AMBER Archive (2004)

Subject: AMBER: entropy implementation in ptraj

From: Raik Grünberg (
Date: Tue Dec 14 2004 - 11:37:18 CST

Hi there,

I have rather extensively used Amber 8 ptraj for the calculation of entropies
from MD trajectories. With some tricks here and there, things have worked out
quite well - much better (and more efficient) than what I got from my own
feeble attempts of implementing this calculation. Thanks a lot for adding
this method to ptraj!

Unfortunately, I couldn't find any reference for how exactly the entropy
estimate is implemented in ptraj. I haven't got any Fortran knowledge, so I
am pretty lost when looking at the source code.

The classic way of calculating the vibrational entropy from the eigenvalues ev
of the mass-weighted (?) covariance matrix C would be:
(1) S = -1/2 kb SUM( ln ev_i )
or S = -1/2 kb ln | C | [Karplus Kushick 1981]
Then there is the famous Schlitter correction (Schlitter, 1993) which adds
some term to the covariance matrix before determining the eigen values:
(2) C' = C + [ M^-1 h^2 / (kb T e^2) ]
(3) S = -1/2 kb ln | C' |
(M is the diagonal vector of masses)

I suppose the latter is what you are using in ptraj, isn't it?

Next question - in ptraj, the entropy contributions from the decreasing eigen
values neatly converge to zero. In my own implementation any such convergence
was usually messed up by many low but non-zero eigen values and it was never
clear where (or if) I should cut the list. This may of course point to some
mistake on my side - Anyway, is ptraj using any trick to force the
eigenvalues to converge on zero?

Thanks a lot for any help!

Raik Grünberg          | Bioinformatique Structurale
                       | Institut Pasteur
Tel: +33/ | Paris, France

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