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applied
sciences
Article
Large-Scale Screening and Machine Learning to
Predict the Computation-Ready, Experimental
Metal-Organic Frameworks for CO2Capture from Air
Xiaomei Deng, Wenyuan Yang, Shuhua Li, Hong Liang *, Zenan Shi * and Zhiwei Qiao *
Guangzhou Key Laboratory for New Energy and Green Catalysis, School of Chemistry and Chemical
Engineering, Guangzhou University, Guangzhou 510006, China; 1705200045@e.gzhu.edu.cn (X.D.);
2111705055@e.gzhu.edu.cn (W.Y.); lish@gzhu.edu.cn (S.L.)
*Correspondence: lhong@gzhu.edu.cn (H.L.); zenanshi@126.com (Z.S.); zqiao@gzhu.edu.cn (Z.Q.)
Received: 19 December 2019; Accepted: 10 January 2020; Published: 13 January 2020
Abstract:
The rising level of CO
2
in the atmosphere has attracted attention in recent years. The
technique of capturing CO
2
from higher CO
2
concentrations, such as power plants, has been
widely studied, but capturing lower concentrations of CO
2
directly from the air remains a
challenge. This study uses high-throughput computer (Monte Carlo and molecular dynamics
simulation) and machine learning (ML) to study 6013 computation-ready, experimental metal-organic
frameworks (CoRE-MOFs) for CO
2
adsorption and diffusion properties in the air with very low
concentrations of CO
2
. First, the law influencing CO
2
adsorption and diffusion in air is obtained as a
structure-performance relationship, and then the law influencing the performance of CO
2
adsorption
and diffusion in air is further explored by four ML algorithms. Random forest (RF) was considered the
optimal algorithm for prediction of CO
2
selectivity, with an Rvalue of 0.981, and this algorithm was
further applied to analyze the relative importance of each metal-organic framework (MOF) descriptor
quantitatively. Finally, 14 MOFs with the best properties were successfully screened out, and it was
found that a key to capturing a low concentration CO
2
from the air was the diffusion performance
of CO
2
in MOFs. When the pore-limiting diameter (PLD) of a MOF was closer to the CO
2
dynamic
diameter, this MOF could possess higher CO
2
diffusion separation selectivity. This study could
provide valuable guidance for the synthesis of new MOFs in experiments that capture directly low
concentration CO2from the air.
Keywords:
CO
2
capture; Monte Carlo; machine learning; metal–organic framework; adsorption;
diffusion
1. Introduction
It is well known that the amount of CO
2
discharged into the atmosphere increases with the
rapid development of industry and population growth. In addition, deforestation, the large amount
of CO
2
and other gases generated by the burning of fossil fuels such as coal, oil, and natural gas
directly discharged into the atmosphere, and the emission of limestone roasting to produce cement
have resulted in global carbon dioxide emissions increasing by 3.8% [
1
]. All of the above factors have
aggravated carbon dioxide emissions, thereby increasing the urgency of counteracting the greenhouse
effect and its associated global warming. The Kyoto Protocol and the Paris Agreement aim to control
greenhouse gas emissions under the United Nations Framework Convention on Climate Change
(UNFCCC), in which CO
2
is listed as a major greenhouse gas that needs to be mitigated or recycled [
2
].
The greenhouse gases include more than CO
2
, however; in fact, the global warming potentials of CH
4
and N
2
O are 25 times and 298 times that of CO
2
, respectively. Nevertheless, due to its relatively large
emission levels, CO
2
accounts for approximately 55% of the total greenhouse gas contribution [
3
,
4
].
Appl. Sci. 2020,10, 569; doi:10.3390/app10020569 www.mdpi.com/journal/applsci
Appl. Sci. 2020,10, 569 2 of 13
Thus, it is obvious that the adsorption and separation of carbon dioxide from the air is particularly
important. In addition, the successful capture of CO
2
could have multifaceted practical values: first,
oil recovery could be improved through appropriate reservoir engineering; second, the captured CO
2
could be used to produce industrial chemicals, including concrete, paint, and fertilizer; third, the CO
2
in the atmosphere could be captured and combined with hydrogen for direct synthesis into liquid
hydrocarbons, which could then be utilized in fuel synthesis and supply, including gasoline and diesel.
The use of raw materials can reduce the proportion of fossil energy to further control CO
2
emissions,
ultimately achieving carbon neutrality or even net negative carbon emissions [5].
