Ewald size-dependence correction in FEP simulation of an electric dipole

From: Ali Mehdizadeh Rahimi (mehdizadehrahimi.a_at_husky.neu.edu)
Date: Wed Sep 12 2018 - 19:34:37 CDT

Dear All,

The problem that I’m interested in is to charge two naked Lennard-Jones
particles to opposite unit charges (create a dipole), starting from zero
charge to the two atom’s final charge (-1 and +1). I want to calculate the
charging free energies of the dipole as I change the distance between the
two atoms (and ultimately obtain a landscape of energy as a function of the
distance between the two atoms to assess the accuracy of a continuum theory
that I’m working on).

I went through the FEP tutorial for charging a spherical sodium ion.

The change that I made to the setup.pgn was to add another sodium segment:

segment SOD1 {

  residue 1 SOD

}

segment SOD2 {

  residue 2 SOD

}

and wrote the outputs to setup.pdb and setup.psf files.

I modified the resulting psf file:

…

       4 !NTITLE

 REMARKS original generated structure x-plor psf file

 REMARKS topology ../common/top_all22_prot.inp

 REMARKS segment SOD1 { first NONE; last NONE; auto angles dihedrals }

 REMARKS segment SOD2 { first NONE; last NONE; auto angles dihedrals }

       2 !NATOM

       1 SOD1 1 SOD SOD SOD -1.000000 22.9898 0

       2 SOD2 2 SOD SOD SOD 1.000000 22.9898 0

….

and the pdb file (e.g. for when the distance between the two oppositely
charged atoms, d, is 6 A):

REMARK original generated coordinate pdb file

ATOM 1 SOD SOD 1 -3.000 0.000 0.000 -1.00 0.00 SOD1
NA

ATOM 2 SOD SOD 2 3.000 0.000 0.000 -1.00 0.00 SOD2
NA

END

and then solvated the dipole in a water box using solvate plugin of VMD and
modified solvate.pdb:

CRYST1 46.000 46.000 46.000 90.00 90.00 90.00 P 1 1

ATOM 1 SOD SOD S 1 -3.000 0.000 0.000 1.00 1.00 SOD1
NA

ATOM 2 SOD SOD S 2 3.000 0.000 0.000 1.00 1.00 SOD2
NA

ATOM 3 OH2 TIP3W 5 -19.332 -9.918 -4.096 1.00 0.00 WT1
O

ATOM 4 H1 TIP3W 5 -19.776 -9.549 -4.899 1.00 0.00 WT1
H

ATOM 5 H2 TIP3W 5 -19.908 -9.621 -3.373 1.00 0.00 WT1
H

….

….

and saved as solvate.fep.

Finally equilibrated the system and ran forward and backward simulations.

What would be the right expression to estimate the error due to the
size-dependence of the energy to the system in my problem since the box is
already charge-neutral?

Thanks a lot for taking the time,
Ali

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