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Force Fields and Numerical Solutions

Force Fields and Numerical Solutions. - within Molecular Dynamics. Christian Hedegaard Jensen. Outline. General Introduction Force Fields Numerical Solutions Test. Outline. General Introduction Force Fields Numerical Solutions Test. General Introduction.

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Force Fields and Numerical Solutions

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  1. Force Fields and Numerical Solutions - within Molecular Dynamics Christian Hedegaard Jensen

  2. Outline • General Introduction • Force Fields • Numerical Solutions • Test

  3. Outline • General Introduction • Force Fields • Numerical Solutions • Test

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

  5. Outline • General Introduction • Force Fields • Numerical Solutions • Test

  6. Force Fields • A force field may look like this (taken from [1])

  7. Force Fields • Dihedral

  8. Force Fields • Lennard-Jones or “Stolen” from [2]

  9. Force Fields • Coulomb • (r) model the effect of a solvent. • This can also be modelled explicitly in which case (r) = 1.

  10. Outline • General Introduction • Force Fields • Numerical Solutions • Test

  11. Numerical Solutions • Predictor-corrector algorithm

  12. Numerical Solutions

  13. Numerical Solutions • Verlet algorithm

  14. 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.

  15. 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.

  16. Outline • General Introduction • Force Fields • Numerical Solutions • Test

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

  18. 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

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

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

  21. 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/classes/ch331/protstructure/olunderstandconfo.html • M.P. Allen and D. J. Tildesley; Computer Simulations of Liquids; Oxford; 1987

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