Mg12O12 and Be12O12 Nanocages as Sorbents and Sensors for H2S and SO2 Gases: A Theoretical Approach.

Theoretical calculations based on the Density Functional Theory (DFT) have been performed to investigate the interaction of H2S as well SO2 gaseous molecules at the surfaces of Be12O12 and Mg12O12 nano-cages. The results show that a Mg12O12 nano-cage is a better sorbent than a Be12O12 nano-cage for the considered gases. Moreover, the ability of SO2 gas to be adsorbed is higher than that of H2S gas. The HOMO-LUMO gap (Eg) of Be12O12 nano-cage is more sensitive to SO2 than H2S adsorption, while the Eg value of Mg12O12 nano-cage reveals higher sensitivity to H2S than SO2 adsorption. The molecular dynamic calculations show that the H2S molecule cannot be retained at the surface of a Be12O12 nano-cage within 300-700 K and cannot be retained on a Mg12O12 nano-cage at 700 K, while the SO2 molecule can be retained at the surfaces of Be12O12 and Mg12O12 nano-cages up to 700 K. Moreover, the thermodynamic calculations indicate that the reactions between H2S as well SO2 with Be12O12 and Mg12O12 nano-cages are exothermic. Our results suggest that we can use Be12O12 and Mg12O12 nano-cages as sorbents as well as sensors for H2S and SO2 gases.

1. Introduction

Recently, great efforts have been made to develop novel gas sensors and detectors as well as gas-removing materials. This is to control the pollutant gases broadly produced from industrial activities and burning fuel, etc. The toxic H2S and SO2 gases are produced as byproducts from SF6 decomposition, which is widely used as an insulating gas in high-voltage transformers and circuit breakers [1,2,3,4]. H2S is mostly found in crude petroleum, natural gas, and coal gasification. In addition, some organic materials decompose, releasing H2S [5,6,7]. H2S is also released in many industries such as the paper industry and biomass fermenters [7,8]. The combustion of sulfur-containing fossil fuels releases SO2 into the air, and SO2 is naturally released as a byproduct of volcanic activity [9,10]. The H2S as well SO2 gases pose several hazards to the environment and human health. H2S exposure leads to coughing, eye irritation, and a runny nose, harms the nervous system by killing the neurons and may cause death [11,12]. Moreover, H2S is a corrosive gas and has devastating impacts on industrial catalysts [7,8]. SO2 interacts with the air resulting in acidic rain which causes the corrosion of metals and disintegration of buildings [9,10]. Furthermore, SO2 causes skin burning, eye irritation and respiratory system inflammation, and may cause death [7,13,14,15]. Therefore, several attempts have been made to utilize many materials as sorbents and detectors for H2S and SO2 gases, such as fullerene-like gallium nitride [16], CuO(111) surface [17], pristine graphene and graphene oxide [18], NH-decorated graphene [8], activated carbon, [19,20], pillared clays [21], zeolites [22], p-CuO/n-ZnO Heterojunction [23], Cu (100) and Au (100) surfaces [24,25], Cu doped MoSe2 [12], monolayer Janus MoSSe [26], aza-macrocycle [27], Cu-modified and Cu-embedded WSe2 monolayers [28], porous N4O4-donor macrocyclic Schiff base [29] and MgO (100) surfaces [10].

Metal oxides have a significant consideration due to their several applications. They are usually utilized as substrates for epitaxial growth of multilayers and clusters, catalytic processes, hydrogen storage materials, sensors and sorbent materials [10,30,31,32,33,34]. Recently, nano-structures have been frequently utilized as gas detectors and sorbents due to their appropriate features such as their tiny size, precision, and reactivity [35,36,37].

Furthermore, Shamlouei et al. reported that nanocages with a X12Y12 structure are the most stable among (XY)n nano-cages [38]. Ren et al. [39] have investigated (BeO)N clusters and found that Be12O12 is one of the most feasible nano-cages. Ziemann and Castleman [40] have proven that a Mg12O12 nano-cage displays unique stability among (MgO)n, n ≤ 90 nano-structures. The Mg-O bond in Mg12O12 nano-cages has an ionic character [38], while the Be-O bond has ionic and covalent characters [41], therefore one can expect different applications for Be12O12 and Mg12O12 nano-cages. Be12O12 and Mg12O12 have several applications; for instance, Be12O12 has been utilized as a catalyst to convert CH4 into CH3OH [42], an electro-conductive sensor for sulfur mustard [43], and a detector and sorbent for Mercaptopyridine [44], and Be12O12 and Mg12O12 have been utilized for hydrogen storage applications [45,46], detection and adsorption of Tabun [47]

According to our knowledge, the interaction of H2S and SO2 gases at the surfaces of Be12O12 and Mg12O12 nano-cages has not been investigated yet. Hence, the present work aims to shed light on the characteristics of the interaction of H2S and SO2 with Be12O12 and Mg12O12 nano-cages for adsorption and sensing applications using DFT calculations.

2. Methods

To investigate the adsorption characteristics of H2S and SO2 molecules onto Be12O12 and Mg12O12 nano-cages, DFT and DFT-D3 methods [48] are used at the B3LYP/6-31G(d,p) level. D3 is a version of Grimme’s dispersion [49]. B3 is Becke’s three-parameter exchange functional [50] and LYP is the correlation functional of Lee, Yang and Parr [51,52]. A geometrical optimization without any restriction is performed for the free gaseous molecules, bare nano-cages and gas/nano-cage complexes. The ionization potential (IP) is calculated as [10,37]: where is the energy of the nano-cage with one electron lost at the same geometrical structure of the neutrally charged nano-cage. The chemical potential (µ), hardness (η) and electrophilicity (ω) are calculated as [53,54]:

Molecular dynamic simulations via the Atom Centered Density Matrix Propagation molecular dynamics model (ADMP) as implemented in Gaussian 09 package are achieved for the investigated nano-cages and gas/nano-cage complexes.

