Grandcanonical TransitionMatrix Monte Carlo (GCTMMC) simulations [1, 510] of CH4 were performed at T = 300 K and 350 K in four metalorganic 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 GCTMMC 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 a standard, conventional set of unbiased Monte Carlo moves, as described below. Since the simulations were run at a high temperature for the model fluid, all windows used conventional TMMC mode without WangLandau initialization.
All simulations were performed using the opensource FEASST Monte Carlo engine [13], version v0.21.1 (commit hash fad5d0d6575a2ed8251d7093e1a250d634cbbcb4).
Other key simulation details common to all simulations are given below:
Fluid Model  TraPPE CH_{4}[11]  
LennardJones cutoff  12A, with linearforce shift tail  
Ewald Parameters  Set according to DL_POLY recipe [14], with relative tolerance 10^{5}  
Standard Move Set 
Translation, weight 0.3 

Total MC Trials  1.0e8 for ZIF8, CuBTC, and IRMOF1; 5.0e8 for UiO66  
Bias update freq  1.0e6  
Physical Parameters  CODATA 2018 [12] 
The adsorbent MOFs were reconstructed from publiclyavailable 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 ignored since the TraPPE CH_{4} particle has no charge [2,3]. LorentzBerthelot mixing rules were used to set the unlikeatom LennardJones parameters.
Simulation details specific to each MOF
ZIF8  CuBTC  UiO66  IRMOF1  
Number of Windows  60  40  80  40 
N_{max}  300  210  480  235 
Unit Cell Replication (N_{x}, N_{y}, N_{z})  (2,2,2)  (1,1,1)  (2,2,2)  (1,1,1) 
Cubic Box Dimensions (A)  34.023240  26.3430  41.40080  25.6690 
Simulation MOF Mass (amu)  21846.91  9677.91  53249.82  6158.94 
MOF Forcefield, Reference 
Snurr [15]  Calero IV [16]  Snurr [17]  DREIDING [18] + mCBAC [19] 
FEASST MOF Particle  data.ZIF8_Snurr_rep222  data.CuBTC_CaleroIV_rep111  data.UiO66_Snurr_rep222  data.IRMOF1_mCBAC_rep111 
Note: all four MOFs have cubic unit cells
The result of each simulation is the PNPD and average potential energy (for each N state). The PNPD may be used to compute the adsorption isotherm by the histogramreweighting procedure described by Siderius and Shen [10]. All systems were single phase and, hence, no phase decomposition of the PNPD was necessary. The pressure for a particular chemical potential was determined from GCTMMC simulation of the bulk CH4 fluid [4]; the PNPD and average potential energy of the bulk fluid are also provided in the associated data repository. Note that the TraPPE CH_{4} fluid is just a LennardJones fluid; the cutoff selected here corresponds to a LennardJones fluid with cutoff of 3.217σ.
The isosteric heat of adsorption was computed as
$$ q_{st} = k_B T \dfrac{<UN><U><N>}{<N^2>  <N>^2}$$
The <...> brackets indicate grandcanonical averages
Various data files used to generate the reference isotherms are available in a Git Repository: https://github.com/dwsideriusNIST/NIST_SRSW_Data/tree/master/CH4_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 TraPPE CH_{4}
Particle number probability distributions and canonical energy averages for both the bulk and adsorbed CH_{4}
Isotherm data files, including the adsorption isotherm and isosteric heat and estimated uncertainties, formatted as AIF files [20]
E. I. Todorov and W. Smith, The DL\_POLY User Manual (version 4.03).
J. M. Castillo, T. J. H. Vlugt, and S. Calero, JPC C 112, 15934, 2008.
P. Ghosh, Y. J. Colón, and R. Q. Snurr, Chem Commun, 50, 11329, 2014.
S. L. Mayo, B.D. Olafson and W. A. Goddard, JPC, 26, 8897, 1990.
C. Zou, D. R. Penley, E. H. Cho, and LC. Lin, JPC C 124, 11428, 2020.
J. D. Evans, V. Bon, I. Senkovska, S. Kaskel, Langmuir, 37, 4222, 2021.