I want to calculate the g(r) of two liquids that are not miscible. I want the effective potential between the molecules in two liquids. I need the g(r) for using iterative Boltzmann inversion to get the potential. So what is the effective way to calculate the radial distribution?
If you have run molecular dynamics simulation of the system with the two liquids, using VMD can be an easy way to calculate the radial distribution function.
Hi Sudharsan,
I'll try and give a "bare-bones" answer.
The question depends on exactly how much detail you need from the radial distribution function (RDF). For example, when you have two immiscible liquids you would generally define the RDF as a function of the z dimension (assuming infinite x and y), meaning the RDF is simply the density profile across the phase boundary, calculated as
g(r) = ρ(z)/ρ0
= N(z) / (ρ0 x L2 δz)
where ρ(z) is the density at z of species 1, ρ0 is the bulk density of species 1, N(z) the number of species 1 at z, and L the length of x=y, and δz the length of the bin in z. This generally has a hyperbolic tangent form as liquids have "soft" interfaces.
However, if you want an RDF as a function of r and z for each point between the liquids, things get a little more tricky. I suggest reading Ashbaugh et al., JACS, 2005, 127, 2808-2809, where Ashbaugh et al. provide a method for an approximate RDF between water-oil at an interface that is shown to be similar to an RDF between water and methane. Alternatively, you can calculate the RDF in the usual way and apply a correction, i.e.
gij(r) = 1/( ρi ρj V dV nf) nij(r)
where ρ is the bulk density, V the volume, and nf the number of frames, and n(r) the number of species at r. The correction needed is a little too robust to post here, but you must account for the region of "lost" correlations depending on the concentration of each species at each point in z, otherwise the g(r) functions will not all plateau at 1. Hope this helps.
Regards,
Quinn
I think that you cannot define a sensible RDF between components that are not in the same phase. As implicitely pointed out by Quinn Alexander Besford perhaps you should try to get information from the density profile, or from distribution functions that take into account not only the distance between the pairs of particles, but also their positions with respect to the interface. But perhaps I have not understood properly the question.
Dear Sudharsan (and others),
Further to my original answer (3 years ago), I've just published the correction needed in the RDF to account for regions of lost density for "mean" interfaces. It may be found in the supporting information of Article Stabilizing Dipolar Interactions Drive Specific Molecular St...
Kind Regards,
Quinn