The adsorption energy (Eads) and the corrected adsorption energy () with basis set superposition error (BSSE) have been estimated as [55]: where , , and are the energies of gas/nano-cage complexes, free gas molecules, and bare nano-cages, respectively. The charge density difference () for the complexes is computed as: where , , and are the charge densities for gas/nano-cage complexes, free gas molecules, and bare nano-cages, respectively.

Thermodynamic calculations are performed via vibrational calculations to predict enthalpies as well free energies for the considered gases, nano-cages, and gas-cages complexes. Enthalpy difference (ΔH) and free energy difference (ΔG) for gas/nano-cage complexes are evaluated as [56]: where , , and are the enthalpies for gas/nano-cage complexes, bare nano-cages and free gas molecules, respectively. where , , and are the free energies for gas/nano-cage complexes, bare nano-cages, and free gas molecules, respectively.

All the calculations have been carried out by Gaussian 09 program package [57]. GaussSum3.0 program is used to visualize the densities of states (DOS) [58]. Atomic charges are calculated for the considered structures via full natural bond orbital (NBO) analyses by using NBO version 3.1 [59].

3. Results and Discussions

3.1. Structural and Electronic Properties of Be12O12 and Mg12O12

The optimized structures for the scrutinized adsorbed gases H2S and SO2, as well the adsorbent nano-cages Be12O12 and Mg12O12, are shown in Figure 1.

Figure 1

The optimized structures for (a) free H2S gas, (b) free SO2 gas, (c) Be12O12, and (d) Mg12O12 nano-cages.

For H2S gas, the S-H bond length and the H-S-H angle are 1.35 Å and 92.52°, respectively, while for SO2 gas, the S-O bond length and the O-S-O angle are 1.46 Å and 119.16°, respectively, in good agreement with previous studies [10,29]. Be12O12, as well Mg12O12 nano-cages are constructed of eight hexagonal and six tetragonal rings. It is noticed that all the metallic (Be and Mg) and O sites are identical. These nano-cages have two metal–oxygen bond types. They are denoted as d1 and d2 in Figure 1, where d1 shares a hexagon ring and a tetragon ring while d2 shares two hexagon rings. The d1 values are 1.58 and 1.95 Å, whereas the d2 values are 1.52 and 1.90 Å for Be12O12 and Mg12O12, respectively, match well with the previous studies [39,60,61,62,63]. Table 1 represents the electronic properties of Be12O12 and Mg12O12 nano-cages.

Table 1

Electronic properties of Be12O12 and Mg12O12 nano-cages. HOMO and LUMO energy levels (eV), HOMO- LUMO gap (Eg, eV), ionization potential (IP, eV), NBO charges (Q, e), chemical potential (µ, eV), hardness (η, eV), electrophilicity (ω, eV), and dipole moment (D, Debye).

	Be12O12		Mg12O12
	Present Study	Previous Studies	Present Study	Previous Studies
HOMO	−8.62	−8.62 [57]	−6.59	−6.58 [57],−6.57 [58],−6.60 [38],−6.58 [59],
				−6.74 [30,31],−6.53 [10]
LUMO	−0.79	−1.07 [57]	−1.75	−1.78 [57],−1.71 [58],−1.80 [38],−1.72 [59]
Eg	7.83	8.29 [43],7.41 [45],7.55 [57]	4.84	4.87 [43],4.83 [45],4.79 [57],4.86 [58,59],4.78 [30,31]
IP	10.27		7.98
QM	1.19		1.44
QO	−1.19		−1.44
µ	−4.71		−4.17	−4.14 [58]
η	3.92		2.42
ω	2.83		3.60
D	0.00		0.01	0.01 [58],0.00 [38],0.07 [59]

M = Be and Mg.

The HOMO–LUMO energy gap (Eg) values for Be12O12 and Mg12O12 are 7.829 and 4.839 eV while the ionization potential (IP) values are 10.273 and 7.983 eV, respectively, in good agreement with the previous studies [10,30,31,39,44,60,61,62,63]. The lower IP value for the Mg12O12 nano-cage suggests its higher ability to donate electrons than the Be12O12 nano-cage. The atomic charges for the investigated nano-cage are calculated via natural bond orbital (NBO) analysis. For Be12O12, the atomic charges for Be and O sites are 1.186 and −1.186 e, while for Mg12O12, the atomic charges for Mg and O sites are 1.442 and −1.442 e, respectively. In other words, the charge polarization for the Mg-O bond is greater than that for the Be-O bond; therefore, the Mg12O12 is expected to be more reactive than Be12O12. This matches the calculated Eg, IP, η, and ω values, where the higher chemical stability and consequently lower reactivity for a molecule are marked by wide Eg, large IP, η, and low ω values [64,65,66,67]. Figure 2 illustrates the molecular electrostatic potential (MESP) for H2S, SO2, Be12O12, and Mg12O12.

