In Silico Screening of Metal-Organic Frameworks for Formaldehyde Capture with and without Humidity by Molecular Simulation

Capturing formaldehydes (HCHO) from indoor air with porous adsorbents still faces challenges due to their low capacity and poor selectivity. Metal-organic frameworks (MOFs) with tunable pore properties were regarded as promising adsorbents for HCHO removal. However, the water presence in humid air heavily influences the formaldehyde capture performance due to the competition adsorption. To find suitable MOFs for formaldehyde capture and explore the relationship between MOFs structure and performance both in dry air and humid air, we performed grand canonical Monte Carlo (GCMC) molecular simulations to obtain working capacity and selectivity that evaluated the HCHO capture performance of MOFs without humidity. The results reveal that small pore size (~5 Å) and moderate heat of adsorption (40–50 kJ/mol) are favored for HCHO capture without water. It was found that the structure with a 3D cage instead of a 2D channel benefits the HCHO adsorption. Atoms in these high-performing MOFs should possess relatively small charges, and large Lennard-jones parameters were also preferred. Furthermore, it was indicated that Henry’s constant (KH) can reflect the HCHO adsorption performance without humidity, in which the optimal range is 10−2–101. Hence, Henry’s constant selectivity of HCHO over water (SKH HCHO/H2O) and HCHO over mixture components (H2O, N2, and O2) was obtained to screen MOFs at an 80% humidity condition. It was suggested that SKH for the mixture component overestimates the influence of N2 and O2, in which the top structures absorb a quantity of water in GCMC simulation, while SKH HCHO/H2O can efficiently find high-performing MOFs for HCHO capture at humidity in low adsorption pressure. The ECATAT found in this work has 0.64 mol/kg working capacity, and barely adsorbs water during 0–1 bar, which is the promising candidate MOF for HCHO capture.


Introduction
Volatile organic compounds (VOCs) include a variety of chemicals, some of which may have short-and long-term adverse health effects. Among the most popular VOCs, formaldehyde (HCHO), is very allergenic and carcinogenic even at very low concentrations [1][2][3]. The World Health Organization (WHO) recommended that a safe concentration of formaldehyde vapor for humans must be below 0.08 ppm (30-min) and a threshold sensory irritation of 0.1 mg/m 3 , which also can be lethal at a concentration of 30 mg/m [4][5][6]. Therefore, the removal of formaldehyde from contaminated air or the industrial process is in demand. The various methods for abating HCHO from indoor areas include photocatalysis [7,8], catalytic oxidation [9,10], and adsorption-based [11,12], and formaldehyde capture has been one of the most promising strategies due to the facile operation [13]. To date, a number of adsorbents including activated carbons [14], zeolites [13], SiO 2 [15,16], AlOOH [17], amine-supported materials [18], etc. have been explored for formaldehyde

HCHO Capture Performance without Humidity
In this work, GCMC simulation was carried out to evaluate the HCHO pressure swing adsorption (PSA) performance of 1668 CoRE-MOFs in dry air between 0.1 and 1 bar. Figure 1 shows the relationship of working capacity (∆W), selectivity (S), and heat of adsorption (Q st ) to the pore size. It is revealed that the highest working capacity is 4.01 mol/kg, the refcode in the Cambridge Structural Database (CSD) is LAVSUY, followed by the DUBWON (3.98 mol/kg), and PARMIG (3.93 mol/kg). It denotes LCD located in the range of 5-6 Å for most MOFs with ∆W > 2 mol/kg and selectivity over 10 3 , presented in Figure 1a. Notably, Bellat et al. [13]. previously reported the total uptake of 2.3 mol/kg (7 wt%) of Ga-MIL-53 at 2000 ppm, room temperature, and Wang et al. [27] found the adsorption