Cite this Article
Raoof Toosi Ali, Reza Shamlouei Hamid, Mohammadi Hesari Asghar. Influence of alkali metal superoxides on structure, electronic, and optical properties of Be12O12 nanocage: Density functional theory study. Chinese Physics B, 2016, 25(9): 094220  
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Influence of alkali metal superoxides on structure, electronic, and optical properties of Be12O12 nanocage: Density functional theory study
Raoof Toosi Ali, Reza Shamlouei Hamid†, , Mohammadi Hesari Asghar
Lorestan University, Chemistry Department, Khorram Abad, Iran

 

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

Abstract
Abstract

The effect of alkali metal superoxides M3O (M = Li, Na, K) on the electronic and optical properties of a Be12O12 nanocage was studied by density functional theory (DFT) and time-dependent density functional theory (TD-DFT). The energy gaps (Eg) of all configurations were calculated. Generally, the adsorption of alkali metal superoxides on the Be12O12 nanocage causes a decrease of Eg. Electric dipole moment μ, polarizability α, and static first hyperpolarizability β were calculated and it was shown that the adsorption of alkali metal superoxides on Be12O12 increases its polarizability. It was found that the absorption of M3O on Be12O12 nanocluster improves its nonlinear optical properties. The highest first hyperpolarizability (β ≈ 214000 a.u.) is obtained in the K3O–Be12O12 nanocluster. The TD-DFT calculations were performed to investigate the origin of the first hyperpolarizabilities and it was shown that a higher first hyperpolarizability belongs to the structure that has a lower transition energy.

PACS: 42.70.Nq;42.70.Mp
Keyword:Be12O12;alkali metal superoxides;hyperpolarizability;DFT calculation
1. Introduction

Materials with large nonlinear optical (NLO) properties are very useful for optical interconnections, optical switching, and signal processing.[1,2] The accurate theoretical determination of hyperpolarizability can make significant contributions to explore new nonlinear optical materials with potential applications in advanced technologies.[3]

Cages with fullerene-like structures can be utilized in new industrial applications such electronic devices, imaging materials, magnetic recording and environmental processes.[4–10] These cages with another substituent lead to the emergence of some physical properties such as a different energy gap and genesis of semiconducting properties.[11–15] Nanocages with the M12X12 formula are most stable energetically among different types of (MX)n structures.[16–22] Moreover theoretical studies demonstrated that the M12X12 cluster built from square and hexagonal rings is more stable than that built from pentagons and hexagons.[22–24] Previously some studies were done to improve the NLO properties of nanocages. For instance, lithium, sodium, and potassium were employed to increase the NLO properties of Mg12O12 and B12O12 nanocages,[25] and similarly transition metal atoms were used to improve the Mg12O12 nanocage.[26] Wu et al. used the alkali superoxide (M3O) to improve the NLO properties of materials and designed novel alkalides with high NLO properties.[27]

In the present work, we report a theoretical study on the interaction of alkali metal superoxides with the Be12O12 nanocage. Structure, energetic, electronic, and optical properties of the compounds are studied using density functional theory.

2. Computational details

The optimized structures of ground state of Be12O12 nanocage, M3O (M = Li, Na, K), and complex of Be12O12 with M3O (M3O@Be12O12) were calculated using density functional theory at the B3LYP/6-311+G(d) level.[28–32]

To find the optimized structures for M3O (M = Li, Na, K) adsorbed on the surface of Be12O12, several different initial configurations were used for optimization: (i) three metal atoms horizontally attached on three oxygen atoms in the hexagonal ring of Be12O12 (3M-H-3O h ring), (ii) two metal atoms vertically attached on two oxygen atoms in the hexagonal ring of Be12O12 (M-V-2O-h ring), (iii) two metal atoms vertically attached on two oxygen atoms in the square ring of Be12O12 (2M-V-2O-s ring). These configurations are illustrated in Fig. 1.

Fig. 1. Different scenarios of M3O on Be12O12: (a) 3M-H-3O h ring, three M metals sit horizontally on a three O atoms hexagonal ring, (b) 2M-V-2O-h ring, two M metals sit vertically on a two O atoms hexagonal ring, (c) 2M-V-2O-s ring, two M metals sit vertically on a two O atoms square ring.

