In recent years, there has been an increasing interest in adsorption of various molecules [1-6] and developing gas storage systems for various applications such as CO2 capture or H2 storage [7-10]. By the same token, the metal-organic framework (MOF) family of materials have attracted particular attention due to their fascinating sorption properties [11-13]. In these materials, inorganic clusters (metals) and organic ligands can be connected to adopt a wide range of different structures, which open the possibility of tuning host-guest interactions in order to explore molecular sieving and adsorption properties unavailable in other materials.
One of the most important MOFs is Zn4O13C24H12 framework called as MOF-5, which was invented in 1999 . This framework has potential applications for H2 storage, CO2 capture, and catalysts . The MOF-5 consists of Zn4O nodes which are linked to terephthalate anions (1,4-BDC = 1,4-benzenedicarboxylate) groups to form a porous material (Fig. 1(a)) . It has been recognized that the MOF-5 occupies either cubic (C-MOF-5) or tetragonal (T-MOF-5) structure [16-20]. Cubic MOF-5 (with ultra-high BET surface area up to 3400 m2/g) has widely been synthesized by using a“diffusion” method  and tetragonal MOF-5 (with a medium surface area) can be synthesized via“direct mixing” approach .
The tetragonal MOF-5 is a distorted cubic MOF-5 . Furthermore, this structure distortion was attributed to the presence of ZnO species extra phase and solvent in the pores [15,18-20]. Zhang and Hang Hu , showed that the composition (Zn4.28O12.8C24H11.3) of cubic MOF-5 sample is consistent with the stoichiometrical formula of Zn4O13C24H12. In contrast, the composition of the tetragonal MOF-5 sample with the calculated formula of Zn4O13C24H12.6(ZnO)1.59(H2O)1.74 was very different from the stoichiometrical formula of Zn4O13C24H12, because ZnO and H2O were present. The presence of H2O might be due to the adsorption of H2O when it was exposed to air. The formation of ZnO species is due to the reaction between zinc nitrate and H2O2 during the synthesis of tetragonal MOF-5.
In our previous work, we have shown that the T-MOF-5 had a lower surface area, lower porosity, smaller and more uniform pore size, and more ZnO molecule than C-MOF-5 . Also in another work, we have synthesized and characterized the C-MOF-5 and T-MOF-5 as adsorbents for H2 and CO2 adsorption . We found that the CO2 adsorption capacity of C-MOF-5 is greater than that of T-MOF-5 and the H2 adsorption capacity of C-MOF-5 is less than that of T-MOF-5 (at 298 K and 25 bar). This behavior was attributed to more ZnO units in T-MOF-5 than C-MOF-5.
According to literature, adsorption of small molecules in MOF-5 occurs first in a site near the Zn cluster in the large pores (site A’ in Fig. 1(b)) [23-27]. Sarmiento-Perez et al  introduced a similar site that is present in the smaller pore (site B’ in Fig. 1(b)). They showed that the site B’ in Fig. 1(b) is the main site for CO2.
As reported in the literature, calculation of the chemical properties of MOF-5 using a representative fragment (such as an organic ligand) is in good agreement with the experimental results [29-31]. Considering the large size of cells in the MOF-5 structure for a quantum mechanics calculation, the model system should be decreased in size. The size reduction can be achieved by separating the H2BDC linker. Accordingly, in this paper, we considered the adsorption behavior of CO2 and H2 molecules on the surface of C-MOF-5 (H2BDC as a representative section) and T-MOF-5 (ZnO-H2BDC as a representative section).
In the current study, we examined the adsorption of H2 and CO2 on the surface of H2BDC and ZnO-H2BDC (as a representative section of C-MOF-5 and T-MOF-5 nanostructures) using DFT calculations. First, we explored the geometric and electronic properties of H2BDC surfaces upon decoration of ZnO (ZnO-H2BDC) by examining binding energies, the charge transfer, density of states, dipole moments and adsorption geometries for the probable position. Then, the relaxed H2BDC and ZnO-H2BDC ligands are theoretically investigated for H2 and CO2 adsorption. In other words, we investigate in detail, the effect of more ZnO molecule in T-MOF-5 nanostructure than C-MOF-5 nanostructure on H2 and CO2 adsorption. We have achieved first-principles calculations to walk around the interaction behavior of the H2 and CO2 with H2BDC and ZnO-H2BDC.
