Section I. Introduction

[ramess101]

@mostafa-razavi

The manuscript provides a biased account of the literature, particularly on thermodynamic integration which they undervalue considerably (see remarks 1.2 and 7.3 and 7.4). This reduces significantly the motivations for a new method.

1.1 This referee does not understand why the authors state that the industrial need for vapor pressure calculations must extend to a reduced temperature of 0.45 only (this target is repeated also later in section II, in section VI page 10,  in section VII page 12 and also in the VIII. Conclusions page 13). Actually, the industrial needs extend over the whole liquid‐vapor coexistence curve down to the triple point. For hydrocarbon solvents (eg isooctane, toluene) the triple point corresponds to a reduced temperature as low as 0.30. Why not setting the target to Tr=0.3 ?  

1.2 The authors state about Gibbs‐Duhem integration that “Ahunbay et al. [FPE, 2004, vol 224, page 73] have tested this approach but their implementation has not been tested below a reduced temperature of 0.55”.  However, in the quoted article there are several examples where thermodynamic integration is applied to reduced  temperatures lower than 0.55 : tetralin (down to Tr = 0.48) , tr‐decalin (down to Tr =0.53), indan (down to Tr=0.46) , propyl cyclohexane (down to Tr=0.47) , hexylbenzene (down to Tr=0.48), propylbenzene (down to Tr=0.53). In Ahunbay’s article it is mentioned that vapor pressure determination is using Kofke’s thermodynamic integration method [ JCP 98 (1993) 4149] as implemented by Ungerer et al. [JCP, 112, (2000), 5499]. In the latter reference the thermodynamic integration method is applied down to Tr = 0.45 for n‐pentane and to n‐dodecane. In other applications on TIP4P water models [Vega et al., JCP 125 (2006), 034503] or on branched alkanes [Bourasseau , FPE 225(2004) 49], and probably many others,  thermodynamic integration was applied  down to lower reduced temperatures than Tr=0.45. The above statement by the authors reveals thus (i) a wrong account of the cited literature (ii) an incomplete survey of the literature (iii) misleading statements on the application range of thermodynamic integration to compute vapor pressures at low reduced temperatures. The first motivation of the authors to develop ITIC must therefore be rejected, because the range of effective application of the GEMC+ TI method is larger than the range set as a target by the authors.   

1.3 It is surprising to read that “the data generated along the integration path are valuable on their own merits”. Indeed, a significant part of the integration path corresponds to supercritical temperatures (Tr=1.2) where many liquids undergo fast degradation by pyrolysis. This is the case for instance of n‐ dodecane, one of the compounds investigated in the manuscript. 

[ramess101]

1.1 This referee does not understand why the authors state that the industrial need for vapor pressure calculations must extend to a reduced temperature of 0.45 only (this target is repeated also later in section II, in section VI page 10, in section VII page 12 and also in the VIII. Conclusions page 13). Actually, the industrial needs extend over the whole liquid‐vapor coexistence curve down to the triple point. For hydrocarbon solvents (eg isooctane, toluene) the triple point corresponds to a reduced temperature as low as 0.30. Why not setting the target to Tr=0.3 ?

I agree that we could probably say that the target is the triple point, and demonstrate that this works with the REFPROP equations by going to whatever Tr the triple point is for dodecane. I feel like we might want to use the notation T_r^{tp} throughout instead of a fixed value of 0.45.

I know we mention that the PR is only valid to about 0.45. But I think the reviewer is correct that we really want the entire phase envelope. I don't think we should limit ourselves to what PR does.

