Learn · Advanced Thermodynamics and Molecular Simulations
Lecture 43 of 60Unit-9
Saving CPU time: short range and long range interactions
Prof. Prateek Kumar Jha · IIT Roorkee
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- Advanced Thermodynamics and Molecular Simulations, IIT Roorkee (at NPTEL)
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- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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All the lectures
- Introduction to the course
- Molecular basis of energy and entropy
- Probability and probability distributions
- Probability distributions and thermodynamic equilibrium
- Energy distribution in molecular systems
- First and second law of thermodynamics
- Reversible and irreversible processes; third law of thermodynamics; legendre transformation; thermodynamic functions for one component system
- Thermodynamic functions for multi-component systems; chemical potential; why do we minimize thermodynamic functions?
- Extensive and intensive variables; gibbs duhem relation; euler theorem; maxwell relations
- Discrete and continuous probabilities; stirling approximation
- Binomial distribution approaches Gaussian distribution for large n; definition of drunkard walk
- Solution of drunkard walk; Lagrange multipliers
- Energy distribution in molecular system revisited; introduction to thermodynamic ensembles
- Canonical ensemble: most probable distribution, partition function
- Definition of temperature; third law of thermodynamics
- Canonical ensemble: Helmholtz free energy, averages and fluctuations, specific heat, deriving ideal gas law
- Partition function of a dense gas; grand canonical ensemble: partition function, most probable distribution
- Computing properties in grand canonical ensemble
- Isothermal isobaric ensemble
- Summary of thermodynamic ensembles; partition function of an ideal gas
- Mixing and phase separation, phase equilibrium of a multiphase multicomponent system, Gibbs phase rule
- Pure component phase diagram; solution thermodynamics: Helmholtz free energy density
- Characterizing mixing and phase separation using Helmholtz free energy density
- Common tangent construction, definition of binodal, spinodal, and critical point
- Osmotic pressure and chemical potential
- Lattice model of liquid solutions I
- Lattice model of liquid solutions II
- Lattice model of liquid solutions III
- Critical review of Lattice model, theoretical basis of molecular dynamics simulation
- Theoretical basis of molecular dynamics simulation.
- Interaction energy and force field
- Liouiville theorem; theoretical basis of Monte Carlo simulation
- Introduction to Monte Carlo simulation method
- Markov chain algorithm, condition for equilibrium and detailed balance
- Metropolis algorithm, periodic boundary condition
- Numerical implementation of Monte Carlo simulation: python examples I
- Numerical implementation of Monte Carlo simulation: python examples II
- Numerical implementation of Monte Carlo simulation: python examples III
- Numerical implementation of Monte Carlo simulation: python examples IV
- Numerical implementation of Monte Carlo simulation: python examples V
- Particle simulations: comparison with quantum chemical and continuum simulations; bridging length and time scales
- Pair potentials
- Saving CPU time: short range and long range interactions
- Bonded and non-bonded interactions, force fields
- Practical aspects of molecular simulations
- Numerical implementation of MD; thermostat and barostat
- MD simulations - efficiency and parallelization, sampling and averaging, analysis of simulation trajectories
- MD simulations - analysis of simulation trajectories (continued), case studies I
- MD simulations - case studies II
- MD simulations - case studies III
- Free energies and phase behavior; extension of canonical ensemble Monte Carlo to other ensembles
- Extension of canonical ensemble Monte Carlo to other ensembles (continued)
- Monte Carlo in Gibbs ensemble and semi-grand canonical ensemble, thermodynamic integration
- Thermodynamic integration (continued); Widom's particle insertion; overlapping distribution method
- Multiple histogram method; umbrella sampling; thermodynamic cycle; potential of mean force; pulling simulations; metadynamics; tackling time scale issues
- Tackling time scale issues (continued); nonequilibrium molecular dynamics; mesoscale simulations: Langevin dynamics and Brownian dynamics, kinetic Monte Carlo simulations; dissipative particle dynamics
- Multiparticle collision dynamics; lattice Boltzmann method; coarse-graining
- Case studies.
- Simulations of chemical reactions using Kinetic Monte Carlo simulations
- Reactive force fields; Ab initio molecular dynamics and other advanced methods; molecular simulations in chemical engineering; concluding remarks