# AMBER Archive (2004)Subject: Re: AMBER: entropy implementation in ptraj

From: David A. Case (case_at_scripps.edu)
Date: Fri Dec 17 2004 - 10:11:29 CST

On Fri, Dec 17, 2004, Raik Gr?nberg wrote:

> 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.

Ptraj just sums the vibrational entropies from each of the modes, and adds the
rigid rotational value and the translational entropy to get the sum. Quantum
mechanical formulas are used for the vibrations (see any textbook on physical
chemistry). Hence, the total S below is just the sum of the three values
immediately below it, and the vibrational entropy is the sum of all of the
individual modes listed below _it_.

You have 3N-6 = 1428 vibrational modes; the final six modes are the
translation/rotation that should have been removed by rms superposition (looks
like this has been done). Hence, you should ignore the final six modes in
your output (they have zero entropy anyway).

>
> 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
>
> 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 ?

Since neither (1) nor (2) is used, these final questions are irrelevant.

...regards...dac

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