CRAFTED - An exploratory database of simulated adsorption isotherms of metal-organic frameworks Felipe Lopes Oliveira12 Conor Cleeton3 Rodrigo Neumann Barros Ferreira1 Binquan

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CRAFTED - An exploratory database of simulated

adsorption isotherms of metal-organic frameworks

Felipe Lopes Oliveira1,2, Conor Cleeton3, Rodrigo Neumann Barros Ferreira1,*, Binquan

Luan4, Amir H. Farmahini3, Lev Sarkisov3, and Mathias Steiner1

1IBM Research, Av. Rep´

ublica do Chile, 330, CEP 20031-170, Rio de Janeiro, RJ, Brazil.

2Department of Organic Chemistry, Instituto de Qu´

ımica, Universidade Federal do Rio de Janeiro, Rio de Janeiro,

RJ, Brazil.

Department of Chemical Engineering, Engineering A, the University of Manchester, Manchester, M13 9PL, United

Kingdom

4IBM Research, 1101 Kitchawan Road, Yorktown Heights, 10519, NY, USA.

*Corresponding author: rneumann@br.ibm.com.

ABSTRACT

Grand Canonical Monte Carlo is an important method for performing molecular-level simulations and

assisting the study and development of nanoporous materials for gas capture application. These

simulations are based on the use of force ﬁelds and partial charges to model the interaction between

the adsorbent molecules and the solid framework. The choice of the force ﬁeld parameters and partial

charges can signiﬁcantly impact the results obtained, however, there are very few databases available to

support a comprehensive impact evaluation. Here, we present a database of simulations of CO

and

adsorption isotherms on 726 metal-organic frameworks taken from the CoRE MOF 2014 database.

We performed simulations with two force ﬁelds (UFF and DREIDING), four partial charge schemes (no

charge, Qeq, EQeq, and DDEC), and three temperatures (273, 298, 323 K). The resulting isotherms

compose the

harge-dependent,

eproducible,

ccessible,

orceﬁeld-dependent, and

emperature-

dependent Exploratory Database (CRAFTED) of adsorption isotherms.

Background & Summary

Carbon capture, storage, and utilization is considered as one of the key strategies required to reduce

anthropogenic carbon dioxide emissions and their impacts on climate change

. The most viable option for

this approach is to focus on CO

capturing from the point sources, such as fossil fuel power plants, fuel

processing plants and other industrial plants where carbon capture technology can be applied to streams

with the industrial scale ﬂow rates

. However, despite several decades of intensive research, carbon capture

in an economically viable way remains an enormous challenge3.

Adsorption processes are considered to be a promising alternative to the conventional absorption

processes due the their low regeneration energy, high selectivity, and high capture capacity

. Combined,

these characteristics may lead to energy-efﬁcient processes for industrial scale capture and utilization

of greenhouse gases (GHG). At the heart of a typical adsorption process for gas separation, such as the

Pressure Swing Adsorption process, is the active adsorbent material; and the efﬁciency of the process

crucially depends on the properties of this material. Within the different adsorbent materials that are

potentially available for this process, crystalline nanoporous materials such as metal-organic frameworks

(MOF)

5–8

, covalent organic frameworks (COF)

9–11

, zeolitic imidazolate frameworks (ZIF)

12–14

, and

zeolites

feature many of the necessary characteristics for a solid sorbent for efﬁcient gas separation

arXiv:2210.09456v1 [cond-mat.mtrl-sci] 17 Oct 2022

under the conditions of interest.

These families of materials contain hundreds of thousands synthesized structures and countless more

hypothetical ones, featuring pores of different size, shape, and chemical characteristics. This creates large

exploration space for studies that seek to identify the best candidates for a given gas capture application.

This endeavour, however, is not possible via a brute-force experimental campaign. The number of large

databases built upon experimental

16–20

and hypothetical

21,22

structures, combined with the continuous

growth of diversity and scope of new materials due to the advancements in digital reticular chemistry,

23,24

make high-throughput computational screening (HTCS) approaches an an imperative strategy for efﬁcient

exploration of the vast chemical landscape of crystalline nanoporous adsorbents25,26.

Most of the HTCS studies for carbon capture and related problems are based on using Grand Canonical

Monte Carlo (GCMC) simulations to generate adsorption data. This data is then used to form some simple

material performance metrics or is passed on to the process level modelling to explore performance of

candidate materials under the realistic process conditions.

