# [gmx-users] Re: What is epsilon_r?

Wed Apr 18 20:24:05 CEST 2012

```Hi,

Thank you, Justin, for your time!

By reading the post that you sent
(http://lists.gromacs.org/pipermail/gmx-users/2004-March/009650.html), it
seems that epsilon_r is just a scale factor.  I interpret this as meaning
that if, for example, I use epsilon_r = 2, then Coulomb interactions will be
scaled down by a factor of 2.  That is, the Coulomb potential
(1/(4*pi*epsilon0))*(q_i q_j)/|r_i - r_j| will be multiplied by 1/2.

But even if my interpretation is correct, what does this mean?  epsilon_r
does not seem to be a reaction field parameter, since the value of epsilon_r
affects the electric potential that I calculate even though I am not using
implicit solvent, nor am I using one of the reaction field electrostatics
methods.  Or, a different way to phrase this is, if most or all modern force
fields are parametrized based on epsilon_r and if one is not using any sort
of implicit or coarse-grained solvent or applying a reaction field
electrostatics method, then why would anyone want to scale down the Coulomb
potential?

Also, I am wondering about the boundary condition for the Ewald method.  It
seems that, for the Ewald method, one must specify the dielectric constant
at the boundary.  For example, the text on liquid simulations by Allen and
Tildesley says (page 157), "... we must specify the nature of the medium
surrounding the sphere, in particular its relative permittivity (dielectric
constant).  The results for a sphere surrounded by a good conductor such as
a metal (epsilon = infinity) and for a sphere surrounded by vacuum (epsilon
= 1) are different [de Leeuw, Perram, and Smith 1980]."

My question is, what epsilon parameter in Gromacs serves this purpose.  One
possibility is epsilon_surface.  However, this does not seem to be the right
parameter, because the manual entry for epsilon_surface says, "Turn it on by
setting it to the value of the relative permittivity of the imaginary
surface around your infinite system."  This wording almost seems to imply
that it is a dipole correction (not a dielectric boundary condition), and
that there is some other parameter that, in fact, controls the "relative
permittivity of the imaginary surface."  Is this true?  If so, what is this
parameter?

Andrew DeYoung
Carnegie Mellon University

Andrew DeYoung wrote:
> Hi,
>
> What is the parameter epsilon_r mentioned in the manual
> (http://manual.gromacs.org/current/online/mdp_opt.html#el)?  The manual
says
> that it is the relative dielectric constant.  My initial thought was that
> this would only be relevant for reaction-field electrostatics, or
somewhere
> where implicit solvent is used.  However, it seems that epsilon_rf (not
> epsilon_r) is used for reaction-field purpose.
>
> I am not using implicit solvent in my system, nor am I using a
> reaction-field method (I am using PME electrostatics); in my system, I am
> using an all-atom description.  Then, does epsilon_r generate "additional"
> dielectric, beyond what naturally arises from the all-atom description of
> the solvent?
>
> Even though I am not using a reaction-field method, epsilon_r is clearly
> affecting something, because when I use g_potential to calculate the
> electric potential, the results vary considerably depending on the value
of
> epsilon_r that I use in my .mdp file.
>
> Do you have any thoughts about what epsilon_r does in an all-atom
descripton
> of a solvent?  Does it provide "additional" charge screening?
>

http://lists.gromacs.org/pipermail/gmx-users/2004-March/009650.html

-Justin

--
========================================

Justin A. Lemkul
Ph.D. Candidate
ICTAS Doctoral Scholar
MILES-IGERT Trainee
Department of Biochemistry
Virginia Tech
Blacksburg, VA
jalemkul[at]vt.edu | (540) 231-9080
http://www.bevanlab.biochem.vt.edu/Pages/Personal/justin

========================================

```