Geometry optimization, the density of states (DOS), and energy analyses were performed to investigate the adsorption phenomena using Gaussian 09 program package  with density functional theory (DFT) at B3LYP/6-31G (d,p) functional/basis set. The 6-31G(d,p) basis set is good for general calculations, besides the B3LYP density functional has been known appropriate for nano-structure studies. The temperature and pressure for all calculations were 298.15 K and 1.0 atm respectively.
A number of possible orientations are considered for H2BDC, ZnO-H2BDC, CO2-H2BDC, H2-H2BDC, CO2-ZnO-H2BDC, and H2-ZnO-H2BDC, but all input geometries resulted in optimization of limited structures, according to Fig. 2.
The adsorption Energy of ZnO on the H2BDC is calculated by:
where is the energy of H2BDC interacting with the ZnO and is the energy of a pristine H2BDC, and is the energy of pristine ZnO. The interaction energy of CO2 or H2 (indexed by CO2/H2) with pristine H2BDC and H2BDC-ZnO are calculated by:
where and correspond to interaction energy of CO2/H2 with H2BDC and ZnO-H2BDC, and are energies of H2BDC and ZnO-H2BDC interacting with the CO2/H2, and is the energy of an isolated CO2/H2. All the mentioned energies of the equations are related to equivalently relaxed minimum energy structures. Also chemical potential () , hardness () , softness (S)  and electrophilicity ()  are calculated by:
where EHOMO and ELUMO are the energies of HOMO and LUMO, respectively.
The charge transferring between CO2/H2 and the surface of both H2BDC and ZnO-H2BDC is calculated from the varying of the charge concentration on CO2/H2 after adsorption and an isolated spice. This calculation has been done by Mullikan charge analysis .
RESULTS AND DISCUSSION
Geometries of isolated pristine H2BDC, ZnO-H2BDC and their interaction with CO2 and H2 have optimized at B3LYP functional at 6-31G(d,p) basis set to allow them to be relaxed. Although the site C in Fig. 2 is the most attractive location for ZnO adsorption, but because this place will be occupied by ZnO molecules, as inorganic cluster, therefore in this study, to investigate the location of extra ZnO adsorption around the H2BDC, the site A, B, and D in Fig. 2 were investigated. In this paper, we will discuss the strongest adsorption site and use the more stable configurations to further study (for all systems). Fig. 3 shows the optimized unit cell of H2BDC and ZnO-H2BDC. The values of adsorption energy, as well as some important parameters for all relaxed systems, are listed in Table 1. The geometric parameters of H2BDC are in good agreement withthe already reported data . According to results, the location D in Fig. 2 is the best location (in front of location A and B) for ZnO adsorption on H2BDC (whit high adsorption energy, -111.5627 kJ/mol).
In order to study the adsorption of H2 and CO2 on H2BDC and ZnO-H2BDC, it is essential to note that there are two possible configurations for CO2 (O end and C end) to be optimized. In this study, we used the more stable configuration. The interaction of H2 and CO2 molecules with H2BDC and ZnO-H2BDC on different positions (site A, B, and D in Fig. 2) has been studied using the above-mentioned method and let them be fully optimized. Fig. 4 shows the optimized unit cell of H2-H2BDC and CO2-H2BDC in three positions (site A, B, and D in Fig. 2). In this study, we found that there are two main sites for H2 and CO2 adsorption (named site A and site B respectively) on H2BDC, while the Eads for adsorption of H2 and CO2 on site D, is very little (as shown in Table 1).
In fact, considering that the organic ligand in MOF-5 is an appropriate representative [29-31], therefore Fig. 4 shows the adsorption behavior of H2 and CO2 on C-MOF-5. Accordingly as noted in the previous sections, the T-MOF-5 had more ZnO molecule than C-MOF-5. The differences between two nanocrystal structures bring about the different behavior in gas adsorption. To investigate the adsorption behavior of H2 and CO2 on T-MOF-5, the adsorption study on ZnO-H2BDC (according to Fig. 3 (b)) was done. Fig. 5 shows the optimized unit cell of H2-ZnO-H2BDC and CO2-ZnO-H2BDC. The H2 and CO2 adsorption energies in ZnO-H2BDC are -7.6125 and -45.6750 kJ/mol, respectively. According to results, we can conclude that, at least in the organic ligand of the MOF-5, the highest and lowest adsorption of H2 (or CO2) is attributed to the T-MOF-5 and C-MOF-5 respectively. Also by changing in structure from cubic to tetragonal, the main site for H2 and CO2 adsorption was changed. According to obtained results, the interaction of H2 (or CO2) on H2BDC and ZnO-H2BDC are in the range of physisorption. That’s while the interaction between ZnO and H2BDC is intermediate between chemisorption and physisorption.
