To clarify my question, I am trying to construct a coarse-grained modeling of an fcc system using the iterative Boltzmann inversion method to compute the pair potential interactions. However, in order to be able to start the iterative process, I first need to use V0(r)=-KBTln(g(r)) as an initial guess for the pair interactions among my CG beads. the g(r) values used in this relation are those computed from the all-atom system. However, as you know the rdf values of a crystalline structure is not continuous and it contains zero values between the peaks where the crystall lattices lie and I have no idea what to do with these zero values as they cannot be used in this relation as ln(0) is meaningless.
Another problem that I have is that I am using lammps software for my simulations and I have used lammps to compute these rdf values but the values do not match the values that I obtained manually using this relation: g(r)=V*dn(r)/4pi*r^2*N*dr
I really appreciate your help and suggestions.
From the computational perspective, it seems justified to offset your g(r) by a small number, let's call it epsilon, just to avoid singularities when calculating log(0). If your algorithm doesn't take days to converge, you can actually verify if the value of epsilon has any effect on the outcome. Then, if your sampling of g(r) is fine enough, discontinuities should not be an issue anymore.
What kind of disagreement between your calculations and the lampps results are you observing? In RDF calculations, some tools omit the 4piR² factor, since it's physical only for spherically symmetric systems.
Thank you so much for your response. I will try to implement your advice.
As for the disagreement between my calculations and that of lammps I must say that they are soooo different. I used the coordination number calculated by lammps to compute the g(r), and the two values differed completely. For example where lammps got a zero g(r) value, I computed a real number. I also mentioned this in lammps mailing list just to make sure that lammps is using the same relation to compute rdf, and they said that the relation I mentioned is a slight simplification and is valid for very large values of N.
Regards,
Melika
Probably showing the two discrepant estimates would help, otherwise I have no idea what could go wrong. The simplification you mention should typically have a very small effect on the asymptotic behavior, so it probably doesn't explain what you're seeing.
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