Figure 2

The molecular electrostatic potential contours (MESP) for (a) free H2S gas, (b) free SO2 gas, (c) Be12O12, and (d) Mg12O12 nano-cages at ±0.001, ±0.002, ±0.004,…, ±0.8 au iso-values. Red and green colors are assigned to negative and positive values, respectively.

It is clear that the S atom is surrounded by negative and positive electrostatic potentials for H2S and SO2 molecules, respectively. Furthermore, the MESP around the SO2 molecule is extended in space more than that of the H2S molecule.

For Be12O12 and Mg12O12 nano-cages, the O atoms and the metallic atoms are surrounded by negative and positive electrostatic potentials, respectively. In addition, the MESP of Mg12O12 is more extended around the nano-cage than that of the Be12O12 nano-cage. This is due to the higher charge polarization of Mg12O12. Therefore, it is expected that the S atoms of H2S and SO2 tend to be attracted to the metallic sites and oxygen sites of the nano-cages, respectively. Furthermore, the electric dipole moment (D) of Be12O12 and Mg12O12 nano-cages are 0.001 and 0.010 Debye, respectively. The low D values are owing to the uniform charge distribution on the nano-cages.

Molecular dynamic (MD) simulations examine the stability of the considered nano-cages at 300, 500, 700 K for a total time of 500 fs. Figure 3 depicts the fluctuation of the potential energy versus the time and the nano-cage geometric configuration at the end of the period.

Figure 3

Potential energy fluctuations during MD simulation as well as the atomic configuration after 500 fs at 300, 500, and 700 K for (a) Be12O12, and (b) Mg12O12 nano-cages.

It is obvious the potential energy trivially varies and no considerable distortion is observed for the nano-cages; this emphasizes the stability of Be12O12 and Mg12O12. In addition, the optimized geometries of discussed nano-cages were verified as true minima on the potential energy surfaces by the absence of imaginary frequencies [68,69,70,71].

3.2. Adsorption of H2S and SO2 Gases

DFT as well DFT-D3 calculations were performed to investigate the adsorption characteristics of the adsorbed gases H2S and SO2 at the surfaces of Be12O12, as well Mg12O12, nano-cages. Four complexes are investigated—H2S/Be12O12, H2S/Mg12O12, SO2/Be12O12, and SO2/Mg12O12. There are several possibilities of the gas interaction with the nano-cage, therefore eight adsorption modes for each complex have been fully optimized without any restrictions. Tables S1 and S2 in the Supplementary Data show the examined adsorption modes for H2S interaction with Be12O12 and Mg12O12, respectively. We found that the H2S prefers to interact via its S atom toward the metallic atom Be or Mg of the nano-cage. Tables S3 and S4 in the Supplementary Data show the examined adsorption modes for SO2 interaction with Be12O12 and Mg12O12, respectively. One can observe that SO2 prefers to interact via its S and O atoms toward the O sites and the metallic atoms, respectively, of the nano-cages. The differences in total electronic energies (ΔE) for the examined orientations are shown in Figure 4.

Figure 4

The differences in total electronic energies (ΔE) for the examined structures calculated at (a) DFT and (b) DFT-D3.

DFT and DFT-D3 calculations show that modes 1, 6, 8, and 1 for H2S/Be12O12, H2S/Mg12O12, SO2/Be12O12, and SO2/Mg12O12, respectively, are the most energetically stable adsorption modes. Figure 5 presents the most energetically stable adsorption modes that have more negative adsorption energy for each complex.

Figure 5

The optimal structures for (a) H2S/Be12O12, (b) H2S/Mg12O12, (c) SO2/Be12O12, and (d) SO2/Mg12O12 complexes.

Table 2 list the adsorption properties of H2S and SO2. Notably, the DFT-D3 calculations give more negative adsorption energy values than DFT calculations.

Table 2

Adsorption properties of H2S as well SO2 on Be12O12 and Mg12O12 nano-cages. Adsorption energies (Eads, eV), Basis set superposition error (BSSE, eV), corrected adsorption energy (, eV), HOMO and LUMO energy levels (eV), HOMO- LUMO gap (Eg, eV), NBO charges (Q, e), and dipole moment (D, Debye).

	H2S	H2S/Be12O12	H2S/Mg12O12
Eads	-	−0.31 (−0.50)	−1.32 (−1.57)
BSSE	-	0.05 (0.05)	0.09 (0.10)
Eadscorr	-	−0.26 (−0.45)	−1.23 (−1.47)
HOMO	−7.31 (−7.31)	−8.20 (−8.22)	−5.93 (−5.95)
LUMO	0.26 (0.26)	−0.67 (−0.68)	−1.94 (−1.93)
Eg	7.56 (7.56)	7.53 (7.54)	3.99 (4.02)
Q_H_2S	0.00 (0.00)	0.23 (0.24)	−0.15 (−0.16)
D	1.33 (1.33)	3.27 (3.22)	5.50 (5.48)
	SO2	SO2/Be12O12	SO2/Mg12O12
Eads	-	−0.83 (−1.07)	−2.33 (−2.52)
BSSE	-	0.38 (0.39)	0.41 (0.41)
Eadscorr	-	−0.45 (−0.68)	−1.93 (−2.11)
HOMO	−9.16 (−9.16)	−8.05 (−8.05)	−6.55 (−6.55)
LUMO	−3.73 (−3.73)	−1.47 (−1.49)	−1.84 (−1.83)
Eg	5.43 (5.43)	6.58 (6.57)	4.71 (4.72)
Q_SO_2	0.00 (0.00)	−0.13 (−0.13)	−0.34 (−0.34)
D	1.94 (1.94)	2.95 (2.83)	4.59 (4.58)

Values between brackets are calculated at B3LYP/6–311g(d,p) with dispersion correction (DFT-D3).

