Journal of Molecular Modeling (2018) 24:205 https://doi.org/10.1007/s00894-018-3750-4
ORIGINAL PAPER
Nonlinear optical properties of aluminum nitride nanotubes doped by excess electron: a first principle study Tang-Mi Yuan 1 & Shao-Li Liu 1 & Zhen-Bo Liu 1
&
Xiao Wang 1 & Wen-Zuo Li 1 & Jian-Bo Cheng 1 & Qing-Zhong Li 1
Received: 23 December 2017 / Accepted: 3 July 2018 # Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract Aluminum nitride nanotubes (AlNNTs) doped by the excess electron, e@AlNNT and M@N-AlNNT (M = Li, Na, K), have been designed and their geometrical, electronic, and nonlinear optical (NLO) properties have been explored theoretically. The results showed that the excess electron narrows the energy gap between HOMO and LUMO values (EH-L) of the doped systems in the range of 3.42–5.37 eV, which is due to a new energy level HOMO formed for the doped excess electron, with higher energy than the original HOMO of AlNNT. Importantly, the doped excess electron considerably increases the first hyperpolarizability (β0) from 130 a.u. of the undoped AlNNT to 646 a.u. for e@AlNNT, 2606 a.u. for Li@N-AlNNT, while 1.14 × 105 a.u. for Na@NAlNNT, and 1.37 × 106 a.u. for K@N-AlNNT. The enormous β0 values for Na@N-AlNNT and K@N-AlNNT are attributed to the low transition energy. These results demonstrate that AlNNTs are a promising material in high-performance NLO nanomaterials for electronic devices. Keywords Aluminum nitride nanotube . Excess electron narrow . HOMO-LUMO energy gap . Nonlinear optical
Introduction Nonlinear optical (NLO) response plays an important role and has potential applications in fields of optoelectronics and photonics [1–3]. It has been the subject of wide academic and industrial interests for decades [4–15]. To find and design high performance NLO materials, scientists have proposed many strategies, such as using molecules with abundant π-electrons [16, 17] and adding electron-donor/acceptor groups [18–22], and they remarkably enhance the NLO response [23–27]. A growing number of research revealed that introducing excess electrons is an effective method for enhancing NLO response in different kinds of systems. Some simple molecular
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00894-018-3750-4) contains supplementary material, which is available to authorized users. * Zhen-Bo Liu
[email protected] * Wen-Zuo Li
[email protected] 1
College of Chemistry and Chemical Engineering, Yantai University, Yantai 264005, People’s Republic of China
clusters with excess electron, such as (FH)2{e}(HF) and (H2O)3{e}, possess excessively large first hyperpolarizability (β0), 8.1 × 106 and 1.7 × 107 a.u. [8, 28]. Doping alkali metals is another method to gain excess electrons for a system. It is known that alkali metals (Li, Na, and K) easily lose the outermost s orbital valence electron. When an alkali metal is doped in a system, the outermost s orbital valence electron becomes a loosely bound excess electron caused by the interaction between alkali metals and the system [13]. Champagne et al. [29] found that doping of an alkali atom enhances the second hyperpolarizability of polyacetylene chains. Chen et al. [30] designed an interesting cup-like compound, Li@calixpyrrole, and found that the excess electron from Li atom plays an important role in enhancing β0. Accompanied with the identification and widely studied carbon nanotubes (CNTs) [31–35], more new nanotube structures with many advantages were found. Group III- and Vbased nanotubes with almost constant band gap nearly independent of tubular diameter and chirality [36–38], have many advantages over CNTs due to their high reactivity of the exterior surface and thermodynamic stability [39]. CNTs have been studied intensively in the NLO research [40–45]. On the other hand, some recent studies on III-V nanostructures showed that doping alkali atoms enhance the NLO response of BN and AlN nanocages considerably
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[46–50]. Zhong et al. found that the distribution of the excess electron plays an important role in increasing β0 of boron nitride nanotubes (BNNTs) [51]. Aluminum nitride nanotubes (AlNNTs) were first experimentally synthesized by Tondare et al. [52] in 2002. Due to their unusual mechanical properties, excellent chemical and thermal stabilities, AlNNTs have potential applications in nanoelectronic devices [53, 54]. Especially, AlNNTs have greater polarity than CNTs and BNNTs [55, 56]. However, there is scarce study on the NLO property of AlNNTs. As expected, the AlNNTs may have large β0 with precious thermal stabilities. In this paper, our aims are to obtain the structures of new doped-AlNNT structures with excess electron, to show the localization of the excess electron inside the AlNNTs of the electride salt molecules, to exhibit the effects of the excess electron and alkali metal on β0, and to reveal the new relationship between the excess electron cloud and β0. We think it is significant for designing new NLO molecules, materials, and electronic devices of AlNNTs with the excess electron.
