[gmx-users] On computing entropies using g_anaeig

[Hari Shankar M]

Gmx-users,

There has been a earlier post on differences in entropies computed using the covariance analysis and normal mode analysis (http://lists.gromacs.org/pipermail/gmx-users/2009-April/041535.html). I discovered the reason for the differences and thought that this information might be useful to others.

1. g_anaeig tool used to compute the entropy, computes entropies from the eigenvalues of the covariance matrix only. So, feeding the eigenvalues obtained from the mass-weighted Hessian to g_anaeig gives meaningless entropy values. Probably, this information should be clearly stated in the manual to prevent any potential abuse of g_anaeig. I compared the results on a diatomic molecule (oxygen) and benzene, and found very different results. The values differ by an order of magnitude. Also, looking at the source code of gmx_anaeig.c, it is clear that the entropies are computed from the covariance eigenvalues and not the eigenvalues of the Hessian. 

2. There is a user-developed code distributed on the gromacs website called 'calc_entropies.pl'. This script can be used to compute entropies from eigenvalues obtained by covariance analysis or normal mode analysis. However, there seems to be a bug in this code. While the conversion of the eigenvalues to eigenfrequencies is done correctly in this code, there is a huge difference in the formula used to compute the entropy in the case of normal modes (for entropy formula refer to Karplus and Kushik 1981 paper). After correcting the entropy formula, I was able to get similar results with either method. If you are interested in the corrected script, you could email me at hari711 at yahoo.com.

I hope this information is helpful for those who are working on entropies.

Best,
Hari
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