Influences of adsorptions of some inorganic molecules on electronic, optical, and thermodynamic properties of Mg<sub>12</sub>O<sub>12</sub> nanocage: A computational approach

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Hesari Asghar Mohammadi, Shamlouei Hamid Reza. Influences of adsorptions of some inorganic molecules on electronic, optical, and thermodynamic properties of Mg₁₂O₁₂ nanocage: A computational approach. Chinese Physics B, 2018, 27(8): 084210 Copy to clipboard

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Influences of adsorptions of some inorganic molecules on electronic, optical, and thermodynamic properties of Mg₁₂O₁₂ nanocage: A computational approach

Hesari Asghar Mohammadi, Shamlouei Hamid Reza^†

Chemistry Department, Lorestan University, Khorram Abad, Lorestan, Iran

† Corresponding author. E-mail: shamlouei.ha@lu.ac.ir

Abstract

According to density functional theory, we investigate the effects of BF₃, BF₄, BCl₃, AlF₃, AlCl₃, AlBr₃, BeF₃, GaF₃, GaCl₃, GaBr₃, NO₃, BS₂, BSO, BO₂, F₂, PF₅, PCl₅, and ASF₅ molecules on the geometric, electronic, linear, and nonlinear optical properties of an Mg₁₂O₁₂ nanocage. The thermodynamic stability and feasibility of the adsorption process are investigated by analyzing the free energy. It is shown that the adsorptions of almost all molecules on the Mg₁₂O₁₂ surface are exothermic. The calculations of the polarizability of these nanoclusters show that among the studied molecules, BeF₃ has the largest influence on the polarizability value (α ≈ 315 a.u., the unit a.u. is short for atomic unit). The static first hyperpolarizability (β₀) value is increased in the presence of these superhalogens. This increase is greatest for BeF₃ and BF₄ of which the highest value of the first hyperpolarizability (β₀ ≈ 5775 a.u.) is related to a BeF₃_c(e@Mg₁₂O₁₂) nanocluster. The adsorption position is a key to estimating the value of increasing the first hyperpolarizability.

PACS: 42.70.Mp

Keyword:Mg₁₂O₁₂ ;polarizability;hyperpolarizability;binding energy;nanocage;DFT calculation

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1. Introduction

Nonlinear optics (NLO) is a branch of optics that describes the nonlinear relationship between dielectric polarization P and electric field E. Nonlinear optical materials have been the subject of broad research in the past few decades because of their potential applications in technological applications such as optical switching, signal processing, information storage, optical communication, laser technology, and chemical and biological species detection.^[1,2]

The systematic study of the NLO properties really become possible since the invention of the laser. The first nonlinear optical laser experiment was performed by Franken et al. by using a ruby laser. They discovered the second harmonic generation (SHG), in which nonlinear optical material mediates the adding-up of two photons with the same frequency to form a new photon with twice the frequency.^[3] The NLO susceptibility χ⁽²⁾ describes the SHG process. The χ⁽²⁾ is a third-rank tensor with 27 components and is related to the first hyperpolarizability β of a molecule.

In recent decades extensive studies have been conducted to develop new compounds with high NLO response and meet the technological requirements for various applications.^[4–14]

In our previous research, we found that the alkali metal oxide adsorption on a Mg₁₂O₁₂ nanocage leads to a huge static first hyperpolarizability.^[15] In another work, we showed that the first hyperpolarizability value increases by substituting a magnesium atom of a Mg₁₂O₁₂ nanocage with a transition metal atom.^[16] The influences of Sc doping on the optical properties of Be₁₂O₁₂, Mg₁₂O₁₂, and Ca₁₂O₁₂ nanocages were investigated.^[17] The effects of superalkalis M₃O (M = Li, Na, and K) on the nonlinear optical properties of C₂₀ fullerene nanoclusters^[18] and Be₁₂O₁₂ nanocage^[19] have been studied.

In this paper, we theoretically study the effects of adsorbing some inorganic molecules on structures, energetic, electronic, thermodynamic, and the linear and nonlinear optical properties of an Mg₁₂O₁₂ nanocage.