Computational details A truncated (4, 0) AlNNT was used to model the nanotube. The geometry structures with all real frequencies were optimized using the density functional theory (DFT) at the B3LYP/6-31+G(d) level. For the calculation of polarizability (α0) and first hyperpolarizability (β0), we took the super-short AlNNT (Fig. S1 in supporting information) as a representative to select the method. The results (Table S1 in supporting information) show that β0 values obtained with the Hartree– Fock (HF) method are closer to those obtained with the more sophisticated second-order Møller−Plesset perturbation (MP2) method than the DFT methods including LC-BLYP, CAM-B3LYP, BHandHLYP, and M06-2X. Thus, the HF method was chosen to calculate polarizability and first Fig. 1 Top and side views of the optimized geometries of AlNNT, e@AlNNT, and M@N-AlNNT (M = Li, Na, K)
hyperpolarizability, with the 6-31+G(d) basis set. The magnitude of the applied electric field is chosen as 0.0010 a.u., due to the little region of β0 values around 0.0010 a.u. (see Table S2 in supporting information). The difference of the dipole moment between the ground state and the excited state (Δμ), oscillator strength (f0), and transition energy (ΔΕ) were roughly calculated at the CIS/6-31+G(d) level. The natural bond orbital (NBO) charges were calculated at the HF/6-31+ G(d) level. In this work, we considered the spin contamination of all the computations on the geometrical optimization and NLO response, and found that the corresponding ⟨S2⟩ values are in the range of 0.752–0.771, which are very close to the value 0.750 for the pure doublet state, indicating that the spin contamination could be negligible and the computational results are reliable. In a weak and stable applied electric field, the energy of the system can be written as: 1 1 E ¼ E 0 −μα F α − ααβ F α F β − βαβγ F α F β F γ ⋯ 2 6
ð1Þ
where E0 is the molecular energy without the applied electrostatic field, and Fα is a component of the applied electric field strength along the α direction; μα, ααβ, and βαβγ are the components of the dipole moment, polarizability, and first hyperpolarizability tensors, respectively. In this paper, we focus on the μ0, α0, and β0 values. Their expressions are written as follows: 1=2 μ0 ¼ μ2x þ μ2y þ μ2z
ð2Þ
1 αxx þ αyy þ αzz 3
ð3Þ
α0 ¼
The static first hyperpolarizability is noted as: 1=2 β0 ¼ β2x þ β2y þ β2z
ð4Þ
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Table 1 The main geometrical parameters of AlNNT, e@AlNNT, and M@N-AlNNT (M = Li, Na, K) (distances in Å and angles in degree) at the B3LYP/6-31+G(d) level
N1-Al1a D(N1, max)b D(N1,min)c Avg.D(N1)d D(Al4)e Avg.d(M-N1)f Angle N1-Al1-N1 Angle Al1-N1-Al1 a
AlNNT
e@AlNNT
Li@NAlNNT
Na@NAlNNT
K@NAlNNT
1.83 4.56 4.56 4.56 4.53
1.84 4.53 4.53 4.53 4.23
123 106
121 104
1.86 4.70 3.88 4.29 4.53 2.40 110 113
1.86 4.40 4.33 4.37 4.53 2.58 112 113
1.86 4.44 4.38 4.41 4.54 2.98 114 113
The bond length between N atoms of N1 layer and Al atoms of Al1 layer
b
The maximum diameter of N1 layer
c
The minimum diameter of N1 layer
d
The average diameter of N1 layer
e
The diameters of Al4 layer
f
The average distance between alkali metal atom and N atoms of N1 layer
where 3 β þ βxyy þ βxzz 5 xxx 3 β y ¼ β yyy þ βyxx þ βyzz 5 3 βz ¼ βzzz þ βzxx þ β zyy 5
βx ¼
All of the calculations were performed with the Gaussian 09 program package [57]. The total density of states (TDOS) were analyzed by Multiwfn software [58].