In contrast, the values for HOMO, LUMO, Eg, Q, and D have no considerable variations between DFT and DFT-D3 calculations. The values show that the interaction of H2S as well SO2 at the surfaces of Be12O12 and Mg12O12 is a chemical interaction, where the values are lower than −0.2 eV [67]. The released adsorption energy is in the following trend SO2/Mg12O12 > H2S/Mg12O12 > SO2/Be12O12 > H2S/Be12O12. One can notice that the ability of the Mg12O12 nano-cage to adsorb the considered gases is higher than that of the Be12O12 nano-cage. This is referred to as the higher ability of the Mg12O12 nano-cage to donate electrons than the Be12O12 nano-cage. Additionally, the ability of the SO2 gas to be adsorbed on the Mg12O12 nano-cage, as well as the Be12O12 nano-cage, is higher than that of H2S gas. Figure 5a shows that the H2S/Be12O12 complex, the S atom of the H2S molecule, is bonded to a Be site at a distance (d1–25) of 2.35 Å, the S-H bond length is the same as that of the free H2S molecule, and there is a negligible increase of the H-S-H angle. The H2S molecule acquires a positive charge of 0.226 e, meaning that a charge transfer has occurred from the H2S molecule to the Be12O12 nano-cage. Figure 5b illustrates the H2S/Mg12O12 complex, while the H2S molecule dissociates into two fragments HS and H. The HS fragment is bonded via its S atom to a Mg site at a distance (d1–25) of 2.40 Å while the H fragment is attached to an O site at a distance (d4–26) of 0.98 Å. Due to that, an obvious deformation has occurred in Mg12O12 where the Mg-O bond length (d1–4) is elongated to 2.99 Å. The net acquired charge by the H2S molecule is −0.146 e, which means the Mg12O12 donates a charge to the H2S. Figure 5c demonstrates the SO2/Be12O12 complex, while the S atom of the SO2 molecule is bonded to an O site at a distance (d2–25) of 1.83 Å, and an O atom of the SO2 molecule is attached to a Be site at a distance (d1–27) of 1.57 Å. While for the SO2 molecule, the bond length (d25–27) is stretched to 1.56 Å and the O-S-O angle is slightly widened to 111.35°. In addition, the Be-O bond length (d1–2) is elongated to 2.62 Å. The SO2 molecule gains a negative charge of 0.127 e, i.e., a charge transfer has occurred from the Be12O12 nano-cage to the SO2 molecule. Furthermore, Figure 5d represents the SO2/Mg12O12 complex; it seems that three bonds are formed between the SO2 molecule and the Mg12O12 nano-cage. The two O atoms of the SO2 molecule are bonded to two Mg sites at distances of (d3–27) 1.98 Å and (d7–26) 2.06Å, while the S atom is attached to an O site at a distance (d2–25) of 1.64 Å. In addition, the two S-O bonds of the SO2 molecule are dilated to 1.54 Å while the O-S-O angle is diminished to 109.6° and the Mg-O bond length (d2–3) is elongated to 2.93 Å. Moreover, the SO2 molecule accepts a negative charge of −0.339 e; therefore, a charge transfer has occurred from the Mg12O12 nano-cage to the SO2 molecule. Additionally, the adsorption of H2S leads to a decrease in the HOMO–LUMO gap (Eg) values of Be12O12 and Mg12O12 by 3.84% and 17.54%, respectively, whereas the adsorption of SO2 leads to a decrease in Eg values by 15.97% and 2.60%, respectively. Therefore, one can say that the Eg of the Be12O12 nano-cage is more sensitive to the SO2 than H2S adsorption while the Eg of the Mg12O12 nano-cage reveals higher sensitivity to H2S than SO2 adsorption.

The electrical conductivity (σ) and recovery time () are important aspects of sensing applications. σ depends on Eg according to the following equation [72,73,74,75,76,77]: where A is a constant, k is Boltzmann’s constant, and T is the temperature. Therefore, the increase of σ value of the Be12O12 nano-cage in the presence of SO2 gas is higher than in the presence of H2S gas, while the increase of σ value of the Mg12O12 nano-cage in the presence of H2S gas is higher than in the presence of SO2 gas. The is related to the Eads as in Equation (11) [78,79]: where is the attempt frequency. In other words, as Eads increases (more negative) the longer becomes. Therefore, in the obtained Eads values, trends as follows: SO2/Mg12O12 > H2S/Mg12O12 > SO2/Be12O12 > H2S/Be12O12. Thus, our results may be fruitful for sensing applications.

To illuminate the features of the interaction between the considered gases and the sorbent nano-cages, our results will be discussed related to the following: (i) NBO atomic charges as well charge density difference analysis (), (ii) bond analysis, and (iii) PDOS analysis.

3.2.1. NBO and Charge Density Difference Analysis

To shed light on the mechanism of H2S and SO2 interaction with the considered nano-cages, NBO analysis, as well as charge density difference () analysis, has been performed. Table 3 lists the atomic NBO charges, as well the electronic configuration of the atoms, for the free H2S, Be12O12, Mg12O12, H2S/Be12O12, and H2S/Mg12O12. The numbering of atoms as shown in Figure 5 is used.