To perform molecular simulations, such as GCMC, one needs a set of parameters that describe the

interactions among the adsorbate molecules, and between the adsorbate molecules and the atoms of the

adsorbent material; this set of parameters is called a force ﬁeld.

Over the years of the development, many force ﬁelds have been developed for various purposes and

several options are available to describe adsorption of gases such as carbon dioxide in materials such as

MOFs. Invariably, the predicted equilibrium adsorption data and, consequently ranking of the materials

and the recommendations of the screening study will depend on the choice of the force ﬁeld.

This poses several fundamental questions. How sensitive is the adsorption data to the choice of the

force ﬁeld parameters? How does this sensitivity vary across different categories or classes of materials?

And ultimately, is a ranking of porous materials for a particular application a robust result or it is contingent

on using a particular force ﬁeld?

To start to explore these questions one needs a representative mass of adsorption data covering typical

choices of the force ﬁeld parameters, materials, gases and conditions. This deﬁnes the remit of the current

article where we tasked ourselves with building such a database (or at least, the ﬁrst block of conditions).

To explain the contents of the database and our approach, let us delve ﬁrst into components of the

classical force ﬁelds and the typical options available for the studies of adsorption of gases in MOFs and

related materials. In the classical force ﬁelds, the non-bonded interactions are modeled as a sum of van

der Waals and Coulomb potentials

. The van der Waals interactions between the adsorbed molecules and

the framework are usually modeled by the Lennard-Jones (LJ) potential, which is an effective potential

with two ﬁtted parameters that can capture most of the intermolecular effects relevant to physisorption.

The parameters for the atoms can be taken from the generic force ﬁelds such as the Universal Force Field

(UFF)

, DREIDING

and TraPPE

, with the interactions between different atom species computed

using mixing rules such as Lorentz-Berthelot31 or Jorgensen32.

The Coulombic interactions are modeled by partial atomic charges assigned to the atoms which need

to be calculated for each material. There are several charge assignment methods available, and they

can be divided into two main groups: i. methods derived from quantum chemistry calculations (e.g.

RESP

, CHELP

, REPEAT

, and DDEC

36–38

) and ii. methods based on charge equilibration (e.g.

Qeq

, PQeq

, EQeq

, and FC-Qeq

). Although there is some consensus that the approaches such as

DDEC (based on electronic structure calculations) are more accurate, methods such as EQeq can present

sufﬁciently good results that, combined with their low computational cost, makes them attractive choices

for HTCS studies43,44.

Lately, there have been several studies evaluating the accuracy of different methods for calculating

partial atomic charges

44–48

, however, little is known about the combined impact of force ﬁeld and partial

2/18

charge selection on material-level analysis and its implication on process-level performance metrics.

Furthermore, the parameters of force ﬁelds such as UFF and DREIDING were ﬁtted employing speciﬁc

partial charge schemes (Gasteiger

for DREIDING and Qeq

for UFF), thus the combination of these

parameters with different charge assignment methodologies, even if more accurate, may not necessarily

generate better results.

These considerations guide us on the choices of the parameters of the force ﬁelds to consider in the

database.

The database contains simulated adsorption isotherms for 726 MOFs selected from the CoRE MOF

2014

database. The simulations were performed for the adsorption of CO

and N

with two force

ﬁelds (UFF and DREIDING), four partial charge schemes (no charge, Qeq, EQeq, and DDEC), at three

temperatures (273, 298, 323 K). The resulting isotherms compose the

harge-dependent,

eproducible,

ccessible,

orceﬁeld-dependent, and

emperature-dependent

xploratory

atabase (

CRAFTED

) of

adsorption isotherms. CRAFTED provides a convenient platform to explore the sensitivity of simulation

outcomes to molecular modeling choices at the material (structure-property relationship) and process

levels (structure-property-performance relationship).

Methods

Structure selection

The 2932 structures present in the CoRE MOF 2014

database were analyzed and 726 structures were

retained in our analysis. This subset of 726 comprises all materials from the CoRE MOF 2014 database

for which all atom types are present in both DREIDING and UFF force ﬁelds. Throughout this work, this

subset of structures will be referred to as “CRAFTED structures”.

Partial charges calculation

The DDEC partial charges

36–38

were taken without modiﬁcation from the CoRE MOF 2014

database.

The EQeq partial charges

were calculated using the the extended charge equilibration method as

implemented in the EQeq software

v1.1.0. The Qeq partial charges

were calculated using the default

implementation available in RASPA51.

