Reviewer 2 Comment 6.1: Finite size effects

[mostafa-razavi]

Reviewer 2 Comment 6.1:

6.1 It seems to this referee that Figure 9 is illustrating the divergence of the pressure determination in the zero density limit when the molecule has internal degrees of freedom. This behavior is frequent when the atomic virial route is used for pressure determination because the atomic virial expresses as PV = nkT + W , where n is the number of atoms (not the number of molecules!) and the virial term W contains contributions from internal forces and from intermolecular forces. Depending on the numerical approximations in computing intra- and intermolecular forces in the atomic virial, Z may not tend toward 1 in the zero density limit. MC predicts better the compressibility factor Z in low density phases, because MC codes are generally using the molecular virial route in which PV = NkT + W' where N is the number of molecules (not the number of atoms) and where the virial W' contains contributions from intermolecular forces only. Thus Z tends toward 1 in the low density limit. If this interpretation is correct, there is no reason to use a large number of molecules for vapor phases in MC. The authors should discuss these points more thoroughly. They may also consider merging the section "Finite size effects" with "Simulation details" .

Our response: In light of the reviewer’s comments, we examined the virial contributions for ethane in greater detail, as shown in the figure below. It is clear from the figure that the intermolecular contribution to the virial is approaching zero as expected, but the bonded contribution deviates significantly from its steady approach to -1 as the density approaches zero. The discrepancy is magnified in the computation of (Z-1)/ρ owing to the division by density. The bonded contribution to the virial is a quantity reported by LAMMPS with little recourse for user intervention. Presumably, the problem is the small number of intermolecular collisions at low density relative to the large number of intramolecular collisions, inhibiting the equilibration of the various components of momentum. To illustrate one manner of correcting for this deficiency, we used a linear extrapolation of the intramolecular virial, enforcing a value of -1 at zero density. Then we recomputed the total virial. As shown below, this procedure reduces the problem, but requires considerably more effort than switching to fixed bond lengths.

We include this figure with a detailed explanation in the Supplementary Material. We also briefly mention the nature of the correction in Section 6.

[ramess101]

@mostafa-razavi

Looks good to me.