[gmx-users] HB lifetime

Omer Markovitch omermar at gmail.com
Thu Oct 2 10:45:24 CEST 2008

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

> 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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