UTF-8Under the Hood255255192
How does molecular dynamics work?
The Molecular Workbench (MW) uses basic physics and a fantastic amount of computation. A few decades ago, a supercomputer would have strained to do this much computing. Because MW can make mistakes, it is important that you know something about how it works.
The model uses Newton's Second Law to compute how atoms move. Here is how it works:
It calculates the forces on each atom using the Lennard-Jones potential.
Then it uses F=ma to determine the acceleration.
The acceleration is used to compute how much the velocity changes.
This gives the velocity of each atom, which is used to move the atom forward a tiny time step.
The PE and KE is computed for every atom.
This whole process is repeated tens of thousands of times each second. The accuracy of the computation depends on the forces not changing too much during each time step. If the time steps and velocities are small, the computations are quite accurate.
MW uses time steps measured in femtoseconds. This is one-millionth of one-billionth of a second or 10-15 seconds. That is a very small step!!!! A femtosecond is to a second as one second is to about 32 million years. Fortunately, computers are able to compute 100,000 steps easily and that is enough time for some interesting things to happen.
MW computes the total kinetic energy by adding up the KE of each atom, KE=(1/2)mv2. The total potential energy comes from adding up the values of the Lennard-Jones potential for every pair of atoms. Then the total energy is computed by adding KE and PE.
It is amazing that the total calculated energy is constant, given how many calculations go into it.
Of course, we know from physics that the total energy MUST be constant, so this is not too surprising. The fact that MW computes that energy is conserved means that the calculations must be fairly accurate.
What are limits of the Molecular Workbench?
In the model below, you can push the limits of the MW. If you go too far, you will know, because the model will not compute the right energy. It will report that energy is not conserved. Since we know that energy is conserved, we cannot trust a model that says that it isn't.
In the following model, you can adjust the time step and heat the system up. Can you break the model?
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</html>-243f9a7575175.075.014truetrue75.075.075.075.01475.075.01475.075.01475.095.0org.concord.modeler.text.BulletIcon$SquareBulletIcon141414true1475.095.0org.concord.modeler.text.BulletIcon$SquareBulletIcon141475.095.0org.concord.modeler.text.BulletIcon$SquareBulletIcon141475.095.0org.concord.modeler.text.BulletIcon$SquareBulletIcon141475.095.0org.concord.modeler.text.BulletIcon$SquareBulletIcon141475.075.01475.075.01475.075.01475.075.01414true1414true1475.075.01475.075.01414true1475.075.01475.075.01475.075.01475.075.01475.075.014true14255 0 0true14truetrue75.075.075.075.01414true1414true1475.075.01475.075.01475.075.075.075.01org.concord.mw2d.activity.AtomContainerpage10$0.mmlfalseorg.concord.modeler.PageXYGraph0Time (fs)Kinetic Energy/ParticlePotential Energy/ParticleTotal Energy/Particlefalse0.060000.0false-0.10.25280350Time (fs)Energy (eV)true400450-333301-1falseRaised Bevel75.075.01org.concord.modeler.PageSliderorg.concord.mw2d.models.MolecularModel01.48199999943375580.100000001490116124.050Time step (femtosec)30060falsetrue{value="3.4319999986886978", label="3.5"}{value="1.4819999994337558", label="1.5"}{value="2.9639999988675116", label="3"}{value="1.0139999996125697", label="1"}{value="2.4959999990463255", label="2.5"}{value="0.5459999997913837", label=".5"}{value="3.9779999984800813", label="4"}{value="1.949999999254942", label="2"}{value="0.15599999994039535", label=".1"}Execute MW scriptorg.concord.modeler.PageButtonHeatorg.concord.mw2d.models.MolecularModel0Heat the system up0.175.075.075.075.0org.concord.modeler.ImageQuestion600250Lowered Etched<html><font face="Verdana" size="4">Insert here a snapshot of a graph for the above system that is <b>not</b> accurate. In the caption, explain why this is inaccurate and how it should be fixed. </font></html>75.075.075.075.0org.concord.modeler.PageTextField600120<html>
<font size=4 face=Verdana>What do you think the largest time step should be? Justify your answer.
</html>1.5 fs seems safe—the total energy remains constant even for 500 atoms. 75.075.075.075.0org.concord.modeler.ActivityButtonHintHint about how to break the system.falseIf the atoms are going further with each step, it is more likely that they will get into trouble. Hint75.075.075.075.075.075.0org.concord.modeler.text.LineIcon40101010<html><body face="Trebuchet MS">
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