Table 3

NBO charges (Q, e) and electronic configuration for free H2S, Be12O12, Mg12O12, H2S/Be12O12, and H2S/Mg12O12.

Structure	Atom	Atomic Charge	Electronic Configuration
			1s	2s	2p	3s	3p
H2S	H	0.134	0.86	-	-	-	-
	S	−0.268	-	-	-	1.76	4.48
Be12O12	Be	1.186	-	0.21	0.59	-	-
	O	−1.186	-	1.69	5.49	-	-
Mg12O12	Mg	1.443	-	-	-	0.21	0.35
	O	−1.443	-	1.84	5.60	-	-
H2S/Be12O12	H26	0.160	0.83	-	-	-	-
	H27	0.159	0.84	-	-	-	-
	S	−0.093	-	-	-	1.73	4.34
	Be1	1.007	-	0.25	0.73	-	-
	O2	−1.191	-	1.68	5.50	-	-
	O4	−1.189	-	1.68	5.50	-	-
	O6	−1.190	-	1.68	5.50	-	-
H2S/Mg12O12	H26	0.509	0.49	-	-	-	-
	H27	0.130	0.86	-	-	-	-
	S	−0.785	-	-	-	1.81	4.97
	Mg1	1.305	-	-	-	0.27	0.41
	O2	−1.452	-	1.83	5.62	-	-
	O4	−1.251	-	1.77	5.47	-	-
	O6	−1.442	-	1.83	5.61	-	-

For the H2S/Be12O12 structure, it is clear that due to the interaction, the 1s orbital of the H26 and H27 atoms loses charges of 0.03 and 0.02 e while the 3s and 3p orbitals of the S atom lose charges of 0.03 and 0.14 e, respectively. On the other hand, the 2s and 2p orbitals of the Be1 atom gain charges of 0.14 and 0.04 e while for the O2, O4, and O6 the 2s orbital loses a charge of 0.01e whereas the 2p orbital gains a charge of 0.01 e. This explains why a total charge of 0.226 e, as shown in Table 2, has been transferred from H2S to the Be12O12 nano-cage and the major of the charge transfer has occurred from the S atom of H2S to the Be1 atom of the Be12O12 nano-cage.

This means the major mechanism of the interaction is the charge transfer mechanism. In addition, a slight loss and gain of charges are observed simultaneously for the O2, O4, and O6; therefore, one can suggest another minor mechanism which is the donation–back donation mechanism. Figure 6a demonstrates for H2S/Be12O12 complex.

Figure 6

Charge density difference () for (a) H2S/Be12O12, (b) H2S/Mg12O12, (c) SO2/Be12O12, and (d) SO2/Mg12O12 complexes. Red color for negative and blue color for positive .

The H and S atoms of the H2S molecule are surrounded by positive values (blue color), which confirms the charge transfer from the H2S molecule to the nano-cage. In addition, the positive (blue color) and negative (red color) values around each of the O2, O4, O6, and S atoms confirm the donation–back donation mechanism. For H2S/Mg12O12 structure, the interaction between H2S and Mg12O12 leads to the following: the 1s orbital of the H26 loses a charge of 0.37 e whereas the 2s and 2p of the O4 atom lose a charge of 0.07 and 0.13 e, respectively. Furthermore, the H27 atom has no change, the 3s and 3p orbitals of the S atom gain charges of 0.05 and 0.49 e, and the 3s and 3p of the Mg gain charges of 0.06 and 0.06 e, respectively. This confirms the dissociation of the H2S molecule into H+ and SH−. Then, the H+ is attached to the O4 atom, while the SH− is attached to the Mg1 atom. Figure 6b shows for the H2S/Mg12O12 complex. The H26 is surrounded by positive values (blue color) while the S atom is surrounded by negative (red color) values which agree with the above discussion. Table 4 illustrates the atomic NBO charges, as well the electronic configuration of the atoms, for the free SO2, Be12O12, Mg12O12, SO2/Be12O12, and SO2/Mg12O12.

Table 4

NBO charges (Q, e) and electronic configuration for free SO2, Be12O12, Mg12O12, SO2/Be12O12, and SO2/Mg12O12.

Structure	Atom	Atomic Charge	Electronic Configuration
			2s	2p	3s	3p
SO2	O	−0.747	1.84	4.89	-	-
	S	1.495	-	-	1.62	2.68
Be12O12	Be	1.186	0.21	0.59	-	-
	O	−1.186	1.69	5.49	-	-
Mg12O12	Mg	1.443	-	-	0.21	0.35
	O	−1.443	1.84	5.60	-	-
SO2/Be12O12	O26	−0.852	1.84	5.00	-	-
	O27	−0.980	1.76	5.21	-	-
	S	1.705	-	-	1.55	2.58
	Be1	1.210	0.22	0.55	-	-
	O2	−1.109	1.75	5.36	-	-
	O4	−1.214	1.69	5.52	-	-
	O6	−1.197	1.69	5.50	-	-
SO2/Mg12O12	O26	−1.003	1.82	5.17	-	-
	O27	−1.049	1.81	5.23	-	-
	S	1.713	-	-	1.51	2.62
	Mg1	1.477	-	-	0.20	0.32
	Mg3	1.468	-	-	0.20	0.32
	Mg7	1.417	-	-	0.21	0.36
	O2	−1.148	1.82	5.32	-	-
	O4	−1.463	1.84	5.62	-	-
	O8	−1.454	1.84	5.61	-	-