Although in this study, the investigations have been done on organic ligand of MOF-5, and according to the overall structure of MOF-5 has not been analyzed, however, the obtained results for H2 adsorption on H2BDC and ZnO-H2BDC (as representative sections of C-MOF-5 and T-MOF-5) are in good agreement with experimental results obtained for H2 adsorption on C-MOF-5 and T-MOF-5 . Also, the experimental results for CO2 adsorption on C-MOF-5 and T-MOF-5  are in contrast to the obtained results in this study for CO2 adsorption on H2BDC and ZnO-H2BDC (little difference in the same temperature and pressure).
As noted in the previous sections and according to our previous experimental results  with changing the structure from cubic to tetragonal, the pore size reduced from 8.67 Å to 6.3 Å. Because the kinetic diameter of hydrogen is very small, then it can be expected that changing the pores size from cubic to tetragonal has little effect on the H2 diffusivity [19,20] and more effect on the bigger molecules (CO2 in this study). Also, Sarmiento-Perez et al  reported that the primary step in the abnormal CO2 adsorption in MOF-5 is due to synergic and significant contributions from all the three: the inorganic cluster, the organic linker and the 3-D structure of the nanopores. Therefore, the agreement between experimental results  and DFT theoretical results presented in this study for H2 adsorption is attributed to the very small kinetic diameter of H2. Accordingly, the difference between experimental results (complete structure)  and theoretical results presented in this work for CO2 adsorption, is attributed to the bigger kinetic diameter of CO2 and high impact of 3-D structure on the adsorption of CO2. However, this difference does not violate the result of CO2 adsorption (in this study).
We believe that the adsorption of ZnO on H2BDC and also the adsorption of H2 and CO2 on H2BDC and ZnO-H2BDC can be interpreted by the amount of net charge transfer. The amounts of charge transferring between H2BDC, ZnO, ZnO-H2BDC, H2, and CO2 were simulated at the B3LYP functional at 6-31G(d,p) basis set. The Mulliken charge analysis is essential analysis for examination the net charge transferring in molecular systems. Table 1 shows the Mulliken charge of interacted ZnO with H2BDC and alsointeracted H2 and CO2 with H2BDC and ZnO-H2BDC. In H2-H2BDC-A complex, H2 detracts about 0.011e− charges to H2BDC. Reverse transfer of charge achieved in ZnO-H2BDC, CO2-H2BDC-B, CO2-H2BDC-D, H2-H2BDC-D, CO2-ZnO-H2BDC, and H2-ZnO-H2BDC complexes whereas ZnO loses about 0.107e− charge from H2BDC and CO2 (also ZnO) loses about 0.101e− (0.059e−) charge from ZnO-H2BDC (also CO2-H2BDC) and H2 (also ZnO) loses about 0.083e− (0.058e−) charge from ZnO-H2BDC (also H2-H2BDC). Also for CO2-H2BDC-B and CO2-H2BDC-D and H2-H2BDC-D complexes no net charge transfer occurs.
As shown in Table 1, significant changes in electronic properties were achieved during adsorption of ZnO on H2BDC. Also, according to results of Table 1, there are no significant changes in the electronic properties of the pristine H2BDC surface during interaction with H2 and CO2 but significant changes in electronic properties were achieved during adsorption of H2 and CO2 on ZnO-H2BDC.
Supporting confirmation was found in the measured dipole moments (µD) of all systems. The dipole moment is related to the particular property of a molecule which considers data of electronic and geometrical properties . The amounts of the size and structures of the dipole moment for H2BDC on ZnO-H2BDC and also for H2 and CO2 on the H2BDC and ZnO-H2BDC are listed in Table 1. Our computations reveal that when ZnO comes close to the H2BDC, the size and directions of µD will change dramatically (from 0.0012 to 2.3339). Also, we found that during H2 and CO2 interaction for all systems, the µD is raised. The µD values of the interacted pristine H2BDC with H2 (site A), H2 (site D), CO2 (site B), and CO2 (site D) are equal to 0.2828, 0.0096, 0.2563 and 0.0034 Debye, respectively. Also the alteration in the µD of ZnO-H2BDC upon interaction with mentioned gas compounds increases in the order of CO2 > H2. Our results reveal that more dipole moment (4.5891 for CO2-ZnO-H2BDC and 3.6621 for H2-ZnO-H2BDC) corresponds to more adsorption energy which is in agreement with the results of charge analysis.
