M-Encapsulated Be12O12 Nano-Cage (M = K, Mn, or Cu) for CH2O Sensing Applications: A Theoretical Study

DFT and TD-DFT studies of B3LYP/6–31 g(d,p) with the D2 version of Grimme’s dispersion are used to examine the adsorption of a CH2O molecule on Be12O12 and MBe12O12 nano-cages (M = K, Mn, or Cu atom). The energy gap for Be12O12 was 8.210 eV, while the M encapsulation decreased its value to 0.685–1.568 eV, whereas the adsorption of the CH2O gas decreased the Eg values for Be12O12 and CuBe12O12 to 4.983 and 0.876 eV and increased its values for KBe12O12 and MnBe12O12 to 1.286 and 1.516 eV, respectively. The M encapsulation enhanced the chemical adsorption of CH2O gas with the surface of Be12O12. The UV-vis spectrum of the Be12O12 nano-cage was dramatically affected by the M encapsulation as well as the adsorption of the CH2O gas. In addition, the adsorption energies and the electrical sensitivity of the Be12O12 as well as the MBe12O12 nano-cages to CH2O gas could be manipulated with an external electric field. Our results may be fruitful for utilizing Be12O12 as well as MBe12O12 nano-cages as candidate materials for removing and sensing formaldehyde gas.


Introduction
Recently, the problem of pollution of the air, soil, and water has attracted the attention of many scientists.There have been several attempts to reduce pollution sources, whether by capturing the pollutants or detecting the contaminated materials.Formaldehyde (CH 2 O) is considered one of these pollutants.That is because of its diverse household uses in addition to its assorted uses in several industries [1][2][3][4][5][6][7][8].CH 2 O gas has a pungent smell and no color [9].Exposure to CH 2 O gas can cause voluminous hazards or even death to humans [10][11][12][13].Accordingly, it is necessary to search for a material capable of removing the CH 2 O or that can be used as a CH 2 O sensor.Beryllium oxide (BeO) has some electronic features, making it a candidate material for this purpose.BeO is a semiconductor possessing an energy gap (E g ) value of 8.21 eV [14].The Be-O bond appears to be a shared behavior of ionic and covalent bonds [15].Several experimental and theoretical efforts have been made to investigate BeO nano-structures, which have been synthesized in various forms such as nano-fibers [16] and nano-particles [17,18].The geometrical and electrical characteristics of diverse nano-clusters of BeO have been inspected, and this has proven that a Be 12 O 12 nano-cage possesses adequate stability [19].Moreover, Be 12 O 12 is a semiconductor with E g = 7.41-8.29 eV [20][21][22][23][24][25].Furthermore, metal oxide gas sensors have desirable properties such as a small size, lower cost, and extended lifetime [26].Accordingly, Be 12 O 12 nanocages are employed for various uses such as a catalyst to convert methane to organic compounds [27]; a sensor for sulfur mustard [23], tabun, mercaptopyridine, formaldehyde, sulfur hydride, and sulfur dioxide [20,22,28,29]; and a hydrogen storage material [25].The impact of Li, Na, and K deposition and encapsulation on the electronic and non-linear optical properties of Be 12 O 12 has been studied [24,28].It was found that the deposition and encapsulation of the alkali metals sharply decreased the E g of the nano-cage to 1.10-1.56eV and 0.68-0.69eV, respectively.Additionally, it proved that the non-linear optical properties of Be 12 O 12 nano-cages could be modified by the alkali metals.The UV-vis spectra for the Be 12 O 12 nano-cage were predicted by Fallahi et al. [22] and Jouypazadeh et al. [23].They found that the λ max absorbance peak for a Be 12 O 12 nano-cage is located at 140 to 150 nm.Kosar et al. [30] found that the encapsulation of Be 12 O 12 with Be, Mg, and Ca atoms led to a red shift that was located at 505 nm, 781 nm, and 1136 nm, respectively.
According to previous studies [45][46][47][48][49][50][51][52], the existence of an external electric field (EF) impacts the geometric structure, substrate-adsorbate interaction, and electrical characteristics.Additionally, the electric field has a significant impact on key sensor properties such as the adsorption energy (E ads ), sensitivity, and recovery time (τ).Our previous study [20] focused on studying the effect of the EF on the interaction characteristics of CH 2 O on a pristine Be 12 O 12 nano-cage in different solvents.It was discovered that the magnitude and orientation of the EF can alter the sensing parameters of Be 12 O 12 for the CH 2 O molecule.
According to our knowledge, there is a deficiency in the investigation of the impact of encapsulation of 3d metal atoms on the electrical, optical, and adsorption features of Be 12 O 12 .Moreover, no work has been interested in the effect of the existence of an EF on the adsorption features of CH 2 O molecules on metal-encapsulated Be 12 O 12 .Therefore, in this work, we sought to study the effect of an alkali metal (K) or a transition metal (Mn or Cu) as well as the effect of an EF on the adsorption characteristics of the CH 2 O molecule on a Be 12 O 12 nano-cage.

