[gmx-users] HB lifetime

Christopher Daub cdaub at vcu.edu
Thu Oct 2 17:05:35 CEST 2008

Hi Omer,

We are aware of your work with Dr. Agmon, and I believe Dr. Luzar has  
spoken with him about it.  I don't understand it enough to say much,  
but I don't think we have substantive disagreements with it.  Of  
course, the questioner was asking about the implementation of the  
Luzar model in Gromacs, so I tried to explain some of the background  
of her ideas.  Perhaps they'll implement your HB model in Gromacs 5...


On Oct 2, 2008, at 4:45 AM, Omer Markovitch wrote:

> Please see my comments below.
> Hi,
> 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.
> I disagree. HB lifetime is only slightly dependent on the exact  
> values of the geometric parameters, around the usual values of R 
> (O...O)= 3.5 Angstrom & angle(O...O-H)= 30 degrees, please see JCP  
> 129, 84505 (a link to the abstract is given below).
> C(t) of a HB obeys the analytical solution of the reversible  
> geminate recombination (see a short review in JCP 129), and so its  
> tail follows a power law: C(t) ~ Keq*(D*t)^-3/2, which is  
> indicative of a 3 dimensions diffusion.
> 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.
> The reversible geminate recombination deals with the A+B <---> C,  
> here A=B=H2O & C=(H2O)2, the bound water dimer.
> From a single fit to C(t) one receives the bimolecular forward &  
> backward rate constants, which are well defined.
> k' you suggest is an apparent unimolecular rate constant, which  
> appears to be more suited for short times.
> 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.
> I have to disagree again. The A+B=C problem has an analytical  
> solution. Technically, ones only need to know how to calculate an  
> error-function and to solve a cubic equation, please see eq. 9, 10  
> at JCP 129.
> The geminate problem is robust in the sense that it describes C(t)  
> of ANY 2 particles, as long as their behavior is controlled by  
> diffusion, it describes the water pair, but should describe also,  
> for example, liquid argon. For the second case, ofcourse, different  
> rate constants are expected.
> One should NOT see JCP 129 as a "proof" that previous works were  
> absolutly wrong !
> Instead, it shows that the postulate by Luzar & Chandler, that C(t)  
> of water is controlled by diffusion, is right, and that with the  
> analytical solution of the geminate problem one can understand some  
> aspects of the water dimer. For example - what causes the  
> activation energies of the forward & backward rate constants to be  
> about similar rather then being different by the strength of 1 HB?
> Hope I was clear.
> Omer Markovitch.
> ** a link to JCP 129, 84505 (2008) http://dx.doi.org/10.1063/1.2968608
> ** supporting information includes a short trajectory movie

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