Carbon monoxide interactions with pure and doped B₁₁XN₁₂ (X = Mg, Ge, Ga) nano-clusters: a theoretical study

Abstract

The goal of this investigation was to study a novel sensor for detecting the toxic gas compounds of CO using B₁₁XN₁₂ (X = Ge, Mg, and Ga) nano-clusters in terms of its energetic, geometric, and electronic structure using DFT calculations by the PBE-D method. The reaction of CO gas with these doping atoms results in a weak interaction and an elongation of X–N bond of B₁₁XN₁₂ nano-clusters. After the adsorption of CO gas over the doped positions of B₁₁XN₁₂ nano-cluster, the conductivity of the adsorbent and the atomic charges in some of the nearby B and N atoms around X atoms were dramatically enhanced. These calculations represent the capabilities of the B₁₁XN₁₂ nano-clusters in designing novel materials based on B₁₁XN₁₂ for potential applications in gas sensing.

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1. Introduction

Carbon monoxide or CO is an extremely poisonous gas to human and animal bodies when encountered in concentrations above 35 ppm. It is a colourless, poisonous and odourless gas; these characteristics make it one of the most fatal gases with a significant role in air pollutants and in human daily life. Due to increasing concern over the safety and health hazards related to this gas, there is an increasing demand of CO sensors.^1–3 Thus, theoretical studies regarding the adsorption and dissociation of CO molecule using the Rh-decorated SWCNT,⁴ Fe–B₁₈N₁₈ cluster,⁵ Al–graphitic boron nitride sheet,⁶ Al/Ga-doped BN nanotube,⁷ FeCo alloy (110) surface,⁸ ZnO (1010) surface,⁹ B₁₂N₁₂ nano-cage,¹⁰ doped h-BN monolayer,¹¹ and transition metal doped BN nanotube¹² have been reported. In particular, theoretical studies have shown that some metal-doped BN nanostructures are promising candidates to act as chemical sensors.^13–17 During the last decade, various types of BN-based nanostructures consisting of nanotubes, nanohorns, nanoparticles, nanosheets, and nano-cages, have attracted considerable attention due to their unique chemical and physical properties.^18–20 B₁₂N₁₂ is one of the known stable class of small III–V nano-clusters with the network of B–N bonds, which is energetically favorable. The 4-membered rings of B₁₂N₁₂ consist of the B–N bonds, which result in angular strain in the network. Since then, B_iN_i clusters have been widely investigated both theoretically and experimentally.^21–26 Recently, Oku et al.²⁷ synthesized B₁₂N₁₂, which can be detected by laser desorption time-of-flight mass spectrometry. Their study indicated that a BN nano-cluster is a structure built from four squares and six hexagons rings. In addition, Matxain and co-workers theoretically studied the electronic structure and the energy differences between covalent and van der Waals dimers using the hybrid B3LYP and MPW1PW91 density functional theory.²⁸ Li et al. proposed bonding character and electronic structure of B₁₂C₆N₆ fullerene using ab initio calculations.²⁹ They found that replacing an N atom with a C atom in the B₁₂N₁₂ nano-cage results in a decrease of the cluster energy gap. Bahrami and co-authors reported a theoretical study of amphetamine adsorption upon the pure P-doped and Al-doped B₁₂N₁₂ nano-cage at the M06-2X/6-311++G** level of theory.³⁰ Based on their results, the pure B₁₂N₁₂ nano-cage has a better condition for detecting amphetamine compared with the P-doped and Al-doped B₁₁N₁₂ nano-cage. Doping in BN nanomaterials can outstandingly alter the electronic properties, which can be utilized to develop its sensing applicability. Previous reports demonstrated the reaction of different molecules with the pure and doped metal BN nanostructures using DFT calculations.^31–33 In this study, we investigated the interaction of CO molecule with the pure Ga, Ge, and Mg atoms of B₁₁XN₁₂ nano-clusters to find whether these adsorbents can be used as a gas sensor in environmental monitoring using DFT calculations.