Methods
The BeO nano-cage was represented by 12 Be-O dimers.Then, as a trial to modify the properties of the beryllium oxide nano-cage (Be 12 O 12 ), an M atom (M = K, Mn, or Cu) was encapsulated into the nano-cage to form MBe 12 O 12 nano-cages (see Figure 1).DFT-D2 computations were performed to inspect the adsorption features of the CH 2 O molecule on the Be 12 O 12 as well as MBe 12 O 12 nano-cages.To estimate the optimized energetic geometrical structures and the electronic properties, the DFT-D2 computations were carried out by utilizing the hybrid functional B3LYP and 6-31 g(d,p) basis set [53].The exchange functional B3 refers to Becke's three parameters, while the correlation functional LYP refers to the correlation functional of Lee, Yang,and Parr [54].The investigated structures were fully optimized under the following cutoff conditions for the total force on an atom (0.129 eV/Å), the root mean square of the force (0.086 eV/Å), the displacement (5.29 × 10 −3 Å), and the root mean square of the displacement (3.53 × 10 −3 Å).
D2 refers to Grimme's dispersion [55,56], which takes into account the van der Waals interactions.The optimal multiplicity M (M = 2S + 1) was examined for the considered nano-cages, where S is the total spin.The dynamic stability for the considered nanocages was checked by utilizing the vibrational frequencies, which were estimated by using the FT-IR spectra as well as a molecular dynamic simulation using the ADMP model.The UV-vis spectra were estimated for the considered structures by using the timedependent DFT (TD-DFT) method.In TD-DFT calculations, an adequate number of excited states (n = 15) is estimated to cover all the probable transitions in the appropriate range (0-2000 nm).
The binding energy per atom (E b ) for the investigated structures was assessed using Equation (1) [57].
Here, E cage is the optimized nano-cage total energy, E i is the single atom energy, and n is the number of the cage atoms.D2 refers to Grimme's dispersion [55,56], which takes into account the van der Waals interactions.The optimal multiplicity M (M = 2S + 1) was examined for the considered nano-cages, where S is the total spin.The dynamic stability for the considered nano-cages was checked by utilizing the vibrational frequencies, which were estimated by using the FT-IR spectra as well as a molecular dynamic simulation using the ADMP model.The UVvis spectra were estimated for the considered structures by using the time-dependent DFT (TD-DFT) method.In TD-DFT calculations, an adequate number of excited states (n = 15) is estimated to cover all the probable transitions in the appropriate range (0-2000 nm).
The binding energy per atom (Eb) for the investigated structures was assessed using Equation (1) [57].
Here, E is the optimized nano-cage total energy, E is the single atom energy, and n is the number of the cage atoms.The ionization potentials (IPs) for the considered cages were evaluated as shown below [5,58]: where E cage + is the energy of the cage after removing an electron while keeping the same geometry of the neutral cage.The Fermi level (E F ), hardness (η), and electrophilicity (ω) were evaluated as shown in Equations ( 3)-( 5), respectively [59,60]: where E HOMO E LUMO are the energies of the highest occupied and the lowest unoccupied molecular orbitals, respectively.The adsorption energy (E ads ) for CH 2 O on a nano-cage was calculated by Equation ( 6): where E CH 2 O/cage , E cage and E CH 2 O are the energies for the CH 2 O/cage complex, the nanocage and the CH 2 O molecule, respectively.For the adsorption of multiple n molecules of CH 2 O gas, the adsorption energy per molecule (E ads ) was calculated by Equation ( 7): where E nCH 2 O/cage is the energy for the nCH 2 O/cage complex.A negative sign for the E ads and E ads indicates an exothermic reaction and more stable products.The Gaussian 09 program was used to achieve all the calculations, whereas the Gauss View 5 was used for the visualization of the results [61].The GaussSum 3.0 program estimated the partial density of states (PDOS) of the adsorbates-substrates [62].The NBO version 3.1 measured the charges of atoms [63].The Multiwfn 3.7 software package was employed to achieve the Quantum Theory of Atoms in Molecules (QTAIM) analysis [64].

Effect of Metal Encapsulation in Be 12 O 12
In this section, the impact of doping on the geometrical, electrical, optical, and magnetic characteristics of the Be 12 O 12 nano-cage was scrutinized.Therefore, full geometrical optimization was performed for the pristine and M-encapsulated Be 12 O 12 nano-cage (M = K, Mn, or Cu).The optimized structures for Be 12 O 12 as well as MBe 12 O 12 are shown in Figure 1.The Be 12 O 12 nano-cage comprises eight hexagonal and six tetragonal rings.Furthermore, the Be-O bonds are distinguished into two types.The first type, denoted by d 1 , is shared between hexagonal and tetragonal rings.The second type, denoted by d 2 , is shared between two hexagonal rings.It is found that d 1 and d 2 have bond lengths of 1.58 and 1.52 Å, respectively, for the Be 12 O 12 nano-cage in good agreement with previous works [20,21,29,65 To investigate the stability of Be 12 O 12 as well as MBe 12 O 12 nano-cages, molecular dynamic (MD) simulations by the ADMP model as implemented in Gaussian 09 were performed.The MD simulations were performed at room temperature (300 K) for 500 fs. Figure S1, in the Supplementary Materials, illustrates the potential energy (PE) fluctuation against time besides the structure of Be 12 O 12 as well as MBe 12 O 12 at the end of the time.One can notice that the PE irrelevantly fluctuates, and unimportant distortion occurs for the cages.Therefore, the Be 12 O 12 and MBe 12 O 12 nano-cages have stable structures.Additionally, in Figure S2, in the Supplementary Materials, the disappearance of the imaginary frequencies for all investigated nano-cages declares that the optimized nanocages are true minima on the potential energy surfaces [66][67][68][69].This is in agreement with our previous work on the Be 12 O 12 nano-cage [29].
One can judge the relative stability as well as relative reactivity of Be 12 O 12 and MBe 12 O 12 nano-cages in terms of the following: E b , HOMO-LUMO energy gap (E g ), IP, E F , η, and ω.Their values are listed in Table 1.The E b is calculated via Equation (1).The E b value for Be 12 O 12 is −5.630 eV, which is in agreement with Sajid et al. [21], while the M encapsulation decreases its value by 8 [20,21,65].[69][70][71][72] that the clusters distinguished by lower E g , IP, and η values and larger ω values are chemically less stable and more reactive.Thus, our results assert that the M-encapsulated Be 12 O 12 nano-cages are chemically higher in reactivity than the Be 12 O 12 nano-cage.
For more intuition, the NBO atomic charges were estimated.As listed in Table 1, for MBe 12 O 12 nano-cages, the K, Mn, and Cu atoms own positive charges of 0.096, 0.237, and 0.108 e.
This indicates the occurrence of charge transfer from the M atoms to the rest of the beryllium oxide nano-cage.Despite the charge transfer that occurred, the charge distribution on the beryllium and oxygen atoms is still symmetric.Therefore, no obvious change in the magnitudes of the dipole moment values of the MBe 12 O 12 nano-cages was observed.Figure 2  Obviously, the M atom is enclosed by positive and negative values of Δ, which indicates the occurrence of a donation-back donation of charges between the metal atom and the rest of the nano-cage atoms.In other words, there is a charge transfer from the M atom to the nano-cage and vice versa.Additionally, the electronic configuration was calculated for M atoms in a free state as well as in the MBe12O12 nano-cages and listed in Table Obviously, the M atom is enclosed by positive and negative values of ∆ρ, which indicates the occurrence of a donation-back donation of charges between the metal atom and the rest of the nano-cage atoms.In other words, there is a charge transfer from the M atom to the nano-cage and vice versa.Additionally, the electronic configuration was calculated for M atoms in a free state as well as in the MBe 12 O 12 nano-cages and listed in Table 2  In Figure 3, the molecular electrostatic potential (MESP) for Be 12 O 12 as well as MBe 12 O 12 nano-cages was displayed.Figure 3a reveals that positive and negative electrostatic potentials surround the Be sites and the O sites, respectively, which is in good agreement with our previous work [20].Figure 3b-d show that the K, Mn, or Cu encapsulation in the nano-cage has no obvious effect on the MESP distribution around the nano-cage.Therefore, the Be and O sites for Be 12 O 12 as well as MBe 12 O 12 nano-cages are expected to perform as electrophilic and nucleophilic sites, respectively.
Furthermore, the PDOS as well as the surfaces of the frontier orbitals (HOMO and LUMO) for Be 12 O 12 and MBe 12 O 12 nano-cages are depicted in Figure 4.As seen in Figure 4a the HOMO and LUMO of the Be 12 O 12 nano-cage are located at −8.463 and −0.253 eV, respectively.Therefore, Be 12 O 12 nano-cage is a wide-band gap semiconductor possessing an E g value of 8.21 eV [14].
Additionally, the HOMO is commonly attributed to the 2p orbitals of the O atoms, whereas the LUMO is commonly attributed to the 2p orbitals of the Be atoms.Thus, the HOMO and LUMO are chiefly localized on the O and the Be sites, respectively.Figure 4b-d show that the presence of the K, Mn, and Cu atoms, respectively, causes noticeable changes in the states attributed to the Be nano-cages, an overlap is observed between the occupied states of the K, Mn, and Cu atoms and the occupied states of the rest of the nano-cage atoms, which indicates an interaction among them has occurred.The electrical conductivity (σ) is governed by the E g value as follows [73][74][75][76][77][78].
where k is Boltzmann's constant, and T is the temperature.Subsequently, the metal doping increases the σ value of the Be 12 O 12 nano-cage.where k is Boltzmann's constant, and T is the temperature.Subsequently, the metal doping increases the σ value of the Be12O12 nano-cage.To scrutinize the influence of metal encapsulation on the optical properties of the Be12O12 nano-cage, the UV-vis spectra for the Be12O12, KBe12O12, MnBe12O12, and CuBe12O12 nano-cages were estimated via TD-DFT calculations and graphed in Figure 5.It is obvious the Be12O12 nano-cage has a λmax absorbance peak in the UV region at 169 nm, which is consistent with previous studies [22,23].Moreover, the KBe12O12 nano-cage has two absorbance peaks; the first peak is located in the visible region at 424 nm, and the second peak is located in the IR region at 1527 nm, while the MnBe12O12 nano-cage has a λmax absorbance peak in the IR region at 889 nm.However, the CuBe12O12 nano-cage has a λmax absorbance peak in the visible region at 431 nm.In other words, the metal encapsulation   [20], it was found that negative and positive electrostatic potentials surround the O atom and CH 2 group, respectively, of the CH 2 O molecule.While Figure 3 shows that positive and negative electrostatic potentials surround the Be and O sites, respectively, of the Be 12 O 12 and MBe 12 O 12 nano-cages.Therefore, the interaction of CH 2 O with the nano-cage is investigated in different orientations, as shown in Figure S3 in the Supplementary Materials.The optimization process for the suggested orientations shows that the CH 2 O molecule always interacts via its O head with the Be site of the nano-cage, as depicted in Figure 6.
obviously affects the optical activity of the Be12O12 nano-cage.The Be12O12 nano-cage is an ultraviolet active compound, while the MBe12O12 nano-cages are active compounds in the visible and IR regions.