2. Computational details

Structural optimizations for the ground state of an Mg₁₂O₁₂ nanocage and XY_n(e@Mg12O₁₂; (XY_n = BF₃, BF₄, BCl₃, AlF₃, AlCl₃, AlBr₃, BeF₃, GaF₃, GaCl₃, GaBr₃, NO₃, BS₂, BSO, BO₂, F₂, PF₅, and PCl₅, ASF₅) were performed by using the density functional method, the unrestricted B3LYP,^[20,21] and 6-31+G(d) basis sets. All the calculations converged to an optimized geometry, which corresponds to a true energy minimum as revealed by the lack of imaginary values in the calculated vibration frequencies. Vibration frequencies are calculated at the same level. All the structural optimizations were performed without any symmetry constraints with the Gaussian 09 package.^[22] A GaussSum program has been used to calculate the electronic density of states (DOS). The energy gap (E_g) that refers to the energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) was calculated from the density of states.

The coulomb-attenuating hybrid exchange-correlation functional method (CAM-B3LYP) with 6-31+G(d) basis sets was used to calculate the dipole moment, polarizability, and first hyperpolarizability.^[23] A natural bond orbital (NBO) charge analysis was performed at the same level for all optimized structures.

In a constant and weak electric field the total energy of the system can be expressed as follows:^[24,25] 1

Here, E⁰ is the molecular energy of the system in the absence of an electric field and F_α is the electric field component along the α direction, is the permanent dipole moment, α_αβ is the static dipole polarizability (linear polarizability), β_αβγ and γ_αβγδ are the first and second hyperpolarizabilities respectively, with indices α, β, γ, δ, … referring to the Einstein summation of distinct tensor components.

The definitions of the total dipole moment (μ), mean polarizability (α), and magnitude of static first hyperpolarizability (β₀) are as follows:^[5,26,27] 2 3 4

3. Results and discussion

3.1. Geometric structure and thermodynamic properties

The optimized ground-state geometry of Mg₁₂O₁₂ is shown in Fig. 1, and the selected bond lengths and bond angles are also depicted in Fig. 1.

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	Fig. 1. (color online) Optimized ground-state geometries of Mg₁₂O₁₂. In the figure, and represent O and Mg, respectively.

An Mg₁₂O₁₂ nanocage is formed from eight 6-member (6-MR) rings and six 4-member (4-MR) rings. There are two distinct Mg–O bonds in the Mg₁₂O₁₂ nanocage, one is shared by two 6-MR rings (B₆₆) and the other by a 4-MR ring and a 6-MR ring (B₄₆) where their lengths are 1.90 Å and 1.95 Å respectively, which is compatible with previous results.^[16,28]

The optimized ground-state geometries for XY_n(e@Mg₁₂O₁₂) where XY_n = BF₃, BF₄, BCl₃, AlF₃, AlCl₃, AlBr₃, BeF₃, GaF₃, GaCl₃, GaBr₃, NO₃, BS₂, BSO, BO₂, F₂, PF₅, PCl₅, and ASF₅ are shown in Fig. 2.

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	Fig. 2. (color online) Optimized ground-state geometries of Mg₁₂O₁₂ and, XY_n(e@Mg₁₂O₁₂) (XY_n = BF₃, BF₄, BCl₃, AlF₃, AlCl₃, AlBr₃, BeF₃, GaF₃, GaCl₃, GaBr₃, NO₃, BS₂, BSO, BO₂, F₂, PF₅, PCl₅, ASF₅). , , , , , , , , , , and represent the O, Mg, B, F, Cl, Al, Be, Ga, N, P, and As atoms, respectively.

In order to determine the thermodynamic feasibility of the adsorption process, the changes of Gibbs free energy (ΔG⁰), the entropy ΔS⁰, and the enthalpy (ΔH⁰) are all obtained at standard temperature and pressure (1.0 atmosphere and 298.15 K) from the vibrational frequency calculation results. The ΔG⁰ is the fundamental criterion to determine whether a process occurs spontaneously. For a given temperature, a process is considered to be spontaneous if the ΔG⁰ has a negative value. Moreover, if ΔH⁰ is positive, the process is endothermic and if it is negative, the process is exothermic. These results are presented in Table 1.

