From the experiment, the energy gap (Eg) of Cu-BTC MOF was experimentally reported to be 3.6 eV . Based on the optimized structure of the Cu-BTC cluster, the energy gap based on the M06-L calculation is predicted to be 1.21 eV which is significantly lower than the experimental value. To obtain a more accurate prediction of the energy gap, single-point calculations were performed on M06-L-optimized structures by using hybrid M06 functional at the combination of 6-311G(d,p) + SDD ECP basis sets. The M06-calculated energy gap of the Cu-BTC cluster was predicted to be 3.55 eV which is consistent with the experimental observation . Therefore, all reported values in this work were obtained by using the M06//M06-L level of theory. The M06 functional predicts the energy gap of M06-L-optimized Fe-BTC, Ni-BTC, Zn-BTC, and Pd-BTC clusters to be 2.33 eV, 3.73 eV, 5.63 eV, and 3.22 eV, respectively.
Optimized structures of adsorption complexes are shown in Figs. 2-3. The adsorption of SO2 molecules on the metal site of five metal paddlewheel units was investigated by the M06//M06-L level of theory. For SO2 adsorption, there are two possible configurations of the adsorbed sulfur dioxide (SO2) for interacting with the metal center of metal-paddlewheel units. One is the interaction between the SO2 molecule on the metal center of paddlewheel units via a terminal oxygen atom (O-bound complex). The other is the interaction via the central sulfur atom of the SO2 molecule (S-bound complex). For the former configuration, the distance between the SO2 oxygen atom and the metal center of paddlewheel units increases from 1.947 Å (Fe-BTC) to 2.648 Å (Pd-BTC). After the adsorption, two S-O bonds become inequivalent in which an S-O bond of SO2 molecule elongates from 1.463 Å to 1.536, 1.484, 1.478, 1.495, and 1.476 Å for the adsorption on Fe-BTC, Ni-BTC, Cu-BTC, Zn-BTC, and Pd-BTC paddlewheels, respectively. The adsorption energy for SO2 on the metal center in the O-bound complex increases as follows: Pd-BTC (–2.90 kcal mol−1) < Cu-BTC (–6.66 kcal mol−1) < Ni-BTC (–12.01 kcal mol−1) < Zn-BTC (–13.60 kcal mol−1) < Fe-BTC (–19.60 kcal mol−1).
For the S-bound configuration, the SO2 molecule was attached to the metal center of paddlewheels via the lone pair centered on the sulfur atom. This mode of adsorption was not found for the adsorption of the Cu-BTC paddlewheel. Starting from the adsorption on the Cu of Cu-BTC via its sulfur atom, the molecule was optimized to bind with BTC ligands via hydrogen bonds as shown in Fig. 2. The adsorption energy is predicted to be –4.16 kcal/mol, which is much smaller than the adsorption of SO2 via its oxygen atom. For the other cases, the S-O bonds of adsorbed SO2 are insignificantly distorted from the isolated values for the adsorption on the metal center of paddlewheel units. Much weaker adsorption energies ranging from -0.68 to –4.42 kcal/mol were found for the adsorption of SO2 molecules on the Fe-, Ni-, Zn-, and Pd-BTC paddlewheels. Among five metal paddlewheels, Pd-BTC weakly interacts with the SO2 molecule both in O-bound or S-bound configurations. These findings agree with the previous studies of the adsorption of SO2 on the coordinatively unsaturated metal center of MOFs (–21.77 for Mg-MOF-74 , –17.22 kcal mol−1 for Zn-MOF-74 , and –15.79 kcal mol−1 for Zn(BDC)(ted)0.5  ), in which the SO2 molecule adsorbs on the metal center via its oxygen atom. From calculated results, Fe-BTC paddlewheel has relatively high adsorption energy for SO2 molecules both in O-bound and in S-bound configurations, indicating that SO2 molecule is captured facilely by Fe-BTC paddlewheel.
