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Material Measurement Laboratory / Chemical Sciences Division

Chemical Informatics Group

TMMC: Reference Adsorption Isotherms for H2O in Metal-organic Frameworks

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Grand-canonical Transition-Matrix Monte Carlo (GC-TMMC) simulations [1, 5-10] of SPC/E H2O were performed at T = 300 K in two metal-organic frameworks (MOFs). The particle number range was divided into windows advanced trial moves were performed to ensure adequate sampling at high densities. The main result of a GC-TMMC simulation is the particle number probability distribution (PNPD), which is constructed by stitching together the particle number distributions from each window. The adsorption isotherm may be determined from the PNPD [10]. At each value of N, average total potential energies U were collected and these quantities were used to compute the isosteric heat of adsorption.

Simulations used an N-dependent set of Monte Carlo moves, as described below. Simulations were initialized with Wang-Landau Monte Carlo, the TMMC collection matrix was accumulated beginning in Wang-Landau stage 18, and the simulation switched to TMMC mode after 20 stages.

All simulations were performed using the open-source FEASST Monte Carlo engine [13], version v0.17.3 (commit hash 7430150742e157258612007c18f1d41fde9308ba).

Other key simulation details common to all simulations are given below:

Fluid Model SPC/E H2O [11]
Lennard-Jones cutoff 10A, with linear-force shift tail
Ewald Parameters Set according to DL_POLY recipe [14], with relative tolerance 10-5

Monte Carlo Move Set
   (N dependent)
ZIF-8 CuBTC

0 < N < 50:
Translation, relative weight 30
Rotation, relative weight 20
Insertion/Deletion, weight 50

 0 < N < 10:
Translation, relative weight 30
Rotation, relative weight 20
Insertion/Deletion, weight 50
50 < N < 300:

Translation, relative weight 30
Rotation, relative weight 20
Insertion/Deletion, weight 50
AVBMC2 Regrowth, weight 1
AVBMC4 Regrowth, weight 1
AVB Insertion/Deletion, weight 1

 10 < N < 200:

Translation, relative weight 30
Rotation, relative weight 20
Insertion/Deletion, weight 50
AVBMC2 Regrowth, weight 1
AVBMC4 Regrowth, weight 1
AVB Insertion/Deletion, weight 1
N > 300: 
Translation, relative weight 30
Single Hydrogen Regrowth, weight 0.6
Two Hydrogen Regrowth, weight 0.4
Configurational Bias Insertion/Deletion, weight 8		 N > 200: 
Translation, relative weight 30
Single Hydrogen Regrowth, weight 0.6
Two Hydrogen Regrowth, weight 0.4
Configurational Bias Insertion/Deletion, weight 8

 
Total Run Time ZIF-8: 28 days ; CuBTC: 7 days
Bias update freq 1.0e5
Physical Parameters CODATA 2018 [12]

The adsorbent MOFs were reconstructed from publicly-available crystal structures and replicated to ensure that the simulation cell was at least twice the cutoff radius in all dimensions. Forcefields for each MOF were taken from published literature. The MOF structure and forcefield are provided in FEASST particle files in the data repository associated with this page (see "Data Availability" below). Coulombic interactions were handled using the Ewald summation method [2,3] (parameters listed in the metadata files). Lorentz-Berthelot mixing rules were used to set the unlike-atom Lennard-Jones parameters.

Simulation details specific to each MOF 

  ZIF-8 CuBTC
Number of Windows 80 64
Nmax 630 500
Unit Cell Replication (Nx, Ny, Nz) (2,2,2) (1,1,1)
Cubic Box Dimensions (A) 34.023240 26.3430
Simulation MOF Mass (amu) 21846.91 9677.91
MOF Forcefield,
Reference		 Snurr [15] Calero IV [16]
FEASST MOF Particle data.ZIF8_Snurr_rep222 data.CuBTC_CaleroIV_rep111

Note: both MOFs have cubic unit cells

The result of each simulation is the PNPD, which may be used to compute the adsorption isotherm by the histogram-reweighting procedure described by Siderius, Hatch, and Shen in a forthcoming publication [10].  The pressure for a particular chemical potential was determined from GC-TMMC simulation of the bulk SPC/E water [4]; the PNPD and average potential energy of the bulk fluid are also provided in the associated data repository.

