Grandcanonical TransitionMatrix Monte Carlo (GCTMMC) simulations [1, 510] of N_{2} were performed at T = 300 K and 350 K in three 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 different combinations of Monte Carlo moves depending on the number of particles, as described below. Low density windows used a conventional set of moves (i.e., no configurational bias) whereas high density windows used a configurational bias strategy known as Dualcut configurational bias (DCCB) Monte Carlo [13]. Additionally, lowdensity windows started in WangLandau biasing mode to quickly generate a guess of the PNPD, later switching to TMMC mode; data from the TMMC phase of the simulation was saved and reported here.
All simulations were performed using the opensource FEASST Monte Carlo engine [14], version v0.21.1 (commit hash fad5d0d6575a2ed8251d7093e1a250d634cbbcb4).
Other key simulation details common to all simulations are given below:
Fluid Model  TraPPE N_{2}[11]  
LennardJones cutoff  12A, with linearforce shift tail correction  
Ewald Parameters  Set according to DL_POLY recipe [15], with relative tolerance 10^{5}  
Standard Move Set 
Translation, weight 0.3 

Advanced Move Set (N ≥ 100) 
Translation, weight 0.1 DCCB Regrowth (single Nitrogen), weight 0.06 DCCB Regrowth (both Nitrogens), weight 0.04 DCCB Growth (full N_{2} particle), weight 0.8 

DCCB Details 
Number of trials per atom: 4 

Total MC Trials  1.0e8  
Bias update freq  1.0e4  
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 handled using the Ewald summation method [2,3] (parameters listed in the metadata files). LorentzBerthelot mixing rules were used to set the unlikeatom LennardJones parameters.
Simulation details specific to each MOF
ZIF8  CuBTC  IRMOF1  
Number of Windows  60  40  40 
N_{max}  350  245  275 
Unit Cell Replication (N_{x}, N_{y}, N_{z})  (2,2,2)  (1,1,1)  (1,1,1) 
Cubic Box Dimensions (A)  34.023240  26.3430  25.6690 
Simulation MOF Mass (amu)  21846.91  9677.91  6158.94 
MOF Forcefield, Reference 
Snurr [16]  Calero IV [17]  DREIDING [19] + mCBAC [20] 
FEASST MOF Particle  data.ZIF8_Snurr_rep222  data.CuBTC_CaleroIV_rep111  data.IRMOF1_mCBAC_rep111 
Note: all three 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 N_{2} fluid [4]; the PNPD and average potential energy of the bulk fluid are also provided in the associated data repository.
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/N2_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 N_{2}
Particle number probability distributions and canonical energy averages for both the bulk and adsorbed N_{2}
Isotherm data files, including the adsorption isotherm and isosteric heat and estimated uncertainties, formatted as AIF files [21]
H. W. Hatch, N. A. Mahynski, and V. K. Shen J Res Natl Inst Stan, 123, 123004, 2018.
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.