Tutorial 7.4:  Search for the Optimum Structure of 24 Atoms of Lennard-Jonesium

INTRODUCTION:

The multiple minimum problem is expected to become more and more serious as the system's number of degrees of freedom grows. In this tutorial, you will run a series of simulated annealing simulations on 24 atoms of Lennard-Jonesium in two and three dimensions, to roughly estimate the success rate in fining the global minimum energy conformation.

PREDICTION:

As you did in Tutorial 7.1, use coins to find the two-dimensional arrangements of 24 discoidal atoms with the maximum number of contacts. Make a sketch of this conformation, which should be the global minimum energy structure for 24 atoms of Lennard-Jonesium in two dimensions.

We will again use a Lennard-Jones potential with a 1 kcal/(mol•Å2) well depth, to make the interatomic attractions strong enough to keep the system condensed at temperatures below about 50K.

SETUP AND RUNNING INITIAL SIMULATION:

Create a new folder for your work on this tutorial.

Open Chimera, Launch Sophia, and initiate a new simulation with:

PDB File: LJ24.pdb

Force Field:   Lennard-Jones

FF Mod File:  LJ_E0_1.0.frcmod

Box length:  3 nm

Non-bond cutoff:  1 nm

In the Sophia Recipe window:

Load and run the recipe: freeMD.json

If you watch the trajectory created by this 100,000 step simulation, you'll see that there is sufficient atomic motion to shake the structure up while keeping most of the atoms together in a cluster. The average temperature in this simulation is therefore a good choice for the initial temperature in simulated annealing. Plot the temperature in the Trajectory Viewer Window, so you can find out what the approximate average temperature was. (You can estimate it to the nearest 10°; the exact average isn't critical.

SETUP AND RUN A SERIES OF TEN SIMULATED ANNEALING SIMULATIONS:

In the Sophia Recipe window, clone the recipe you have just run.

Make all ingredients deletable and delete ingredient 1 (the recipe that has already been run).

Edit the new ingredient 1, changing only the following settings:

Initialize velocities:  xy

Thermostat:  Rescale

Initial temperature:  (Use the value you determined in the step above.)

Final temperature:  3K    (You don't have to take the system all the way to 0K.)

Make nine copies of this recipe by clicking the "clone" button nine times. You should have a total of 10 ingredients in the recipe.

Run all ingredients. Your energy plot should resemble the one in the figure.

ANALYSIS:

xxx . How many times did you find the global minimum? When you compare your results with the LJ10 simulation in Tutorial ttt, do you agree that the search grows more difficult with more degrees of freedom?

THE 3D SEARCH:

xxx . How many times did you find the global minimum? Do you agree that the search grows more difficult with more degrees of freedom?