I’m trying to calculate Normalized Velocity Autocorrelation Function. Everything seems okay but the final results increase slightly higher than 1. While they’ve been normalized and should decay from 1 (because the velocity is being damped). I explain the python code I’ve written for calculating VAC. Can anyone say what is wrong about it?
First, I calculate velocities in each step: Vx=X(t+1)-X(t); Vy=Y(t+1)-Y(t); Vz=Z(t+1)-Z(t).
Then I calculate Kinetic Energy: E=0.5*m*(Vx^2+Vy^2+Vz^2)
Then I calculate VAC using this formula:
C(t)= / < ΔE(0)^2>
Which
ΔE(t) = E(t) -
Angular brackets denote averaging over a statistical ensemble. I use Arithmetic mean of kinetic energy of all atoms in each step for and then calculate ΔE(t) by above equation.
Then I use ΔE at first step for ΔE(0) and calculate C(t). But C(t) doesn’t decay from 1 (As expected) and increases slightly above 1 and then decays:
1.0
1.0411723327434699
1.0712715905255132
1.0869666718390047
1.086815165390184
1.0734484829458877
1.048255640992866
1.0137467150895072
0.9668091110022087
0.906007463426958
0.8319494116214141
0.7513883561991619
0.666062512398385
…
Ehsan Moradpur-Tari ,
There are a bunch of resources on github that can help you understand how to perform the VACF analysis and what maybe going wrong with your script. Here is one nice python class written by Qijing Zheng that does VACF and pair correlation analysis:
https://github.com/QijingZheng/VASP_XDATCAR
I also wrote a script a while back that does VACF but using LAMMPS dump files:
http://u.arizona.edu/~stefanb/Codes/dump2VDOS.py
Good luck,
Stefan
Dear Ehsan,
from your formulas, it looks like you are not calculating the VACF, but the correlation of kinetic energy fluctuations.
To get the VACF, the correct formula is:
c(t)= < vi(t)*vi(0) >,
Where * denotes the scalar product. I just found online this nice page, you might want to check it:
ftp://ftp.dl.ac.uk/ccp5/DL_POLY/Democritus/Theory/vaf.html
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