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1. Liquid-vapor coexistence properties

Liquid-vapor coexistence properties obtained by grand-canonical transition-matrix Monte Carlo and histogram re-weighting [3-7]. Mean values and standard deviations of the saturation pressure, density, potential energy per molecule, and activity (chemical potential- see below) for each phase are reported.

Basic simulation parameters are given below.
METHOD: Grand-canonical transition-matrix Monte Carlo and histogram re-weighting
V/σ3: 343
TRUNCATION:

LJ-

Electrostatics-

  

3.5σ + standard long range corrections

3.5σ + Ewald summation
Prob. of Disp./Rot. Move 0.70
Prob, of Ins/Del. Move: 0.30
Biasing Function Update Frequency
 1.0E5 trials
Simulation Length:  > 1.0E9 trials
 


Liquid-Vapor Phase Coexistence Properties:
 

|µi|* = 1.0

  
T* ρvap*
 +/- ρliq* +/- psat* +/- uvap* +/- uliq* +/- ln zsat +/-
1.00 0.01494 1.E-05 0.7551 8.E-04 0.01345 1.E-05 -0.2038 3.E-04 -6.165 6.E-03 -4.41053 5.E-04
1.05 0.02122 2.E-05 0.7321 4.E-04 0.01942 2.E-05 -0.2736 2.E-04 -5.939 4.E-03 -4.11690 8.E-04
1.10 0.02947 3.E-05 0.7068 6.E-04 0.02717 2.E-05 -0.3607 4.E-04 -5.696 5.E-03 -3.85567 6.E-04
1.15 0.04013 3.E-05 0.6786 5.E-04 0.03691 1.E-05 -0.4695 2.E-04 -5.435 4.E-03 -3.62468 3.E-04
1.20 0.05394 2.E-05 0.6477 2.E-04 0.04889 2.E-05 -0.6053 5.E-04 -5.159 2.E-03 -3.41951 8.E-05
1.25 0.07217 7.E-05 0.6128 3.E-04 0.06343 4.E-05 -0.7800 9.E-04 -4.859 2.E-03 -3.23641 4.E-04
1.30 0.09755 9.E-05 0.5711 2.E-04 0.08078 3.E-05 -1.0227 1.E-03 -4.521 2.E-03 -3.07275 7.E-05
 

|µi|* = 2.0
T* ρvap*
 +/- ρliq* +/- psat* +/- uvap* +/- uliq* +/- ln zsat +/-
1.65 0.02163 3.E-05 0.6975 7.E-04 0.02787 2.E-05 -1.094 2.E-03 -9.881 9.E-03 -4.2973 5.E-04
1.70 0.02774 1.E-05 0.6753 4.E-04 0.03528 1.E-05 -1.279 2.E-03 -9.589 6.E-03 -4.1185 2.E-04
1.75 0.03550 4.E-05 0.6515 8.E-04 0.04414 5.E-05 -1.498 2.E-03 -9.288 1.E-02 -3.9533 7.E-04
1.80 0.04520 2.E-05 0.6255 5.E-04 0.05454 2.E-05 -1.746 2.E-03 -8.964 6.E-03 -3.8005 3.E-04
1.85 0.05785 1.E-04 0.5968 4.E-04 0.06675 4.E-05 -2.048 4.E-03 -8.619 5.E-03 -3.6588 4.E-04
1.90 0.07499 2.E-04 0.5628 6.E-04 0.08100 7.E-05 -2.434 4.E-03 -8.230 6.E-03 -3.5277 4.E-04

 