Results and discussion Optimized structures M@N-AlNNT (M = Li, Na, K) is obtained by doping Li, Na, or K atom to the N-rich edge of AlNNT. The optimized Table 2 The selected NBO charges of some important atoms in AlNNT, e@AlNNT, and M@N-AlNNT (M = Li, Na, K) and HOMO-LUMO energy gap (EH-L) (eV)
structures with all real frequencies of AlNNT, e@AlNNT, and M@N-AlNNT (M = Li, Na, K) are shown in Fig. 1, and the main geometrical parameters are listed in Table 1. In this work, the N atoms at the same layer are defined as Nn-cluster, while the Al atoms at the same layer are defined as Alncluster (in which n = 1–4, see Fig. 1). We focus on the structure parameters of N-tip and Al-tip. As shown in Table 1, the N1-Al1 bond length of e@AlNNT is 1.84 Å and it is almost equal in M@N-AlNNT (M = Li, Na, K) (1.86 Å), both of which are larger than that of the undoped AlNNT (1.83 Å). Doping an alkali metal atom deforms the circular of N–tip, especially for Li@N-AlNNT, which can be seen from top views of undoped and doped AlNNT structures in Fig. 1. The maximum diameter D(N1, max) and minimum diameter D(N1, min) of N1 layer are listed in Table 1. In regard to Li@N-AlNNT, D(N 1 , max) is larger than D(N 1 , min) (4.70 Å vs 3.88 Å). The average diameters of N 1 (Avg.D(N 1 )) (4.29-4.53 Å) of the doped structures are smaller than that of the undoped AlNNT (4.56 Å). The
AlNNT
e@AlNNT
Li@NAlNNT
Na@NAlNNT
K@NAlNNT
q(M) q(N1)
−1.83
−1.82
0.78 −1.86
0.65 −1.88
0.65 −1.34
q(Al1) q(N2) q(Al2) q(N3) q(Al3) q(N4) q(Al4) EH-L
2.13 −2.16 2.16 −2.16 2.14 −2.16 1.90 9.45
2.12 −2.16 2.15 −2.16 2.14 −2.17 1.71 4.37
1.97 −2.17 2.16 −2.16 2.14 −2.16 1.90 5.37
2.03 −2.17 2.16 −2.16 2.14 −2.16 1.90 3.57
0.78 0.13 −0.13 0.40 −0.49 0.25 −0.02 3.42
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Fig. 2 The frontier molecular orbitals (HOMO, HOMO-1, and LUMO) of AlNNT, e@AlNNT, and M@N-AlNNT (M = Li, Na, K). The energies (eV) of the corresponding frontier molecular orbitals are also shown
values of Avg.D(N1) for M@N-AlNNT (M = Li, Na, K) increase with the atomic number of M from 4.29 to 4.41 Å. For the diameters of the Al4 layer (D(Al 4 )), the D(Al 4 ) of e@AlNNT is obviously smaller than that of the undoped AlNNT (4.23 Å vs 4.53 Å). D(Al 4 ) of M@N-AlNNT (M = Li, Na, K) is between 4.53 and 4.54 Å, indicating the doped alkali metal atom has almost no effect on D(Al4). The average distance between M (M = Li, Na, K) atom and N1 increases with the atomic number, and it increases in the order of 2.40 Å (M = Li) < 2.58 Å(Na) < 2.98 Å(K). In
contrast to the original AlNNT (123o), the angles of N1Al1-N1 (110-121o) for the four doped structures reduce obviously. The angle of Al1-N1-Al1 in e@AlNNT (104o) is a bit smaller than that of the undoped AlNNT (106 o ). However, the angle of Al1-N1-Al1 in M@N-AlNNT (M = Li, Na, K) (113o) is larger than that of the undoped AlNNT. Therefore, the values of the main geometrical parameters of e@AlNNT and M@N-AlNNT (M = Li, Na, K) including some bond lengths, diameter, distance between atom and atom, and bond angles, are different from the undoped
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Fig. 3 The total density of states (TDOS) of AlNNT, e@AlNNT, and M@N-AlNNT (M = Li, Na, K). The corresponding frontier molecular orbitals are shown as the insets
AlNNT, indicating that the doped electron or alkali metal atoms induce the structure alteration.
