# MM Force Fields: Part 1¶

Abstract

## How do you find a global minimum when there’s so many local minima?¶

• Systematically search all the coordinates?
• Impossible ($$~N^100$$)
• Dynamics and quench (MD/Monte Carlo)
• Run a dynamics simulation at a high temperature and periodically cool it down to see which structure it relaxes in to
• Simulated annealing (MD/Monte Carlo)
• Heat the system up and cool it down slowly (similar to dynamics and quench)
• Evolutionary/Genetic Algorithms
• Allow “good” geometries to survive and share properties and “bad” ones to die
• Not a likely option

### Phase Space¶

The space that’s characterised by the momentum and the position of the particles within the system

• $$r=(q,p)$$
• $$r=(q_{1x},q_{1y},q_{1z},p_{1x},p_{1y},p_{1z},...)$$

In the image below, the middle plot shows the trajectory of momentum ($$p$$) and position ($$q$$). Since it is harmonic, the plot is elliptical

#### Are you following this phase space in small enough time steps?¶

• If the steps are too big, the trajectory may differ from the realistic (infinitely small) steps taken in reality
• Think, broken physics in games
• The image below shows an example of a normal phase space trajectory