uptake of 3.34 mol/kg in MIL-101(Cr) at 150 ppm and then can up to 5.49 mol/kg after being post-modified by ethylenediamine. The highest working capacity in this work is larger than the capacity of MOFs without modification in the experiment, which indicated that there are promising MOFs awaiting discovery. In addition, most MOFs with large working capacities (>2 mol/kg) have relatively small LCDs (4-6 Å), which is nearly double the formaldehyde dynamic diameter (2.43 Å) [34]. This may be ascribed to the suitable interaction of MOFs in such a pore size, which reflected in the moderate heat of desorption (40~50 kJ/mol). A similar phenomenon of pore size dependence for gas adsorption also can be found in Wilmer et al.'s [35]. CH 4 storage work and Banerjee et al.'s [36] Xe/Kr separation work. Moreover, Figure 1b indicated that the selectivity fluctuates with the heat of desorption, while higher Q st benefits from the increase of selectivity. When the LCD > 10 Å, it was found that most structures exhibit poor HCHO capture performance (∆W < 2.0 mol/kg, S < 10 3 and Q st < 40 kJ/mol). However, as presented in Figure S1, it was noted that excessive strong interaction leads to the HCHO being difficult to desorb during the PSA process, which will be discussed later. pressure. This work offers the molecular understanding of the rational design of highperforming MOFs for HCHO removal both in dry and humid air.

HCHO Capture Performance without Humidity
In this work, GCMC simulation was carried out to evaluate the HCHO pressure swing adsorption (PSA) performance of 1668 CoRE-MOFs in dry air between 0.1 and 1 bar. Figure 1 shows the relationship of working capacity (ΔW), selectivity (S), and heat of adsorption (Qst) to the pore size. It is revealed that the highest working capacity is 4.01 mol/kg, the refcode in the Cambridge Structural Database (CSD) is LAVSUY, followed by the DUBWON (3.98 mol/kg), and PARMIG (3.93 mol/kg). It denotes LCD located in the range of 5-6 Å for most MOFs with ΔW > 2 mol/kg and selectivity over 10 3 , presented in Figure 1a. Notably, Bellat et al. [13]. previously reported the total uptake of 2.3 mol/kg (7 wt%) of Ga-MIL-53 at 2000 ppm, room temperature, and Wang et al. [27] found the adsorption uptake of 3.34 mol/kg in MIL-101(Cr) at 150 ppm and then can up to 5.49 mol/kg after being post-modified by ethylenediamine. The highest working capacity in this work is larger than the capacity of MOFs without modification in the experiment, which indicated that there are promising MOFs awaiting discovery. In addition, most MOFs with large working capacities (>2 mol/kg) have relatively small LCDs (4-6 Å), which is nearly double the formaldehyde dynamic diameter (2.43 Å) [34]. This may be ascribed to the suitable interaction of MOFs in such a pore size, which reflected in the moderate heat of desorption (40~50 kJ/mol). A similar phenomenon of pore size dependence for gas adsorption also can be found in Wilmer et al.'s [35]. CH4 storage work and Banerjee et al.'s [36] Xe/Kr separation work. Moreover, Figure 1b indicated that the selectivity fluctuates with the heat of desorption, while higher Qst benefits from the increase of selectivity. When the LCD > 10 Å, it was found that most structures exhibit poor HCHO capture performance (ΔW < 2.0 mol/kg, S < 10 3 and Qst < 40 kJ/mol). However, as presented in Figure  S1, it was noted that excessive strong interaction leads to the HCHO being difficult to desorb during the PSA process, which will be discussed later. In indoor air, formaldehyde is generally found in trace amounts with very low partial pressure, which adsorbs in Henry's law region. Thus, Figure 2a presented the correlation between adsorption performance and KH. It was found that the MOFs exhibited poor ΔW and S when KH was small than 10 −2 mol/(kg·Pa), which can be ascribed to the poor interaction