The results of Table 1 show that ΔG⁰ values are all negative except for F₂₋a(e@Mg₁₂O₁₂), F₂₋b(e@Mg₁₂O₁₂), and PCl₅₋b(e@Mg₁₂O₁₂). The negative value of ΔG⁰ indicates the feasibility and spontaneous nature of the adsorption process, and also the negative value of ΔH indicates that the adsorption of superhalogens on Mg₁₂O₁₂ nanocage is exothermic.

Table 1.

Calculated values of energy gap E_g (in unit eV), the energy of the highest occupied molecular orbital E_HOMO (in unit eV), the energy of the lowest unoccupied molecular orbital E_LUMO (in unit eV), the binding energy E_b (in units kcal/mol), entropy change ΔS (in units cal/mol), free energy ΔG (in units kcal/mol), and enthalpy change ΔH (in units kcal/mol).

System	E_g	E_HOMO	E_LUMO	E_b	ΔH	ΔS	ΔG
Pristine	4.80	−6.58	−1.78	–	–	–	–
BF₃₋a(e@Mg₁₂O₁₂)	4.87	−6.82	−1.95	−60.6	−61.2	−41.5	−48.8
BF₄₋a(e@Mg₁₂O₁₂)	1.54	−6.93	−5.39	−96.0	−96.6	−45.7	−83.0
BF₄₋b(e@Mg₁₂O₁₂)	1.74	−6.79	−5.05	−93.0	−93.6	−37.4	−82.4
BCl₃₋b(e@Mg₁₂O₁₂)	4.94	−6.83	−1.89	−68.1	−68.7	−41.1	−56.4
AlF₃₋a(e@Mg₁₂O₁₂)	4.82	−6.80	−1.98	−83.7	−84.3	−41.7	−71.8
AlF₃₋b(e@Mg₁₂O₁₂)	4.77	−6.75	−1.98	−82.1	−82.7	−41.5	−70.3
AlF₃₋c(e@Mg₁₂O₁₂)	4.62	−6.6	−1.98	−56.3	−56.9	−39.5	−45.2
AlCl₃₋b(e@Mg₁₂O₁₂)	4.86	−6.87	−2.01	−75.8	−76.4	−39.9	−64.5
AlBr₃₋b(e@Mg₁₂O₁₂)	4.9	−6.78	−1.88	−91.3	−91.8	−41.0	−79.6
BeF₃₋a(e@Mg₁₂O₁₂)	1.83	−6.77	−4.94	−120.6	−121.2	−41.8	−108.7
BeF₃₋b(e@Mg₁₂O₁₂)	0.96	−6.23	−5.27	−96.9	−97.5	−30.3	−88.5
BeF₃₋c(e@Mg₁₂O₁₂)	0.96	−6.23	−5.27	−94.1	−94.7	−34.3	−84.4
GaF₃₋a(e@Mg₁₂O₁₂)	4.8	−7.10	−2.30	−80.2	−80.8	−44.9	−67.4
GaF₃₋b(e@Mg₁₂O₁₂)	4.65	−6.74	−2.09	−97.1	−97.7	−42.8	−85.0
GaF₃₋c(e@Mg₁₂O₁₂)	4.77	−6.83	−2.06	−90.2	−90.8	−51.2	−75.5
GaCl₃₋b(e@Mg₁₂O₁₂)	4.8	−6.84	−2.04	−76.7	−77.3	−40.1	−65.3
GaCl₃₋c(e@Mg₁₂O₁₂)	4.83	−7.09	−2.26	−58.9	−59.5	−44.7	−46.1
GaBr₃₋a(e@Mg₁₂O₁₂)	3.7	−5.96	−2.26	−143.8	−144.4	−37.0	−133.3
GaBr₃₋b(e@Mg₁₂O₁₂)	3.23	−5.52	−2.29	−148.8	−149.3	−37.8	−138.1
NO₃₋b(e@Mg₁₂O₁₂)	1.5	−6.82	−5.32	−35.4	−36.0	−40.4	−24.0
NO₃₋c(e@Mg₁₂O₁₂)	1.97	−6.72	−4.75	−33.3	−33.9	−38.5	−22.4
BS₂₋a(e@Mg₁₂O₁₂)	1.52	−6.63	−5.11	−17.6	−18.1	−32.9	−8.3
BS₂₋b(e@Mg₁₂O₁₂)	2.04	−6.75	−4.71	−64.3	−64.9	−36.1	−54.2
BSO₋a(e@Mg₁₂O₁₂)	2.17	−6.72	−4.55	−68.5	−69.1	−38.0	−57.8
BO₂₋ a(e@Mg₁₂O₁₂)	1.73	−6.65	−4.92	−56.8	−57.3	−35.7	−46.7
BO₂₋b(e@Mg₁₂O₁₂)	1.85	−6.61	−4.76	−55.6	−56.2	−34.2	−46.0
F₂₋a(e@Mg₁₂O₁₂)	1.86	−6.59	−4.73	0.3	−0.3	−26.0	7.4
F₂₋b(e@Mg₁₂O₁₂)	1.90	−6.59	−4.69	−0.2	−0.80	−30.0	8.1
PF₅₋b(e@Mg₁₂O₁₂)	4.91	−6.89	−1.98	−69.7	−70.2	−42.0	−57.7
PCl₅₋b(e@Mg₁₂O₁₂)	1.70	−6.45	−4.75	−4.2	−4.80	−26.1	3.0
PCl₅₋c(e@Mg₁₂O₁₂)	2.49	−6.86	−4.37	−68.8	−69.4	−39.5	−57.6
AsF₅₋b(e@Mg₁₂O₁₂)	4.41	−6.84	−2.43	−89.1	−89.7	−44.8	−76.3

