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

2. 1-12-20052 Outline General Introduction Force Fields Numerical Solutions Test

3. 1-12-20053 Outline General Introduction Force Fields Numerical Solutions Test

4. 1-12-20054 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. 1-12-20055 Outline General Introduction Force Fields Numerical Solutions Test

6. 1-12-20056 Force Fields A force field may look like this (taken from [1])

7. 1-12-20057 Force Fields Dihedral

8. 1-12-20058 Force Fields Lennard-Jones or “Stolen” from [2]

9. 1-12-20059 Force Fields Coulomb →  (r) model the effect of a solvent. →This can also be modelled explicitly in which case  (r) = 1.

10. 1-12-200510 Outline General Introduction Force Fields Numerical Solutions Test

11. 1-12-200511 Numerical Solutions Predictor-corrector algorithm

12. 1-12-200512 Numerical Solutions

13. 1-12-200513 Numerical Solutions Verlet algorithm

14. 1-12-200514 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. 1-12-200515 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. 1-12-200516 Outline General Introduction Force Fields Numerical Solutions Test

17. 1-12-200517 Test 1. What is the following ? →Coublumb interaction →Lennard-Jones interaction →Verlet interaction

18. 1-12-200518 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. 1-12-200519 Test How is the force on a particle (in one direction) found from the potential ? →

20. 1-12-200520 Answers Question 1. Lennard-Jones interaction Question 2. To ”solve” N2 at constant Temperature Question 3.

21. 1-12-200521 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/hjakubows ki/classes/ch331/protstructure/olunderst andconfo.html M.P. Allen and D. J. Tildesley; Computer Simulations of Liquids; Oxford; 1987