Zeo++

The following document was adapted from  Prof. Randy Snurr's group  and was originally authored by  Prof. Kaihang Shi .

Overview

The two tools most people consider for computing textural (i.e. geometric, pore-related) properties of porous materials are  Zeo++  and  PoreBlazer  (PB). Examples of how to compute various properties are described below.

Pore Volume and Void Fraction

Helium Void Fraction

This is preferrable when you try to compare experimental excess adsorption data with your simulation results. Relevant equations can be found in Ref. [2] (see Eq. 6-9). RASPA is recommended for this task. Recommended parameters are as follows.
Title
Recommended Value
Comments
He atom probe  [Å]
2.64
From Ref. [3,4]. Default for PBE is 2.58.
He atom probe  [K]
10.9
From Ref. [3,4]. Default for PB is 10.22.
Temperature [K]
298
Standard experimental condition.
vdW cutoff radius [Å]
12.8
Framework force field
UFF
Combining rules
Lorentz-Berthelot


Probe-Occupiable (PO) Pore Volume

This property is useful when the experimental pore volume is estimated from nitrogen adsorption (assuming adsorbed nitrogen has bulk liquid density) [4]. The recommended command to get this property in Zeo++ is
network -ha -r UFF.rad -volpo 1.86 1.86 100000
where UFF framework atom radii are used (-r UFF.rad) with high accuracy (-ha).

The PO volume calculation (-volpo) uses a nitrogen probe with radius of 1.86 Å (corresponding to the size of nitrogen molecule in TraPPE force field) [5] to access both the availability of the network and the PO pore volume. A total of 100,000 points are sampled across the entire unit cell and Monte Carlo integration is used to determine the result (105 sampling point is enough in most cases with accuracy up to the second decimal place).
Do not compute the probe-center (PC) pore volume (i.e. the -vol flag). It has been shown that this property systematically underestimate the Helium pore volume [2].

Cavity Dimensions

Largest Free Sphere

This property corresponds to the common definition of the pore limiting diameter (PLD). It is the largest probe that can cross the simulation cell in at least one dimension via a diffusive pathway.

Largest Included Sphere

This property corresponds to the common definition of the largest cavity diameter (LCD). It is the largest cavity in a porous material.

Largest Included Sphere Along Free Sphere Path

The largest included sphere along the free sphere path This is a unique property provided by Zeo++. It is the LCD along the accessible network path. This property should be reported if the network accessibility is considered in GCMC simulations.

The recommended command to get these properties in Zeo++ is:
network -ha -r UFF.rad -res
The output file will report three values, from left to right, they are 1) the largest included sphere, 2) the largest free sphere and 3) the largest included sphere along free sphere path.

Surface Area

Both Zeo++ and PB calculate the surface area accessible to the center of the probe which compares favorably with the experimental surface area estimated using the BET method (however, if a more sensible comparison is desired, the ‘true monolayer surface area’ should be calculated in the simulation [6]). The algorithm consists of generating random points on the surface of a sphere centered at each framework atom with the radius of
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where σ_p and σ_s are the LJ size parameter for probe and solid atom, respectively; then tests are performed to check if sampling points overlap with other constructed spheres. If not, those sampling points are counted towards the calculation of the geometric surface area. The major difference between the implementation in PB and Zeo++ is that PB takes k=2^(1/6)=1.122 [2], while k=1 in Zeo++. There is no way to change k in both software unless modifying the source code. The easiest way to reach agreement in surface area calculations between PB and Zeo++ is to modify radius for nitrogen probe atom, channel accessing probe, and framework atoms to account for the difference in k.

The recommended command to get this property in Zeo++ is:
network -ha -r UFF.rad -sa 1.86 1.86 1000
where a nitrogen probe is used to access both the availability of the network and the surface area. A total of 1,000 points are sampled at a distance of 1.86 Å from each framework atom surface, and Monte Carlo integration is used to determine the result. Using 1,000 sampling points roughly gives the accuracy up to the first decimal points. Because this sampling is performed for each framework atom, considering the computational time, 1,000 points is a good choice. Note that PB uses fewer sampling points (500) by default to access the surface area.

Please be noted that ‘ASA’ reported in the final output is the surface area in the accessible network. If your GCMC simulation inserts molecules in the entire simulation box, the total surface area should be reported for consistency, i.e., total area = ASA + NASA.