Table 1.

The values of ΔG⁰ for F₂₋a(e@Mg₁₂O₁₂), F₂₋b(e@Mg₁₂O₁₂), and PCl₅₋b(e@Mg₁₂O₁₂) are all positive and this can be explained with a small amount of binding energy (Table 1).

3.2. Electronic and optical property

The values of energy gap E_g, which corresponds to the difference between the energy of the highest occupied molecular orbital (HOMO) and the energy of the lowest unoccupied molecular orbital (LUMO) are listed in Table 1. Mg₁₂O₁₂ nanocage is an intrinsic semiconductor with E_g = 4.8 eV. The plots of the calculated electronic densities of states (DOSs) for all mentioned structures are depicted in Fig. 3.

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Fig. 3. (color online) Plots of the densities of states for Mg₁₂O₁₂ and XY_n(e@Mg₁₂O₁₂ (XY_n = BF₃, BF₄, BCl₃, AlF₃, AlCl₃, AlBr₃, BeF₃, GaF₃, GaCl₃, GaBr₃, NO₃, BS₂, BSO, BO₂, F₂, PF₅, PCl₅, and ASF₅). The red curve denotes the total DOS spectrum (scaled by 0.5), the blue curve represents the alpha DOS spectrum, and the green curve refers to the beta DOS spectrum. E_g is the energy gap.

In some structures, such as GaBr₃₋a(e@Mg₁₂O₁₂) and GaBr₃₋b(e@Mg₁₂O₁₂, the value of E_HOMO goes up while the E_LUMO is almost constant, so the value of energy gap E_g decreases. In some other structures, the main reason for E_g decreasing is the displacement of the E_LUMO energy downward and E_HOMO is almost constant. In some of these structures, E_g is constant. In Fig. 4, the variation trends of energy gap E_g, E_HOMO, and E_LUMO of all nanostructures are illustrated in Fig. 4.

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	Fig. 4. (color online) Plots of E_g, E_LUMO, and E_HOMO for nanostructures based on Mg₁₂O₁₂.

