Overview

COURSE OUTLINE: 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.

Syllabus

Advanced Thermodynamics and Molecular Simulations.
Lecture 01-Introduction to the course.
Lecture 02: Molecular basis of energy and entropy.
Lecture 03: Probability and probability distributions.
Lecture 04: Probability distributions and thermodynamic equilibrium.
Lecture 05: Energy distribution in molecular systems.
Lecture 06: First and second law of thermodynamics.
Lecture 07- Reversible and irreversible processes; third law; legendre transformation....
Lecture 08- Thermodynamic functions for multi-component systems; chemical potential....
Lecture 09-Extensive and intensive variables; gibbs duhem relation; euler theorem; maxwell relations.
Lecture 10- Discrete and continuous probabilities; stirling approximation.
Lecture 11- Binomial distribution approaches gaussian distribution for large n....
Lecture 12- Solution of drunkard walk; lagrange multipliers.
Lecture 13: Energy distribution in molecular system revisited.
Lecture 14: Canonical ensemble: most probable distribution, partition function.
Lecture 15: Definition of temperature; third law of thermodynamics.
Lecture 16: Canonical ensemble: Helmholtz free energy, averages and fluctuations, specific heat.
Lecture 17: Partition function of a dense gas; grand canonical ensemble: partition function.
Lecture 18: Computing properties in grand canonical ensemble.
Lecture 19: Isothermal isobaric ensemble.
Lecture 20: Summary of thermodynamic ensembles; partition function of an ideal gas.
Lecture 21: Mixing and phase separation, phase equilibrium of a multiphase multicomponent system.
Lecture 22: Pure component phase diagram; Solution thermodynamics: Helmholtz free energy density.
Lecture 23: Characterizing mixing and phase separation using Helmholtz free energy density.
Lecture 24: Common tangent construction, definition of binodal, spinodal, and critical point.
Lecture 25: Osmotic pressure and chemical potential.
Lecture 26: Lattice model of liquid solutions I.
Lecture 27: Lattice model of liquid solutions II.
Lecture 28: Lattice model of liquid solutions III.
Lecture 29: Critical review of Lattice model, theoretical basis of molecular dynamics simulation.
Lecture 30: Theoretical basis of molecular dynamics simulation.
Lecture 31: Interaction energy and force field.
Lecture 32: Liouiville theorem; theoretical basis of Monte Carlo simulation.
Lecture 33: Introduction to Monte Carlo simulation method.
Lecture 34: Markov chain algorithm, condition for equilibrium and detailed balance.
Lecture 35: Metropolis algorithm, periodic boundary condition.
Lecture 36: Numerical implementation of Monte Carlo simulation: python examples I.
Lecture 37: Numerical implementation of Monte Carlo simulation: python examples II.
Lecture 38: Numerical implementation of Monte Carlo simulation: python examples III.
Lecture 39: Numerical implementation of Monte Carlo simulation: python examples IV.
Lecture 40: Numerical implementation of Monte Carlo simulation: python examples V.
Lecture 41: Particle simulations: comparison with quantum chemical and continuum simulations.
Lecture 42: Pair potentials.
Lecture 43: Saving CPU time: short range and long range interactions.
Lecture 44: Bonded and nonbonded interactions, force fields.
Lecture 45: Practical aspects of molecular simulations.
lecture 46: Numerical implementation of MD; thermostat and barostat.
Lecture 47: MD simulations - efficiency and parallelization, sampling and averaging.
Lecture 48: MD simulations - analysis of simulation trajectories (continued), case studies I.
Lecture 49: MD simulations - case studies II.
Lecture 50: MD simulations - case studies III.
Lecture 51: Free energies and phase behavior; extension of canonical ensemble monte carlo....
Lecture 52: Extension of canonical ensemble monte carlo to other ensembles (continued).
Lecture 53: Monte carlo in gibbs ensemble and semi-grand canonical ensemble....
Lecture 54: Thermodynamic integration (continued); widom's particle insertion....
Lecture 55: Multiple histogram method; umbrella sampling; thermodynamic cycle....
Lecture 56:Tackling time scale issues (continued); nonequilibrium molecular dynamics....
Lecture 57: Multiparticle collision dynamics; lattice boltzmann method; coarse-graining.
Lecture 58: Case studies.
Lecture 59: Simulations of chemical reactions using kinetic monte carlo simulations.
Lecture 60: Reactive force fields; ab initio molecular dynamics and other advanced methods ....