Adsorption of CH2O on M-Doped Be12O12
To examine the interaction characteristics of the CH2O molecule with the Be12O12 and MBe12O12 nano-cages, an optimization was carried out for the free CH2O, the bare nanocages (Be12O12 and MBe12O12), and the CH2O/nano-cages (CH2O/Be12O12 and CH2O/MBe12O12) complexes.Our calculations show that the bond lengths of the C-O and C-H bonds for the CH2O molecule are 1.21 and 1.11 Å, respectively.The geometrical parameters for the bare Be12O12 and MBe12O12 nano-cages were discussed in the previous section.Additionally, in our previous work [20], it was found that negative and positive electrostatic potentials surround the O atom and CH2 group, respectively, of the CH2O molecule.While Figure 3 shows that positive and negative electrostatic potentials surround the Be and O sites, respectively, of the Be12O12 and MBe12O12 nano-cages.Therefore, the interaction of CH2O with the nano-cage is investigated in different orientations, as shown in Figure S3 in the Supplementary Materials.The optimization process for the suggested orientations shows that the CH2O molecule always interacts via its O head with the Be site of the nano-cage, as depicted in Figure 6.
One can see that the distance between the CH2O and the Be12O12 nano-cage (dBe1-O1 = 1.76 Å) is longer than that between the CH2O and the MBe12O12 nano-cage (dBe1-O1 in the range 1.49-1.50Å).Moreover, the C-O bond length of the CH2O molecule is elongated by 0.83%, 10.74%, 11.57%, and 11.57% for the CH2O/Be12O12, CH2O/KBe12O12, CH2O/MnBe12O12, and CH2O/CuBe12O12, respectively.Furthermore, the CH2O adsorption elongates the bond lengths between the adsorbing site (Be1) and the neighboring oxygen sites (O2, O3, and O4); this elongation is higher for the CH2O/MBe12O12 complexes than that for the CH2O/Be12O12 complex.Table 5.The estimated topological parameters.Electron densities (ρ), Laplacian of charge density (∇ 2 ρ), kinetic electron density (G(r)), potential energy density (V(r)), and energy density (H(r)).All units are in au.The kind of bond can be distinguished by the BCP parameters [83][84][85].As reported, the ionic bond, weak hydrogen bond, and van der Waals interaction are characterized by ∇ 2 ρ > 0, H(r) > 0, −G(r)/V(r) > 1.Furthermore, the strong interaction is categorized by ∇ 2 ρ >10 −1 au, and the weak interaction is categorized by ∇ 2 ρ < 10 −1 au.Additionally, the partly covalent interaction is categorized by ∇ 2 ρ > 0 and H(r) < 0. Our results show that for the CH 2 O/Be 12 O 12 complex, there are two BCPs; the first BCP is Be1-O1, which has a ∇ 2 ρ of 0.327 au, H(r) of 0.005 au, and −G(r)/V(r) ratio of 1.069, while the other BCP is O2-H1, which has a ∇ 2 ρ of 0.054 au, H(r) of 0.002 au, and −G(r)/V(r) ratio of 1.200 complexes, respectively.These results categorize the interaction as an ionic interaction with a partially covalent character.Therefore, one can say that the presence of the metal atom has an obvious role in altering the character of the interaction between the CH 2 O molecule and the nano-cages.Furthermore, the higher ρ values [80]  O molecule.In addition, the essential sensing factor, the recovery time (τ), depends on the E ads as in the following equation [20,86,87].
where ν o is the attempt frequency, k is Boltzmann's constant, and T is the temperature.Therefore, the τ value is in the following trend: MnBe 12 O 12 > KBe 12 O 12 > CuBe 12 O 12 > Be 12 O 12 .