For SO2/Be12O12 structure, one can observe, that the 2s of the O27 and the 3s and 3p of the S atom lose charges of 0.08, 0.07, and 0.10 e, respectively, while the 2p of the O26 and O27 atoms gain charges of 0.11 and 0.32 e, respectively. Therefore, the positive charge of the S atom and the negative charge of the O27 atom increase; consequently, they are attached to the O2 negative and Mg1 positive sites of the nano-cage, respectively. Moreover, for the Be1 atom, the 2s gains a charge of 0.01 e while the 2p loses a charge of 0.04 e, whereas for the O2 atom, the 2s gains a charge of 0.06 e while the 2p orbital loses a charge of 0.13 e. Therefore, one can say that there is a charge transfer from the Be12O12 nano-cage to the SO2 molecule greater than the charge transferred from the SO2 molecule to the Be12O12 nano-cage. This explains why SO2 has a total charge of −0.127 e, as shown in Table 2. for the SO2/Be12O12 complex is demonstrated in Figure 6c. It is clear that both the adsorbed SO2 molecule and the sorbent Be12O12 nano-cage are surrounded by positive and negative values (blue and red colors) which confirms the donation–back donation mechanism for the interaction. For the SO2/Mg12O12 structure, one can notice that the 2s of the O26 and O27 loses charges of 0.02 and 0.03 e while the 2p gains charges of 0.28 and 0.34 e, respectively. Moreover, the 3s and 3p of the S atom lose charges of 0.11 and 0.06 e, respectively. Therefore, the net atomic charges of the O atoms of the SO2 become more negative while the S atom becomes more positive, consequently, the O26 and O27 are attracted to the Mg7 and Mg3 positive sites while the S atom is attracted to the O2 negative site of the Mg12O12 nano-cage, whereas for the Mg12O12, the 2s and 2p of the O2 atom lose charges of 0.02 and 0.28 e while the rest atoms of the nano-cage have little gains and loss of charges. for the SO2/Mg12O12 complex is illustrated in Figure 6d. It is clear that the adsorbed SO2 molecule is surrounded by negative values greater than the positive values, which confirm the donation–back donation mechanism for the interaction.

3.2.2. Bond Analysis

Bond order and overlap population are estimated for the free adsorbed gasses as well gas/nano-cage complexes. As the overlap value decreases, the interaction between the two atoms decreases and vice versa whereas the values close to zero mean no interaction while overlapping positive and negative values indicate the bonding and anti-bonding states, respectively [71,75,80]. Table 5 concerns the free H2S molecule, H2S/Be12O12, and H2S/Mg12O12 complexes.

Table 5

Overlap population and bond order of H2S, H2S/Be12O12, and H2S/Mg12O12.

Structure	H2S		H2S/Be12O12		H2S/Mg12O12
	Overlap Pop.	Bond Order	Overlap Pop.	Bond Order	Overlap Pop.	Bond Order
S–H26	0.304	0.979	0.316	0.974	0.042	0.097
S–H27	0.304	0.979	0.313	0.972	0.266	0.956
S–M1	-	-	0.074	0.279	0.273	0.717
O4–H26	-	-	0.000	0.002	0.289	0.835
M1–O4	-	-	0.206 (0.220) *	0.538 (0.602) *	0.035 (0.183) *	0.106 (0.520) *

* Values between brackets are for the bare nano-cage. M = Be and Mg.

For H2S/Be12O12, the overlap population and bond order values of the S-H26 and S-H27 bonds are slightly changed with respect to the free H2S molecule, while overlapping population and bond order values of 0.074 and 0.279, respectively, are observed for the S-Be1 bond. This indicates the formation of a weak bond between the H2S molecule and the B12O12 nano-cage. On the other hand, for H2S/Mg12O12, the low overlap population and bond order values for the S-H26 bond indicate the dissociation of the H2S molecule. In addition, high overlapping population and bond order values for S-Mg1 and O4-H26 indicate bond formation between the S atom and the Mg1 atom and between the H26 atom and the O4 atom. Furthermore, the overlapping population and the bond order values for the Mg1-O4 are decreased to 0.035 and 0.106 rather than 0.183 and 0.520 for the bare nano-cage, respectively, indicating a bond weakness has occurred. This reveals the strong interaction between the H2S molecule and the Mg12O12 nano-cage. Table 6 is interested in the free SO2 molecule, SO2/Be12O12, and SO2/Mg12O12 complexes.

Table 6

Overlap population and bond order of SO2, SO2/Be12O12, and SO2/Mg12O12.

Structure	SO2		SO2/Be12O12		SO2/Mg12O12
	Overlap Pop.	Bond Order	Overlap Pop.	Bond Order	Overlap Pop.	Bond Order
S-O26	0.242	1.773	0.302	1.706	0.203	1.290
S-O27	0.242	1.773	0.116	1.138	0.156	1.219
S-O2	-	-	−0.015	0.564	0.079	0.892
M1-O27	-	-	0.262	0.614	0.000	−0.010
M3-O27	-	-	0.022	0.022	0.192	0.464
M7-O26	-	-	0.057	0.118	0.207	0.495
M1-O2	-	-	−0.006 (0.220) *	0.028 (0.602) *	0.113 (0.183) *	0.267 (0.520) *
M3-O2	-	-	0.215 (0.220) *	0.452 (0.602) *	0.033 (0.183) *	0.103 (0.520) *

* Values between brackets are for the bare nano-cage. M = Be and Mg.

