Jaynes (1957). Information Theory and Statistical Mechanics.

Computer Simulations

• M. P. Allen, D. J. Tildesley (2017). Computer Simulation of Liquids.

Contents

• 1. Motivation
• 2. Thermodynamics
• 3. Entropy
• 4. Statistical Method
• 5. Information Theory
• 6. Canonical Ensemble
• 7. Rigid-Rotor–Harmonic-Oscillator Approximation
• 8. Computational Thermochemistry
• 9. Classical Statistical Mechanics
• 10. Molecular Dynamics