Further, the values of dipole moment, polarizability, and hyperpolarizability for all above-mentioned structures are calculated by the CAM-B3LYP method. The values of the dipole moment, polarizability, and hyperpolarizability of nanostructures are presented in Table 2.

The results in Table 2 indicate that for all of the studied cases the dipole moment μ is considerably increased except for the systems F₂₋a(e@Mg₁₂O₁₂) and F₂₋b(e@Mg₁₂O₁₂) in which the values of μ are both nearly zero. This property can be explained with nearly zero charge on the F₂ molecule (Table 2).

Table 2.

Values of permanent dipole moment μ (in unit a.u.), polarizability α (in unit a.u.), first hyperpolarizability β₀ (in unit a.u.), and q for the systems considered in this work.

The results in Table 2 show that by the adsorption of mentioned molecules on the Mg₁₂O₁₂ surface, in all cases, the polarizability value increases. Several trends are evident for polarizability in Table 2. First, the polarizability increases in the same configuration as GaF₃(e@Mg₁₂ O₁₂) > AlF₃(e@Mg₁₂O₁₂) > BF₃ (e@Mg₁₂O₁₂). This trend can be explained by the fact that in each group of the periodic table, the polarizability increases from top to bottom, the polarizability of the Ga atom is greater than those of Al and B. The polarizability increases in the same configuration as AlBr₃(e@Mg₁₂ O₁₂) > AlCl₃(e@Mg₁₂ O₁₂) > AlF₃(e@Mg₁₂ O₁₂). Similarly, this trend can be explained as previously discussed (i.e., the amount of polarizability increases with the replacement of atoms in the lower row of the periodic table). Second, from left to right across a row of the periodic table, polarizability decreases (BeF₃(e@Mg₁₂ O₁₂) > BF₃(e@Mg₁₂ O₁₂)).

Like polarizability, the results indicate that as a consequence of adsorption of all selected molecules on the Mg₁₂O₁₂ surface, the first hyperpolarizability value is increased. The quantities that β increases in these systems are very different, which depend on the type of adsorbing molecules and the adsorption geometry. It is clearly shown that the locations of the mentioned molecule adsorption on the Mg₁₂O₁₂ for all XY_n(e@Mg₁₂O₁₂) nanoclusters play an important role in increasing the calculated value of first hyperpolarizability (β₀). For example, first hyperpolarizability values of BO₂(e@Mg₁₂O₁₂) in a and b conformation are 17.0 a.u. and 3935.9 a.u., respectively.

4. Conclusions

In this work, we have studied the influences of adsorptions of some inorganic molecules on the electronic, optical, and thermodynamic properties of Mg₁₂O₁₂ nanocage by using the DFT method. The main results of this research can be summarized as follows.

(i) It is shown that almost all considered molecules each have an exothermic adsorption energy on the Mg₁₂O₁₂ surface.

(ii) The effects of XY_n molecules on the energy gap of the nanocage depend on the type of molecule and the position of adsorption.

(iii) For all studied systems, with the increase of adsorption of molecules the polarizability value increases.

(iv) The effects of adsorbing molecules on the polarizability depend on the type of molecule and the adsorption geometry, and it is shown that the polarizability increases in the same configuration as GaF₃(e@Mg₁₂O₁₂) > AlF₃(e@Mg₁₂O₁₂) > BF₃(e@Mg₁₂O₁₂) and increases for the similar structures as BeF₃(e@Mg₁₂O₁₂) > BF₃(e@Mg₁₂O₁₂.

(v) Additionally it is shown that the first hyperpolarizability value increases in each of all studied cases. Like the E_g and polarizability results, the value of the first hyperpolarizability depends on the type of adsorbing molecule and the adsorption geometry, however the sensitivity of hyperpolarizability to adsorption position is higher, and it is a key to estimating the value of increasing the first hyperpolarizability.

(vi) The large values of β₀ for the systems studied above suggest that these compounds may have potential applications in NLO materials.

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