2. Computational details

To study the structural parameters and electronic properties of the pure B₁₁XN₁₂ (X = Ge, Mg, and Ga) nano-cluster and that interacted with a CO molecule, we carried out density functional theory (DFT) calculations. The goal is to calculate equilibrium geometries, adsorption energies, Mulliken population charge analysis (MPA), molecular electrostatic potential (MEP), frontier molecular orbital (FMO), and density of states (DOS) analyses for these complexes. All the geometry optimizations and energy calculations were performed using GAMESS software³⁴ at the level of density functional theory (DFT) using PBE functional augmented with an empirical dispersion term (PBE-D) and 6-311G** standard basis set. Moreover, the corresponding optical adsorption spectra were obtained through time-dependent density functional theory (TD-DFT) calculations in the gas phase regime.^35–37 The relaxed structures were further subjected to the computations for harmonic vibrational frequencies at the PBE functional. For all the systems, the SCF convergence limit was set to 10⁻⁶ a.u. over energy and electron density. The basis set superposition error (BSSE) for the adsorption energy was corrected by implementing the counterpoise method.^38,39 The adsorption energies (E_ad) for each of the structures were determined at 298.15 K and 1 atm using the following formulae:

E_ad = E_B12N12–CO − (E_B12N12 + E_CO) + E_BSSE (1)

E_ad = E_B11XN12–CO − (E_B11XN12 + E_CO) + E_BSSE (2)

where E_B11XN12–CO is the total energy of the B₁₁XN₁₂ nanocage interacting with the CO molecule. E_nano-cage and E_TM-nano-cage are the total energies of the pure and B₁₁XN₁₂, respectively, and E_CO is the total energy of an isolated CO molecule. The electrophilicity index (ω) concept was stated for the first time by Parr et al.^40,41 Chemical potential (μ) is defined according to the following equation:

μ = −χ =−1/2(I + A) (3)

Electronegativity (χ) is defined as the negative of chemical potential, as follows: χ = −μ. According to Koopmans theorem,⁴² chemical hardness (η) can be approximated by the following equation:

η = 1/2(I − A) (4)

I(−E_HOMO) is the ionization potential and (−E_LUMO) is the electron affinity of the molecule. E_HOMO is the energy of the highest occupied molecular orbital and E_LUMO is the energy of the lowest unoccupied molecular orbital of the considered structure. Softness (S) and electrophilicity index are determined by the following equations, respectively:

S = 1/2η (5)

ω = (μ²/2η) (6)

3. Results and discussion

First, the B₁₂N₁₂ nano-cage was optimized as an adsorbent for detection of CO molecule at the gas phase using PBE-D method and 6-311G** standard basis set (see Fig. 1). Then, two stable states of the CO adsorption were considered, which locates the C and O over top of a B atom of B₁₂N₁₂ nano-cage. When CO molecule is adsorbed from C and O heads toward the boron atom of the adsorbent, the adsorption energies and distances of CO physisorption are −0.27 eV (II: 1.655 Å) and −0.06 eV (III: 3.176 Å) respectively (Table 1). Regarding previous studies, the adsorption of a CO molecule over (5, 5) SWCNT and capped CNT in their most stable states are about −0.147 and −0.02 eV.^1,43 Baierlea et al. and Beheshtian et al. showed that the BN nanotubes have physical interactions with CO molecule in the range of about −0.13 and −0.06 eV.^13,44 Our results were in agreement with the study of Beheshtian and co-workers, who reported a DFT study of CO molecule in reaction with B₁₂N₁₂ nano-cluster.¹⁰ They showed that CO can be adsorbed over the nano-cluster with the adsorption energy of 0.15–0.30 eV. It was found that the length of C≡O bond (1.1386 Å at the PBE-D) after reaction with B₁₂N₁₂ is slightly smaller than that of a free CO molecule (1.357 Å), which is close to the reported experimental value of 1.128 Å.⁴⁵ By Mulliken charge analysis, a charge transfer of about 0.172e (C head) and 0.019e (O head) occurs from CO molecule (electron donor) to B₁₂N₁₂ nano-cluster. In Fig. 1, the density of states are shown for the different CO-adsorptions over the B₁₂N₁₂ nano-cluster discussed above. Compared with the DOS of the pristine nano-cluster, the adsorption of CO molecule alters the electronic structure of B₁₂N₁₂, as shown in Fig. 1. This indicates a remarkable change (II) of energy gap (E_g) of about 45.8%. The DOS plots of the complex clearly reveal that the LUMO level has a distinct change after the adsorption process.

Fig. 1 Optimized structures and density of state spectra of CO and B₁₂N₁₂ nano-clusters.