[ramess101]

1.2 The authors state about Gibbs‐Duhem integration that “Ahunbay et al. [FPE, 2004, vol 224, page 73] have tested this approach but their implementation has not been tested below a reduced temperature of 0.55”. However, in the quoted article there are several examples where thermodynamic integration is applied to reduced temperatures lower than 0.55 : tetralin (down to Tr = 0.48) , tr‐decalin (down to Tr =0.53), indan (down to Tr=0.46) , propyl cyclohexane (down to Tr=0.47) , hexylbenzene (down to Tr=0.48), propylbenzene (down to Tr=0.53). In Ahunbay’s article it is mentioned that vapor pressure determination is using Kofke’s thermodynamic integration method [ JCP 98 (1993) 4149] as implemented by Ungerer et al. [JCP, 112, (2000), 5499]. In the latter reference the thermodynamic integration method is applied down to Tr = 0.45 for n‐pentane and to n‐dodecane. In other applications on TIP4P water models [Vega et al., JCP 125 (2006), 034503] or on branched alkanes [Bourasseau , FPE 225(2004) 49], and probably many others, thermodynamic integration was applied down to lower reduced temperatures than Tr=0.45. The above statement by the authors reveals thus (i) a wrong account of the cited literature (ii) an incomplete survey of the literature (iii) misleading statements on the application range of thermodynamic integration to compute vapor pressures at low reduced temperatures. The first motivation of the authors to develop ITIC must therefore be rejected, because the range of effective application of the GEMC+ TI method is larger than the range set as a target by the authors.

I have not looked closely at the literature cited here. How do we need to respond to this?

[ramess101]

1.3 It is surprising to read that “the data generated along the integration path are valuable on their own merits”. Indeed, a significant part of the integration path corresponds to supercritical temperatures (Tr=1.2) where many liquids undergo fast degradation by pyrolysis. This is the case for instance of n‐ dodecane, one of the compounds investigated in the manuscript.

As Dr. Elliott mentioned, we need to clarify this point as to why this is an advantage. The fact that some of these compounds are unstable at the higher temperatures is not really a limitation, in my opinion.

[mostafa-razavi]

I have not looked closely at the literature cited here. How do we need to respond to this?

Ahunbay paper [FPE, 2004, vol 224, page 73]

The reviewer is right. In Ahunbay et al. [FPE, 2004, vol 224, page 73], in a lot of cases, Tr min is below 0.55.

	Tr min	Tr min
Compound	NPT	GE
propylcyclopentane	0.50	0.68
propylcycohexane	0.46	0.67
trans-decalin	0.52	0.67
tetralin	0.53	0.68
indan	0.45	0.66
2,3-dimethylpentane	NN	0.74
2,4-dimethylpentane	0.67	0.72
propylbenzene	0.47	0.70
hexylbenzene	0.44	0.71

FYI: In Ahunbay et al. [FPE, 2004, vol 224, page 73], they perform GEMC when T>Tb. When T<Tb, NPT simulations are performed (where P=0) to get rhoL sat in conjunction with Gibbs-Duhem integration along Clasius-Clapeyron line to obtain Psat. Note that this method do not rigorously calculate rhoV sat, hence they only report rhoV for GEMC results. Also, they use parallel tempering method do increase efficiency of NPT simulations at low temperatures.

So I'm going to change this part of introduction:

As another alternative, Kofke \cite{Kofke1993b} developed a method called Gibbs-Duhem integration 
which makes use of the Clapeyron equation to numerically integrate and proceed along the saturation 
line starting from one single coexistence point. The Gibbs-Duhem method can solve the insertion 
problem, but it provides a limited extension beyond the starting coexistence point, and it relies on a 
second method to obtain the initial coexistence point. Ahunbay et al. \cite{Ahunbay2004} have applied 
this approach but their implementation has not been tested below a reduced temperature of 0.55.

to

As another alternative, Kofke \cite{Kofke1993b} developed a method called Gibbs-Duhem integration
which makes use of the Clapeyron equation to numerically integrate and proceed along the saturation
 line starting from one single coexistence point. The Gibbs-Duhem method can solve the insertion 
problem, but it relies on a second method to obtain the initial coexistence point. Ahunbay et al. 
\cite{Ahunbay2004} have applied this approach in conjunction with GEMC method to obtain the initial 
coexistence point, NPT simulations to estimate saturation liquid densities, and parallel tempering 
method \cite{Yan1999} to increase the efficiency of low temperature simulations. Their implementation is 
tested at reduced temperatures above 0.45 for several compounds, however it does not provide 
saturation vapor density unless it is calculated directly from GEMC simulation.

Let me know if you have a suggestion.

[ramess101]

@mostafa-razavi

I think this is good.