that limited the HCHO adsorption. As for those structures with KH > 10 1 mol/(kg·Pa), it is suggested that strong interaction benefits the selectivity of HCHO over N2 and O2. However, as shown in Figure S2, the overlarge host-adsorbate interaction causes the HCHO extremely hard to desorb, which is not conducive to HCHO capture. It In indoor air, formaldehyde is generally found in trace amounts with very low partial pressure, which adsorbs in Henry's law region. Thus, Figure 2a presented the correlation between adsorption performance and K H . It was found that the MOFs exhibited poor ∆W and S when K H was small than 10 −2 mol/(kg·Pa), which can be ascribed to the poor interaction that limited the HCHO adsorption. As for those structures with K H > 10 1 mol/(kg·Pa), it is suggested that strong interaction benefits the selectivity of HCHO over N 2 and O 2 . However, as shown in Figure S2, the overlarge host-adsorbate interaction causes the HCHO extremely hard to desorb, which is not conducive to HCHO capture. It was indicated that 10 −2 ≤ K H ≤ 10 1 was favored for high working capacity and moderate selectivity that benefits HCHO capture. Such a result suggests that K H can be used to pre-screen adsorbents for HCHO capture in dry air. Moreover, the correlation between atom distribution in Int. J. Mol. Sci. 2022, 23, 13672 4 of 13 crystal (MaxER, MinER) and ∆W was also investigated. Notably, as shown in Figure S3a, the MaxER = MinER = 0.33 indicated that the MOF crystal is cubic topology and x, y, z axisymmetric. For MinER = 0, the structures tend to be 2-D layers. Hence, when the MinER is close to 0, it means the pore of structures tends to be a channel instead of a cage. In Figure 2b, it was found that MaxER near 0.4 and MinER located in 0.2-0.3 are favored for high working capacity, while most structures with MaxER > 0.6 and MinER < 0.1 exhibit low working capacity. Compared with the channel, 3D cages with different properties in each direction were preferred in HCHO capture. was indicated that 10 −2 ≤ KH ≤ 10 1 was favored for high working capacity and moderate selectivity that benefits HCHO capture. Such a result suggests that KH can be used to prescreen adsorbents for HCHO capture in dry air. Moreover, the correlation between atom distribution in crystal (MaxER, MinER) and ΔW was also investigated. Notably, as shown in Figure S3a, the MaxER = MinER = 0.33 indicated that the MOF crystal is cubic topology and x, y, z axisymmetric. For MinER = 0, the structures tend to be 2-D layers. Hence, when the MinER is close to 0, it means the pore of structures tends to be a channel instead of a cage. In Figure 2b, it was found that MaxER near 0.4 and MinER located in 0.2-0.3 are favored for high working capacity, while most structures with MaxER > 0.6 and MinER < 0.1 exhibit low working capacity. Compared with the channel, 3D cages with different properties in each direction were preferred in HCHO capture. We further analyzed the correlation between adsorption performance and the force field of atoms in MOFs, including average positive/negative charge(APC/ANC) and LJ parameters. According to Figure 3a, APC < 0.2 (ANC > −0.2) and APC > 0.5 (ANC < −0.5) exhibit poor working capacity, which the APC located in 0.2-0.5 for most structures with ΔW > 0.2 mol/kg. As shown in Figure S4a, it was suggested that the enhancement of LJ interaction always favors the increase in HCHO capacity. The excessive interaction makes the HCHO difficult to desorb from the MOFs in Figure S4b, which led to a decrease in working capacity, similar to the tendency found in KH. Furthermore, as shown in Figure  3b, the selectivity of HCHO over N2 and O2 scatter in a wide range (1-10 7 ), can be divided into three parts according to the LJ parameters. For those MOFs with 0 < Aε < 1.5 and 0 < Aσ < 0.12, they have large enough pore volume ( Figure S4c), but the