Table 1 Calculated bond length, adsorbate-surface distance D/Å, adsorption energy E_ad/eV, HOMO energies (E_HOMO/eV), LUMO energies (E_LUMO/eV), dipole moment (DM/Debye), Fermi level energies (E_F/eV) and HOMO–LUMO energy gap (E_g/eV) for the pure B₁₂N₁₂ nano-cluster

System	Ead/eV	D/Å	C–O/Å	B–N/Å	EHOMO/eV	Eg/eV	ELUMO/eV	ΔEg%	EF/eV	DM/Debye
CO	—	—	1.1386	—	−8.87	7.03	−1.84	—	−5.36	0.226
I	—	—	—	1.493	−6.91	5.0	−1.91	—	−4.41	0.00
II	−0.27	1.655	1.136	1.563	−6.52	2.71	−3.81	−45.8	−5.17	3.62
III	−0.06	3.176	1.139	1.495	−6.90	4.81	−2.09	−3.80	−4.50	0.182

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In this stage, first, the optimized structures and density of states of the perfect B₁₂N₁₂ nano-cluster with doped transition metal atoms containing Mg, Ge, and Ga are used to calculate the adsorption of a CO molecule, as shown in Fig. 2. The length of Mg–N, Ge–N, and Ga–N bonds of the doped nano-cluster are calculated with values of 2.079, 1.946, and 1.921 Å, respectively. In a similar study, Li et al. generated a similar structure by replacing N with C atom in the B₁₂N₁₂ nano-cage using ab initio calculations.²⁹ Soltani et al.⁷ determined the length of a Ga–N bond of a B₁₁XN₁₂ nano-cage to be about 2.072 Å. As reported in Table 2, the angles of the N–Mg–N, N–Ge–N, and N–Ga–N bonds of B₁₁XN₁₂ nano-cluster were found to be about 69.66°, 76.92°, and 79.76°, respectively. As shown in Fig. 2, all the doped systems with Mg, Ge, and Ga atoms in B₁₁XN₁₂ nano-cluster belong to C_s point group, while the point group symmetry of B₁₂N₁₂ nano-cage is T_h.⁴⁶ In the B₁₁XN₁₂ nano-cluster, metal atoms move slightly out of the cluster form leading to a significant change of the local geometry of the nano-cluster. The point charges over the Mg, Ge, and Ga atoms in B₁₁XN₁₂ nano-cluster are 0.621, 0.720, and 0.739e, while the corresponding values for N atoms are about −0.522, −0.512, and −0.503e, respectively. To better understand the properties of crucial transition states for the X-doped B₁₁XN₁₂ nano-cluster, we plotted frontier molecular orbitals (HOMO and LUMO) for these systems. These orbitals play an important role in governing many chemical reactions, and they are also responsible for charge transfer properties (see Fig. 3). By comparison, it is found that the HOMO and LUMO energy levels can be significantly changed due to doping atoms because the energy gap of the nanoclusters reduces in the process of CO adsorption. From HOMO and LUMO analysis, it is easily seen that there is a uniform shift of the HOMO level to the upper energy region due to the mutual charge transfer and the interaction between N atoms of the nano-cluster and dopant atoms.

Fig. 2 Optimized structures, infrared and density of state spectra of B₁₁XN₁₂ nano-clusters.

Table 2 The obtained structural parameters for a single CO adsorption over the pure and B₁₁XN₁₂ nano-clusters

System	RC=O	RGa–N	RGe–N	RMg–N	RN–Ga–N	RN–Ge–N	RN–Mg–N
GaB11N12	—	1.921	—	—
State I	1.144	1.923	—	—	117.889	—	—
State II	1.133	1.938	—	—	114.828	—	—
State III	1.132	1.937	—	—	114.707	—	—
State IV	1.137	1.910	—	—	120.488	—	—
GeB11N12	—		1.946
State I	1.164	—	1.922	—	—	107.243	—
State II	1.140	—	1.947	—	—	105.975	—
State III	1.137	—	1.934	—	—	107.591	—
State IV	1.138	—	1.890	—	—	105.814	—
MgB11N12	—			2.079
State I	1.132	—	—	2.098	—	—	105.671
State II	1.138	—	—	2.064	—	—	105.079
State III	1.146	—	—	2.088	—	—	110.126
State IV	1.203	—	—	2.010	—	—	106.710

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Fig. 3 Crucial transition states of B₁₁XN₁₂ structures with the largest component coefficient marked.

