# 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**

**Legendre Transforms**

**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**