In principle, if no experimental comparison is needed, the probe diameter should be that of the adsorbate of interest [7].

Pore Size Distribution (PSD)

Zeo++ and PB use different algorithms for the PSD calculation [8, 11]. Personally, I prefer PB in this case which implements a classical algorithm related to the cumulative pore volume. It should also be noted that there is a flaw in Zeo++’s PSD algorithm when the probe diameter is significantly smaller than the material’s atoms (refer to the  Warnings  section in the documentation). A nitrogen probe of radius of 1.86 Å is recommended for measuring the network accessibility.

General Comments

  • When computing textural properties, they should be consistent with any reported GCMC simulations. For example, the total properties should be reported if the network accessibility is not considered in GCMC simulations.
  • The input framework atom radii should be consistent with those used in GCMC simulations if any were carried out. For general tasks, the sigma values (Lennard-Jones diameters) from universal force field (UFF) [1] are recommended. Be sure to specify the atom radius with `-r` flag in Zeo++. Zeo++ uses the CCDC atom radius by default. PB uses the UFF radius by default.

References

[1] A.K. Rappe, C.J. Casewit, K.S. Colwell, W.A. Goddard, W.M. Skiff, UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations, J. Am. Chem. Soc. 114 (1992) 10024–10035.  https://doi.org/10.1021/ja00051a040 .
[2] L. Sarkisov, R. Bueno-Perez, M. Sutharson, D. Fairen-Jimenez, Materials Informatics with PoreBlazer v4.0 and the CSD MOF Database, Chem. Mater. 32 (2020) 9849–9867.  https://doi.org/10.1021/acs.chemmater.0c03575 .
[3] J.O. Hirschfelder, C.F. Curtiss, R.B. Bird, Molecular Theory of Gases and Liquids, Wiley, New York, 1964.  https://doi.org/10.1063/1.3061949 .
[4] D. Ongari, P.G. Boyd, S. Barthel, M. Witman, M. Haranczyk, B. Smit, Accurate Characterization of the Pore Volume in Microporous Crystalline Materials, Langmuir. 33 (2017) 14529–14538.  https://doi.org/10.1021/acs.langmuir.7b01682 .
[5] Y.-S. Bae, A.Ö. Yazaydın, R.Q. Snurr, Evaluation of the BET Method for Determining Surface Areas of MOFs and Zeolites that Contain Ultra-Micropores, Langmuir. 26 (2010) 5475–5483.  https://doi.org/10.1021/la100449z .
[6] D.A. Gómez-Gualdrón, P.Z. Moghadam, J.T. Hupp, O.K. Farha, R.Q. Snurr, Application of Consistency Criteria To Calculate BET Areas of Micro- And Mesoporous Metal–Organic Frameworks, J. Am. Chem. Soc. 138 (2016) 215–224.  https://doi.org/10.1021/jacs.5b10266 .
[7] T. Düren, F. Millange, G. Férey, K.S. Walton, R.Q. Snurr, Calculating Geometric Surface Areas as a Characterization Tool for Metal−Organic Frameworks, J. Phys. Chem. C. 111 (2007) 15350–15356.  https://doi.org/10.1021/jp074723h .
[8] L.D. Gelb, K.E. Gubbins, Pore Size Distributions in Porous Glasses: A Computer Simulation Study, Langmuir. 15 (1999) 305–308.  https://doi.org/10.1021/la9808418 .
[9] L. Sarkisov, A. Harrison, Computational structure characterisation tools in application to ordered and disordered porous materials, Mol. Simul. 37 (2011) 1248–1257.  https://doi.org/10.1080/08927022.2011.592832 .
[10] T.F. Willems, C.H. Rycroft, M. Kazi, J.C. Meza, M. Haranczyk, Algorithms and tools for high-throughput geometry-based analysis of crystalline porous materials, Microporous Mesoporous Mater. 149 (2012) 134–141.  https://doi.org/10.1016/j.micromeso.2011.08.020 .
[11] M. Pinheiro, R.L. Martin, C.H. Rycroft, A. Jones, E. Iglesia, M. Haranczyk, Characterization and comparison of pore landscapes in crystalline porous materials, J. Mol. Graph. Model. 44 (2013) 208–219.  https://doi.org/10.1016/j.jmgm.2013.05.007 .