Recently, carbon engineering has developed a series of capture technologies that remove carbon
dioxide directly from the air. Carbon dioxide can be removed from the atmosphere using biological,
chemical, or physical processes [
6
]. These methods have certain limitations, however. For example,
biological processes are very economical, but they are usually very slow and ineffective. As for
chemical processes, the waste of carbon resources and volatilization of organic solvents during these
actions lead to further environmental pollution, equipment corrosion, and complex post-treatment
issues. The traditional technique for separating carbon dioxide is solvent washing, such as the use of
an alcohol amine solution [
7
–
10
]. Although this conventional method can reduce the concentration of
carbon dioxide in the air, it is extremely expensive, the solvent is difficult to regenerate, the operation
is complicated, and it consumes a great deal of energy [
11
]. In fact, the energy consumption of solvent
washing is 3 to 4 times that of CO
2
captured from exhaust gas [
12
]. Given these drawbacks, there
is an urgent need to find a more efficient, convenient, and energy-saving technique to replace the
traditional carbon dioxide capture method. Adsorption separation is a potential technique. It is
not only inexpensive, but also simple in terms of operation and equipment, and relatively low in
energy consumption when the adsorbent is regenerated (the regeneration process of adsorbents is
to desorb the adsorbed substances). Conventional adsorbents, however, including activated carbon,
zeolite, silica gel, and metal oxides have poor scavenging effects on carbon dioxide in the air due to
inferior separation selectivity and regeneration difficulty. For example, silica gel, which has amorphous
properties, does not have a continuous uniform porous structure and exhibits unfavorable diffusion
properties [
11
]. Therefore, the development of a new type of adsorbent is imperative. In recent years,
studies have shown that the use of metal-organic frameworks (MOFs) to adsorb and separate carbon
dioxide can not only make up for the shortcomings of the above adsorbents, but also feature the
advantages of high selectivity and being non-polluting. The MOF is an organic–inorganic hybrid
material with intramolecular pores formed by the self-assembly of organic ligands and inorganic metal
ions or clusters by coordination bonds [
13
]. Compared with common adsorbents, MOFs exhibit many
advantages such as various structures and properties, large specific surface area, high porosity, and
structural control. Therefore, they are widely used in gas adsorption [
11
] and separation [
14
–
19
],
as well as general materials in processes including storage [
20
], optics [
21
], catalysis [
22
–
25
], and
drug delivery [
26
,
27
]. To date, thousands of MOFs have been synthesized, some of which have
been utilized in the attempt to capture CO
2
from the air. Peng et al. [
28
] designed and synthesized
2 incorporated MOFs to study their stability and ability to capture CO
2
from the air. Liu et al. [
11
]
used an amine-functionalized MOF and an ultra-microporous MOF to capture CO
2
directly from
the air, and further investigated the performance of CO
2
capture and the reproducibility of MOFs
under humid conditions. Osama et al. [
29
] synthesized an isomorphic MOF SIFSIX-3-Cu with uniform
adsorption sites for capturing CO
2
from the air. Since CO
2
capture from the air has a very high
selectivity of MOF, when the traditional approach is used to screen MOFs for the best-performing
candidates, it not only consumes a great deal of manpower and material resources, but also has an
extended study period and causes pollution to a certain extent. With the continuous advancement and
development of computers, molecular simulation is playing an increasingly important role in the field
of materials science [
30
]. Some studies have used high-throughput molecular simulation calculation
methods to screen large numbers of MOFs in a database, thereby successfully screening MOFs with
high selectivity and high working capacity based on different target performance requirements. For
Appl. Sci. 2020,10, 569 3 of 13
example, Wilmer et al. adsorbed pure carbon dioxide, nitrogen, and methane using more than 130,000
hypothetical MOFs, and proposed a relationship between structural properties (pore size, volume, and
surface area) and chemical functions, as well as evaluation criteria for the separation of carbon dioxide
from adsorbents [
31
]. In the presence of nickel dilution, Watanabe et al. combined pore size analysis
with classical simulation to screen 1163 MOFs as membrane materials for CO
2
/N
2
separation [
32
].
Lin et al. screened hundreds of thousands of theoretically predicted zeolites and zeolite MOFs and
identified a number of potential materials for capturing carbon dioxide [
33
]. Based on 105 MOFs, Wu
et al. proposed the relationship of CO
2
/N
2
adsorption selectivity with porosity and the isosteric heat of
adsorption [
34
]. Fernandez et al. [
35
] used advanced machine-learning (ML) algorithms to quickly
identify 292,050 hypothetical high-performance MOFs for pure CO
2
adsorption (0.15 bar and 1 bar).
These screening studies, however, were aimed at capturing high concentrations of CO
2
. Given that the
concentration of CO
2
in the atmosphere is comparatively low relative to the concentrations of natural
gas and other components, it is undoubtedly a challenge to discover efficient MOF materials that can
directly capture CO2from the air.
To date, given that there have been 6013 MOFs reported, finding the appropriate MOFs for a
specific system in such a large database is undoubtedly a daunting task. This study focused on the
aforementioned MOF simulation of the adsorption and diffusion performances of CO
2
, N
2
, and O
2
in infinite dilutions in order to identify materials with excellent performance in terms of both static
adsorption and kinetic adsorption. The influencing factors affecting the adsorption and diffusion
of CO
2
were obtained by univariate analysis. Next, multivariate analyses, namely 4 ML algorithms
(back propagation neural network (BPNN), decision tree (DT), random forest (RF), and support
vector machine (SVM)), were explored in depth. Finally, we adopted the optimal algorithm model.
The parameters affecting CO
2
selectivity were predicted, and 14 types of MOFs with the same diffusion
selectivity and adsorption selectivity were selected.
2. Materials and Methods
2.1. Molecular Model
In this work, we used molecular simulation to screen the capability of 6013 computation-ready,
experimental MOFs (CORE-MOFs version 2) [
36
] to capture CO
2
from the air. Their crystal structures
were derived from the Cambridge Crystallographic Data Centre (CCDC), and their parameters were
compiled and verified by Chung et al. [
37
]. We removed all solvent and ligand molecules prior to
running the simulation. Each MOF used 5 structural parameters, namely, volumetric surface area
(VSA), largest cavity diameter (LCD), pore-limiting diameter (PLD), porosity
φ
, density
ρ
, and an
energy parameter: heat of adsorption. Both LCD and PLD were calculated using the Zeo++ software
package [
38
]. The VSA and
φ
were calculated using the N
2
of 3.64 Å and He of 2.58 Å as probes in
the RASPA software package [
39
]. If VSA is close to or equal to 0, this indicates that the MOF cannot
accommodate N
2
molecules [
40
]. We used NVT-Monte Carlo (NVT-MC) simulation, where N is the
number of particles, V is the volume of the system, and T is the temperature of the system. The Q
st
of
each gas was calculated in an infinite dilution state.
The force field parameters for the 3 gas components CO
2
/N
2
/O
2
were from the transferable
potentials for phase equilibria (TraPPE) force field [
41
] and are listed in Table S2 The CO
2
molecule has
a C-O bond length of 1.16 Å and a bond angle
∠
OCO of 180
◦
. N
2
is considered as a 3-point model,
and the bond length of N-N is 1.10 Å. Oxygen is also a 3-point atom, and the O-O bond length is 1.21 Å.