The next stage involved search for a suitable nano-cluster for CO detection. After full optimization, adsorption states of CO molecule over the X-doped B₁₂N₁₂ nano-cluster using PBE method were studied and are reported in Table 3. This method has shown to obtain reasonable results for dative B–N bonds in comparison with other methods.⁴⁷ In these interactions (Fig. 4–6), the CO molecule has electrostatic contact with the X-doped B₁₂N₁₂ nano-clusters. The observed trend for the B₁₁GaN₁₂ nano-cluster with CO molecule was found to be III > II > IV > I. In contrast, these values in the B₁₁MgN₁₂ were found to be III > I > II > IV, which means that the B₁₁MgN₁₂ is more stable than B₁₁GaN₁₂, whereas CO molecule is physisorbed toward B₁₁GeN₁₂ nano-cluster, which mainly stems from the van der Waals interaction, as can be seen in Table 3. According to the relative energy values, B₁₁GeN₁₂ is the least stable among all the species that interacted with the CO molecule. The minus value of adsorption energy in the interaction between adsorbent and adsorbate, representing that the CO molecule configuration has a very weak physical bond with the doping atoms of the nano-cluster. The weak type of interactions between adsorbate and adsorbent can be remarkable in gas detection because such ineffective interactions represent that the desorption of the adsorbate could be easy and the device can benefit from short recovery times.⁴⁸ If E_ad is significantly decreased, considerable shorter recovery time is expected. τ = υ₀⁻¹e^{(−E_ad/k_BT)}, where T is temperature, k_B is the Boltzmann constant (8.62 × 10⁻⁵ eV K⁻¹), and υ₀ is the attempt frequency. According to this equation, the B₁₁XN₁₂ nano-cluster should be a good CO sensor with quick response as well as short recovery time. Upon the interaction of the CO molecule with X-doped B₁₂N₁₂ nano-cluster, the Mg–N, Ga–N, and Ge–N bond lengths shift to 2.098, 1.938, and 1.890 Å, respectively, with a resulting change in hybridization from sp² to sp³. As a result, the adsorption of CO over the B₁₁GaN₁₂ and B₁₁MgN₁₂ nano-clusters leads to the elongation of the bond length but in the B₁₁GeN₁₂, it shortens the bond-length (Table 2). Bahrami and co-workers studied the effects of Al-doped and P-doped B₁₂N₁₂ nano-cage at the M06-2X method.³⁰ They showed that the distance between the Al and the N atoms is about 1.97 Å. In addition, they reported that the adsorption of amphetamine on the surfaces of the perfect Al-doped and P-doped B₁₂N₁₂ nano-cages are found at −1.63, −2.48, and −0.33 eV, respectively. The results of these reports revealed that the Al-doped B₁₁N₁₂ can be used as an adsorbent in the environmental system.

Table 3 Calculated bond length, adsorbate-surface distance D/Å, adsorption energy E_ad/eV, HOMO energies (E_HOMO/eV), LUMO energies (E_LUMO/eV), work function (Φ/eV), dipole moment (DM/Debye), Fermi level energies (E_F/eV) and HOMO–LUMO energy gap (E_g/eV) for X-doped B₁₁N₁₂ nano-cluster

System	Ead/eV	D/Å	EHOMO/eV	Eg/eV	ELUMO/eV	ΔEg%	EF/eV	Φ/eV	DM/Debye
GaB11N12	—	—	−7.47	3.74	−3.73	—	−5.60	1.87	2.654
State I	−0.200	2.511	−6.36	2.83	−3.53	24.33	−4.95	1.42	6.492
State II	−0.657	2.148	−6.17	1.45	−4.72	61.23	−5.44	0.72	6.478
State III	−0.668	2.148	−6.19	1.45	−4.70	60.16	−5.44	0.74	2.556
State IV	−0.221	1.671	−6.28	5.023	−3.81	33.96	−5.04	1.23	4.562
GeB11N12	—	—	−6.38	4.41	−1.97	—	−4.18	2.21	1.673
State I	−0.132	2.179	−4.423	2.88	−1.54	−34.74	−2.98	1.44	1.577
State II	−0.067	3.476	−3.981	2.34	−1.64	−46.82	−2.81	1.17	1.188
State III	−0.163	1.685	−6.288	4.93	−1.36	11.68	−3.83	2.47	1.8203
State IV	−0.059	3.466	−6.270	4.73	−1.54	7.26	−3.91	2.37	1.840
MgB11N12	—	—	−6.10	3.14	−2.96	—	−4.53	1.57	5.249
State I	−0.589	2.270	−5.86	1.44	−4.42	54.14	−5.14	0.72	7.246
State II	−0.356	2.351	−5.90	4.741	−4.21	46.18	−5.0	0.79	5.38
State III	−0.871	1.681	−5.92	2.93	−2.99	6.69	−4.45	1.46	6.85
State IV	−0.073	1.358	−5.90	2.41	−3.49	23.25	−4.70	1.21	4.061

