[gmx-users] HB lifetime

Christopher Daub cdaub at vcu.edu
Tue Sep 30 17:45:01 CEST 2008

> From: Laercio Pol Fachin <laercio_pf at yahoo.com.br>
> Date: September 30, 2008 9:50:48 AM EDT
> To: gmx-users at gromacs.org
> Subject: [gmx-users] Hydrogen Bond Lifetime
> Reply-To: laercio_pf at yahoo.com.br, Discussion list for GROMACS  
> users <gmx-users at gromacs.org>
> Hi, all.
> I am analyzing the hydrogen bond lifetime of water molecules around  
> polar atoms of my molecule. However, I have faced different HB  
> lifetime definitions in different sources. A sample of what I  
> obtained employing g_hbond is below:
> "g_hbond -f .xtc -s .tpr -n .ndx -ac .xvg -b 0 -e 10000"
> Type      Rate (1/ps)  Time (ps)  DG (kJ/mol)
> Forward         0.797      1.254       5.089
> Backward        0.061     16.475      11.474
> One-way         1.323      0.756       3.835
> Integral        0.948      1.055       4.661
> Relaxation      2.195      0.456       2.579
> # In GROMACS 3.3 manual, page 171, it is said that "the integral of  
> C(t) gives a rough estimate of the average H-bond lifetime", which  
> points to a HB lifetime of 1.055 ps (right?);
> # On the other hand, in previous discussion in this list, I have  
> found that "according to Luzar the time corresponding to the  
> forward rate constant should be regarded as 'the' hbond lifetime",  
> which points to a HB lifetime of 0.797;
> Can anyone please clarify such points?


The HB definitions and associated lifetimes are a bit arbitrary, so  
there' s always going to be some ambiguity here.  That being said,  
the reason the integral of the HB correlation function C(t) isn't an  
ideal definition is that C(t) is only roughly exponential.  Same  
argument goes for getting the lifetime from a fit to C(t), or looking  
for the time where C(t)=1/e, or similar simple approximations.

What Luzar recommends is to think about an equilibrium between bound  
and unbound molecules, so that they interact with a forward and a  
backward rate constant k and k'.  k gives the forward rate, ie. the  
HB breaking rate, and k' gives the HB reformation rate... they are  
not equal due to the diffusion of unbound molecules away from the  
solvation shell.  There are a few advantages of going this route, not  
the least of which is that you tend to get similar lifetimes  
regardless of small changes in the HB definition, and whether you use  
geometric or energetic criteria, etc.

Extracting these rate constants is a bit tricky (I usually do it by  
hand), but I guess gromacs has a scheme to do it... I haven't  
actually looked at it (though I really should!).  I'd recommend some  
caution though, a scheme that works well for HB's between water  
molecules in bulk may need to be adjusted to properly model HB's  
between water and polar atoms.

So in this case, the "best" rate constant is probably 0.797 ps-1 or a  
time of 1.254 ps, which is only a bit slower than in bulk water.  I'm  
very surprised that the backward rate constant is so small though...  
this is about 1 ps-1 in bulk water! I've never seen k'  be this small...

Exhaustive details about the HB dynamics issues can be found eg. here:

A. Luzar, JCP 113, 10663 (2000)

Hope this helps,
Chris Daub
(currently postdoc with Dr. Luzar).
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