Grand Canonical Monte Carlo simulations

Atomistic Grand Canonical Monte Carlo (GCMC) simulations were performed using a force ﬁeld-based

algorithm as implemented in RASPA

51,52

v2.0.45. Interaction energies between non-bonded atoms were

computed through a combination of Lennard-Jones (LJ) and Coulomb potentials

Ui j(ri j) = 4εi j "σi j

ri j 12

−σi j

ri j 6#+1

4πε

qiqj

ri j

(1)

where

and

are interacting atom indexes and

ri j

is their interatomic distance.

εi j

and

σi j

are the well

depth and diameter, respectively. The LJ parameters between atoms of different types were calculated

using the Lorentz-Berthelot mixing rules

εi j =pεiiεj j,σi j =σii +σj j

2(2)

3/18

LJ parameters for framework atoms were taken from Universal Force Field (UFF)

or DREIDING

(see Table 1). The parameters for the adsorbed molecules were taken from the TraPPE

force ﬁeld (see

Table 2). All simulations were performed with 10,000 Monte Carlo cycles. Swap (insertion or deletion

with with a probability of 50% for each), translations, rotations, and re-insertions moves were tried with

probabilities 0.5, 0.3, 0.1, and 0.1, respectively. To avoid the use of long initialization cycles, each isotherm

was calculated in a single simulation, with each pressure point of the simulation starting from the result

of the previous one. The uptake values for each pressure were obtained by averaging over the GCMC

equilibrium phase, determined using the Marginal Standard Error Rule. For more information, please refer

to section Automatic transient regime detection and truncation.

All atoms in the MOF were held ﬁxed at their crystallographic positions. The number of unit cells

used was different for each MOF to ensure that the perpendicular lengths of the supercell were greater

than twice the cutoff used. The cutoff for Lennard-Jones and charge-charge short-range interactions was

12.8 Å and the Ewald sum technique was applied to compute the long-range electrostatic interactions with

a relative precision of 10

–6

. The Lennard-Jones potential was shifted to zero at the cutoff. Fugacities

needed to impose equilibrium between the system and the external ideal gas reservoir at each pressure

were calculated using the Peng-Robinson equation of state

with the critical parameters for each gas

taken from Table 3. All GCMC uptake data report the absolute adsorption value in mol/kg units.

The enthalpy of adsorption was computed as

∆H=hU·Ni−hUihNi

hN2i−hNi2−RT (3)

where

is the number of adsorbates on the simulation box and

is the potential energy

. All the

adsorption enthalpy values are reported in kJ/mol and are the values as calculated by RASPA without

further modiﬁcation.

Lennard-Jones parameters

The Lennard-Jones parameters for DREIDING and UFF force ﬁelds used in the calculations for the

framework atoms are shown in Table 1. For simplicity, only the atoms that are present in both UFF and

DREIDING are shown. The TraPPE parameters used for the gas molecules are present in Table 2. The

critical parameters used in the Peng-Robinson equation to calculate the fugacity are present in Table 3.

Automatic equilibration detection and truncation

To eliminate the use of long initialization cycles, the Marginal Standard Error Rule (MSER)

was applied

to automatically detect the ideal truncation point using the pyMSER package v1.0.12

, so that the

averages were taken only over the equilibrated phase of the simulation. The output of this method is the

equilibrated average of the observable, alongside an uncertainty metric. Here we used the uncorrelated

standard deviation, as explained in the next sub-section.

The MSER deﬁnes the start of the equilibrated region ˆ

d(n)by solving the minimization problem:

d(n) = argmin

0≤k≤n−2

gn(k)where gn(k) = 1

(n−k)2

n−1

∑

j=k

(Yj−¯

Yn,k)2=S2

n,k

n−k(4)

The Left-most Local Mininum (LLM) version of MSER was used in a batched data with batch size of

4/18

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CRAFTED-Anexploratorydatabaseofsimulatedadsorptionisothermsofmetal-organicframeworksFelipeLopesOliveira1,2,ConorCleeton3,RodrigoNeumannBarrosFerreira1,*,BinquanLuan4,AmirH.Farmahini3,LevSarkisov3,andMathiasSteiner11IBMResearch,Av.Rep´ublicadoChile,330,CEP20031-170,RiodeJaneiro,RJ,Brazil.2Departmento...

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CRAFTED - An exploratory database of simulated adsorption isotherms of metal-organic frameworks Felipe Lopes Oliveira12 Conor Cleeton3 Rodrigo Neumann Barros Ferreira1 Binquan

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