The models of 3 gases are shown in Figure S1, The atomic charge of MOF was estimated using the MOF
electrostatic-potential-optimized charge scheme (MEPO-Qeq) method [
42
], which accurately evaluated
electrostatic interactions. Due to the advantages of the MEPO-Qeq method with fast and accurate,
it is widely used in various systems of adsorption-MOF [
43
–
45
]. The Lennard–Jones (LJ) electrostatic
parameters were obtained from the universal force field (UFF) [
46
] and are listed in Table S1 Data from
previous studies had shown that the UFF–TraPPE force field combination could accurately predict
Appl. Sci. 2020,10, 569 4 of 13
the adsorption and diffusion behaviors of these 3 gases in MOFs [
40
,
47
,
48
]. The Lorentz–Berthelot
combination rule was used to calculate the cross-LJ parameters.
2.2. Screening Methods
In MOFs, the values of Henry’s constant Kand the diffusion coefficient Dof CO
2
, N
2
, and O
2
were estimated using Monte Carlo (MC) and molecular dynamics (MD) simulations with the same
set, respectively. In principle, a single gas molecule should be added to an MOF to simulate infinite
dilution, while in reality, we added 30 gas molecular models to each MOF, ignoring the force between
the gas models, thus being equivalent to the independent simulation of each gas molecule. Ultimately,
the simulation results of the 30 independent molecules were statistically averaged. Throughout the
simulation, the MOF frame was assumed to be rigid and the simulation elements were extended
to at least 24 Å along the three-dimensional periodic boundary conditions. A 12 Å spherical cutoff
with long-range correction was used to calculate the LJ interaction, while the Ewald sum was used to
calculate the electrostatic interaction. In each MOF, the MC simulation ran 100,000 cycles, with the
first 50,000 used for balancing and the last 50,000 used for overall averaging. Each cycle consisted of n
trials (n: number of adsorbed molecules), including translation, rotation, regeneration, and exchange
(exchange movement, including insertion and deletion). In the MD simulation, the 30 gas molecules
had an MD duration of 10 ns at each MOF, and 5 ns was ultimately selected for statistical averaging.
After the sampling analysis of dozens of MOFs, it was found that further increases of cycle time and
MD duration had little effect on the simulation results. All MCs and MDs were simulated using the
RASPA software package [39].
3. Results and Discussion
3.1. Univariate Analysis
In order to investigate the relationship of CO
2
adsorption and diffusion properties in N
2
+O
2
with
the MOF structure during static adsorption and kinetic adsorption, we first analyzed the relationship
among adsorption selectivity S
ads
, diffusion selective S
diff
, and the LCD of CO
2
/N
2
+O
2
, as shown
in Figure 1. Obviously, most MOFs with large adsorption selectivity and diffusion selectivity have
relatively small LCDs. Figure 1a indicates that when the LCD is 2.8–6.5 Å, the adsorption selectivity
of CO
2
/N
2
+O
2
decreases, and when the LCD is >15 Å, the adsorption selectivity gradually becomes
stable, tending to 5, as depicted by the red line in Figure 1This is because CO
2
has a strong quadrupole
moment, and even in infinitely large pores it is preferentially adsorbed compared to N
2
and O
2
.
The trend of gas separation is consistent with the trends of previous reports [
49
,
50
]. Figure 1b presents
the relationship between S
diff
and LCD. Similar to S
ads
, the larger diffusion selectivity (S
diff
>1) only
occurs in the LCDs ranging from 2.4–5 Å, since the kinetic diameter of CO
2
is less than the kinetic
diameters of O
2
and N
2
(the kinetic diameters of CO
2
, O
2
, and N
2
are 3.3, 3.46, and 3.64 Å, respectively).
When the LCD of an MOF is small, the CO
2
molecules with smaller diameters diffuse faster, so the
diffusion selectivity S
diff(CO2/N2+O2)
is larger. As the LCD increases, the diffusion selectivity gradually
decreases. When the LCD is >15 Å, the diffusion selectivity tends to be stable and fluctuates at around
0.36. Comparison of Figure 1a,b reveals that the adsorption selectivity is generally >1, while it is rare
for the diffusion selectivity to be >1. Because CO
2
has a strong quadrupole distance, it has a strong
interaction force with MOF molecules, thus hindering the diffusion of CO
2
and resulting in a slower
diffusion rate, which may be even smaller than the diffusion rates of N2and O2.
Figure 1c,d show the relationships of S
ads
and S
diff
to the PLD, respectively. Comparing the panels
in Figure 1reveals that the PLD and LCD display the same trend in their relationships to the S
ads
and
S
diff
of CO
2
/N
2
+O
2
. Larger S
ads
and S
diff
values appear when the LCD and PLD are small, and S
ads
and S
diff
both decrease with increasing PLD or LCD, eventually tending toward stability. Therefore,
there is a greater possibility of finding MOFs with simultaneously high S
ads
and S
diff
among MOFs
with small PLDs and LCDs.
Appl. Sci. 2020,10, 569 5 of 13
Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 13
5 1015202530
10-3
100
103
106
109
S
ads(CO2/(N2+O2))
LCD (Å)
(a)
5 1015202530
10-3
10-2
10-1
100
101
102
S
diff(CO2/(N2+O2))
LCD (Å)
(b)
51015
10-3
100
103
106
109
1012
S
ads(CO2/(N2+O2))
PLD ( )
(c)
51015
10-2
10-1
100
101
102
S
diff(CO2/(N2+O2))
PLD
(
Å
)
(d)
Figure 1. The relationships of (a) Sads (CO2/N2+O2) and (b) Sdiff (CO2/N2+O2) with (c) largest cavity diameter
(LCD) and (d) pore-limiting diameter (PLD).
