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

[Markus Deserno]

Folks,

>> One can take that point of view, but of course the Bjerrum length is then 
>> still measurable,
>> since I can measure the bulk dielectric constant. And I'd like to point out 
>> that as long as
>> the local packing effects are small, the potential of mean force is a valid 
>> approximation.
>> Unfortunately the case of water is really pushing this limit, since the 
>> Bjerrum length is
>> so small. But in solvents with a lower dielectric constant I expect the 
>> discrepancies to
>> become bigger.
> 
> Did you mean the last sentence as written? In lower dielectric constant it 
> should become less problematic, right? The Bjerrum length is then larger than 
> the molecular size, and the "granularity" of the medium is less important. 

Oh dear me. SMALLER of course---that was my whole point.
In my defense: It *is* Sunday morning...

> But my point was: The Bjerrum length _not_ measured by taking two charges and 
> pushing them together until the work you have spent is k_B T. Its definition 
> is stems from the asymptotic behaviour, and that is by definition the 
> dielectric permittivity. 

I see no deep problem here.

>> It is important to stress here that the "free energy" because this means 
>> that is invalid to simulate two charges in water for different distances, 
>> calculate the mean electrostatic energy energy for all distances and use 
>> this energy for the definition of the Bjerrum length. Ulf's suggestion could 
>> be understood like that. The thing that we work with in implicit solvent 
>> simulations is not an energy as for an atomistic system, but it is a Free 
>> Energy where all implicit degrees of freedom have been integrated out. 

Of course. We would not measure the electrostatic *energy* as a function of 
distance. We need
the potential of mean force. And that we get from integrating the force.

>> Let's please not forget why I started this discussion: All I wanted to make 
>> sure is that
>> we understand that the Bjerrum length is a physical concept that is 
>> independent of
>> modeling. If one wants to model water, then the physics tells us what the 
>> Bjerrum length
>> ought to be at the end of the day. If you would like to use the theorists 
>> view that it is
>> just a convenient way of writing a bulk Poisson equation, I'm all with you, 
>> but still,
>> that length is then physical and is characteristic of the solvent, just like 
>> the dielectric
>> constant is, and it will also depend on temperature. Hence, the physical 
>> quantity Bjerrum
>> length ought to be distinguished from an input parameter in some Espresso 
>> script.
> 
> That sounds fair to me, as long as we make clear: Every microscopic model has 
> its own Bjerrum length, for a given temperature. It depends all on the 
> microscopic model how large it is. 

I agree if you mean the following: The potential of mean force between two 
charges in
some medium depends on the medium. Or if you'd like to phrase it in terms of 
models:
The potential of mean force between two charges in some model depends on that 
model.
Yes, because all the other degrees of freedom (everything but your two charges) 
needs
to be integrated out, and for that everything else in your medium/model matters.

However, when we talk about the Bjerrum length of water, we are talking about 
something
that has a physical meaning, and it should not depend on the model you are 
using. Whatever
model you use, you need to tweak its input parameters in such a way that at the 
end of the
day you get 7 Angstrom. And that might even mean to set the value of some model 
parameter,
which somebody decided to call "Bjerrum length", to a value which is distinctly 
not the value
of the Bjerrum length of water. That's hopefully agreed upon by everybody by 
now. I'm simply
warning against the misleading question "Does the Bjerrum length of water 
change if I go from
an implicit to an explicit solvent representation?". The Bjerrum length 
doesn't, but some model
input parameters might.

Best,

Markus



> 
> Cheers and have a nice sunday!
> Stefan