Electronic properties of SO2 adsorption complexes
Attempts have been made to investigate the change of electronic properties of metal paddlewheels after the adsorption of SO2 molecule. Based on the adsorption energies between the O-bound and S-bound complexes, the O-bound complex is energetically preferred for the adsorption on the metal-paddlewheel clusters. From NBO analysis, the NBO charge of the metal center is predicted to be +1.121e, +1.037e, +0.996e, +1.277e, and +0.711e for Fe(II), Ni(II), Cu(II), Zn(II), and Pd(II) cations in the paddlewheel clusters, respectively. NBO analysis reveals the amount of electron transfer and the orbital interaction between the adsorbing molecule and the metal center of metal-paddlewheel units. The results from the NBO analysis are tabulated in Table 1. Excepting the adsorption on the Fe-BTC, the charge of the adsorbed SO2 molecule changes from zero to +0.024e, +0.080e, +0.127e, and +0.096e for the adsorption on Pd-BTC, Cu-BTC, Ni-BTC, and Zn-BTC, respectively. The NBO results indicate that the SO2 gas molecule acts as an electron donor molecule for the adsorption on the Pd-, Cu, Ni-, and Zn-BTC paddlewheels. For Fe-BTC, the HOMO and LUMO orbitals of Fe-BTC are localized on the metal centers of Fe-BTC. Fe centers of Fe-BTC can either provide electrons from the metal center or accept electrons. The direction of electron transfer between the Fe-BTC to the adsorbed SO2 molecule is attributed to the Lewis character of Fe in the paddlewheel. From the FMO diagram, the |LUMOFe-BTC – HOMOSO2| gap and the |LUMOSO2 – HOMOFe-BTC| is predicted to be 5.73 eV and 2.47 eV, respectively. It was found that the gap of |LUMOFe-BTC – HOMOSO2| is larger than the |LUMOSO2 – HOMOFe-BTC| gap. Therefore, it might be expected that the electron transfer from the Fe center to the SO2 molecule is the preferable route. NBO analysis showed that 0.247e was transferred from Fe-BTC to the adsorbed SO2 molecule, suggesting that SO2 acts as an electron acceptor molecule. Furthermore, the spin density localized on atoms of adsorbed SO2 is increased as compared with the isolated SO2 molecule. For S-bound configuration, the charge of adsorbed SO2 molecule becomes positive after the adsorption on the Fe-, Ni-, Zn- and Pd-BTC paddlewheels, indicating the SO2 molecule behaves as a nucleophile for donating an electron to the LUMO orbital of the paddlewheel. As a result, the net charge of SO2 is +0.118e, +0.289e, +0.153e, and +0.036e for the adsorption on Fe-, Ni-, Zn-, and Pd-BTC paddlewheels, respectively. From NBO population analysis, it was found that there is no correlation between the adsorption energy of SO2 and the amount of electron transfer between the SO2 molecule and the substrate.
From the frontier molecular orbitals (FMO) viewpoint (cf. Fig. 4), the highest occupied molecular orbital (HOMO) of SO2 shows the participation of all three atoms of the SO2 molecule. Either O atom or S atom of SO2 molecule can act as an electron donor center to the available unoccupied orbital of the metal center. The adsorption energy of the S-bound configuration on M-BTC paddlewheels (M = Fe, Ni, Cu, and Zn) is much smaller than the adsorption energy of the O-bound configuration in the corresponding systems. NBO population analysis reveals that the NBO charge of oxygen atoms and the sulfur atom of SO2 molecule is –0.758e and +1.517e, respectively. From the electrostatic viewpoint, the metal center having a higher charge density tends to have a stronger interaction with a negative charge of the SO2 oxygen atom. Therefore, the adsorption energy of SO2 adsorbed on Ni-BTC, Zn-BTC, Fe-BTC is significantly greater than that on Cu-BTC and Pd-BTC. On the other hand, the more positive charge the metal center, the weaker the SO2 via its sulfur atom is adsorbed on the metal center. The weak interaction between the metal center and the SO2 molecule in the S-bound configuration is due mainly to the electrostatic repulsion between the positive charge of metal and the positive charge of the SO2 sulfur atom. It could be summarized that the interaction between the SO2 molecule and the metal cluster is mainly governed by the electrostatic interactions, corresponding with the adsorption of styrene oxide on metal-paddlewheel clusters as reported previously [17, 18].
