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...
Cheers,
Chris.
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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