Figure 2a shows that Sads (CO2/N2+O2) increases monotonically with increasing Qst, indicating that
Qst may be the main parameter during the adsorption process. Since the concentration of CO2 in the
atmosphere is low, it is close to the infinite dilution state. Hence, the selectivity is strongly
dependent on the isosteric heat of adsorption of CO2 in the infinite dilution state. The larger Sdiff
(CO2/N2+O2) in Figure 2b occurs when the VSA is close to zero. As the VSA continues to increase, Sdiff
(CO2/N2+O2) gradually decreases, and eventually stabilizes. This is because when the VSA is close to
zero, the MOF molecule either cannot pass any or only passes a small amount of CO2 molecules.
When the VSA is large, all the gas molecules can pass through the MOF molecule. Therefore, the
separation of CO2 cannot be achieved, i.e., the diffusion selectivity is substantially unchanged.
Figure S11b,c indicate the relationship of adsorption selectivity with porosity and VSA, respectively.
It can be observed that both of these parameters exert weak influences on adsorption selectivity.
0 20 40 60 80 100
10-1
102
105
108
1011
1014
S
ads(CO2/(N2+O2))
Q
st (kJ/mol)
(a)
0 1000 2000 3000
10-3
10-2
10-1
100
101
102
S
diff(CO2/(N2+O2))
VSA
(
m2/cm3
)
(b)
Figure 2. The relationships between (a) Sads (CO2/N2+O2) and Qst, (b) Sdiff (CO2/N2+O2) and volumetric surface
area (VSA).
Figure 1.
The relationships of (
a
) S
ads (CO2/N2+O2)
and (
b
) S
diff(CO2/N2+O2)
with (
c
) largest cavity diameter
(LCD) and (d) pore-limiting diameter (PLD).
Figure 2a shows that S
ads (CO2/N2+O2)
increases monotonically with increasing Q
st
, indicating that
Q
st
may be the main parameter during the adsorption process. Since the concentration of CO
2
in the
atmosphere is low, it is close to the infinite dilution state. Hence, the selectivity is strongly dependent
on the isosteric heat of adsorption of CO
2
in the infinite dilution state. The larger S
diff(CO2/N2+O2)
in
Figure 2b occurs when the VSA is close to zero. As the VSA continues to increase, S
diff(CO2/N2+O2)
gradually decreases, and eventually stabilizes. This is because when the VSA is close to zero, the MOF
molecule either cannot pass any or only passes a small amount of CO
2
molecules. When the VSA is
large, all the gas molecules can pass through the MOF molecule. Therefore, the separation of CO
2
cannot be achieved, i.e., the diffusion selectivity is substantially unchanged. Figure S11b,c indicate the
relationship of adsorption selectivity with porosity and VSA, respectively. It can be observed that both
of these parameters exert weak influences on adsorption selectivity.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 13
5 1015202530
10-3
100
103
106
109
S
ads(CO2/(N2+O2))
LCD (Å)
(a)
5 1015202530
10-3
10-2
10-1
100
101
102
S
diff(CO2/(N2+O2))
LCD (Å)
(b)
51015
10-3
100
103
106
109
1012
S
ads(CO2/(N2+O2))
PLD ( )
(c)
51015
10-2
10-1
100
101
102
S
diff(CO2/(N2+O2))
PLD
(
Å
)
(d)
Figure 1. The relationships of (a) Sads (CO2/N2+O2) and (b) Sdiff (CO2/N2+O2) with (c) largest cavity diameter
(LCD) and (d) pore-limiting diameter (PLD).
Figure 2a shows that Sads (CO2/N2+O2) increases monotonically with increasing Qst, indicating that
Qst may be the main parameter during the adsorption process. Since the concentration of CO2 in the
atmosphere is low, it is close to the infinite dilution state. Hence, the selectivity is strongly
dependent on the isosteric heat of adsorption of CO2 in the infinite dilution state. The larger Sdiff
(CO2/N2+O2) in Figure 2b occurs when the VSA is close to zero. As the VSA continues to increase, Sdiff
(CO2/N2+O2) gradually decreases, and eventually stabilizes. This is because when the VSA is close to
zero, the MOF molecule either cannot pass any or only passes a small amount of CO2 molecules.
When the VSA is large, all the gas molecules can pass through the MOF molecule. Therefore, the
separation of CO2 cannot be achieved, i.e., the diffusion selectivity is substantially unchanged.
Figure S11b,c indicate the relationship of adsorption selectivity with porosity and VSA, respectively.
It can be observed that both of these parameters exert weak influences on adsorption selectivity.
0 20 40 60 80 100
10-1
102
105
108
1011
1014
S
ads(CO2/(N2+O2))
Q
st (kJ/mol)
(a)
0 1000 2000 3000
10-3
10-2
10-1
100
101
102
S
diff(CO2/(N2+O2))
VSA
(
m2/cm3
)
(b)
Figure 2. The relationships between (a) Sads (CO2/N2+O2) and Qst, (b) Sdiff (CO2/N2+O2) and volumetric surface
area (VSA).
Figure 2.
The relationships between (
a
) S
ads (CO2/N2+O2)
and Q
st
, (
b
) S
diff(CO2/N2+O2)
and volumetric
surface area (VSA).
