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

[Markus Deserno]

Folks,

this is a beautiful example of the confusion that arises if one does not

distinguish between the physics one wants to describe and the computer

variables one types into one's favorite simulation engine.

The Bjerrum length is the distance at which the electrostatic part of the

free energy of interaction between two unit charges is equal to the thermal

energy. I concede that my previous email didn't have the important word "free"

in it. But anyways, this is how it is defined, and no computer simulation

software in the world will change that. Whether one uses implicit solvent

or explicit solvent, at the end of the day, it must be true that if you put

two unit charges at that distance into your simulation, their potential of

mean force in that solvent is equal to the thermal energy.

Now, in ESPResSo the Bjerrum length is apparently used as an input

parameter for electrostatics. That is partially convenient, but also partially

confusing. Stefan is right that if you use an implicit solvent water model,

you would type in 7 Angstrom at that point, while if you have an explicit

water model there, there is no need to account for a dielectric constant,

since it will be created explicitly by the solvent. Electrostatic interactions

then don't have a dielectric permittivity in them, and one can account that

by using a value for the Bjerrum length corresponding to vacuum, and

that is about 56nm (not Angstrom!). But that only means that the parameter

in the script is set to that value. The Bjerrum length in your simulation should

be 7A. If it is not, you are simply not simulating water. (In fact, it probably

is not, since hardly any model is perfect in giving the right dielectric constant,

and you certainly wouldn't know just by guessing it.)

I also disagree that it's impossible to measure the Bjerrum length. Of course

it is possible. All you need to do is to measure the potential of mean force

between two unit charges in your system as a function of distance, and look

for the distance where it is equal to the thermal energy. This has been done.

As Stefan suggests, you could alternatively calculate the dielectric constant

of your system and calculate the Bjerrum length from there.

So again: My main point here is: Please don't lose the physics out of sight.

It is all fair and square if your simulating day in and day out to think about

the values of your input parameters. But it is all too easy to forget that the

value of the input parameters and the physical meaning of the things they

are supposed to represent are not necessarily the same. I have witnessed

too often to count that people waste weeks of research by that. In this case:

Yes, if you want to simulate an explicit water model, you cannot set the value

of the Bjerrum length input parameter in the Espresso Script to 7 Angstrom.

And yet, that does not mean that suddenly the Bjerrum length is different.

It means that the physics is the same but the model is different, and what

is called "Bjerrum length" in the input script is no longer the Bjerrum length.

ESPResSo was developed in a time where nobody wanted to simulate

explicit water with it, and hence it was natural to call the strength parameter

of the electrostatic interaction the Bjerrum length, since people always used

implicit models. Now that explicit models are used as well, you simply have

to jury-rig the code and make it do what you want. You crank up the input

parameter of the Bjerrum length to its vacuum value. But that doesn't mean

that the value of the Bjerrum length depends on the model. The Bjerrum

length is a physics concept and must be model independent. Instead, the

input parameters of the model must be adapted such as to reflect the right

physics. Sadly, the input parameters were given physical names, and this

now may or may not cause confusion.

To be fair: Jezreel probably asked about the input parameter in the first

place. But the language was confusing. Maybe I'm just a bit too pedantic

to point all of this out, but in my experience it is helpful to keep a very clean

line between the physics one wishes to describe and how to algorithmically

implement this. Using a clear language is never a mistake.

Best,

Markus Deserno

-- 

Dr. Markus Deserno ++1-412-268-4401 (office)
Associate Professor of Physics ++1-412-681-0648 (fax)
Carnegie Mellon University ++1-412-268-8367 (Amanda Bodnar)
5000 Forbes Avenue www.cmu.edu/biolphys/deserno/

Pittsburgh, PA 15213, USA address@hidden

On Oct 5, 2013, at 9:19 PM, Jezreel Castillo <address@hidden> wrote:

Thank you very much. It has been very informative.

Respectfully,

Jezreel

On Sun, Oct 6, 2013 at 12:33 AM, Stefan Kesselheim <address@hidden> wrote:

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