Effect of EF
In the present section, the influence of EF on the electronic properties of the CH 2 O molecule, Be 12 O 12 as well as MBe 12 O 12 nano-cages, and the CH 2 O/Be 12 O 12 as well as CH 2 O/MBe 12 O 12 complexes was examined.The EF was considered in the range of −514 to +514 kV/mm with a step of 102.8 kV/mm.All the investigated structures are fully optimized for each EF value.The direction of the EF relative to the investigated structures is sketched in Figure 9.The influence of the EF on the dipole moment for the CH 2 O molecule and the Be 12 O 12 nano-cage, as well as the MBe 12 O 12 nano-cages, was investigated.Because the EF was applied in the X-axis direction, the change in the dipole moment was only evident in its x-component.mized for each EF value.The direction of the EF relative to the investigated structures sketched in Figure 9.The influence of the EF on the dipole moment for the CH2O molecu and the Be12O12 nano-cage, as well as the MBe12O12 nano-cages, was investigated.Becau the EF was applied in the X-axis direction, the change in the dipole moment was on evident in its x-component.It is seen that with the varying of the EF from −514 to +514 kV/mm, the dipole mome of the investigated nano-cages decreases from 0.311, 2.041, 0.901, and 0.420 Debye −0.311, −2.032, −0.903, and −0.427 Debye for Be12O12, KBe12O12, MnBe12O12, and CuBe12O respectively.It is worth noticing that the polarity of the dipole moment is inverted as t EF direction is inverted.Additionally, the rate of change in the dipole moment with t EF is in this trend: KBe12O12 > MnBe12O12> CuBe12O12> Be12O12.These results manifest th the EF affects the charge distribution for the CH2O molecule, Be12O12, and MBe12O12 nanocages.This is emphasized by Figure 10b-f, which demonstrates the charge density difference (Δρ) for the CH2O molecule, Be12O12, and MBe12O12 nano-cages for EF values of −514 and +514 kV/mm.The dipole moment of a molecule plays an important role in its reactivity with the surrounding medium [88].Therefore, it is expected that the EF would have an obvious impact on the CH2O adsorption on the Be12O12 as well as MBe12O12nano-cages.
The manipulation of the EF on the CH2O adsorption on the Be12O12 and MBe12O12 nano-cages has been completed under the same criteria mentioned above.The Eads values for the CH2O/Be12O12 and CH2O/MBe12O12 complexes are estimated and plotted against the EF in Figure 11.It is seen that by increasing the negative EF, the value of Eads is gradually enhanced for the CH2O/Be12O12 complex up to 3.4% at EF = −514 kV/mm with respect to their value at zero EF.Meanwhile, the values of Eads are gradually inhibited for CH2O/KBe12O12, CH2O/MnBe12O12, and CH2O/CuBe12O12 complexes up to 4.8%, 3.6%, and 6.2%, respectively, at EF = −514 kV/mm with respect to its value at zero EF.On the other side, by increasing the positive EF, the value of Eads is gradually inhibited for the CH2O/Be12O12 complex up to 3.1% at EF = +514 kV/mm with respect to its value at zero EF.Meanwhile, the values of Eads are gradually enhanced for CH2O/KBe12O12, CH2O/MnBe12O12, and CH2O/CuBe12O12 complexes up to 4.2%, 3.5%, and 6.4%, respectively, at EF = +514 kV/mm with respect to their value at zero EF.Therefore, the Eads values for CH2O/Be12O12 and CH2O/MBe12O12 complexes are dominated by either the value or direction of the EF.These results could be explained in terms of the mechanism of CH2O interaction with the nanocage.For the CH2O/Be12O12 complex, as mentioned before, there is a charge transfer from the CH2O molecule to the Be12O12 nano-cage.Looking at Figure 9b,c, one can see that the negative EF induces a negative Δρ value on the oxygen head of the CH2O molecule and a positive Δρ value on the side of the Be12O12 nano-cage facing the CH2O molecule.This in turn encourages the charge transfer and, consequently, enhances the Eads value.In contrast, the positive electric field induces a positive Δρ value on the oxygen head of the CH2O molecule and a negative Δρ value on the side of the Be12O12 nano-cage facing the CH2O molecule.This discourages the charge transfer and, consequently, inhibits the Eads value.This could be confirmed by Figure 12, which shows the NBO charges of the CH2O molecule (Q ) vs. electric field.It is clear that the positive Q for the CH2O/Be12O12 complex increases as the negative EF increases and decreases as the positive EF increases.Thus, the Eads value is enhanced by increasing the negative EF and inhibited by increasing the positive EF (see Figure 11).On the other side, for the CH2O/MBe12O12 complexes, the interaction has occurred due to the charge transfer from the MBe12O12 nanocage to the CH2O molecule.Looking at Figure 9d-f, it is clear that for negative EF values, the induced positive Δρ value on the side of the MBe12O12 nano-cage facing the CH2O molecule inhibits this charge transfer and consequently inhibits the Eads values.Whereas for the positive EF values, the induced negative Δρ value on the side of the MBe12O12 nano-cage facing the CH2O molecule encourages the charge transfer and thus enhances the Eads values.This can be confirmed by Figure 12, where the negative Q for CH2O/MBe12O12 complexes decreases as the negative EF increases and decreases as the positive EF increases.Thus, the Eads value is inhibited as the negative EF increases and enhanced as the positive EF increases (see Figure 11).
Figure 13 represents the impact of the EF on the Eg for the Be12O12 and MBe12O12 nanocages as well as the CH2O/Be12O12 and CH2O/MBe12O12 complexes.It is clear that the EF has a negligible impact on the Eg values of the Be12O12 and MBe12O12 nano-cages.Figure 13a declares that the Eg value for the CH2O/Be12O12 complex increases as the negative EF increases and decreases as the positive EF increases.On the other side, Figure 13b-d show that the Eg values for the CH2O/KBe12O12, CH2O/MnBe12O12, CH2O/CuBe12O12 complexes increase as the negative EF decreases and the positive EF increases.Therefore, according to Equation ( 8), the electric conductivity (σ) for the CH2O/Be12O12 and CH2O/MBe12O12 complexes can be controlled by the EF.Here, σ for the CH2O/Be12O12 complexes will increase by increasing the positive EF, while for the CH2O/MBe12O12 complexes, σ will increase by increasing the negative EF.   10) and represented in Figure 14.
∆E g values at EF = 0 were −41.2%,To investigate the electrical sensitivity dependence on the EF, the percentage of the variance of Eg (ΔEg) by the adsorption for CH2O/Be12O12 and CH2O/MBe12O12 complexes versus the EF is estimated by Equation (10) and represented in Figure 14.To investigate the electrical sensitivity dependence on the EF, the percentage of t variance of Eg (ΔEg) by the adsorption for CH2O/Be12O12 and CH2O/MBe12O12 complex versus the EF is estimated by Equation (10) and represented in Figure 14.