weak interaction limited the adsorption of HCHO, which makes the selectivity lower than 10 4 . As for those structures with Aε > 3 and Aσ > 0.21, the tiny pore volume cannot afford higher capacity, which also makes it unsuitable for HCHO capture. Therefore, it was suggested that 1.5 ≤ Aε ≤ 3.0 and 0.12 ≤ Aσ ≤ 0.21 are beneficial to the enhancement of selectivity, and most structures with S > 10 5 are located in this range. Moreover, it was also found that the high selectivity accompanied by satisfying capacity in Figure S4d, which indicated the combined moderate charge and LJ parameters, favors the HCHO capture performance of MOFs. We further analyzed the correlation between adsorption performance and the force field of atoms in MOFs, including average positive/negative charge(APC/ANC) and LJ parameters. According to Figure 3a, APC < 0.2 (ANC > −0.2) and APC > 0.5 (ANC < −0.5) exhibit poor working capacity, which the APC located in 0.2-0.5 for most structures with ∆W > 0.2 mol/kg. As shown in Figure S4a, it was suggested that the enhancement of LJ interaction always favors the increase in HCHO capacity. The excessive interaction makes the HCHO difficult to desorb from the MOFs in Figure S4b, which led to a decrease in working capacity, similar to the tendency found in K H . Furthermore, as shown in Figure 3b, the selectivity of HCHO over N 2 and O 2 scatter in a wide range (1-10 7 ), can be divided into three parts according to the LJ parameters. For those MOFs with 0 < Aε < 1.5 and 0 < Aσ < 0.12, they have large enough pore volume ( Figure S4c), but the weak interaction limited the adsorption of HCHO, which makes the selectivity lower than 10 4 . As for those structures with Aε > 3 and Aσ > 0.21, the tiny pore volume cannot afford higher capacity, which also makes it unsuitable for HCHO capture. Therefore, it was suggested that 1.5 ≤ Aε ≤ 3.0 and 0.12 ≤ Aσ ≤ 0.21 are beneficial to the enhancement of selectivity, and most structures with S > 10 5 are located in this range. Moreover, it was also found that the high selectivity accompanied by satisfying capacity in Figure S4d, which indicated the combined moderate charge and LJ parameters, favors the HCHO capture performance of MOFs.
The top 10 MOFs with excellent formaldehyde capture performance are listed in Table 1. Among them, the best MOF is LAVSUY, with 6.62 Å LCD, 0.43 MaxER, 0.50 e APC, 0.16 kcal/mol Aε, 1.18 × 10 −2 mol/(kg·Pa) K H , which was predicted to have 4.01 mol/kg working capacity and 2722 selectivity. As shown in Figure S3c, the LAVSUY has bcu (bodycentered cubic) topology, Y nodes connected by 1,3,5-Benzenetricarboxylic acid. In addition, other top-performance MOFs exhibited similar structural characteristics. For example, LCD located in 4.25-6.62 Å, MaxER in 0.37-0.56, APC in 0.16-0.59, Aε in 0.13-0.23 kcal/mol, K H in 7.37 × 10 −2 -2.68 × 10 −1 mol/(kg·Pa), and other descriptors are provided in Table S2, which is quite consistent with the suitable range for HCHO capture found in previous results. The top 10 MOFs with excellent formaldehyde capture performance are listed in Table 1. Among them, the best MOF is LAVSUY, with 6.62 Å LCD, 0.43 MaxER, 0.50 e APC, 0.16 kcal/mol Aε, 1.18 × 10 −2 mol/(kg·Pa) KH, which was predicted to have 4.01 mol/kg working capacity and 2722 selectivity. As shown in Figure S3c, the LAVSUY has bcu (body-centered cubic) topology, Y nodes connected by 1,3,5-Benzenetricarboxylic acid. In addition, other top-performance MOFs exhibited similar structural characteristics. For example, LCD located in 4.25-6.62 Å, MaxER in 0.37-0.56, APC in 0.16-0.59 , Aε in 0.13-0.23 kcal/mol, KH in 7.37 × 10 −2 -2.68 × 10 −1 mol/(kg·Pa), and other descriptors are provided in Table S2, which is quite consistent with the suitable range for HCHO capture found in previous results. The adsorption isotherm of HCHO, N2, and O2 mixture components