Appl. Sci. 2020,10, 569 6 of 13
In addition to adsorption and diffusion selectivity, the Henry coefficient of CO
2
reflects the
adsorption performance of CO
2
in the infinite dilution state, helping to explain the capture performance
of MOFs for air with very low CO
2
concentration. Figure 3a clearly shows the tendency of K
N2
to
change with enthalpy. When the porosity
φ
is small, the MOF has no space due to the limited pore
volume, and only a small amount of N
2
can be adsorbed; therefore, K
N2
is small. When
φ
is in the
range of 0–0.29, K
N2
increases significantly with increasing
φ
. When
φ
>0.29, K
N2
slows down and
gradually stabilizes with increasing
φ
. Figure 3b compares the Henry coefficients of the 3 gases. It can
be seen that the trends of the Henry coefficients of N
2
and O
2
are almost the same; however, CO
2
is different. First, in most MOFs, the Henry coefficient values of CO
2
are basically larger than the
Henry coefficient values of N
2
and O
2
. Second, when LCD >20 Å, the K
CO2
value tends to be level,
and eventually stabilizes. The Henry coefficient of CO
2
is still higher than the coefficients of N
2
and
O
2
, which also leads to MOF selectivity >1 when the LCD is infinite, as seen in Figure 1a Finally, it can
be observed that only a few MOFs can be identified for which the CO
2
Henry coefficient can be >10
−1
mmol/g/Pa. Observing these MOF structures reveals that most have smaller or open metal sites. The
above univariate analysis can only determine the relationship between individual parameters and
performance. Q
st
, PLD and LCD are considered to have dramatic impacts on adsorption selectivity and
diffusion selectivity, but their variable influences cannot be analyzed quantitatively. We will further
utilize 4 types of ML algorithms to obtain additional information about structure-performance.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 13
In addition to adsorption and diffusion selectivity, the Henry coefficient of CO2 reflects the
adsorption performance of CO2 in the infinite dilution state, helping to explain the capture
performance of MOFs for air with very low CO2 concentration. Figure 3a clearly shows the tendency
of KN2 to change with enthalpy. When the porosity ϕ is small, the MOF has no space due to the
limited pore volume, and only a small amount of N2 can be adsorbed; therefore, KN2 is small. When ϕ
is in the range of 0–0.29, KN2 increases significantly with increasing ϕ. When ϕ > 0.29, KN2 slows down
and gradually stabilizes with increasing ϕ. Figure 3b compares the Henry coefficients of the 3 gases.
It can be seen that the trends of the Henry coefficients of N2 and O2 are almost the same; however,
CO2 is different. First, in most MOFs, the Henry coefficient values of CO2 are basically larger than the
Henry coefficient values of N2 and O2. Second, when LCD >20 Å, the KCO2 value tends to be level, and
eventually stabilizes. The Henry coefficient of CO2 is still higher than the coefficients of N2 and O2,
which also leads to MOF selectivity >1 when the LCD is infinite, as seen in Figure 1a Finally, it can be
observed that only a few MOFs can be identified for which the CO2 Henry coefficient can be >10−1
mmol/g/Pa. Observing these MOF structures reveals that most have smaller or open metal sites. The
above univariate analysis can only determine the relationship between individual parameters and
performance. Qst, PLD and LCD are considered to have dramatic impacts on adsorption selectivity
and diffusion selectivity, but their variable influences cannot be analyzed quantitatively. We will
further utilize 4 types of ML algorithms to obtain additional information about
structure-performance.
0.0 0.2 0.4 0.6 0.8 1.0
10-17
10-14
10-11
10-8
10-5
10-2
K
N2
(mmol/g/Pa)
φ
(a)
5 1015202530
10-13
10-10
10-7
10-4
10-1
102
105 K CO2
K N2
K O2
K
LCD (Å)
(b)
Figure 3. Henry coefficient KN2 versus (a) ϕ and (b) LCD.
3.2. Machine Learning
Currently, machine learning has been used to predict the performance of materials and to filter
high-performance materials from large databases [51]. Aiming to discover a better machine
prediction method suitable for this system, we individually compared the simulations of the 4 ML
algorithms commonly used in big data analysis, i.e., the BPNN, DT, RF, and SVM. Among them,
BPNN is a kind of forward signal propagation with error back propagation in which the gradient
descent algorithm continuously adjusts the weight and threshold until the error is less than a set
threshold. Some parameters of BPNN were set: the training function is Levenberg–Marquardt, the
transfer function is a hyperbolic tangent sigmoid transfer function, and the performance evaluation
function is the mean square error (MSE). The number of hidden layer neurons was 18, the maximum
number of training was 1000, the training required an accuracy of 0.001, and the learning rate was
0.01. DT is a traditional method for data classification and screening. Under the condition that the
probability of occurrence takes place in various situations, probability analysis is employed to
analyze data with the dendritic model to obtain the expected values. The random forest algorithm is
composed of multiple decision trees. The setting parameters of DT were: standard CART
(classification and regression tree) used to select the best split predictor at each node. The criteria of
splitting and pruning are the MSE function. After optimizing and pruning, the minimum number of
branch node observations was 10, the minimum number of leaf node observations was 4, and the
maximal number of decision splits was 1. RF uses the method of randomly selecting split attribute
Figure 3. Henry coefficient KN2 versus (a)φand (b) LCD.
3.2. Machine Learning
Currently, machine learning has been used to predict the performance of materials and to filter
high-performance materials from large databases [
51
]. Aiming to discover a better machine prediction
method suitable for this system, we individually compared the simulations of the 4 ML algorithms
commonly used in big data analysis, i.e., the BPNN, DT, RF, and SVM. Among them, BPNN is a kind
of forward signal propagation with error back propagation in which the gradient descent algorithm
continuously adjusts the weight and threshold until the error is less than a set threshold. Some
parameters of BPNN were set: the training function is Levenberg–Marquardt, the transfer function
is a hyperbolic tangent sigmoid transfer function, and the performance evaluation function is the
mean square error (MSE). The number of hidden layer neurons was 18, the maximum number of
training was 1000, the training required an accuracy of 0.001, and the learning rate was 0.01. DT is a
traditional method for data classification and screening. Under the condition that the probability of
occurrence takes place in various situations, probability analysis is employed to analyze data with the
dendritic model to obtain the expected values. The random forest algorithm is composed of multiple
decision trees. The setting parameters of DT were: standard CART (classification and regression
tree) used to select the best split predictor at each node. The criteria of splitting and pruning are the
MSE function. After optimizing and pruning, the minimum number of branch node observations
was 10, the minimum number of leaf node observations was 4, and the maximal number of decision
splits was 1. RF uses the method of randomly selecting split attribute sets to construct a decision tree.
