Velocity auto-correlation

[vjramana]

I wish to get some explanation on calculating velocity auto-correlation for water molecules in a box.

I have done 100 ns molecular dynamics simulation on 1445 water molecules in a box. Also I have calculated velocity for each water molecule in a frame. A frame contains 1445 water molecules, so for each frame I have 1445 velocity values. I have total 10000 frames.

Now I want to calculate the velocity auto-correlation function for this system. I am confused if I shall need to calculate average velocity for each frame (average for 1445 molecules in one frame) - this means I will have 10000 averaged velocities, each value will represent velocity from each frame (total 10000 frames).


And then calculate the velocity auto-correlation function?

I appreciate any explanation.

Thanks in advance.
Vijay

 

[LightHero]

The velocity auto-correlation function (VACF) is used to measure the correlation between the velocity of a particle at two different points in time. In order to calculate the VACF, you will need to calculate the average velocities for each frame (averaged over all 1445 molecules in the frame). Then, you can calculate the correlation between each pair of frames by subtracting the average velocity of each frame from the average velocity of the other frame and multiplying the result by the average of the products of the velocities of individual molecules in each frame. You can then sum up all these correlations to get the VACF.