obtained from GCMC simulation for the top 3 MOFs (LAVSUY, DUBWON, and PARMIG) are presented in Figure 4a-c. All MOFs almost were Type I adsorption isotherm [37] defined by IUPAC and exhibited ultra-high capacity with extremely low N2 and O2 capacity. It is worthy of note that the DUBWON and PARMIG seem to reach the saturation capacity when the pressure is larger than 0.8 bar, whereas the LAVSUY probably tends to have a higher capacity as the pressure continues to increase. Moreover, combined with the snapshots of  The adsorption isotherm of HCHO, N 2, and O 2 mixture components obtained from GCMC simulation for the top 3 MOFs (LAVSUY, DUBWON, and PARMIG) are presented in Figure 4a-c. All MOFs almost were Type I adsorption isotherm [37] defined by IUPAC and exhibited ultra-high capacity with extremely low N 2 and O 2 capacity. It is worthy of note that the DUBWON and PARMIG seem to reach the saturation capacity when the pressure is larger than 0.8 bar, whereas the LAVSUY probably tends to have a higher capacity as the pressure continues to increase. Moreover, combined with the snapshots of Figure S3c-e, the density plots in Figure 4d-f illustrated that the HCHO majority adsorb in the center of the cage close to the metal nodes of MOFs, which is consistent with the results of Figure 2b.

HCHO Capture Performance with Humidity
As we mentioned before, the competitive adsorption between HCHO and H 2 O would heavily influence the HCHO capture performance in humid air. However, estimating the HCHO capture performance for a large quantity of MOFs via GCMC simulation or experiment is extremely time-consuming [38]. It was proposed that the K H of water can be adapted to identify whether the MOFs are hydrophilic or hydrophobic in HCHO capture. Moreover, the results in dry air suggested that K H are the dominant factor to determine the HCHO capture performance. Thus, regarding the heavy competition between water and HCHO, there are two Henry's selectivity (SK H ) were calculated to screen out suitable MOFs in humid air, type 1: HCHO over water, type 2: HCHO over water, N 2, and O 2 . As shown in Figure 5a, it was found that the LCD of the top 3 MOFs for SK H HCHO/H 2 O is located in a wide range (5-13 Å). Whereas the small LCD (~5 Å) exhibited better performance for SK H HCHO/(H 2 O + N 2 + O 2 ) in Figure 5b, similar to the trend found in dry air.

HCHO Capture Performance with Humidity
As we mentioned before, the competitive adsorption between HCHO and H2O would heavily influence the HCHO capture performance in humid air. However, estimating the HCHO capture performance for a large quantity of MOFs via GCMC simulation or experiment is extremely time-consuming [38]. It was proposed that the KH of water can be adapted to identify whether the MOFs are hydrophilic or hydrophobic in HCHO capture. Moreover, the results in dry air suggested that KH are the dominant factor to determine the HCHO capture performance. Thus, regarding the heavy competition between water and HCHO, there are two Henry's selectivity (SKH) were calculated to screen out suitable MOFs in humid air, type 1: HCHO over water, type 2: HCHO over water, N2, and O2. As shown in Figure 5a, it was found that the LCD of the top 3 MOFs for SKH HCHO/H2O is located in a wide range (5-13 Å). Whereas the small LCD (~5 Å) exhibited better performance for SKH HCHO/(H2O + N2 + O2) in Figure 5b, similar to the trend found in dry air.  