Force Fields and Numerical Solutions

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Force Fields and Numerical Solutions

• - within Molecular Dynamics

Christian Hedegaard Jensen
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Outline

• General Introduction
• Force Fields
• Numerical Solutions
• Test

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Outline

• General Introduction
• Force Fields
• Numerical Solutions
• Test

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General Introduction

• From last time we have that the problem is
• Force Fields What is V ?
• Numerical Solutions How to solve the equation
  numerically ?

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Outline

• General Introduction
• Force Fields
• Numerical Solutions
• Test

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Force Fields

• A force field may look like this (taken from 1)

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Force Fields

• Dihedral

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Force Fields

• Lennard-Jones
• or

Stolen from 2
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Force Fields

• Coulomb
• ?(r) model the effect of a solvent.
• This can also be modelled explicitly in which
  case ?(r) 1.

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Outline

• General Introduction
• Force Fields
• Numerical Solutions
• Test

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Numerical Solutions

• Predictor-corrector algorithm

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Numerical Solutions
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Numerical Solutions

• Verlet algorithm

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Numerical Solutions

• Errors
• If you start with slightly perturbed initial
  conditions the trajectories will diverge from
  each other eventually.
• Fluctuations in energy. For longer time steps the
  Verlet algorithm is better.

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Numerical Solutions

• Thermostats (If you want to sample at constant
  temperature)
• Example Andersen Thermostat
• Pick random atom/molecule at intervals
• Set the velocity so that it is chosen randomly
  from the Maxwell-Boltzmann distribution
• This corresponds to introducing collisions with
  virtual heat bath particles.

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Outline

• General Introduction
• Force Fields
• Numerical Solutions
• Test

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Test

• 1. What is the following ?
• Coublumb interaction
• Lennard-Jones interaction
• Verlet interaction

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Test

• The Andersen is used for what ?
• To solve N2 at constant Energy
• To calculate forces in the system
• To solve N2 at constant Tempreture

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Test

• How is the force on a particle (in one direction)
  found from the potential ?

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Answers

• Question 1. Lennard-Jones interaction
• Question 2. To solve N2 at constant Temperature
  
• Question 3.

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References

• 1 N. Rathore et al. Density of states
  simulations of proteins J. Chem. Phys. v.118 n.
  9 4285 2002
• 2 http//employees.csbsju.edu/hjakubowski/classe
  s/ch331/protstructure/olunderstandconfo.html
• M.P. Allen and D. J. Tildesley Computer
  Simulations of Liquids Oxford 1987