UV-vis Spectra Investigation
Herein, the effect of the adsorption of the CH 2 O molecule as well as the EF on the spectra of the examined nano-cages was considered.The UV-vis spectra for the CH 2 O/Be 12 O 12 and CH 2 O/MBe 12 O 12 complexes are predicted for EF values of −514, 0, and +514 kV/mm, and these are displayed in Figure 15a-c, respectively.It is worth noting that the effect of the EF on the UV-vis spectra of bare nano-cages is studied, and it is found that the EF has no noticeable effect.It is clear that at EF values of −514, 0, and +514 kV/mm, the CH 2 O/Be 12 O 12 complex has a λ max absorbance peak in the UV region at 224, 252, and 260 nm, respectively.Comparing these results with Figure 5, one can observe that the adsorption of CH 2 O causes a red shift for the UV-vis spectrum of the Be 12 O 12 .The negative EF value decreases the red shift value of λ max , while the positive EF increases it.Furthermore, at zero EF, the CH 2 O/KBe 12 O 12 exhibits three peaks located at 324 nm, 509 nm, and 810 nm in the UV, visible, and IR regions of the spectra, respectively.The presence of the EF shifts these peaks to 328, 536, and 896 nm at negative EF and to 316, 484, and 736 nm at positive EF.When compared with Figure 5, the Kbe 12 O 12 nano-cage has a peak in the visible region at 424 nm, whereas the adsorption of CH 2 O induces a red shift in this peak to 536, 509, and 484 for EF values of −514, 0, and +514 kV/mm, respectively.Moreover, at EF values of −514, 0, and +514 kV/mm, the CH 2 O/MnBe 12 O 12 exhibits one prominent peak in the visible region of the spectra, which is located at 460, 463, and 448 nm, respectively.In comparison with Figure 5, it is evident that the MnBe 12 O 12 nano-cage has one peak in the IR region (889 nm), while the adsorption of CH 2 O causes a blue shift for λ max to the visible region.Additionally, Figure 5 7) and graphed in Figure 16a.It is seen that as n increases, the negative value of the E ads decreases.Nevertheless, the E ads values remain within the bounds of chemical adsorption for all n values.
In Figure 16b, the relationship between E g and n is illustrated.It is observed that for KBe 12 O 12 and MnBe 12 O 12 , as n increases up to n = 3 and 2, respectively, the E g decreases after which there is no significant change.Conversely, for CuBe 12 O 12 , the E g decreases as n increases, reaching a minimum at n = 4, and then it rises again.According to Equations ( 8) and (10), it is noted that for all the investigated nano-cages, the electrical conductivity (σ) and the electrical sensitivity at all values of n > 1 are higher than their values at n = 1.Furthermore, the highest electrical conductivity (σ) and electrical sensitivity are recorded for CuBe 12 O 12 at n = 4.

Effect of Concentration
This section concerns the impact of CH2O concentration on the adsorption charac istics.The adsorption of n molecules (n = 1-6) on the surface of the MBe12O12 was inv gated to form nCH2O/MBe12O12 complexes.The nCH2O/MBe12O12 complexes were f optimized.The adsorption energies per molecule (E ) were estimated by Equation and graphed in Figure 16a.It is seen that as n increases, the negative value of the increases, reaching a minimum at n = 4, and then it rises again.According to Equations ( 8) and (10), it is noted that for all the investigated nano-cages, the electrical conductivity (σ) and the electrical sensitivity at all values of n > 1 are higher than their values at n = 1.Furthermore, the highest electrical conductivity (σ) and electrical sensitivity are recorded for CuBe12O12 at n = 4.

Conclusions
This work is a DFT and TD-DFT study that investigates the capability of the M atomencapsulated Be12O12 nano-cage to capture or sense CH2O gas; M = K, Mn, or Cu.The molecular dynamic simulations and the frequency calculations assert that the Be12O12 and MBe12O12 nano-cages are stable structures.In contrast, the values of the binding energies per atom (Eb), the ionization potential (IP), the hardness (η), and the electrophilicity (ω)

Conclusions
This work is a DFT and TD-DFT study that investigates the capability of the M atomencapsulated Be 12 O 12 nano-cage to capture or sense CH 2 O gas; M = K, Mn, or Cu.The molecular dynamic simulations and the frequency calculations assert that the Be 12 O 12 and MBe 12 O 12 nano-cages are stable structures.In contrast, the values of the binding energies per atom (E b ), the ionization potential (IP), the hardness (η), and the electrophilicity (ω) prove that the M-encapsulated Be 12 O 12 is chemically more reactive than the Be 12 O 12 cage.In addition, the encapsulation of the M atom into the Be 12 O 12 nano-cage increases its basicity, narrows its energy gap, and alerts its optical activity from an ultraviolet active compound into active compounds in the visible and IR regions.
Moreover, the calculated adsorption energies confirm that the CH 2 O adsorption on the Be 12 O 12 as well as the MBe 12 O 12 is chemisorption, while the presence of the M atom improves the adsorption of the CH 2 O molecule on the nano-cage.Moreover, the QTAIM analysis confirms that the presence of the metal atom plays an obvious role in altering the character of CH 2 O interaction with the nano-cages from pure ionic interaction into an ionic interaction with a partially covalent character.Additionally, the CH

Figure 3 .
Figure 3.The molecular electrostatic potential maps (MESP) for (a) Be 12 O 12 , (b) KBe 12 O 12 , (c) MnBe 12 O 12 , and (d) CuBe 12 O 12 nano-cages.To scrutinize the influence of metal encapsulation on the optical properties of the Be 12 O 12 nano-cage, the UV-vis spectra for the Be 12 O 12 , KBe 12 O 12 , MnBe 12 O 12 , and CuBe 12 O 12 nanocages were estimated via TD-DFT calculations and graphed in Figure5.It is obvious the Be 12 O 12 nano-cage has a λ max absorbance peak in the UV region at 169 nm, which is consistent with previous studies[22,23].Moreover, the KBe 12 O 12 nano-cage has two absorbance peaks; the first peak is located in the visible region at 424 nm, and the second peak is located in the IR region at 1527 nm, while the MnBe 12 O 12 nano-cage has a λ max absorbance peak in the IR region at 889 nm.However, the CuBe 12 O 12 nano-cage has a λ max absorbance peak in the visible region at 431 nm.In other words, the metal encapsulation obviously affects the optical activity of the Be 12 O 12 nano-cage.The Be 12 O 12 nano-cage is an ultraviolet active compound, while the MBe 12 O 12 nano-cages are active compounds in the visible and IR regions.

3. 2 .
Adsorption of CH 2 O on M-Doped Be 12 O 12 To examine the interaction characteristics of the CH 2 O molecule with the Be 12 O 12 and MBe 12 O 12 nano-cages, an optimization was carried out for the free CH 2 O, the bare nano-cages (Be 12 O 12 and MBe 12 O 12 ), and the CH 2 O/nano-cages (CH 2 O/Be 12 O 12 and CH 2 O/MBe 12 O 12 ) complexes.Our calculations show that the bond lengths of the C-O and C-H bonds for the CH 2 O molecule are 1.21 and 1.11 Å, respectively.The geometrical parameters for the bare Be 12 O 12 and MBe 12 O 12 nano-cages were discussed in the previous section.Additionally, in our previous work
One can see that the distance between the CH 2 O and the Be 12 O 12 nano-cage (d Be1-O1 = 1.76 Å) is longer than that between the CH 2 O and the MBe 12 O 12 nano-cage (d Be1-O1 in the range 1.49-1.50Å).Moreover, the C-O bond length of the CH 2 O molecule is elongated by 0.83%, 10.74%, 11.57%, and 11.57% for the CH 2 O/Be 12 O 12 , CH 2 O/KBe 12 O 12 , CH 2 O/MnBe 12 O 12 , and CH 2 O/CuBe 12 O 12 , respectively.Furthermore, the CH 2 O adsorption elongates the bond lengths between the adsorbing site (Be1) and the neighboring oxygen sites (O2, O3, and O4); this elongation is higher for the CH 2 O/MBe 12 O 12 complexes than that for the CH 2 O/Be 12 O 12 complex.