All calculations were performed using the Gaussian 09W.[33] The electronic density of states (DOS) for all structures was calculated using the GaussSum program.[34] The spin-unrestricted approach was applied to describe the geometry optimization, electronic structure, and NLO properties of the M3O–Be12O12 nanocluster and the functional Coulomb-attenuated hybrid exchange–correlation functional (CAM-B3LYP)[35] was used to predict the large molecular system. This functional also provided good quality results for the electronic excitation energies.[36–39]

The electronic properties of the cluster including the frontier molecular orbitals, which correspond to the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), ionization potential (I), electron affinity (A), chemical potential (μ), global hardness (η), softness (S), global electrophilicity (ω), index electronegativity (χ) and the maximum amount of electronic charge index (ΔNmax) were calculated. All the electronic properties can be obtained through the HOMO–LUMO orbitals.[40–47] The calculated HOMO-LUMO energy gap Eg, chemical hardness η, chemical potential μ, electrophilicity index ω, and maximum amount of electronic charge index ΔNmax are in atomic units.

The simplest polarizability α characterizes the ability of an electric field to distort the electronic distribution of a molecule related to the linear optical properties. Higher order polarizabilities (hyperpolarizabilities β, γ, etc.) describe the nonlinear response of atoms and molecules related to a wide range of phenomena in nonlinear optics.[48] The energy of an uncharged liner molecule in a weak, homogenous electric field can be written as

where E0 is the energy of the unperturbed molecule, Fi is the field at the origin μi, and αij, βijk, and Vijkl are the components of the dipole moment, i.e., the polarizability, the first and the second order hyperpolarizability, respectively.

Using the two-level model,[49–51] the relation between the hyperpolarizibility and other time dependent properties are obtained by the following relation:

where ΔE, f, and Δμ are the transition energy, the oscillator strength, and the difference in the dipole moments between the ground state and the crucial excited state respectively. In this model, β is inversely proportional to ΔE3, so ΔE is the decisive factor in the first hyperpolarizability.[52–54]

Because of the dependence of the first hyperpolarizability on the ground state and the excited state properties, the time-dependent density functional theory (TD-DFT) calculations at the CAM-B3LYP/6-31+G(d) level were performed to obtain the excitation energy and the differences of the dipole moments between the ground state and the excited state as well as the oscillator strength f0.

3. Results and discussion
3.1. Geometrical structure

The optimized structures and geometrical parameters of the Be12O12 nanocage are depicted in Fig. 2. As seen in Fig. 2, the Be12O12 nanocage consists of six square and eight hexagonal rings. Two different bonds exist within this nanocage: one is shared between two hexagons (hh) and the other is between a square ring and a hexagon (hs). The bond lengths (l) of hh-bonds and hs-bonds in Be12O12 nanoclusters are 1.520 Å and 1.577 Å, respectively, which is in accordance with Ref. [25]. The density of states plots for the Be12O12 nanocage are shown in Fig. 2. The energies of HOMO (ɛHOMO) and LUMO (ɛLUMO) as well as the energy gap (Eg) calculated from the DOS spectrum are −8.64 eV, −1.04 eV, and 7.60 eV, respectively, which confirms the semiconductor character of the nanocage. After optimization of the Be12O12 nanocage, the M3O superoxides were placed in different sites of it (Fig. 1), and then their structures were optimized. The optimized structures of the M3O–Be12O12 nanoclusters are depicted in Figs. 3–5.

Fig. 2. The optimized geometry of the pristine Be12O12 nanocluster.
Fig. 3. The structures and the total density of states of the Be12O12 nanocluster beside Li3O super alkali metal after optimization at the B3LYP/6-311+g(d) level: (a) 3Li-H-3O h ring, (b) 2Li-V-2O-h ring, (c) 2Li-V-2O-s ring.
Fig. 4. The structures and the total density of states of the Be12O12 nanocluster beside Na3O super alkali metal after optimization at the B3LYP/6-311+g(d) level: (a) 3Na-H-3O h ring, (b) 2Na-V-2O-h ring, (c) 2Na-V-2O-s ring.
Fig. 5. The structures and the total density of states of the Be12O12 nanocluster beside K3O super alkali metal after optimization at the B3LYP/6-311+g(d) level: (a) 3K-H-3O h ring, (b) 2K-V-2O-h ring, (c) 2K-V-2O-s ring.

The bond lengths of Be–O located between two hexagonal rings (hh) and a hexagonal ring and a square ring for the M3O–Be12O12 nanocage are listed in Table 1. As seen in Table 1, the existence of M3O on the surface of the Be12O12 nanocage drastically affects its structure and highly deforms it. According to Table 1, the larger effect is seen in the Na3O case and the smaller effect is observed in the K3O case, especially for the 2D structure. Both interaction distances between M of the superoxide and O of the Be12O12 nanocage was studied and the results are gathered in Table 2.

Table 1.

The bond lengths of Be–O in hh and hs rings for all optimized structures of M3O–Be12O12.

.
Table 2.

Interaction distance (in units of Å) between M or O of M3O and Be or O of Be12O12.

.