The parameters for RF were set as: number of trees 200, minimum leaf size 10. The number of variables
Appl. Sci. 2020,10, 569 7 of 13
randomly selected in the variable subset of the node split in each tree was 2. SVM is an algorithm for
binary classification of data through supervised learning, and employs mathematical transformation
methods to divide data with a certain centralized structure into rules. We chose the support vector
machine regression model of Statistics and Machine Learning Toolbox in MATLAB 2016b to predict,
where the kernel function is radial basis function (Gaussian), the kernel scale parameter is set as “auto”,
and the loss function is epsilon-insensitive. The box constraint (also called the penalty coefficient, C)
was 0.0567, and the half width of epsilon-insensitive band (
ε
) was set as 0.0057. In the radial basis
kernel function, Gamma =1/(2
σ2
), where
σ
is the parameter of the kernel function, which can affect the
complexity of the SVM regression algorithm. In our study, the value of gamma was 7.125. The solver of
convex quadratic programming is sequential minimal optimization (SMO). Before training and testing,
we first processed the data set out-of-order, and then randomly divide it into training and testing
sets based on a ratio of 7:3. More detailed descriptions of ML algorithms are listed in the supporting
information, and the corresponding diagrams of each algorithm are shown in Figures S2–S5.
We used BPNN, RF, DT, and SVM to predict the adsorption selectivity, and took the logarithm of
the adsorption selectivity in order to reduce the differences associated with the varying magnitudes
of the data. The 4 ML for predicting the correlation coefficient Rvalue of the adsorption selectivity
are listed in Table 1The results of the testing and training are shown in Figure 4and Figure S12.
The distribution trends of the points in Figure 4a–d are all straight lines inclined upward. The different
colors from top to bottom in the figure represent an increase in the number of points, and most of
the points are concentrated on the diagonal, indicating that the prediction results are good. Figure 4
reveals that RF has the highest correlation coefficient value (0.982), while the support vector machine
algorithm has the lowest (0.886). Thus, the prediction accuracy obtained by the RF algorithm is
the highest. Therefore, among the 4 ML algorithms, the structure-performance relationship of RF
on adsorption selectivity obtains more information, and the prediction results are the best. RF has
good generalization ability and strong model learning ability, and this type of ML is suitable for the
system. To verify the accuracy of four ML algorithms, we performed 5 repeated predictions, listed in
Table S3. The repeated prediction results do not vary significantly, confirming that the RF algorithm is
a suitable model. Because RF introduces two kinds of randomness (sampling randomness and feature
randomness), it has strong generalization ability. In previous studies, random forest algorithms also
exhibited the best prediction results [
52
,
53
]. Whether the overfitting of the model is an important
issue. We used combinations of different descriptors and 5 times 5-fold cross-validation to verify
the RF model. The results showed that the selected model was not overfitting. During the material
screening process, the relative importance of parameters may affect the ultimate screening results.
We selected the best RF algorithm to predict the relative importance of each descriptor. The relative
importance percentages are shown in Figure 5and Table S7. We used mean squared error (MSE) to
evaluate the relative importance of the 6 descriptors; the greater the percentage of relative importance
of the resulting descriptors, the higher the relative contribution of the specific descriptor. According to
the results presented in Figure 5, the percentage of Q
st
is the largest, thus indicating that Q
st
exerts the
greatest impact on the adsorption selectivity. The relative importance of the MOF descriptors to the
adsorption selectivity is Q
st
>
ρ
>LCD >VSA
≥φ
>PLD. The importances of VSA and
φ
are very
close, indicating that the effects of two descriptors on adsorption selectivity are roughly equal. From a
material science point of view, the larger the
φ
, the larger the VSA. This may be the reason why the
effects of these parameters are essentially the same.
Table 1.
The 4 ML algorithms for predicting the correlation coefficient Rvalue of the adsorption selectivity.
ML Algorithms R Value
Train Test
BPNN 0.982 0.979
RF 0.994 0.981
DT 0.985 0.969
SVM 0.915 0.886
Appl. Sci. 2020,10, 569 8 of 13
Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 13
Figure 4. The test results of four machine-learning (ML) algorithms predicted versus simulated
Sads(CO2/N2+O2) using ρ, ϕ, VSA, LCD, PLD and heat of adsorption. (a) back propagation neural network
(BPNN), (b) random forest (RF), (c) decision tree (DT), (d) support vector machine (SVM). The color
of point represents the number of metal-organic frameworks (MOFs), and the unit of number is a
base-10 logarithm of MOF numbers.
Table 1. The 4 ML algorithms for predicting the correlation coefficient R value of the adsorption
selectivity.
ML Algorithms R Value
Train Test
BPNN 0.982 0.979
RF 0.994 0.981
DT 0.985 0.969
SVM 0.915 0.886
Figure 4.
The test results of four machine-learning (ML) algorithms predicted versus simulated
S
ads(CO2/N2+O2)
using
ρ
,
φ
, VSA, LCD, PLD and heat of adsorption. (
a
) back propagation neural
network (BPNN), (
b
) random forest (RF), (
c
) decision tree (DT), (
d
) support vector machine (SVM).
The color of point represents the number of metal-organic frameworks (MOFs), and the unit of number
is a base-10 logarithm of MOF numbers.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 13
LCD VSA PLD
0
10
20
30
40
50
60
φ
Relative importance(%)
MOF Descriptors
ρ
Q
st
Figure 5. Predicted by the Random Forest, the relative importance of the six descriptors for
adsorption selectivity.