For SO2/Be12O12, the S-O27 and Be1-O2 bonds are weakened as indicated by the low values of the overlap population and bond order, while the high overlap population and bond order values for the Be1-O27 bond indicate bond formation. On the other hand, for SO2/Mg12O12, the decrease in the S-O26, S-O27, and Mg3-O2 overlapping population and bond order values indicates the weakness of these bonds while the bond order of 0.892, 0.464, and 0.495 for the S-O2, Mg-O27, and Mg-O26, respectively, confirms the formation of these bonds. In other words, one bond is formed between the SO2 and the nano-cage for the SO2/Be12O12 complex, whereas three bonds are formed for the SO2/Mg12O12 complex. This explains the higher adsorption energy for SO2/Mg12O12 than SO2/Be12O12.

3.2.3. PDOS Analysis

Figure 7 illustrates the surfaces of the HOMO and LUMO as well as the PDOS for the free H2S molecule, the bare Be12O12, and Mg12O12 nano-cages, as well the H2S/Be12O12 and H2S/Mg12O12 complexes.

Figure 7

HOMO, PDOS, LUMO for (a) H2S, (b) Be12O12, (c) H2S/Be12O12, (d) Mg12O12, and (e) H2S/Mg12O12 complexes.

Figure 7a shows three occupied states for the H2S molecule at −12.36, −10.12, and −7.30 eV; the H atom states located at −12.36 and −10.12 eV; and the S atom states located at −12.36, −10.12, and −7.35 eV. The S atom states for free H2S molecule are disappeared in the H2S/Be12O12 complex, as shown in Figure 7c. Furthermore, new states for the S atom are observed in the H2S/Be12O12 complex; these states overlap with the Be and O states, which emphasizes the interaction between the H2S molecule with the nano-cage. For instance, the states of the S, Be, and O atoms of the complex are overlapped at −8.20 eV, which is the HOMO of the complex. The HOMO surface of the complex displays the contribution of the S, Be, and O atoms. Comparing Figure 7b,c, one can observe the adsorption of the H2S molecule rises the HOMO and LUMO of Be12O12 by 0.43 and 0.13 eV, respectively; therefore, a decrease of 0.30 eV in the HOMO–LUMO gap has been recorded. For H2S/Mg12O12 complex, Figure 7e, it is clear that there is an overlap between the H and O states at −12.92 eV, which is due to the interaction between H26 and O4 in the complex. Moreover, the occupied states of the S atom are located at −9.70, −6.51, and −5.93 eV, i.e., they are shifted up with respect to the free H2S, which confirms the strong interaction between the H2S and Mg12O12 nano-cage. In addition, comparing Figure 7d,e, one can see that HOMO rises by 1.02 eV while LUMO lowers by 0.19 eV. Thus, H2S adsorption narrows the HOMO–LUMO gap by 0.85 eV. It is worth noticing that only the states of S and O atoms appear in the HOMO states, and this agrees with the obtained HOMO surface for the H2S/Mg12O12 complex. Figure 8 demonstrates the surfaces of HOMO and LUMO, as well PDOS, for the free SO2 molecule, bare Be12O12, and Mg12O12 nano-cages, as well SO2/Be12O12 and SO2/Mg12O12 complexes.

Figure 8

HOMO, PDOS, LUMO for (a) SO2, (b) Be12O12, (c) SO2/Be12O12, (d) Mg12O12, and (e) SO2/Mg12O12 complexes.

Comparing Figure 8a–c, it is clear that there are dramatic changes in the states due to the adsorption of the SO2 molecule on the Be12O12 nano-cage, where the states of SO2 overlap with the states of Be12O12. For example, one can observe the appearance of the S atom and the O atoms of the SO2 and Be12O12 in the HOMO states of the SO2/Be12O12 at −8.05 eV. This is confirmed by the HOMO surface for the SO2/Be12O12 complex. Based on the interaction, the HOMO of the nano-cage rises by 0.57 eV and the LUMO lowers by 0.68 eV, in turn, narrowing the HOMO–LUMO gap by 1.25 eV. Comparing Figure 8a,d,e, one can observe that adsorption of the SO2 molecule on the Mg12O12 nano-cage leads to intense changes in the states of the SO2 as well as the states of the Mg12O12, which confirms the occurrence of a strong interaction. Moreover, the HOMO of the nano-cage increases by 0.04 while the LUMO decreases by 0.08 eV; consequently, the HOMO–LUMO gap is slightly decreased by 0.12 eV.

3.3. Molecular Dynamic Simulations

To examine the impact of the temperature on the adsorption process of the investigated gases, molecular dynamic (MD) simulations at 300, 500, and 700 K for a total time of 500 fs are performed for H2S/Be12O12, H2S/Mg12O12, SO2/Be12O12, and SO2/Mg12O12 complexes. MD simulations are carried out via the ADMP model. Figure 9a,b illustrates the potential energy fluctuations for H2S/Be12O12 and H2S/Mg12O12, respectively, as well as the atomic configuration after 500 fs at the inspected temperatures.

Figure 9

Potential energy fluctuations during MD simulation for (a) H2S/Be12O12, and (b) H2S/Mg12O12 and the atomic configuration after 500 fs at 300, 500, and 700 K.