 

|µi|* = 3.0
T* ρvap*
 +/- ρliq* +/- psat* +/- uvap* +/- uliq* +/- ln zsat +/-
2.65 0.01041 2.E-05 0.6897 1.E-03 0.01984 3.E-05 -3.383 6.E-03 -19.048 2.E-02 -5.1594 3.E-04
2.70 0.01259 4.E-05 0.6749 8.E-04 0.02359 3.E-05 -3.689 2.E-02 -18.773 1.E-02 -5.0252 4.E-04
2.75 0.01522 2.E-05 0.6585 2.E-04 0.02790 3.E-05 -4.020 1.E-02 -18.465 2.E-03 -4.8978 5.E-04
2.80 0.01839 3.E-05 0.6409 5.E-04 0.03283 4.E-05 -4.378 1.E-02 -18.146 1.E-02 -4.7765 9.E-04
2.85 0.02222 7.E-05 0.6227 1.E-03 0.03844 5.E-05 -4.764 1.E-02 -17.823 2.E-02 -4.6609 5.E-04
2.90 0.02683 8.E-05 0.6040 1.E-03 0.04479 8.E-05 -5.174 1.E-02 -17.494 2.E-02 -4.5510 4.E-04
2.95 0.03259 6.E-05 0.5834 6.E-04 0.05187 7.E-05 -5.641 8.E-03 -17.138 5.E-03 -4.4459 7.E-04
3.00 0.04003 1.E-04 0.5610 7.E-04 0.06001 9.E-05 -6.189 1.E-02 -16.773 1.E-02 -4.3462 2.E-04

 

Other Important Simulation Parameters:

Listed below are other relevant simulation parameters. Included are the activity  used in the simulation ln zsim, the maximum number of particles sampled Nmax, and the Ewald parameters α and Kmax. Referring to Eq. 5.21 of Ref. [1], α is a dimensionless parameter controlling how fast the real part of the Ewald sum is dampened. The quantity α/L, where L is the simulation box length, is equivalent to κ in Eq. 5.21 of Ref. [1]. Kmax is represents the largest inverse lattice vector that is included in the reciprocal-space part of the Ewald summation. The chosen parameters yield an estimated error in the dimensionless electrostatic energy per particle in the saturated liquid to be no more than 0.001.  For those who are interested,  raw macrostate distributions and average total potential energies at each macrostate can be downloaded.

|µi|* = 1.0

T* α Kmax Nmax ln zsim
1.00 5.5 6 305 -4.40
1.05 5.5 6 300 -4.11
1.10 5.5 6 295 -3.85
1.15 5.5 6 290 -3.62
1.20 5.5 6 285 -3.41
1.25 5.5 6 280 -3.23
1.30 5.5 6 275 -3.06

 

|µi|* = 2.0

T* α Kmax Nmax ln zsim
1.65 5.5 6 300 -4.29
1.70 5.5 6 295 -4.11
1.75 5.5 6 290 -3.95
1.80 5.5 6 285 -3.79
1.85 5.5 6 280 -3.66
1.90 5.5 6 275 -3.53

 

|µi|* = 3.0

T* α Kmax Nmax ln zsim

In addition to the standard Monte Carlo moves mentioned above, aggregation-volume bias (AVB) moves [1-3] were employed due to the strongly associating nature of the dipole interaction at this dipole strength. AVB trial displacement were performed according to the AVBMC2 scheme described in Ref. [2]. Thirty percent of the trial moves  consisted of AVB moves (30% of these moves were AVBMC2 while the remaining 70% were AVB insertions/deleteions).
2.65 5.6 6 295 -5.15
2.70 5.6 6 290 -5.02
2.75 5.6 6 285 -4.89
2.80 5.6 6 280 -4.73
2.85 5.6 6 275 -4.66
2.90 5.6 6 270 -4.54
2.95 5.6 6 265 -4.45
3.00 5.6 6 260 -4.35

 

 

REFERENCES

[1] B. Chen and J. I. Siepmann, J. Phys. Chem. B 105, 11275, (2001).

[2] B. Chen, J. I. Siepmann, K. J. Oh, and M. L. Klein, J. Chem. Phys. 115, 10903 (2001).

[3] V. K. Shen and D. W. Siderius, J. Chem. Phys., 140, 244106, (2014).

[4] V. K. Shen and J. R. Errington, J. Phys. Chem. B 108, 19595, (2004).

[5] V. K. Shen and J. R. Errington, J. Chem. Phys. 122, 064508, (2005).

[6] V. K. Shen, R. D. Mountain, and J. R. Errington, J. Phys. Chem. B 111, 6198, (2007).

[7] D. W. Siderius and V. K. Shen, J. Phys. Chem. 117, 5681, (2013).