Figure 6 .
Figure 6.Optimized structures for (a) CH 2 O/Be 12 O 12, (b) CH 2 O/KBe 12 O 12, (c) CH 2 O/MnBe 12 O 12 , and (d) CH 2 O/CuBe 12 O 12 .One can notice that the CH 2 O adsorption on the Be 12 O 12 as well as the MBe 12 O 12 nanocages is a chemisorption.Meanwhile, the E ads values for the CH 2 O/MBe 12 O 12 complexes are more negative than the E ads value for the CH 2 O/Be 12 O 12 complex.In other words, the presence of the M atom enhances the CH 2 O adsorption on the nano-cage.Thus, the Be 12 O 12 as well as MBe 12 O 12 nano-cages can be utilized as removal materials for formaldehyde gas, whereas the MBe 12 O 12 nano-cages are more efficient than the pristine Be 12 O 12 nano-cage for this purpose.Furthermore, it was found in previous studies that the E ads of CH 2 O on the B 3 O 3 monolayer [79], Ti-functionalized porphyrin-like C70 fullerenes [80], carbon nano-tube (CNT) [81], Pd-loaded CNT [81], BeO nano-tube [82], Zn 12 O 12 nano-cage [4], and Al-deposited Zn 12 O 12 nano-cage [4] are −0.402,−1.862, −0.106, −1.299, −1.088, −1.27, and −2.23 eV, respectively.Therefore, the present work shows that KBe 12 O 12 and MnBe 12 O 12

(
red color) Δρ values.This means the CH2O molecule loses and gains char ing the donation-back donation mechanism between the CH2O molecule cages.It is worth noticing that the high dipole moment values for the CH the CH2O/MBe12O12 complexes in Table3refer to the charge redistributio CH2O molecule and the nano-cages.

Figure 9 .
Figure 9. (a) Electric field direction relative to the nano-cage, and the charge density difference (∆ρ) isovalue surfaces at 0.00005 au for EF values of −514 and +514 kV/mm for (b) CH 2 O, (c) Be 12 O 12 , (d) KBe 12 O 12 , (e) MnBe 12 O 12 , and (f) KBe 12 O 12 .∆ρ = ρ E=±514 − ρ E=0 , X-component of dipole moment (D x ) in Debye.Red and blue colors represent negative and positive ∆ρ values, respectively.Therefore, the x-component only of the dipole moment was considered.Figure 10a shows the dipole moment for the CH 2 O molecule versus EF.It is clear that with the EF varying from −514 to +514 kV/mm, the dipole moment of the CH 2 O molecule decreases.The dipole moments versus EF for the Be 12 O 12 and MBe 12 O 12 nano-cages are illustrated in Figure 10b.

Figure 10 .
Figure 10.Dipole moment vs. electric field at different mediums for (a) CH 2 O, (b) Be 12 O 12 and MBe 12 O 12 substrates, and (c) CH 2 O/Be 12 O 12 and CH 2 O/MBe 12 O 12 complexes.It is seen that with the varying of the EF from −514 to +514 kV/mm, the dipole moment of the investigated nano-cages decreases from 0.311, 2.041, 0.901, and 0.420 Debye to −0.311, −2.032, −0.903, and −0.427 Debye for Be 12 O 12 , KBe 12 O 12 , MnBe 12 O 12 , and CuBe 12 O 12 , respectively.It is worth noticing that the polarity of the dipole moment is inverted as the EF direction is inverted.Additionally, the rate of change in the dipole moment with the EF is in this trend: KBe 12 O 12 > MnBe 12 O 12 > CuBe 12 O 12 > Be 12 O 12 .These results manifest that the EF affects the charge distribution for the CH 2 O molecule, Be 12 O 12 , and MBe 12 O 12 nano-cages.This is emphasized by Figure 10b-f, which demonstrates the charge density difference (∆ρ) for the CH 2 O molecule, Be 12 O 12 , and MBe 12 O 12 nano-cages

Figure 11 .
Figure 11.Adsorption energies (E ads ) for CH 2 O/Be 12 O 12 and CH 2 O/MBe 12 O 12 complexes.It is seen that by increasing the negative EF, the value of E ads is gradually enhanced for the CH 2 O/Be 12 O 12 complex up to 3.4% at EF = −514 kV/mm with respect to their value at zero EF.Meanwhile, the values of E ads are gradually inhibited for CH 2 O/KBe 12 O 12 , CH 2 O/MnBe 12 O 12 , and CH 2 O/CuBe 12 O 12 complexes up to 4.8%, 3.6%, and 6.2%, respectively, at EF = −514 kV/mm with respect to its value at zero EF.On the other side, by increasing the positive EF, the value of E ads is gradually inhibited for the CH 2 O/Be 12 O 12 complex up to 3.1% at EF = +514 kV/mm with respect to its value at zero EF.Meanwhile, the values of E ads are gradually enhanced for CH 2 O/KBe 12 O 12 , CH 2 O/MnBe 12 O 12 , and CH 2 O/CuBe 12 O 12 complexes up to 4.2%, 3.5%, and 6.4%, respectively, at EF = +514 kV/mm with respect to their value at zero EF.Therefore, the E ads values for CH 2 O/Be 12 O 12 and CH 2 O/MBe 12 O 12 complexes are dominated by either the value or direction of the EF.These results could be explained in terms of the mechanism of CH 2 O interaction with the nano-cage.For the CH 2 O/Be 12 O 12 complex, as mentioned before, there is a charge transfer from the CH 2 O molecule to the Be 12 O 12 nano-cage.Looking at Figure 9b,c, one can see that the negative EF induces a negative ∆ρ value on the oxygen head of the CH 2 O molecule and a positive ∆ρ value on the side of the Be 12 O 12 nano-cage facing the CH 2 O molecule.This in turn encourages the charge transfer and, consequently, enhances the E ads value.In contrast, the positive electric field induces a positive ∆ρ value on the oxygen head of the CH 2 O molecule and a negative ∆ρ value on the side of the Be 12 O 12 nano-cage facing the CH 2 O molecule.This discourages the charge transfer and, consequently, inhibits the E ads value.This could be confirmed by Figure 12, which shows the NBO charges of the CH 2 O molecule (Q CH 2 O ) vs. electric field.It is clear that the positive Q CH 2 O for the CH 2 O/Be 12 O 12 complex increases as the negative EF increases and decreases as the positive EF increases.Thus, the E ads value is enhanced by increasing the negative EF and inhibited by increasing the positive EF (see Figure11).On the other side, for the CH 2 O/MBe 12 O 12 complexes, the interaction has occurred due to the charge transfer from the MBe 12O 12

Figure 12 .
Figure 12.NBO charges of CH 2 O molecule (Q CH 2 O ) vs. electric field for CH 2 O/Be 12 O 12 and CH 2 O/MBe 12 O 12 complexes.