Figure 6 was presented to illustrate the relationship between Henry constant selectivity and chemical descriptor, including MPC, MNC, Aσ, and Aε. It was found that the SK H HCHO/H 2 O depend significantly on the charge since they are nonpolar adsorbates. In Figure 6a, it was found that most SK H HCHO/H 2 O > 10 MOFs with MPC < 2. As for MPC ≥ 2, a large quantity of MOFs exhibited SK H HCHO/H 2 O < 10 −2 due to the strong Coulombic interaction between MOFs and water. Moreover, as shown in Figure S5a Figure 6 was presented to illustrate the relationship between Henry constant selectivity and chemical descriptor, including MPC, MNC, Aσ, and Aε. It was found that the SKH HCHO/H2O depend significantly on the charge since they are nonpolar adsorbates. In Figure 6a, it was found that most SKH HCHO/H2O > 10 MOFs with MPC < 2. As for MPC ≥ 2, a large quantity of MOFs exhibited SKH HCHO/H2O < 10 −2 due to the strong Coulombic interaction between MOFs and water. Moreover, as shown in Figure S5a,c, it was suggested that top MOFs for SKH HCHO/H2O exhibited low void fraction and high LJ descriptors (Aσ > 0.2 and Aε > 3), including ECAHAT (LCD~12 Å). Moreover, as shown in Figure 6b, high Aσ and Aε also benefit the increment of SKH HCHO/(H2O + N2 + O2), which indicated that Lennard-jones interaction is a dominant role in determining the HCHO capture performance in humid air. Moreover, in Figure S5b,d, it was found most MPC > 2 MOFs have extremely large KH for water that is not favored both in SKH HCHO/H2O and SKH HCHO/(H2O + N2 + O2).  Table 2. JAVTAC has a maximum SKH HCHO/H2O, which is 418.76, followed by WOJJOV (194.11), and ECAHAT (144.74). Notably, it was found that all the MOFs in Table  2 have extremely low KH of N2 and O2, which indicated they probably have a poor affinity toward N2 and O2. Indeed, as shown in Figure S6, SKH HCHO/(H2O + N2 + O2) is almost   Figure 6 was presented to illustrate the relationship between Henry constant selectivity and chemical descriptor, including MPC, MNC, Aσ, and Aε. It was found that the SKH HCHO/H2O depend significantly on the charge since they are nonpolar adsorbates. In Figure 6a, it was found that most SKH HCHO/H2O > 10 MOFs with MPC < 2. As for MPC ≥ 2, a large quantity of MOFs exhibited SKH HCHO/H2O < 10 −2 due to the strong Coulombic interaction between MOFs and water. Moreover, as shown in Figure S5a,c, it was suggested that top MOFs for SKH HCHO/H2O exhibited low void fraction and high LJ descriptors (Aσ > 0.2 and Aε > 3), including ECAHAT (LCD~12 Å). Moreover, as shown in Figure 6b, high Aσ and Aε also benefit the increment of SKH HCHO/(H2O + N2 + O2), which indicated that Lennard-jones interaction is a dominant role in determining the HCHO capture performance in humid air. Moreover, in Figure S5b,d, it was found most MPC > 2 MOFs have extremely large KH for water that is not favored both in SKH HCHO/H2O and SKH HCHO/(H2O + N2 + O2).  Table 2. JAVTAC has a maximum SKH HCHO/H2O, which is 418.76, followed by WOJJOV (194.11), and ECAHAT (144.74). Notably, it was found that all the MOFs in Table  2 have extremely low KH of N2 and O2, which indicated they probably have a poor affinity toward N2 and O2. Indeed, as shown in Figure S6, SKH HCHO/(H2O + N2 + O2) is almost  Table 2. JAVTAC has a maximum SK H HCHO/H 2 O, which is 418.76, followed by WOJJOV (194.11), and ECAHAT (144.74). Notably, it was found that all the MOFs in Table 2 have extremely low K H of N 2 and O 2 , which indicated they probably have a poor affinity toward N 2 and O 2 . Indeed, as shown in Figure S6  In order to verify Henry's constant screening results, the GCMC simulations were implemented for six MOFs (JAVTAC, WOJJOV, ECAHAT, DORDUK, DOTTUC, and OHOMIH) to obtain the adsorption isotherm under 80% humidity conditions in 298 K. As shown in Figure 7d-f, all of the structures selected by SK H HCHO/(H 2 O + N 2 + O 2 ) are highly hydrophilic structures that adsorb a lot of water (>4 mol/kg) in low pressure (0.1 bar). The JAVTAC has a higher formaldehyde uptake in lower pressure and is in agreement with Henry's law. However, when the pressure gradually increases to 1.0 bar, the water molecules with polar functional groups occupy the adsorption sites preferentially, and the strong competitive adsorption of water molecules hinders the capture of HCHO [12]. The water