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