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Fig. 4 Optimized structures, infrared and density of state spectra of B₁₁MgN₁₂ nano-clusters interacting with a CO molecule.

Fig. 5 Optimized structures, infrared and density of state spectra of B₁₁GaN₁₂ nano-clusters interacting with a CO molecule.

Fig. 6 Optimized structures, infrared and density of state spectra of B₁₁GeN₁₂ nano-clusters interacting with a CO molecule.

To better understand the nature of CO adsorption over the electronic properties of adsorbent, we have carried out the electronic density of states (DOSs) analysis. The GaussSum program was used to obtain DOS results.⁴⁹ The DOS spectrum of these structures represent the HOMO–LUMO gaps of the X-doped BN nano-clusters. E_g of Mg-doped, Ga-doped, and Ge-doped B₁₂N₁₂ nano-clusters are 3.14, 3.74, and 4.41 eV, while this value in the pure nano-cluster is about 5.0 eV. However, there is noticeable change in resistivity when the E_g for structures is decreased when compared to that of B₁₂N₁₂ nano-cluster. Oku and co-workers experimentally determined that the energy gap of the pure B₁₂N₁₂ nano-cluster is about 5.1 eV between HOMO and LUMO.²⁷ Thus, the accuracy of the theoretical calculation is close to the experimental data as mentioned above. In the most stable configurations, after the CO adsorption toward the Mg, Ga, and Ge atoms of B₁₁XN₁₂ nano-clusters, ΔE_g of these configurations significantly changed by about 54.14%, 61.23%, and 46.82%, respectively. This result implies that the electronic properties of the B₁₁GaN₁₂ nano-cluster are very sensitive to the CO adsorption in comparison with the pure B₁₂N₁₂ nano-cluster. Zhang et al. have shown that the graphitic BN sheet that by replacing Al-dopant and defects have high sensitive to the CO gas compared to the pure model.⁶ Moreover, their results indicated that the vacancy-defect g-BN has more change of energy gap than Al-dopant g-BN. As seen in Table 3, DOS spectrum in the CO/B₁₁GaN₁₂ complex (State II) near both of the valence and conduction levels have distinct changes in comparison with that in the B₁₂N₁₂. The valence level (−3.981 eV) of the CO/B₁₁GeN₁₂ complex (State II) exhibits a distinct change when compared to that of B₁₂N₁₂ (−6.38 eV). DOS spectrum for the CO/B₁₁GeN₁₂ complex (State I) revealed that the conduction level (−4.42 eV) of this complex exhibits a distinct change in comparison with that of B₁₂N₁₂ (−2.96 eV). This reports leads to a slight reduction in the work function that is important in the field emission applications. The values of Φ for the adsorption of CO gas, in the most stable models (Table 3), upon the Mg, Ga, and Ge atoms of B₁₁XN₁₂ nano-cluster are considerably decreased from 1.57, 1.87, and 2.21 eV to 0.72 (State I), 0.72 (State II), and 1.17 eV (State II), respectively. The decrement in the work function (Φ) values reveals that the field emission properties of the nano-clusters are more noticeable on the adsorption of CO gas because the electrons can be pulled from the surface more easily.^50,51 In Fig. 7, the crucial excited states for the interaction of CO molecule with B₁₁XN₁₂ nano-cluster are provided, where the electron cloud in their LUMO, LUMO+3, and LUMO+5 are dominant over the CO molecule, while electron cloud in their HOMO orbitals do not have the same distribution of the electron density. To explore the interaction mechanism between CO and the B₁₁XN₁₂ nano-cluster, we studied molecular electrostatic potential (MEP) maps for these processes, where the positive charges over the X-doped B₁₂N₁₂ nano-cluster are represented by the blue colors (see Fig. 8). MEP plots are computed at an isovalue of 0.0004 e au⁻³. As demonstrated in these configurations, the CO molecule with blue color (positive charge) acts as an electron donor in the adsorption process. Most negative and natural regions of the MEP plots are colored yellow and green, respectively. Table 4 implies to the values of the quantum molecular descriptors computed for the adsorption of CO gas toward the B₁₁XN₁₂ nano-cluster. When CO gas reacts with the Mg-, Ga-, and Ge-doped B₁₂N₁₂ nano-cluster, the global hardness in the position of Ga and Mg dopants have the highest amount of hardness, while the lowest amount is in relation with the Ge dopant. In addition, when CO gas interacts with the B₁₁XN₁₂ nano-cluster, the η values have significant gain from 1.87, 1.57 and 2.21 eV in the Ga-, Mg-, and Ge-doped B₁₂N₁₂ nano-cluster to 2.54 eV (III), 2.59 eV (V), and 2.56 eV (V) after the adsorption of CO, respectively (see Table 4). For the suitable species, B₁₁GaN₁₂/CO, the global hardness of the complex is significantly increased and the electrophilicity of the complex is significantly reduced, indicating that the reactivity of the complex is decreased and also indicating that the stability of the complex is increased.⁵² The electrophilicity index of the Ga-, Mg- and Ge-doped B₁₂N₁₂ nano-clusters were higher than that of the CO molecule, suggesting a charge transfer from adsorbate to adsorbent.^53–55