SO2 sensing properties of M-BTC paddlewheels (M = Fe, Ni, Cu, Zn, and Pd)
The DOS analysis was used to provide more detailed data of electronic structure and the contribution of atomic orbitals to the chemical bonds. The DOS plots for the noninteracting system of five metal paddlewheels and SO2-adsorption complex in the O-bound configuration on five metal paddlewheels are illustrated in Figs. 5-9. After the adsorption of SO2 on the metal center of paddlewheels, the huge change in PDOS of adsorbed SO2 happens for the adsorption on the Fe-, Ni, Cu, and Zn-BTC paddlewheels. For the adsorption on Fe-BTC, the peak at the energy of –6.16 eV, which is the HOMO state of the adsorption complex, shows the strong hybridization between the Fe d-orbitals and the orbitals of the SO2 molecule. As a result, the peak of the energy at –3.60 eV in spin b, which is a π* antibonding orbital of SO2 molecule, is reduced by half as compared to that of the non-interacting system, indicating that the electrons of the Fe-BTC paddlewheel partially fill in the LUMO orbital of SO2 molecule (cf. Fig. 5). This leads to the elongation of the S-O bonds. The Wiberg bond order of S-O bonds is changed from 1.55 in the isolated molecule to 1.10 and 1.42, respectively. The result shows that a S-O bond of adsorbed SO2 has a single bond character. Excepting the Fe-BTC system, the SO2 adsorption introduces an impurity state, which becomes the LUMO state of the adsorption complex. Besides the electrostatic interaction between the Ni center of Ni-BTC and the oxygen atom of SO2, it was found that there is a s-donation interaction from the SO2 HOMO orbital to the empty Ni-3d orbital as shown in Fig. 6. The hybridization between two orbitals appears in the DOS pot at the energy of –12.44 eV. As a result, the Wiberg bond order of S-O bonds is reduced to be 1.38 and 1.61, respectively.
Unlike the SO2-adsorption on Fe-BTC and Ni-BTC, the overlap of SO2 orbitals and d-orbitals of Zn and Cu cations creates a small hybridization at the energy of -16.2 eV and -12.3 eV, suggesting the small electron transfer exists between HOMO orbital of SO2 molecule and unoccupied d-orbital of these paddlewheels (cf. Figs 7-8). The PDOS analysis is consistent with the quality of electron transfer between two fragments as shown in Fig. 3. Most of the electron density difference is observed at the adsorbed SO2 fragment greater than the bond between the SO2 oxygen atom and the metal center of paddlewheels. In the case of Zn-BTC system, the more polarization of adsorbed SO2 molecule is mainly induced by the Zn(II) cation in the paddlewheel unit. These results suggest that the interaction between SO2 and Zn-BTC in the O-bound configuration is more ionic than that found in the Fe-BTC system. The attachment of SO2 to the Zn center of the Zn-BTC paddlewheel not only results in the distortion of the SO2 molecule but also leads to modification of the TDOS of the system as compared to that of the non-interacting system. For the adsorption of SO2 on the Pd-BTC (cf. Fig. 9), the PDOS plots for the s-, p-, d- orbitals of the metal atom of the non-interacting system and the SO2 adsorption complex are almost identical, indicating that there is no strong orbital interaction between the adsorbed molecule and the metal center.
The change in the energy difference between the HOMO energy and the LUMO energy (Eg), affected by the adsorption of the targeted molecule is used to be a proper indicator to predict the gas-sensing performance of materials as described in the following equation [32-34]:
s a exp (–Eg/kBT) (2)
From the equation, a slight change in energy gap (Eg) results in a significant change in electronic conductivity (s) of a system. Based on the calculated adsorption energies, the trend of energies for the SO2 adsorption on the metal center via O-bound configuration is Pd-BTC< Cu-BTC < Ni-BTC < Zn-BTC < Fe-BTC, respectively. Even though, Fe-BTC has the strongest interaction with the SO2 molecule, the Eg of the Fe-BTC paddlewheel adsorbed by the SO2 molecule is insignificantly changed by –0.02 eV (–0.8%) as compared to the Eg of isolated Fe-BTC paddlewheel (cf. Fig. 5). Similarly, the Eg of Cu-BTC after the adsorption of the SO2 molecule on the Cu center is also identical to that of the isolated Cu-BTC paddlewheel (cf. Fig. 7). The calculated results indicate that Cu-BTC and Fe-BTC paddlewheels are not appropriate metal paddlewheel-based centers for SO2 sensors. Because of the strong interaction with the SO2 molecule, it suggests that Fe-BTC is one of the candidate metal paddlewheels as an SO2 adsorbent. From the population analysis, the Eg of Ni-BTC and Zn-BTC paddlewheels is changed after adsorbing SO2 gas. The Eg is decreased by –0.18 eV (–5.5%), –0.67 eV (–18.0%), and –2.31 eV (–41.0%) for the adsorption of SO2 on Pd-BTC, Ni-BTC, and Zn-BTC paddlewheels, respectively. Because the adsorption effect of SO2 on Pd-BTC is very weak as compared to that on Ni-BTC and Zn-BTC systems. Therefore, this effect has a small influence on the conductivity of the system. These calculated results showed that Ni-BTC and Zn-BTC paddlewheels display sensitivity to SO2 gas as sensors.