# [gmx-users] correlation functions

rams rams rams.crux at gmail.com
Fri Sep 12 22:49:39 CEST 2008

```Dear users,

I am trying to obtain the rotational correlation times using gromacs tools.
Though there are a couple of methods suggested by Xavier and others, I am
trying to test it completely with gromacs tools.

The basic idea is as suggested in the following article (also the article is
suggested by David van der Spoel)

What NMR relaxation Can Tell Us about the Internal Motion of an RNA Hairpin:
A Molecular Dynamics Simulation Study", J. Chem. Theory Comput, 2006, 2,
1228.

The way I understood is the following:

1. The correlation functions we calculate from the MD simulations they are
total correlation functions (i.e., they contain both overall tumbling and
internal correaltions). So we have to separate them i.e.,

C(t) = C0(t) * CI(t)

In the above mentioned article, they obtaind the internal correlation
functions from the MD trajectories, by translating and rotating the each
conformation onto a reference structure (i.e., if I understand correctly,
they have created a translational and rotational free trajectory here) and
then they have used this trajecotry to obtain the internal correaltion
functions and eventually used these functions to obtain the internal
correlation times by fitting it to different models like Lipari-Szabo etc.

I did removed the rotational and translational motions from my trajectory
and created a rotational and translational free trajectory by the following:

trjconv -fit rot+trans

Then used g_rotacf to obtain the correlation funcitons of internal motions
(N-H bond vectors).

These correlation functions were tried to fit to S^2+(1-S^2)*exp(-t/t1) to
obtain the S^2 order parameters and the correlation time (t1). But the order
parameters I am getting are too small.

Then they mentioned that the rotational correlation function is obtained
from the above relation. Is it a straightforward, algebraic division ? I am

I tried to get them by a simple numerical division but the rotational
correlation functions I obtained are not exponentially decaying functions
rather they linearly increase with time. I am not sure where I am making
mistake.

Also, How accurate the generated rotational and transational free trajectory
is ? Since my S^2 order parameters are not comparable to experimental
values, i cannot judge based on them.

I also tried to fit the total correlation function C(t) with
exp(-t/to)*(S^2+(1-S^2)*exp(-t/te)) . surprisingly the "to" (overall
rotational time), S^2 and "te" (internal correlation times) are comparable
to experimental values, the fit also very gud though its not an accurate
method to do it.

I am sorry for quite lengthy email. But surely it will be helpful to others
also. I can be more explicit if some one interested to know.