4. Best Metal-Organic Frameworks (MOFs)
We selected 5 limiting conditions for Sads (CO2/N2+O2) and Sdiff (CO2/N2+O2), and chose 14 optimal MOFs
from the 6013 MOFs, as listed in Table 2 of the 14 materials, HIQPEE exhibited the largest Sdiff, which
was as much as 62.27 Å. NORGOS displayed the largest Sads, which also corresponded to its
maximum heat of adsorption. In comparison, the optimal MOF selected by this study is also more
selective at higher Qst (4712.33) under the same conditions than that predicted by Wu et al. (433) [30]
at Qst = 47.8 kJ/mol and Ravichandar Babarao et al. (500) [54]. It was discovered that diffusion
selectivity is generally lower than adsorption selectivity. The diffusion of CO2 is the key property in
determining the performance of MOFs for low concentrations of CO2 during the kinetic adsorption
process. For these 14 MOFs, the LCD, ϕ, and PLD ranges of the six descriptors also corresponded to
those in the previous univariate analysis. Especially for PLDs, the optimal range of 2.66–3.64 Å only
spans 1 Å, which is also very close to the kinetic diameter of the 3 gases. In such strictly restricted
channels, only CO2 molecules can enter and be adsorbed, greatly increasing the probability of CO2
being captured at low concentrations. Therefore, the analysis of the optimal MOF revealed that a
PLD with a kinetic diameter close to CO2 is a key condition for good CO2 diffusion performance,
further resulting in the excellent performance of the MOF in capturing CO2 from the air, and thus
providing effective guidance for the design and synthesis of new MOFs.
Table 2. Best computation-ready, experimental metal-organic frameworks (CoRE-MOFs).
No CSD Code
a LCD b ϕ VSA c
(m2/cm3) PLD d (Å) Ρ (kg/m3) Qst_CO2
(kJ/mol) SdiffCO2/(N2+O2) SadsCO2/(N2+O2)
1 REYCEF 3.75 0.08 0 2.83 1646.40 26.02 8.21 6.25
2 JAHNEM 3.50 0.05 0 2.66 1714.62 27.01 6.18 6.77
3 HOJLEY 3.63 0.14 0 2.83 1410.99 32.65 5.00 7.45
4 KASPOL 4.04 0.19 16.26 2.93 1665.95 34.05 36.55 7.68
5 XUNJOG 3.25 0.07 0 2.67 1737.75 26.41 5.31 11.12
6 HIQPII 3.87 0.15 9.46 3.12 1472.40 35.20 55.67 11.24
7 YUBFUX 4.58 0.16 98.56 3.64 1786.84 30.52 5.79 11.51
8 HIQPEE 3.84 0.15 7.68 3.12 1440.14 35.31 62.27 12.39
9 FEJKEM 3.46 0.09 0.33 3.09 2132.02 30.00 15.01 15.72
10 FALQIU 5.08 0.12 82.58 3.14 1977.64 34.40 5.38 22.97
11 FALQOA 6.06 0.12 83.34 3.07 2004.41 35.03 6.76 24.10
12 TOXNAX 3.80 0.28 4.42 2.83 1346.52 42.65 5.02 25.15
13 OFIWIK 4.20 0.05 5.99 3.14 1866.86 39.64 27.42 25.66
14 NORGOS 4.95 0.13 45.40 3.43 1728.90 51.67 12.92 4712.33
a CSD Code is the code of MOFs in the Cambridge Structure Database; b LCD: largest cavity diameter; c VSA: volumetric
surface area; d PLD: pore-limiting diameter.
Figure 5.
Predicted by the Random Forest, the relative importance of the six descriptors for
adsorption selectivity.
Appl. Sci. 2020,10, 569 9 of 13
4. Best Metal-Organic Frameworks (MOFs)
We selected 5 limiting conditions for S
ads (CO2/N2+O2)
and S
diff(CO2/N2+O2),
and chose 14 optimal
MOFs from the 6013 MOFs, as listed in Table 2of the 14 materials, HIQPEE exhibited the largest
S
diff
, which was as much as 62.27 Å. NORGOS displayed the largest S
ads
, which also corresponded
to its maximum heat of adsorption. In comparison, the optimal MOF selected by this study is also
more selective at higher Q
st
(4712.33) under the same conditions than that predicted by Wu et al.
(433) [
30
] at Q
st
=47.8 kJ/mol and Ravichandar Babarao et al. (500) [
54
]. It was discovered that diffusion
selectivity is generally lower than adsorption selectivity. The diffusion of CO
2
is the key property in
determining the performance of MOFs for low concentrations of CO
2
during the kinetic adsorption
process. For these 14 MOFs, the LCD,
φ
, and PLD ranges of the six descriptors also corresponded to
those in the previous univariate analysis. Especially for PLDs, the optimal range of 2.66–3.64 Å only
spans 1 Å, which is also very close to the kinetic diameter of the 3 gases. In such strictly restricted
channels, only CO
2
molecules can enter and be adsorbed, greatly increasing the probability of CO
2
being captured at low concentrations. Therefore, the analysis of the optimal MOF revealed that a PLD
with a kinetic diameter close to CO
2
is a key condition for good CO
2
diffusion performance, further
resulting in the excellent performance of the MOF in capturing CO
2
from the air, and thus providing
effective guidance for the design and synthesis of new MOFs.
Table 2. Best computation-ready, experimental metal-organic frameworks (CoRE-MOFs).
No CSD
Code aLCD bφVSA c
(m2/cm3)PLD d
(Å)
P
(kg/m3)
Qst_CO2
(kJ/mol) SdiffCO2/(N2+O2) SadsCO2/(N2+O2)
1 REYCEF 3.75 0.08 0 2.83 1646.40 26.02 8.21 6.25
2 JAHNEM 3.50 0.05 0 2.66 1714.62 27.01 6.18 6.77
3 HOJLEY 3.63 0.14 0 2.83 1410.99 32.65 5.00 7.45
4 KASPOL 4.04 0.19 16.26 2.93 1665.95 34.05 36.55 7.68
5 XUNJOG 3.25 0.07 0 2.67 1737.75 26.41 5.31 11.12
6 HIQPII 3.87 0.15 9.46 3.12 1472.40 35.20 55.67 11.24
7 YUBFUX 4.58 0.16 98.56 3.64 1786.84 30.52 5.79 11.51
8 HIQPEE 3.84 0.15 7.68 3.12 1440.14 35.31 62.27 12.39
9 FEJKEM 3.46 0.09 0.33 3.09 2132.02 30.00 15.01 15.72
10 FALQIU 5.08 0.12 82.58 3.14 1977.64 34.40 5.38 22.97
11 FALQOA 6.06 0.12 83.34 3.07 2004.41 35.03 6.76 24.10
12 TOXNAX 3.80 0.28 4.42 2.83 1346.52 42.65 5.02 25.15
13 OFIWIK 4.20 0.05 5.99 3.14 1866.86 39.64 27.42 25.66
14 NORGOS 4.95 0.13 45.40 3.43 1728.90 51.67 12.92 4712.33
a
CSD Code is the code of MOFs in the Cambridge Structure Database;
b
LCD: largest cavity diameter;
c
VSA:
volumetric surface area; dPLD: pore-limiting diameter.