Figure 13
Figure 13 represents the impact of the EF on the E g for the Be 12 O 12 and MBe 12 O 12 nano-cages as well as the CH 2 O/Be 12 O 12 and CH 2 O/MBe 12 O 12 complexes.It is clear that the EF has a negligible impact on the E g values of the Be 12 O 12 and MBe 12 O 12 nano-cages.Figure 13a declares that the E g value for the CH 2 O/Be 12 O 12 complex increases as the negative EF increases and decreases as the positive EF increases.On the other side, Figure 13b-d show that the E g values for the CH 2 O/KBe 12 O 12 , CH 2 O/MnBe 12 O 12 , CH 2 O/CuBe 12 O 12 complexes increase as the negative EF decreases and the positive EF increases.Therefore, according to Equation (8), the electric conductivity (σ) for the CH 2 O/Be 12 O 12 and CH 2 O/MBe 12 O 12 complexes can be controlled by the EF.Here, σ for the CH 2 O/Be 12 O 12 complexes will increase by increasing the positive EF, while for the CH 2 O/MBe 12 O 12 complexes, σ will increase by increasing the negative EF.To investigate the electrical sensitivity dependence on the EF, the percentage of the variance of E g (∆E g ) by the adsorption for CH 2 O/Be 12 O 12 and CH 2 O/MBe 12 O 12 complexes versus the EF is estimated by Equation (10) and represented in Figure 14.

Figure 14 .
Figure 14.The change percentage for HOMO-LUMO energy gap (∆E g ) vs. electric field.

Figure 16 .
Figure 16.(a) E ads and (b) Eg against the number of adsorbed CH2O molecules.

Figure 16 .
Figure 16.(a) E ads and (b) E g against the number of adsorbed CH 2 O molecules.
]. Whereas the metal encapsulation into Be 12 O 12 elongates d 1 and d 2 bonds to be 1.62 and 1.57Å for KBe 12 O 12 , 1.60 and 1.55 Å for MnBe 12 O 12 , and 1.61 and 1.55 Å for CuBe 12 O 12 .
.77%, 7.63%, and 4.01% for KBe 12 O 12 , MnBe 12 O 12 , and CuBe 12 O 12 , respectively.This indicates that the MBe 12 O 12 nano-cages are lower in stability and consequently higher in reactivity than the Be 12 O 12 nano-cage.Moreover, the E g value for Be 12 O 12 is 8.210 eV and it decreased to 0.685, 1.057, and 1.568 eV for KBe 12 O 12 , MnBe 12 O 12 , and CuBe 12 O 12 , respectively, which is in good agreement with previous studies

Table 2 .
The electronic configurations for M atom in a free state and MBe 12 O 12 nano-cages.

Table 3
lists the adsorption features of CH2O on MBe12O12 nano-cages.

Table 3
lists the adsorption features of CH 2 O on MBe 12 O 12 nano-cages.

CH 2 O/Be 12 O 12 CH 2 O/KBe 12 O 12 CH 2 O/MnBe 12 O 12 CH 2 O/CuBe 12 O 12
nano-cages as CH2O sorbent materials are more efficient than those mentioned in the previous studies.In addition, the CH 2 O adsorption decreases the E g value for Be 12 O 12 and CuBe 12 O 12 by 39.31% and 44.13%, respectively, and increases its value for KBe 12 O 12 and MnBe 12 O 12 by 87.74% and 43.42%, respectively.For a more detailed explanation of the results, NBO atomic charge analysis, charge density difference (∆ρ) analysis, QTAIM analysis, and PDOS analysis were performed.The NBO atomic charge analysis shows that for the CH 2 O/Be 12 O 12 complex, the CH 2 O molecule earns a positive charge of 0.148 e due to a charge transfer from the CH 2 O molecule to the Be 12 O 12 nano-cage.On the other side, for CH 2 O/MBe 12 O 12 complexes, the CH 2 O molecule acquires negative charges of 0.703, 0.960, and 0.960 e.Furthermore, the positive charges for K, Mn, and Cu rose by 0.347, 0.333, and 0.470 e for CH 2 O/KBe 12 O 12 , CH 2 O/MnBe 12 O 12 , and CH 2 O/CuBe 12 O 12 , respectively; i.e., a charge transfer has occurred from the MBe 12 O 12 nano-cages, mainly from the metal atom to the CH 2 O molecule.This may be owing to the lower IP value and consequently higher ability to donate electrons (higher basicity) for the MBe 12 O 12 nano-cages than the Be 12 O 12 nano-cages.Additionally, the electronic configurations of 2s and 2p orbitals for the O and C atoms of CH 2 O were estimated for the free CH 2 O, CH 2 O/Be 12 O 12, and CH 2 O/MBe 12 O 12 complexes (see Table 4).

Table 4 .
The electronic configurations for 2s and 2p orbitals for oxygen and carbon atoms of CH 2 O for free CH 2 O, CH 2 O/Be 12 O 12, and CH 2 O/MBe 12 O 12 .It is clear that the interaction of the CH 2 O molecule with the Be 12 O 12 as well as the MBe 12 O 12 nano-cages is accompanied by losing electrons from the 2s and gaining electrons to the 2p orbitals of the oxygen atom.Whereas for the carbon atom, the 2s orbital has an insignificant change in its electronic configuration, while the 2p orbital loses electrons for the CH 2 O/Be 12 O 12 complex and gains electrons for the CH 2 O/MBe 12 O 12 complexes.This means a donation-back donation mechanism has happened between the CH 2 O molecule and the nano-cages.Figure 7 demonstrates the charge density difference (∆ρ) for CH 2 O/Be 12 O 12 as well as the CH 2 O/MBe 12 O 12 complexes.One can see that the CH 2 O molecule for all the investigated complexes is surrounded by positive (blue color) and negative (red color) ∆ρ values.This means the CH 2 O molecule loses and gains charges, emphasizing the donation-back donation mechanism between the CH 2 O molecule and the nano-cages.It is worth noticing that the high dipole moment values for the CH 2 O/Be 12 O 12 and the CH 2 O/MBe 12 O 12 complexes in Table 3 refer to the charge redistribution between the CH 2 O molecule and the nano-cages.For more insight into the nature of the CH 2 O adsorption on the Be 12 O 12 as well as the MBe 12 O 12 nano-cage, the QTAIM analysis was accomplished.Figure S4, in the Supplementary Materials, shows the bond critical points (BCP) of type (3,−1) for the CH 2 O/Be 12 O 12 and the CH 2 O/MBe 12 O 12 complexes.The topological parameters are stated in

