# Re: AMBER: entropy implementation in ptraj

From: Raik Grünberg <graik.web.de>
Date: Fri, 17 Dec 2004 15:44:13 +0100

Dear David,

> On Tue, Dec 14, 2004, Raik Gr?nberg wrote:
> > 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.
>
> Without knowing more about which ptraj commands you used, it's hard to
> answer this question. It sounds like you are going along a path that

Here are the ptraj commands I am using (fitting and slicing of the trajectory
is done outside ptraj):

trajin in.crd
matrix mwcovar name mwc
analyze matrix mwc vecs 0 thermo

>
> > Next question - in ptraj, the entropy contributions from the decreasing
> > eigen values neatly converge to zero.
>
> I guess I would have to see part of the output you are referring to. The
> entropy contribution should go to zero for *increasing* frequencies. Note
> that with the quasiharmonic approach, it can be very difficult to get a
> converged result for the entropy; see, e.g. Fig. 2 in

I've attached an output file from ptraj. If I understand it correctly, the
increasing frequencies given in the output, stem from decreasing eigenvalues
of the diagonalized mass-weighted covariance matrix. My question (1) is
whether the entropy is directly calculated from that matrix C:
S = 1/2 kB ln | C |
or whether ptraj applies the Schlitter quantum mechanical correction to C:
C' = C + ( M^-1 h^2 / (kB T e^2) ) [M is the atom mass vector]
or if ptraj uses an alltogether different formula.

Question (2) refers to the entropy contributions of the different modes that
are listed by ptraj, for example:

freq. E Cv S
cm**-1 kcal/mol cal/mol-kelvin cal/mol-kelvin
--------------------------------------------------------------------------------
Total 2098.702 1798.606 2849.239
translational 0.888 2.979 52.025
rotational 0.888 2.979 50.480
vibrational 2096.926 1792.648 2746.734
1 1.826 0.592 1.986 11.381
2 1.903 0.592 1.986 11.299
3 2.180 0.592 1.986 11.029
4 2.345 0.592 1.986 10.884
5 2.639 0.592 1.986 10.649
.........
1425 1694.561 2.424 0.037 0.005
1426 1701.617 2.434 0.036 0.005
1427 1710.082 2.446 0.035 0.005
1428 1727.559 2.471 0.033 0.004
1429 70075.282 100.184 0.000 0.000
1430 71219.408 101.819 0.000 0.000

If the entropy is calculated with a formula like S = 1/2kB ln |C|, each
contribution should be related to a single eigenvalue of C
S_mode = 1/2 kB ln ev_mode

The funny thing is that the contributions listed by ptraj are always positive.
That means there are apparently no eigenvalues < 1 . I was wondering whether
ptraj, for example, divides all eigenvalues by the smallest or uses any other
trick to ensure that eigenvalues are always >= 1 ?

Many thanks for any hint!
Raik

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Received on Fri Dec 17 2004 - 15:53:01 PST
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