For H2S/Be12O12, Figure 9a, although the fluctuation of the potential energy is small, the distance (d1–25) between H2S and Be12O12 nano-cage increased with time. As well as the temperature increases, the increment in the distance increases, where the d1–25 values at the end of the time increase to 3.32, 7.38, and 9.55 Å for temperatures 300, 500, and 700 K, respectively. Therefore, one suggests that the Be12O12 nano-cage cannot retain H2S on its surface, especially at high temperatures. For H2S/Mg12O12, Figure 9b, at the temperature of 300 K, the fluctuation of the potential energy is small, and the Mg12O12 nano-cage preserves the dissociated H2S molecule on its surface with no significant changes in the geometrical structure of the complex, while at the temperatures of 500 and 700 K, a high fluctuation of the potential energy is observed until 120–130 fs, when the fluctuation decreases. In addition, the dissociation of the H2S molecule is diminished. At the end of the time, at 500 K, the H2S is retained on the Mg12O12 nano-cage at a distance of 2.65 Å while at 700 K the d1–25 increases to 6.79 Å. Furthermore, Figure 10a,b demonstrates the potential energy fluctuations for SO2/Be12O12 and SO2/Mg12O12, respectively, as well as the atomic configuration after 500 fs at the inspected temperatures.

Figure 10

Potential energy fluctuations during MD simulation for (a) SO2/Be12O12, and (b) SO2/Mg12O12 and the atomic configuration after 500 fs at 300, 500, and 700 K.

It is clear that no significant fluctuation of the potential energy is observed. Moreover, at the end of the time, there is a trivial deformation in the geometrical structure of the SO2/Be12O12 and SO2/Mg12O12 complexes. Therefore, one proposes that Be12O12 and Mg12O12 nano-cages can retain the SO2 molecule on their surface at temperatures up to 700 K.

3.4. Thermodynamic Properties

For gas adsorption, enthalpy difference (ΔH) and free energy difference (ΔG) are imperative thermodynamic parameters for determining the strength and the spontaneity of the reaction. Therefore, thermodynamic calculations for H2S/Be12O12, H2S/Mg12O12, SO2/Be12O12, and SO2/Mg12O12 complexes have been performed in the temperature range 300–700 K. Figure 11a signifies ΔH for the investigated complexes.

Figure 11

(a) ΔH and (b) ΔG for H2S/Be12O12, H2S/Mg12O12, SO2/Be12O12, and SO2/Mg12O12 complexes.

ΔH values for all considered complexes are negative, which specifies the reactions between H2S as well SO2 with Be12O12 and Mg12O12 nano-cages are exothermic. Furthermore, as the temperature increases, the negative ΔH values decrease, which indicates the reactions are stronger at lower temperatures. In addition, for the same gas, ΔH values are more negative for the Mg12O12 nano-cage than the Be12O12 nano-cage, while for the same nano-cage, ΔH values are more negative for SO2 gas than H2S gas. This confirms the above discussion of the high ability of the Mg12O12 nano-cage to absorb the investigated gases and the high ability of the SO2 gas to attach to the considered nano-cages. Figure 11b shows ΔG for the examined complexes. Spontaneous and non-spontaneous reactions are characterized by negative and positive ΔG values, respectively, while low negative ΔG values indicate the capability to reverse the reaction [46,66,67,68]. For the H2S/Be12O12 complex in the temperature range, ΔG values are positive, which indicates a non-spontaneous reaction, while for the SO2/Be12O12 complex, the reaction is spontaneous at low temperatures, and beyond T = 400 K, the reaction turns into a non-spontaneous reaction. Furthermore, for the H2S/Mg12O12 and SO2/Mg12O12 complexes in the temperature range, ΔG values are negative, which indicates a spontaneous reaction. In addition, the reaction is capable of being reversed in the H2S/Mg12O12 complex easier than in the SO2/Mg12O12 complex.

4. Conclusions

Structural and electronic properties of the considered Be12O12 and Mg12O12 nano-cages as well their stability are scrutinized. Mg12O12 exhibits lower Eg, IP, η, and higher ω values than those for Be12O12; therefore, Mg12O12 is more reactive than the Be12O12 nano-cage. Molecular dynamics calculations emphasize the stability of the investigated nano-cages. In addition, the interaction of H2S and SO2 gases at the surfaces of the inspected nano-cages have been studied, and the features of the interaction are examined in the point of the NBO atomic charges, charge density difference analysis (), bond analysis, and PDOS. values show that the ability of the Mg12O12 nano-cage to adsorb the considered gases is higher than that of the Be12O12 nano-cage. Furthermore, the ability of SO2 gas to be adsorbed is higher than that of H2S gas. Furthermore, H2S gas dissociates at the Mg12O12 surface. In addition, adsorption of H2S leads to a decrease in the HOMO–LUMO gap (Eg) values of Be12O12 and Mg12O12 by 3.84% and 17.54%, respectively, whereas the adsorption of SO2 leads to a decrease in Eg values by 15.97% and 2.60%, respectively. At high temperatures, MD calculations declare that the Be12O12 and Mg12O12 nano-cages do not retain the H2S on their surfaces, while SO2 is retained at low and high temperatures. Moreover, the thermodynamic calculations show that the reactions between H2S and SO2 with Be12O12 and Mg12O12 nano-cages are exothermic. Furthermore, at the temperature range of 300–700 K, the H2S reaction with Mg12O12 and Be12O12 is spontaneous and non-spontaneous, respectively, while the SO2 reaction with Mg12O12 is spontaneous, whereas the SO2 reaction with Be12O12 is spontaneous at temperatures up to 400 K. In addition, the reaction is capable to be reversed in the H2S/Mg12O12 complex easier than in the SO2/Mg12O12 complex.