uptake then exhibits an s-shaped isotherm and finally reaches a higher water loading in structures. As for WOJJOV, the water exhibited a similar trend with JAVTAC, while the HCHO uptake maintains at 0.9 mol/kg. For the ECAHAT, the water uptake is extremely low during the whole pressure range, and it has a 0.64 mol/kg working capacity between 0.1 bar and 1 bar, and 465 selectivity of HCHO over H 2 O, N 2, and O 2 , which is a promising candidate for HCHO capture under humidity conditions. In this study, it was indicated that SK H HCHO/H 2 O can be recognized as a critical descriptor in low pressure. It remains a challenge to find a suitable descriptor for screening MOFs under humidity conditions in high pressure with reasonable computation cost.

MOFs Database
All MOF structures were obtained from the computation-ready, experimental (CoRE) MOF database Version 1.0 [39], which the solvent and disorder structures were removed from Cambridge structural database (CSD) by Chung and co-workers. The structure with density derived electrostatic and chemical (DDEC) [40] charges containing 2932 structures were developed by Nazarian [41]. After removing the structures with zero accessible surface area (ASA), there are 1668 structures to perform formaldehyde capture screening. The ASA, largest cavity diameter (LCD), pore limiting diameter (PLD), and available pore volume (Va) were computed using the 1.86 Å nitrogen probe in zeo++0.3. Helium void fraction (VF) and Henry's constant of MOFs toward H2O, HCHO, N2 and O2 were obtained by the Widom particle insertion method.

Grand Canonical Monte Carlo
CoRE MOFs containing 1668 structures carrying DDEC charges were employed for high-throughput screening. GCMC simulations were implemented to obtain the adsorption performance of these structures in RASPA 2.0. During the screening stage, 4 × 10 4 Monte Carlo cycles were performed to estimate the adsorption isotherms of each MOF, including the initial 2 × 10 4 cycles of equilibration run, and the other 2 × 10 4 cycles of the production run. Four Monte Carlo moves of insertion, deletion, rotation, and translation were implemented with equal probability. Identity change of adsorbate molecules for

MOFs Database
All MOF structures were obtained from the computation-ready, experimental (CoRE) MOF database Version 1.0 [39], which the solvent and disorder structures were removed from Cambridge structural database (CSD) by Chung and co-workers. The structure with density derived electrostatic and chemical (DDEC) [40] charges containing 2932 structures were developed by Nazarian [41]. After removing the structures with zero accessible surface area (ASA), there are 1668 structures to perform formaldehyde capture screening. The ASA, largest cavity diameter (LCD), pore limiting diameter (PLD), and available pore volume (V a ) were computed using the 1.86 Å nitrogen probe in zeo++0.3. Helium void fraction (VF) and Henry's constant of MOFs toward H 2 O, HCHO, N 2 and O 2 were obtained by the Widom particle insertion method.

Grand Canonical Monte Carlo
CoRE MOFs containing 1668 structures carrying DDEC charges were employed for high-throughput screening. GCMC simulations were implemented to obtain the adsorption performance of these structures in RASPA 2.0. During the screening stage, 4 × 10 4 Monte Carlo cycles were performed to estimate the adsorption isotherms of each MOF, including the initial 2 × 10 4 cycles of equilibration run, and the other 2 × 10 4 cycles of the production run. Four Monte Carlo moves of insertion, deletion, rotation, and translation were implemented with equal probability. Identity change of adsorbate molecules for multicomponent adsorption was performed with the two-fold probability of insertion, deletion, rotation, and translation moves. The simulation temperature was maintained at 298 K, and the pressure ranges from 0.

