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# Advanced Thermodynamics and Molecular Simulations

## Syllabus

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 ....

### Taught by

IIT Roorkee July 2018