Fig. 7 Crucial transition states of the B₁₁XN₁₂ structures interacting with CO with the largest component coefficient marked.

Fig. 8 Calculated electrostatic potentials with a density isosurface of 0.0004 electrons au⁻³. The scale bar is in atomic units.

Table 4 Calculated quantum molecular descriptors for the CO molecule interacting with the B₁₁XN₁₂ nano-cluster

System	I/eV	A/eV	η/eV	μ/eV	ω/eV	χ/eV	S/eV
GaB11N12	7.47	3.73	1.87	−5.6	8.38	5.6	0.27
State I	6.16	1.244	2.46	−3.70	2.79	3.70	0.20
State II	6.38	1.383	2.49	−3.88	3.02	3.88	0.20
State III	6.57	1.483	2.54	−4.03	3.18	4.03	0.196
State IV	6.310	1.287	2.51	−3.80	2.87	3.80	0.199
State V	6.482	1.197	2.64	−3.84	2.79	3.84	0.189
GeB11N12	6.38	1.97	2.21	−4.18	3.95	4.18	0.226
State I	4.423	1.545	1.44	−2.98	3.09	2.98	0.347
State II	3.981	1.636	1.17	−2.81	3.63	2.81	0.426
State III	6.288	1.363	2.46	−3.83	2.97	3.83	0.203
State IV	6.270	1.540	2.37	−3.91	3.22	3.91	0.211
State V	6.328	1.212	2.56	−3.77	2.78	3.77	0.195
MgB11N12	6.10	2.96	1.57	−4.53	6.53	4.53	0.318
State I	5.901	1.086	2.41	−3.49	2.53	3.49	0.207
State II	5.948	1.207	2.37	−3.58	2.70	3.58	0.210
State III	5.958	0.990	2.48	−3.47	2.43	3.47	0.201
State IV	6.178	1.318	2.43	−3.75	2.89	3.75	0.205
State V	6.077	0.903	2.59	−3.49	2.35	3.49	0.193

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In addition, to investigate the stability of X-doped B₁₂N₁₂ nano-clusters, the calculation of the harmonic frequencies for all the adsorption models is needed. The vibrational frequencies of the Mg–N, Ga–N, and Ge–N in B₁₁XN₁₂ nano-clusters are at 590, 610 and 562 cm⁻¹, respectively. IR vibrational spectrum indicates two active vibration modes (B–N bond) of B₁₂N₁₂ at 755 and 1375 cm⁻¹ by the PBE-D method, which are in good agreement with the corresponding theoretical values of 1294 and 825 cm⁻¹ by Pokropivny et al.⁵⁶ and 1649 and 909 cm⁻¹ by Jensen and Toftlund.⁵⁷ Calculations over CO/B₁₁MgN₁₂ complex shows that the bond at 2190 cm⁻¹ can be assigned to C–O molecule, while the values appearing at 1922 and 2159 cm⁻¹ corresponds to the C–O stretching mode (from C head) of the CO adsorbed over B₁₁GeN₁₂ and B₁₁GaN₁₂ nano-clusters, respectively.