To more understand the electronic properties of the organic ligand of C-MOF-5 and T-MOF-5 during adsorption, the density of states (DOS) as the electron density of HOMO-LUMO was calculated for H2BDC and ZnO-H2BDC and also their complex was formed with H2 and CO2 molecule (see Table 1). Quantum mechanically, the interaction between two reactants takes place because of the interaction of frontier molecular orbitals . HOMO and LOMU have the aptitude to contribute electrons and detract electrons, respectively. However, if a molecule has high HOMO energy, then it will be more unstable and contrariwise because of more reactivity [38,39]. The HOMO and LUMO energy orbitals for H2BDC and ZnO-H2BDC are found to be (-7.38 eV, -2.12 eV) and (-6.18 eV, -3.10 eV), respectively. After ZnO doping of H2BDC (Zn-H2BDC) and adsorption of H2 and CO2 molecule on the surface of H2BDC and ZnO-H2BDC, some changes occur in electronic properties.
The HOMO-LUMO energy gap (Eg) is one of the key parameters to recognize the stability as well as the conductivity of resulted adsorptions. Higher Eg results in more stability and less conductivity of resulted complex. The band gaps of the pristine H2BDC and ZnO-H2BDC as well as complex forms of CO2-H2BDC-B, CO2-H2BDC-D, H2-H2BDC-A, H2-H2BDC-D, H2-ZnO-H2BDC CO2-ZnO-H2BDC are calculated and are listed in Table 1. Adsorption behaviors of H2 and CO2 on H2BDC and ZnO decorated H2BDC (ZnO-H2BDC) are mixed. For pristine H2BDC, the band gap is almost the same on H2 and CO2 adsorption but for ZnO-H2BDC-H2 and ZnO-H2BDC-CO2, the band gap increases from 3.08 eV (for ZnO-H2BDC) to 3.88 eV and 3.82 eV, respectively. The calculations revealed the highest Eg value for interacted ZnO-H2BDC with H2 and CO2, which again correlates well with the high adsorption energies of H2 and CO2 on ZnO-H2BDC compared to H2BDC.
The change in Eg leads to changes in conductivity. The relationship between conductivity and Eg can be given by :
where is the electric conductivity, k is the Boltzmann constant and T is the temperature. According to this equation, a small decrease in Eg leads to significantly higher electrical conductivities. According to results, pristine H2BDC is not a good adsorbent for H2 and CO2 (particularly for H2) molecule but adsorption of ZnO on H2BDC significantly enhances its ability towards H2 and CO2 adsorption (particularly for CO2).
Next, we analyzed the densities of states (DOSs) as well as the electron density of HOMO-LUMO to realize how the adsorption of ZnO affects the electronic structure of H2BDC. Fig. 6 plots the DOSs as well as the electron density of HOMO-LUMO for H2BDC and ZnO-H2BDC near the Fermi level (EF). According to Table 1 and Fig. 5, for pristine H2BDC, the Fermi level (EFL) is slightly changed from -4.75 eV to -4.79 eV, -4.76 eV, -4.79 eV and -4.75 eV for CO2-H2BDC-B, CO2-H2BDC-D, H2-H2BDC-A, and H2-H2BDC-D, respectively. For ZnO-H2BDC, the EFL is changed a lot from -4.64 eV to -3.92 eV and -4.08 eV for CO2-ZnO-H2BDC and H2-ZnO-H2BDC, respectively. After comparing the DOS of H2BDC and ZnO-H2BDC with that of their interacted forms, we found that the ZnO doping of H2BDC (ZnO-H2BDC) causes a significant shift of the occupied orbitals of H2BDC to high energy levels and observed some change evidence of hybridization in the case of ZnO-H2BDC systems.
Also according to Fig. 6, The HOMO and LUMO in H2BDC are uniformly dispersed over the entire skeleton of the pristine organic ligand. The effect of H2 and CO2 adsorption on H2BDC is almost negligible. The decoration of ZnO on H2BDC brings quite significant changes regarding both energies and densities. Adsorption of ZnO on the surface of H2BDC increases the energy of HOMO but decreases the energy of LUMO which ultimately results in a decrease in the band gap (from 5.26 to 3.08).
