Re: [ESPResSo-users] Bjerrum Length for Explicit Solvent

[Stefan Kesselheim]

Dear Jezreel, Marcus and Espressis,

On Oct 5, 2013, at 6:20 PM, Markus Deserno <address@hidden> wrote:

> Jezreel,
> 
> the Bjerrum length is the distance at which two unit charges experience
> an electrostatic interaction energy equal to the thermal energy. For water,
> this is about 7 Angstrom, independent of whether the solvent is treated
> explicitly or implicitly. It would be rather unphysical if this physical 
> quantity
> depended on the way you implement a solvent in your computer program.
> It is rather the other way around: Whatever you do to your computer model,
> you must make sure that physical parameters are reproduced, and the
> Bjerrum length is one such.

I'm not sure if should agree on that. When you create a solvent model with 
dipoles, partial charges, or whatever you do not know its dielectric constant. 
You know however the dielectric constant of the medium, you embed it in, 
typically this is vacuum. In vacuum at room temperature the Bjerrum length is 
around 56 Angstrom. This is the number you would put into you electrostatics 
algorithm. 
The dielectric constant of the medium is a result of a simulation, and can be 
used to define (!) a Bjerrum length in the medium. 
I think this is important: l_B is not the distance where the electrostatic 
energy is unity, but the distance at which it would be unity, if the medium 
were a homogeneous dielectric with the measured dielectric constant. This also 
means: there is no way of measuring the Bjerrum length, except for in vacuum.
If you treat a solvent implicitly, the Bjerrum length is an input parameter, of 
course.

To make an example: If you want say TIP3P water in Espresso, you create all 
particles and bonds and such things, and use the vacuum Bjerrum length for the 
electrostatics algorithm. You can measure a dielectric constant and from that 
determine the Bjerrum length of the solution. Next you can create an implicit 
solution model, where you plug in the Bjerrum length you have obtained before, 
and compare its properties to the original explicit model.

I hope I caused not more confusion and that that helps.
Cheers
Stefan