Herein, we use a TD-PBE/6-311G** calculation to study the optical properties of a CO molecule interacting with the B₁₁XN₁₂ nano-cluster.⁵⁸ In Table 5, we have presented the lowest excitation modes of the four most stable configurations of the adsorbing CO systems. For pure B₁₁GaN₁₂ systems, we have two considerable peaks at the energies of 2.44 and 2.66 eV because they are related to the H−1− > L and H−2− > L vertical transitions. In this case, the H → L transition has very low intensity, which shows the wave functions of the HOMO and excitation modes to the adsorption state. As for I and IV states, the first excitation energy interval is between 2.54–2.85 eV, while for II and III states, the lowest excitation energy range is about 1.5 eV. In all the considered CO adsorbed states, the contribution of the H → L excitation has a noticeable growth. Similar trends also can be seen in corresponding Mg- and Ge-doped systems. Although the lowest excitation modes have a red shift in comparison with Ga-doped BN nanocage, in these cases, HOMO and LUMO have similar radial distribution on the cluster, which consequently results in low dipole moment and oscillation strength.

Table 5 Selected excitation energies (eV, nm), oscillator strength (f), and relative orbital contributions calculated with the PBE method

Methods	Energy/eV	Wavelength/nm	Oscillator strength (f)	Assignment
a H and L are the highest occupied (HOMO) and lowest unoccupied molecular orbitals (LUMO), respectively.
Ga doping	2.44	508	0.0040	H−1 → L^a (100%)
	2.66	465	0.0070	H−2 → L (100%)
State I	2.85	435	0.0016	H → L+1 (100%)
	2.90	428	0.0002	H−1 → L (100%)
State II	1.52	817	0.0084	H → L (99%)
	1.54	804	0.0003	H−1 → L (99%)
State III	1.51	818	0.0035	H → L (96%)
	1.53	806	0.0003	H−1 → L (99%)
State IV	2.54	488	0.0004	H−1 → L (100%)
	2.82	439	0.0105	H−2 → L (99%)
Mg doping	0.66	1891	0.0010	H → L (100%)
	1.17	1061	0.0006	H−1 → L (99%)
State I	0.71	1740	0.0011	H → L (100%)
	1.22	1013	0.0008	H−1 → L (99%)
State II	0.70	1780	0.0012	H−1 → L (99%)
	1.21	1024	0.0008	H−2 → L (64%)
State III	0.75	1646	0.0005	H−1 → L (99%)
	1.12	1101	0.0007	H−2 → L (98%)
State IV	1.47	840	0.0016	H−1 → L (100%)
	1.76	703	0.0020	H−2 → L (100%)
Ge doping	1.352	917	0.0020	H−1 → L (100%)
	1.433	865	0.0014	H−2 → L (100%)
State I	1.973	628	0.0001	H → L (98%)
	2.09	593	0.0032	H−1 → L (100%)
State II	1.46	848	0.0006	H−1 → L (100%)
	1.61	772	0.0021	H−2 → L (100%)
State III	1.41	878	0.0020	H−1 → L (100%)
	1.48	835	0.0011	H−2 → L (100%)
State IV	1.40	887	0.0020	H−1 → L (100%)
	1.47	842	0.0012	H−2 → L (100%)

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4. Summary

We have carried out density functional theory calculations over the adsorption of CO gas upon the Mg-, Ge-, and Ga-doped B₁₂N₁₂ nano-cluster. It was found that CO gas is weakly adsorbed over the B₁₁XN₁₂ nano-cluster due to van der Waals interaction between CO and the adsorbent. In addition, a slight reduction of the charge transfers in the adsorption process from CO to B₁₁XN₁₂ nano-cluster in comparison with the pure nano-cluster was observed. From the calculated results, we conclude that the electronic structure of the B₁₁GaN₁₂ undergoes a dramatic change after the CO adsorption process in comparison with the B₁₁MgN₁₂ and B₁₁GeN₁₂ nano-clusters. The B₁₁GaN₁₂ nano-cluster can act as a suitable sensor in the detection of CO gas by significantly changing the energy gap and work function of an adsorbent.

Acknowledgements

We thank the Sayad Shirazi Hospital, Golestan University of Medical Sciences, Gorgan, Iran. We also thank the Jaber Ebne Hayyan Unique Industry researchers Company, Gorgan city, Iran.

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