Table 5 .
r) * The atom numbering shown in the Figure6is used.
. This indicates the formation of a pure ionic bond between the O1 atom of the CH 2 O molecule and the Be1 site of the Be 12 O 12 nano-cage.Meanwhile, a weak hydrogen bond is found between the H1 atom of the CH 2 O molecule and the O2 site of the Be 12 O 12 nano-cage.For CH 2 O/MBe 12 O 12 complexes, only one BCP exists between the O1 atom of the CH 2 O molecule and the Be1 site of the MBe 12 O 12 nano-cage.This BCP has ∇ 2 ρ values of 0.858, 0.879, and 0.867, −G(r)/V(r) ratios of 1.005, 1.000, and 1.005, and H(r) values of −0.002, −0.001, and −0.001 for CH 2 O/KBe 12 O 12 , CH 2 O/MnBe 12 O 12 , and CH 2 O/CuBe 12 O 12 for the CH 2 O/MBe 12 O 12 complexes explain the higher adsorption of the CH 2 O molecule than the CH 2 O/Be 12 O 12 complex.Figure 8 depicts the HOMO and LUMO surfaces and the PDOS for the CH 2 O molecule, CH 2 O/Be 12 O 12 , and CH 2 O/MBe 12 O 12 complexes.Figure 8a shows four occupied states of the CH 2 O molecule located at −7.30, −10.86, −12.24, and −13.44 eV.Looking at Figure 8b-e, obvious changes in the occupied states of the CH 2 O molecule indicate a strong reaction between the CH 2 O and the nano-cages.Regarding Figure 8b, one can see the HOMO of Be 12 O 12 rises to −7.87 eV and an acceptor state is created at −2.89 eV; thus, the E g value decreases from 8.21 to 4.98 eV.Looking at Figure 4b-d, it is obvious that there are occupied states located at −2.13, −2.28, and −3.54 eV, which are attributed to the metal atoms for KBe 12 O 12 , MnBe 12 O 12 , and CuBe 12 O 12 , respectively.As seen in Figure 8c-e, these states disappear for the complexes CH 2 O/KBe 12 O 12 , CH 2 O/MnBe 12 O 12 , and CH 2 O/CuBe 12 O 12 .This confirms that the adsorption of the CH 2 O leads to a charge loss from the metal atom.Additionally, new occupied states assigned to CH 2 O appear at −2.67, −3.01, and −2.90 eV for CH 2 O/KBe 12 O 12 , CH 2 O/MnBe 12 O 12 , and CH 2 O/CuBe 12 O 12 , respectively.This confirms that the adsorption of the CH 2 O leads to a charge transfer from the MBe 12 O 12 to the CH 2 O molecule.Furthermore, the adsorption of the CH 2 O molecule causes a shift for LUMO states from −1.44, −1.22, and −1.98 eV to −1.38, −1.49, and −2.02 eV for KBe 12 O 12 , MnBe 12 O 12 , and CuBe 12 O 12 , respectively.Accordingly, the E g values increase from 0.69 and 1.06 eV to 1.29 and 1.52 eV for KBe 12 O 12 and MnBe 12 O 12 nano-cages, respectively, while E g value decreases from 1.57 to 0.88 eV for CuBe 12 O 12 nano-cage.Consequently, due to the CH 2 O adsorption and Equation (8), the electrical conductivity is increased for the Be 12 O 12 and CuBe 12 O 12 , whereas it is decreased for the KBe 12 O 12 and MnBe 12 O 12 .Therefore, the Be 12 O 12 and CuBe 12 O 12 nano-cages can be utilized as electrical sensors for the CH 2 87.8%, 38.9%, and −44.1% for CH 2 O/Be 12 O 12 , CH 2 O/KBe 12 O 12 , CH 2 O/MnBe 12 O 12 , and CH 2 O/CuBe 12 O 12 complexes, respectively.It is clear that the variance in value and the direction of the EF has a negligible effect on ∆E g for the CH 2 O/Be 12 O 12 complex.Whereas for the CH 2 O/KBe 12 O 12 , CH 2 O/MnBe 12 O 12 , and CH 2 O/CuBe 12 O 12 complexes, as the negative EF increases, the ∆E g values are lowered, reaching 58.2%, 24.4%, and −55.0%, as the positive EF increases, the ∆E g values are rising, reaching 114.2%, 53.4%, and −34.4%, respectively.Therefore, the electrical sensitivity of Be 12 O 12 to the adsorption of CH 2 O molecules is independent of the EF, while the electrical sensitivity of MBe 12 O 12 depends on the EF.
shows that the CuBe 12 O 12 nano-cage is optically active in the visible region with a λ max value of 431 nm.Meanwhile, the CH 2 O/CuBe 12 O 12 has peaks in the visible region at 452 and 596 nm at an EF value of −514 kV/mm, 332, 429, and 563 nm at an EF value of 0 kV/mm, and 328, 408 and 528 nm at an EF value of +514 kV/mm.From the above discussion, one can summarize the following: (i) the adsorption of a CH 2 O molecule affects the UV-vis spectra of Be 12 O 12 as well as the MBe 12 O 12 .(ii)TheEF has no effect on the UV-vis spectra of Be 12 O 12 as well as the MBe 12 O 12 .(iii)TheEF has an obvious effect on the UV-vis spectra of CH 2 O/Be 12 O 12 as well as CH 2 O/MBe 12 O 12 .In other words, the adsorption of the CH 2 O molecule causes changes in the colors of the MBe 12 O 12 nano-cages; consequently, they could be employed as bare-eye sensors for the CH 2 O molecule.3.5.Effect of ConcentrationThis section concerns the impact of CH 2 O concentration on the adsorption characteristics.The adsorption of n molecules (n = 1-6) on the surface of the MBe 12 O 12 was investigated to form nCH 2 O/MBe 12 O 12 complexes.The nCH 2 O/MBe 12 O 12 complexes were fully optimized.The adsorption energies per molecule (E ads ) were estimated by Equation ( 2 O adsorption decreases the E g value for Be 12 O 12 and CuBe 12 O 12 by 39.31% and 44.13%, respectively, and increases its value for KBe 12 O 12 and MnBe 12 O 12 by 87.74% and 43.42%, respectively.It is found that the existence of an external static electric field (EF) can enhance or inhibit the adsorption energies of CH 2 O molecules on the Be 12 O 12 as well as the MBe 12 O 12 nano-cages, depending on the value and the orientation of the EF.Furthermore, the EF has an obvious influence on the E g of CH 2 O/MBe 12 O 12 complexes and, consequently, on their electrical conductivity.Thus, the electrical sensitivity of MBe 12 O 12 nano-cages to CH 2 O gas can be controlled via EF.Moreover, the CH 2 O adsorption makes a red shift for the UV-vis spectrum of the Be 12 O 12 and causes obvious changes in the absorption peaks of the MBe 12 O 12 nano-cages in the visible region.Additionally, the EF has an obvious effect on the UV-vis spectra of CH 2 O/Be 12 O 12 as well as the CH 2 O/MBe 12 O 12 complexes.Based on these results, the Be 12 O 12 as well as the MBe 12 O 12 nano-cages are candidate materials for removing and sensing the formaldehyde gas.The MBe 12 O 12 nano-cages may be utilized as electrochemical and naked-eye sensors for CH 2 O gas.