Course Overview

This course aims to impart knowledge of advanced thermodynamics concepts and molecular simulation methods. Unlike the standard undergraduate chemical engineering thermodynamics, we will follow a rather physics-based treatment of thermodynamics based on statistical mechanics concepts and molecular theories. The thermodynamics part to be covered in first half of the course would be used in the discussion of molecular simulations to be covered in the second half of the course.

The main emphasis will be on the underlying physics and algorithms; use of software packages will not be described in the lectures. However, programming/software projects may be given as assignments. Use of any programming language (e.g., C, C++, Python, etc.) or software (e.g., LAMMPS, GROMACS, etc.) is allowed. At the successful completion of the course, students are expected to be able to

1. Apply thermodynamic concepts in the understanding of chemical engineering problems and their research work

2. Identify the molecular simulation approach best suited for a problem, perform simulation and analyze results. The latter might involve a more detailed reading of the simulation approach and the programming/software.

Tentative list of topics

1. Probability, Distributions, and Thermodynamic Equilibrium. Laws of Thermodynamics

2. Partition Function, Thermodynamic Functions and Thermodynamic Ensembles, Maxwell Relations, Phase Space, Averages and Fluctuations, Boltzmann Approximation

3. Gibbs Phase Rule and Phase Equilibrium, Equations of State, Solution Thermodynamics, Phase equilibrium, Osmotic Pressure, Chemical Potential, Mixing and Phase Separation, Theory of electrolytes

4. Monte Carlo Simulations: Setting up a Simulation, Types of Boundary conditions, Detailed Balance, Numerical Implementation, Analysis and Interpretation of Results, Advanced Sampling Strategies

5. Molecular Dynamics Simulations in Various Ensembles: Numerical Integration of Equations of Motion, Temperature and Pressure Control, Force-Fields, Analysis and Interpretation of Results, Efficiency and Parallelization

6. Methods for Free Energy Calculations: Thermodynamic Integration, Widom’s Particle Insertion Method, Umbrella Sampling, and Other Advanced Strategies

7. Non-equilibrium Simulations: Langevin Equations, Brownian Dynamics, Kinetic Monte Carlo (kMC) Simulations, and Other Methods

Textbooks

* Mcquarrie, D.A. Statistical Mechanics, Univ Science Books; 1st edition, 2000

* Hanson, R.M. and Green, S. Introduction to Molecular Thermodynamics, University Science Books, 2008

Shell, M.S. Thermodynamics and Statistical Mechanics. Cambridge University Press, 2015

Frenkel, Daan, and Berend Smit. Understanding molecular simulation: from algorithms to applications. Vol. 1. Academic press., Book available Online at https://www.sciencedirect.com/book/9780122673511/understanding-molecular-simulation , 2001

Tildesley, D. J., and M. P. Allen. "Computer simulation of liquids." 2^nd Ed, Oxford University Press, 2017

Andrew R. Leach. Molecular modelling: principles and applications. Pearson Education, 2001