Force Field
During molecular simulation, the Lennard-Jones (LJ) and Coulomb potentials were used to describe the non-bonded interactions between MOFs and adsorbates.
Herein, ij represents the two interacting atoms, where ε is the depth of the potential wall, σ ij is the finite distance at which the inter-particle potential is zero, r ij is the distance between the particles. All the LJ parameters of MOFs were taken from UFF force field [42], and the LJ parameters for N 2 and O 2 were adapted from the TraPPE force field [43]. The Lorentz-Berthelot mixing rule was applied for inter-atomic LJ interactions. q i and q j are the atomic partial charges of two interacting atoms, and ε 0 is the vacuum permittivity constant. Long-range Coulombic interaction was described by the Ewald method [44] with a cutoff of 12.8 Å. We calculate the average sigma of LJ interaction and the average epsilon of LJ interaction, represented as Aσ and Aε.
The water model we adapted is the Tip4p force field, for it can well represent the water adsorption property in hydrophobic MOFs [45]. The force field parameters of formaldehyde were taken from Hantal et al.'s study [46] in which the planar formaldehyde model was employed. The bond lengths of H-C and C=O are 1.101 and 1.203 Å, respectively, and the angle of H-C=O is 121.8 • . In this model, only the C and O atoms carry fractional charges of +0.45 × 10 1 and −0.45 × 10 1 , respectively, and a dipole moment of 2.6 D along C=O bond vector was applied. The N 2 and O 2 force field are taken from TraPPE. All of the parameters of adsorbates are summarized in Table S1.

The Descriptor of MOF Characteristic
There are nine descriptors that were collected from the crystallographic information file (CIF) to describe the structural/energetic features of MOFs. LCD is defined as the diameter of the largest sphere that can fit in the pore of MOF. The MaxER and MinER is the maximum and minimum value of variance explained by principal component analysis (PCA) for atom distribution in three directions of the unit cell, in which MaxER = MinER = 0.33 stands for the isotropic crystal. MPC/MNC is the most positive/negative charge of atoms in a unit cell. As for APC/ANC, the average positive/negative charge per unit volume was calculated. Furthermore, Aσ and Aε is the average σ/ε of an atom in the Lennard-Jones interaction. These descriptors were verified to possess significant correlations with the HCHO capture performance of MOFs.

Conclusions
In this work, we perform high-throughput computational screening of CoRE MOFs for HCHO capture with and without humidity conditions. In the dry air, working capacity and selectivity were adopted to evaluate the HCHO capture performance. It was found that small pore size (5-6 Å) and moderate heat of adsorption (40-50 kJ/mol) are favored for HCHO capture. Such high-performing structures probably have a 3D cage instead of a 2D channel with moderate charge and Lennard-jones parameters (0.2 ≤ APC ≤ 0.5, 1.5 ≤ Aε ≤ 3.0, and 0.12 ≤ Aσ ≤ 0.21) that benefit to the HCHO adsorption. Moreover, it was indicated that K H is the dominant factor to determine the HCHO capture performance, for which 10 −2 -10 1 mol/(kg·Pa) is preferred. The density plot of HCHO adsorption and adsorption isotherm verified that the top3 working capacity MOFs (LAVSUY, DUBWON, and PARMIG) are suitable for the removal of HCHO without H 2 O's existence.
The can be recognized as a critical descriptor in low pressure, which all structures barely adsorb water. The simulation suggested that ECAHAT was a promising candidate for HCHO capture under 80% humidity conditions in 1 bar, 298 K, which have 0.64 mol/kg working capacity and high selectivity (reach 465).