1. Molecular Modelling - Lecture 3
Molecular Dynamics

2. Molecular Dynamics Computational approach to statistical mechanics
beyond the static view of the molecule
dynamic motions can explain the wide range of thermally accessible states and thereby connect structure and function
Many different methods and sampling approaches to deal with the sampling problem
1 fs timestep means one million steps for a ns

3. Molecular Dynamics - Initial System Settings
Structure
Solvation
water and salt ions
Ensemble - NVE (microcanonical ensemble), NVT, NPT ...
velocity
initial velocity vector is set randomly so that the total kinetic energy of the system corresponds to the expected value at the target temperature
set velocities from a Gaussian distribution
Equilibration
exchange between kinteic and potential energies
stable when both terms, and total energy, converge to fluctuate about a value

5. Periodic Boundary Conditions
Model system placed in unit cell and considered to have infinitely many images in space
Any space-filling polyhedra
cubic
hexagonal prism
truncated octahedrao
rhombic dodecahedra

6. Reducing the Computational Cost
Non-bonded interactions most time-consuming part of a simulation N2
Truncating Long-Range forces and the minimum image convention :
Interaction for a molecule i are only counted between it and it’s closest image
Simple cut-off truncation of potential creates problems with consistent potential and force

7. Truncating Long-Range forces and the minimum image convention
Switching
Use smoothing functions to smoothly switch off the interaction between a “cut-on” and a “cut-off” distance.

8. Truncating Long-Range forces and the minimum image convention
Shifting
alters function more gradually over entire range

9. Truncating Long-Range forces and the minimum image convention
atom-based or group-based

11. MD - simple application: Simulated Annealing
special case of either MD (`quenched' MD) or MC simulation, in which the temperature is gradually reduced during the simulation.
Often, the system is first heated and then cooled
the system is given the opportunity to surmount energetic barriers in a search for conformations with energies lower than the local-minimum energy found by energy minimization.
can lead to more realistic simulations of dynamics at low temperature
more expensive than energy minimization.