Results

Temperature = 300K

Adsorption Isotherm of SPC/E Water in ZIF-8 at 300 K.
Adsorption Isotherm of SPC/E Water in ZIF-8 at 300 K.

Vertical dotted lines identify estimates of the adsorbed phase limits of stability. The dashed line identifies the equilibrium phase transition.
Credit: NIST
Adsorption Isotherm of SPC/E Water in CuBTC at 300 K.
Adsorption Isotherm of SPC/E Water in CuBTC at 300 K.

Vertical dotted lines identify estimates of the adsorbed phase limits of stability. The dashed line identifies the equilibrium phase transition.
Credit: NIST

Data Availability

Various data files used to generate the reference isotherms are available in a Git Repository: https://github.com/dwsideriusNIST/NIST_SRSW_Data/tree/master/H2O_REF_ISOTHERMS

Files in the repository include:
FEASST particle files for the MOF materials [includes atomic coordinates and the forcefield parameters]
FEASST particle file for SPC/E Water
Particle number probability distributions for both the bulk and adsorbed water
Isotherm data files, including the adsorption isotherm and estimated uncertainties, formatted as AIF files [20]

References

  1. J. R. Errington, J. Chem. Phys. 118, 9915 (2003).
  2. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford University Press, New York, 1989).
  3. D. Frenkel and B. Smit, Understanding Molecular Simulation, 2nd ed. (Academic, San Diego, 2002)., pp.37-38.
  4. J. R. Errington and A. Z. Panagiotopoulos, J. Chem. Phys., 109, 1093 (1998).
  5. J. R. Errington and V. K. Shen, J. Chem. Phys., 123, 164103 (2005).
  6. V. K. Shen and D. W. Siderius, J. Chem. Phys., 140, 244106, 2014.
  7. V. K. Shen and J. R. Errington, JPC B 108, 19595, 2004.
  8. V. K. Shen and J. R. Errington, JCP 122, 064508, 2005.
  9. V. K. Shen, R. D. Mountain, and J. R. Errington, JPC B 111, 6198, 2007.
  10. D. W. Siderius, H. W. Hatch, and V. K. Shen, "Flat-Histogram Monte Carlo Simulation of Water Adsorption in Metal-organic Frameworks," in preparation.
  11. H. J. C. Berendsen, J. R. Grigera, and T. P. Straatsma, J. Phys. Chem., 91, 6269-6271 (1987).
  12. CODATA Internationally recommended 2018 values of the Fundamental Physical Constants
  13. H. W. Hatch, N. A. Mahynski, and V. K. Shen J Res Natl Inst Stan, 123, 123004, 2018.

  14. E. I. Todorov and W. Smith, The DL\_POLY User Manual (version 4.03).

  15. H. Zhang and R. Q. Snurr, JPC C, 121, 24000, 2017.

  16. J. M. Castillo, T. J. H. Vlugt, and S. Calero, JPC C 112, 15934, 2008.

  17. P. Ghosh, Y. J. Colón, and R. Q. Snurr, Chem Commun, 50, 11329, 2014.

  18. S. L. Mayo, B.D. Olafson and W. A. Goddard, JPC, 26, 8897, 1990.

  19. C. Zou, D. R. Penley, E. H. Cho, and L-C. Lin, JPC C 124, 11428, 2020.

  20. J. D. Evans, V. Bon, I. Senkovska, S. Kaskel, Langmuir, 37, 4222, 2021.

Created September 13, 2023, Updated September 20, 2023