1-12-20051 Force Fields and Numerical Solutions Christian Hedegaard Jensen - within Molecular Dynamics.

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Presentation transcript:

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

Outline General Introduction Force Fields Numerical Solutions Test

Outline General Introduction Force Fields Numerical Solutions Test

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

Outline General Introduction Force Fields Numerical Solutions Test

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

Force Fields Dihedral

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

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

Outline General Introduction Force Fields Numerical Solutions Test

Numerical Solutions Predictor-corrector algorithm

Numerical Solutions

Numerical Solutions Verlet algorithm

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.

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.

Outline General Introduction Force Fields Numerical Solutions Test

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

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

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

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

References [1] N. Rathore et al.; Density of states simulations of proteins; J. Chem. Phys.; v.118 n ; 2002 [2] ki/classes/ch331/protstructure/olunderst andconfo.html M.P. Allen and D. J. Tildesley; Computer Simulations of Liquids; Oxford; 1987