5. Conclusions
Firstly, we simulated the adsorption and diffusion properties of CO
2
, N
2
, and O
2
in 6013
CoRE-MOFs using high-throughput MC +MD. Then, we investigated the correlation among adsorption
selectivity and diffusion selectivity for CO
2
and MOF descriptors by the univariate analysis. The Q
st
and PLD were considered to be the most important for S
ads (CO2/N2+O2)
and S
diff(CO2/N2+O2)
, respectively.
In conjunction with multivariate analysis, a comparison of 4 ML algorithms revealed that the RF had
the best prediction results for adsorption selectivity, with an Rvalue of 0.982. This indicated that
the RF method was the most suitable for the predictions of the capture of low CO
2
concentrations in
MOF. The relative importance analysis of the RF algorithm quantitatively indicated that the relative
importance of the MOF descriptors on adsorption selectivity is Q
st
>
ρ
>LCD >VSA
≥φ
>PLD.
It was also confirmed that Q
st
is the most important parameter, while the VSA and
φ
are relatively
less important. Through this high-throughput screening, 14 types of MOFs with optimal adsorption
selectivity and diffusion selectivity were obtained. After comparison, it was found that their adsorption
selectivity was generally higher than their diffusion selectivity. The diffusion separation performance of
CO
2
is the key property in determining the performance of MOFs on low concentrations of CO
2
during
Appl. Sci. 2020,10, 569 10 of 13
the kinetic adsorption process. This study provides experimental guidance for the determination
of MOFs that effectively capture CO
2
from the air, and indicates that advanced ML algorithms can
accelerate the research and development of new materials.
Supplementary Materials:
The following are available online at http://www.mdpi.com/2076-3417/10/2/569/s1:
Figure S1: Models of N
2
, O
2
and CO
2
, Figure S2: Back propagation neural network, Figure S3: Decision tree,
Figure S4: Random forest, Figure S5: Support vector machine, Figure S6: Diffusion coefficient D
i
versus (a) LCD,
(b–d) Q
st
(D
i
: the diffusion coefficient of different gases, (a,b) CO
2
, (c) N
2
, (d) O
2
), Figure S7: Henry coefficient
K
CO2
versus (a)
φ
, (b) PLD, (c) Q
st
and (d) VSA, Figure S8: Henry coefficient K
N2
versus (a)
φ
, (b) PLD, (c) Q
st
and (d)
VSA, Figure S9: Henry coefficient K
O2
versus (a)
φ
, (b) PLD, (c) Q
st
and (d) VSA, Figure S10: Diffusion selectivity
S
diff(CO2/(N2+O2))
versus (a) LCD, (b)
φ
, (c) PLD and (d) VSA, Figure S11: Adsorption selectivity S
ads (CO2/N2+O2)
versus (a) LCD, (b)
φ
, (c) PLD and (d) VSA, Figure S11: The training results of four machine learning predicted
versus MC simulated log
10
(S
ads (CO2/N2+O2)
) using density, void fraction, volumetric surface area, density, LCD,
PLD and heat of adsorption. (a) BPNN, (b) RF, (c) DT and (d) SVM. The color of point represents the number of
MOF, and the unit of mumber is a base-10 logarithm of MOF numbers, Table S1: Lennard-Jones parameters of
MOFs, Table S2: Lennard-Jones parameters and charges of adsorbates, Table S3: The training and testing Rvalues
of adsorption selectivity using repeat 5 time-four ML. Table S4 Prediction using RF models with different descriptor
combinations. Table S5 Prediction using repeat 5 times-RF models with different descriptor combinations. Table
S6 The results of predicted RF with ktimes k-fold cross validation. Table S7: Predicted by the RF the relative
importance of the six descriptors for adsorption selectivity. Formula S1: S
ads (CO2/N2+O2)
indicates the adsorption
selectivity of CO
2
/N
2
+O
2
;K
i
represents the Henry coefficient of component i(CO
2
, N
2
and O
2
), Formula S2:
S
diff(CO2/(N2+O2))
represents the diffusion selectivity of CO
2
/N
2
+O
2
;D
i
represents the diffusion coefficient of
component i.
Author Contributions:
X.D., Z.S., H.L. and Z.Q. conceived the idea. Z.Q. calculated all the materials’ structural
parameters and obtained valid data about the structure descriptors and performance. X.D., W.Y. and Z.S. analyzed
the relationship between structure descriptors and performance. X.D. and S.L. used univariate analysis to obtain
the influence law of affecting CO
2
adsorption and diffusion in air and Z.S. used ML algorithms to predict the MOF
performance. X.D. and Z.S. wrote the original draft. H.L. and Z.Q. wrote the manuscript with contributions from
all authors. All authors have read and agreed to the published version of the manuscript.
Funding:
This research was funded by the National Natural Science Foundation of China (Nos. 21978058,
21676094, and 21576058).
Acknowledgments:
We gratefully thank the National Natural Science Foundation of China (Nos. 21978058,
21676094, and 21576058) for financial support.
Conflicts of Interest: The authors declare no conflict of interest.
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