I have been wondering how one can determine the atomic radius from the radial distribution function (RDF) of a specific type of atom. Let's say I have a liquid argon system and generate the RDF from a molecular dynamics (MD) simulation. My goal is to check whether the RDF is well-represented, and I thought that one way to do this might be to determine the atomic radius from the RDF and compare it to known values.
Now, my question arises from the fact that I read that the atomic radius should be approximately half the distance at which the first (and most intense) peak appears in $g(r)$. This makes sense because it would mean that the highest probability of finding another atom is at a distance of about twice the atomic radius, which suggests that the atoms are effectively "touching."
However, I do not fully understand why $g(r)$ has nonzero values at distances smaller than this. Intuitively, I would expect $g(r)$ to start at zero and remain zero until $r=2r_0$ (where $r_0$ is the atomic radius), since at shorter distances, two atoms should not be able to overlap. Why, then, do we observe nonzero values of $g(r)$ for distances smaller than this?
Is this effect due to the way the simulation treats atoms as point particles rather than hard spheres?
Edit: I forgot that my intuition tells me that where the value of $g(r)$ starts to be non-zero, this should be value of the radius, but I am not sure at all.