[gmx-users] New shell water model, tabulated bonding interactions, and the documentation.

[Eric Shamay]

Over the past couple days I've attempted to implement the water model
developed by Ishiyama & Morita (J. Phys. Chem. C 2007, 111, 721-737) using a
combination of the shell polarization technique and tabulated potentials for
the bonded terms, among other things. Before elaborating below, the
documentation I found was pretty weak for the tabulated bond potentials, and
forum posts were limited in scope, so I'd like to gather some information
from those in the know such that the wiki and documentation may be updated
on this front. Furthermore, as I slowly understand and make progress, I'll
most likely post follow-ups with more questions to round out the discussion.

>From the paper above, the water model is composed of 5 sites - Oxygen (O),
Hydrogen (2x H), center of mass (G), and an auxiliary site (M) along the
bisector a distance 0.021 nm from the O. All the nonbonding terms are given,
and the intramolecular potential is as follows:

U_intra_i = Sum(n=2,6: K_n*(r1^n + r2^n)) + 1/2*K_theta*r3^2 +
K_r_theta*r3*(r1+r2) + K_r_r'*r1*r2

Where r1 and r2 are the O-H bond displacements from the equilibrium value,
and r3 is the H-H displacement. The first term is a sum with force constants
K_2, K_3,...,K_6 multiplied by the corresponding bond displacement
exponentials, and is where I planned to use a tabulated bond potential a la
the '-tableb' option for mdrun. The higher-order terms have been found
necessary for reproducing the OH vibrational red-shifting in calculated IR,
Raman, and SFG spectra. The 2nd term is the standard harmonic term but for
the H-H bond. The 3rd and 4th terms are bond-angle and bond-bond cross
terms, and are readily available in the gromacs suite already.

Turning to the tabulated potentials, this is where my questions begin. I've
calculated the 3 columns needed in a table_b0.xvg type of file: x, f(x),
f'(x) -- corresponding to the bondlength, potential, and first derivative of
the potential (a.k.a. the force), respectively. In doing so I've assumed
units of nm, kJ/mol/nm, and kJ/mol/nm^2, respectively. The function, f(x),
is as follows:

f(x) = K_2*x^2 + K_3*x^3 + K_4*x^4 + K_5*x^5 + K_6*x^6

It's rather straightforward, and gives a clean analytical solution for the
first derivative:

f'(x) = 2*K_2*x + 3*K_3*x^2 + 4*K_4*x^3 + 5*K_5*x^4 + 6*K_6*x^5

Question: Is the analytical version what I sohuld put in the 3rd column, or
should I use a finite difference method? Using the analytical version
produced a warning that my potential derivative values are an average of
164% off from the internally calculated ones - does that message mean
anything? Does it mean that I'm doing things right? Furthermore, why bother
with this 3rd column if it is something already calculated (and compared to)
by gromacs?

Using a tabspace (resolution) of 1000 datapoints per nm, I constructed a
3-column table, table_b0.xvg, and added the following to the .itp file's [
bond ] section:

[ bonds ]
; pair-potential harmonic bonds O-H terms
1 2 8 0 1.
1 3 8 0 1.

(where 1 == Oxygen; 2,3 == hydrogens)

This signifies that a lookup table will be used (with exclusions) and that
the potential will be multiplied by a force constant of 1.0 kJ/nm/mol --
effectively not changing the tabulated value.

Question: Does this all sound sane so far? Is that value of 1.0 for the
force constant actually keeping the potential term unaltered? Furthermore,
what changes if I use the function type 8(w/exclusions) vs. 9 (w/o
exclusions)?? What is being excluded if I use 8, and what does it mean if
something is excluded from bonding terms? Where are the intra-molecular
bonding exclusions defined?

Next step is to run the simulation. All is similar to previous successful
simulations in terms of my mdp input file, but I add the option of 'mdrun
-tableb table.xvg' in order to use the tabulated bond potentials for my O-H
bonds.

Question: is -tableb the only parameter needed to pass information about the
tabulated data for mdrun and simulations? Are any options necessary in the
.mdp run input file?

Once I get some confirmation about the above I'll feel confident enough to
boldly stride towards finessing the water model .itp file for sharing, and
more coherent documentation. I'm sure others have come across this issue
before, and it would be great to have some type of example fully
illustrating use of the tabulated potential data in a simulation.


~Eric
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