Molecular Dynamics

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Molecular Dynamics

• Joint Presentation by
• Nitin Sharma
• Yong Chen

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• Introduction
  
• Brief overview of Molecular Dynamics Simulations.
• Principal steps involved
• Main steps in molecular dynamics simulations
• Discussion of results
• Some simulation results will be presented by Yong

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What is Molecular Dynamics Simulation ?

• A motion picture that follows molecules as they
  dart to fro, twisting, turning, colliding with
  one another.

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Principal steps involved

• Construction of a model
• Calculation of molecular trajectories
• Analysis of those trajectories to obtain property
  values.

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Construction of a model

• Model for molecular interactions
• Intermolecular force law or equivalently an
  intermolecular potential energy function.
• Model for system environment interactions.
• Periodic boundary conditions are used for bulk
  fluid
• For simulations in which surface effects are to
  be analyzed interaction of the liquid molecules
  with the solid surface molecules are considered.

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Hard Sphere
u(r)
r
r1r2
Soft Sphere
is determined by the equilibrium distance
is the depth of the potential
Lennard-Jones Potential
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Calculation of Molecular Trajectories

• Positions are obtained by numerically solving the
  differential equation of motions (Newtonian
  dynamics)
• Algorithms for Molecular Dynamics
• Verlets Algorithm
• General Predictor-Corrector Algorithms

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Verlets Algorithm

• Third order in time accuracy
• Two step method estimates x(tdt) from the
  current position x(t) and the previous position
  x(t-dt)
• Not self starting
• Simple, stable for moderately large time steps.
• (time step should be large enough to sample
  large phase space, should be small compared to
  mean time between collisions)

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General-Predictor Corrector Algorithms

• Predict the position x(tdt) and velocity v(tdt)
  at the end of the next step.
• Evaluate the forces at tdt using the predicted
  position.
• Correct the predictions using some combination of
  the predicted and previous values of position and
  velocity.

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Analysis of trajectories to obtain property values

• Systems at equilibrium
• Isolated system containing fixed energy, number
  of molecules volume (NVE-molecular dynamics)
• Time averages of the properties can be computed
  once the system has relaxed to equilibrium.
• Systems at non-equilibrium
• External force applied to the system
• Used to compute transport coefficients, shear
  viscosity, bulk viscosity, thermal conductivity
  and diffusion coeffcient.