As seen in Table 1, the interaction distances between Li atoms in the Li3O–Be12O12 case are lower than those in the Na3O–Be12O12 and K3O–Be12O12 cases, which may be the result of the smaller atomic diameter of lithium. For all configurations, the binding energies which are related to the feasibility of forming M3O@Be12O12 were calculated and reported in Table 3. Among these systems, K3O@Be12O12 has the highest binding energy and is more stable than the others.

Table 3.

The binding energy of the system for all considered configurations.

.
4. Electronic properties

The HOMO and LUMO orbitals and the calculated energy gap for all considered conformations are gathered in Table 4. As seen in Table 4 (and mentioned previously), the obtained HOMO and LUMO energies and consequently Eg for pristine Be12O12 are −8.64 eV, −1.04 eV, and 7.6 eV, respectively. It is shown that the HOMO and LUMO energies are lowered by the M3O presence. However, a larger decrease takes place on the HOMO energy, so Eg reduces for all M3O–Be12O12 nanocages. Moreover, the highest reduction in Eg occurs in the case of K3O–Be12O12 (−89.87%). The M3O molecules have high densities of electrons, their excess electrons are injected to the clusters via interaction and a new HOMO level with higher energy locating between the original HOMO and LUMO of the pristine cluster is formed, this may explain the narrowing of the Eg.

Table 4.

Electric properties of the pristine form and M3O adsorbed Be12O12 nanocages.

.

The other quantum chemical quantities such as chemical potential μ, global electrophilicity ω, ionization potential I, electron affinity A, softness S, global hardness η, index electronegativity χ, and maximum amount of electronic charge index ΔNmax, which are related to Eg, were calculated for all optimized conformations and given in Table 4.

4.1. Optical properties

The electric dipole moment μ, polarizability α, and first order static hyperpolarizability β of pristine Be12O12 and M3O–Be12O12 were calculated using DFT theory at the CAM-B3LYP/6-31+G (d,p) level. The dipole moments of the mentioned structures are presented in Table 5. The dipole moment obtained for pristine Be12O12 is 0 Debye and the surprising order of the dipole moment increasing is as follows: Li3O–Be12O12 <K3O–Be12O12 <Na3O–Be12O12.

Table 5.

Calculated dipole moments for all configurations. All components and μtot are in units of Debye.

.

The polarizability α and the first hyperpolarizability for all structures were calculated and reported in Table 6. The minimum polarizability is observed in the interaction with Li3O, and the highest polarizability is observed in the interaction with K3O. Additionally, the polarizability improvement which can be seen as the result of K3O adsorption on the Be12O12 nanocage is considerable in comparison to others. Similarly, it is observed that the first hyperpolarizability of the nanocage is considerably enhanced by the M3O adsorption. The K3O adsorbed on Be12O12 leads to the highest first hyperpolarizability improvement. The dipole moment, polarizability, and first hyperpolarizability are plotted simultaneously to show their trends in Fig. 7.

Table 6.

Polarizability, polarizability variation, and first hyperpolarizability of all structures. The values are in units of a.u.

.
Fig. 6. The energy gaps Eg of Be12O12 nanoclusters for all configuraions.
Fig. 7. Relationships of dipole moment, polarizability, and first order hyperpolarizability.
4.2. TD-DFT

Time-dependent density functional theory calculations at the CAM-B3LYP/6-31+G(d) level were used to obtain the transition excited state properties such as excitation energies E and oscillator strengths f. The major electric transition CT and transition moment of all configurations are listed in Table 7.

Table 7.

TD-CAM-B3LYP/6-31+G(d) calculated results of transition energy ΔEgn, transition moment μgn, oscillator strength fng, and the major electric transitions obtained for all conformations.

.

The modifications of hyperpolarizibility β for all structures are compared to energy changes ΔEgn in Fig. 8. In Fig. 8, it is clearly seen that the excitation energy inversely relates to the hyperpolarizibility. A small change of the transition energy leads to a drastic change in hyperpolarizability (with inverse of 3 powers). Configuration 3(a) has the largest transition energy ΔEgn which corresponds to the smallest hyperpolarizability β. On the other hand, the minimum ΔEgn and the maximum first hyperpolarizability belong to K3O–Be12O12, which corresponds to the results obtained previously.

Fig. 8. The first hyperpolarizibility and excitation energy for different configurations.
5. Conclusion

We performed DFT study of the effect of M3O on the structure, electric and optical properties of Be12O12 nanocluster to suggest a way to improve its NLO properties. It was found that the adsorption of super alkali metals on Be12O12 leads to decreased Eg and increased polarizability. The hyperpolarizibility is drastically affected by the presence of super alkali metals. The K3O–Be12O12 has the highest change in hyperpolarizibility by about 200000 a.u. The relation between the transition energy ΔEgn and the first hyperpolarizability β was explored by TD-DFT calculations.

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