# [gmx-users] How Coulomb energy terms are calculated?

vincenzo moreschini vmprivateer at mail.com
Thu Jun 21 13:11:41 CEST 2012

```Dear users,

I'm trying to understand the way gmx calculates non-bonded interactions
and I set up a toy system composed of two water molecules with initial
coordinates:

1SOL     OW    1   0.3758265   0.5507358   0.8927467
1SOL    HW1    2   0.3234106   0.4695494   0.8670300
1SOL    HW2    3   0.3936553   0.6061094   0.8114085
2SOL     OW    4   0.0000000   0.0000000   0.0000000
2SOL    HW1    5   0.1000000   0.0000000   0.0000000
2SOL    HW2    6  -0.0333313   0.0942816   0.0000000

and zero velocities. Modifying spce.itp I put HW charges=0 so that only
Oxygens matter. Calculating distance between
atom 1 and 4 and then the Coulomb term as f*q*q/r I get 89.5803168839 kj/mol
with f taken from the manual (138.935), q=-0.8476 and r=1.1142495905.

The I set nstlist=rcoulomb=rvdw=rlist=0.0 pbc=no and nstype simple. Doing 1
step of sim I get:

Energies (kJ/mol)
Bond          Angle        LJ (SR)   Coulomb (SR)      Potential
3.65337e-10    5.85205e-05   -1.36690e-03    8.95803e+01    8.95790e+01
Kinetic En.   Total Energy    Temperature Pressure (bar)
5.31575e-11    8.95790e+01    8.52446e-10    0.00000e+00

Playing with constraints does changes nothing, as I think it should.

However, when I insert the correct charges (0.4238) for hydrogen atoms,
using the same set up I get

Energies (kJ/mol)
Bond          Angle        LJ (SR)   Coulomb (SR)      Potential
3.65337e-10    5.85205e-05   -1.36690e-03    2.76599e-01    2.75290e-01
Kinetic En.   Total Energy    Temperature Pressure (bar)
3.13252e-12    2.75290e-01    5.02337e-11    0.00000e+00

But summing the values of the 9 Coulomb interactions present in the systems
(6 atoms -> 6*(6-1)/2 -bonded terms)
by hand I get about twice i.e. 0.479870592 kjmol-1.
Given that I made no errors (I shouldn't since I pasted formulas in a xls
sheet and checked but only death and taxes are sure) what am I missing?

thank you

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