The effect of ZnO doping of H2BDC (ZnO-H2BDC) and H2 and CO2 adsorption on H2BDC and ZnO-H2BDC, and on the electronic structure of the H2BDC, ZnO-H2BDC, CO2-H2BDC-B, H2-H2BDC-A, CO2-H2BDC-D, H2-H2BDC-D, CO2-ZnO-H2BDC, and H2-ZnO-H2BDC can be seen in MEP map, shown in Fig. 7. According to Fig. 7(a and b), the pristine H2BDC has symmetrical potential (due to symmetrical structure) and ZnO atom has positive potential. Also, as shown in Fig. 7(c,d,e and f) the adsorption of H2 and CO2 molecules on H2BDC does not affect on the intensification of positive or negative charge of H2BDC (particularly for adsorption on-site D Fig. 7(e and f)). For ZnO-H2BDC, the Zn and O atoms have positive and negative potential (respectively) whereas the atoms in the H2BDC have almost neutral potential. The negative and positive potential on H2BDC was changed in ZnO decorated H2BDC (ZnO-H2BDC). Upon adsorption of H2 and CO2 (particularly for CO2) molecule on ZnO-H2BDC, the negative potential is regenerated on the H2BDC. The MEP analysis also shows that upon H2 and CO2 adsorption, the position of positive potential also shifts to close around of Zn.
We have also calculated the global indices of reactivity for CO2, H2, ZnO, H2BDC, ZnO-H2BDC, CO2-H2BDC-B, CO2-H2BDC-D, CO2-ZnO-H2BDC, H2-H2BDC-A, H2-H2BDC-D and H2-ZnO-H2BDC systems in order to evaluate how the adsorption of ZnO affects the chemical properties of H2BDC for H2 and CO2 adsorption (Table 2). The energies of LUMO correspond to the electron affinity (define as A) whereas the energies of HOMO can approximately be taken equivalent to ionization potential (define as I) . The ionization potential (I) for pristine H2BDC is very high and does not decrease upon adsorption of H2 and CO2. The decoration of the H2BDC with ZnO causes a reduction in ionization potential. Also, the ionization potential decreases when H2 and CO2 molecules are adsorbed on ZnO decorated H2BDC. The band gap represents the softness (S) or hardness (η) of a compound. A compound with large band gap is expected to be hard, and conversely. After decoration of the H2BDC with ZnO, the band gap decreases from 2.63 to 1.54 and it is expected that these complexes (ZnO-H2BDC) are very soft. According to Table 2, after adsorption of H2 and CO2 on H2BDC the softness values approximately remain unchanged, but after adsorption of H2 and CO2 on ZnO-H2BDC, the softness values declined. The increase in chemical reactivity is electrophilic in nature because the electrophilicity of ZnO-H2BDC (6.990 eV) is higher than the H2BDC (4.289 eV).
We have shown theoretically for the first time that how H2 and CO2 adsorption on cubic and tetragonal structure of MOF-5 are different. Accordingly, we optimized the geometries for pristine H2BDC as well as ZnO doped H2BDC and their interaction with H2 and CO2. Firstly we investigated the possible positions of ZnO on H2BDC. Among the three sites around H2BDC (site A, B, and D) for ZnO adsorbed H2BDC, the site D is more stable than site A and B. According to obtained results, at least in the organic ligand of the MOF-5, the highest and lowest adsorption of CO2 and H2 is attributed to the T-MOF-5 and C-MOF-5 respectively. Also among the three sites around H2BDC (site A, B, and D) by a change in structure from cubic (H2BDC) to tetragonal (ZnO-H2BDC), the main site for H2 and CO2 adsorption was changed from A and B to D site. Our calculations determine that ZnO-H2BDC system (as a representative section of T-MOF-5) has much higher adsorption energy, and higher net charge transfer value than pristine H2BDC (as a representative section of C-MOF-5).
This is a qualitative, exploratory study in which the authors are laying the groundwork for future researches on this subject. It is exploratory because no other researches have been conducted on this specific subject.
The authors acknowledge Iran Nanotechnology Initiative Council for financial support.
CONFLICT OF INTEREST
The authors declare that there are no conflicts of interest regarding the publication of this manuscript.