The electronic properties The detailed NBO charge population is shown in Table 2. Significantly, the NBO charges of N and Al atoms in e@AlNNT (in Fig. 1) are almost the same as those in the undoped AlNNT, except the charges (q(Al4)) of Al4. The q(Al4) in e@AlNNT is 1.71, which is smaller than that (1.90) of the corresponding Al atom in the undoped AlNNT. As such, the charge of four Al atoms of Al4 decreases by 0.76 in all. Therefore, the excess electron is mainly distributed on the four Al atoms of Al4-cluster, as can be embodied in the HOMO of e@AlNNT in Fig. 2. For M@N-AlNNT (M = Li, Na, K), the alkali atom exhibits a positive charge (0.78 for Li, 0.65 for Na and K), showing that charge transfer exists from alkali M atom to the AlNNT. The M@N-AlNNT (M = Li, Na,
Table 3 Polarizability α0 (a.u.), first hyperpolarizability β0 (a.u.) at the HF level, the difference between the ground and excitedstate dipole moments Δμ (a.u.), oscillator strength f0, and the transition energy ΔE (eV) at the CIS level
AlNNT e@AlNNT Li@N-AlNNT Na@N-AlNNT K@N-AlNNT
K) structure can be taken as alkali metal positive ion plus negatively charged AlNNT(M+-e@N-AlNNT) structures. The q(N 2), q(Al 2), q(N3), q(Al 3), q(N4 ), and q(Al 4) in M@N-AlNNT (M = Li and Na) are almost the same as that in the undoped AlNNT, while the q(N1) and q(Al1) are decreased compared with the undoped AlNNT. The q(N1) and q(Al1) of Li@N-AlNNT are −1.86 and 1.97, becoming more negative compared to those in the undoped AlNNT (q(N1) = −1.83 q(Al1) = 2.13). This result indicates that the transferred electron of the Li atom is almost distributed to the N1 and Al1 atoms, which is close to the Li atom. It is also the same as for Na@N-AlNNT. Interestingly, the case of K@N-AlNNT is quite different from Li@N-AlNNT and Na@N-AlNNT. The charge distribution in K@N-AlNNT is dramatically different from that in the undoped AlNNT. Compared with the charge distribution in the undoped AlNNT, the doping K atom influences not only the charge of N1 and Al1 atoms but also the atoms that are far away from the K atom. All the N atoms in
α0
β0
Δμ
f0
ΔΕ
9Δμf0/ ΔΕ3
355 415 398 1353 1315
130 646 2606 1.14 × 105 1.37 × 106
0.752 0.248 3.02 1.12 2.71
0.211 0.193 0.178 0.216 0.211
6.49 2.95 3.21 0.690 0.657
105 338 2943 1.34 × 105 3.65 × 105
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1.4x10
5
4.0 10
5
6
3.0 10
/ 0
5
2.0 10
10000 times 5
1.0x10
0
(a.u.)
1.2x10
3
Fig. 4 The first hyperpolarizabilities (β0) at the HF level and the two-level approximate (Eq. (5))
E (a.u.)
205
5
1.0 10
4
5.0x10
0.0
0.0 AlNNT
K@N-AlNNT become more positive. For instance, the charge of N4 in the undoped AlNNT is negative (−2.16) and it becomes positive (0.25) in K@N-AlNNT. Thus, the excess electron affects the charge distribution of AlNNT, especially the doped K atom. The HOMO-LUMO energy gap (EH-L) of the undoped AlNNT and all doped structures was examined in order to explore the effect of excess electron doping. As we can see in Table 2, EH-L of the undoped AlNNT is 9.45 eV. The doping excess electron endows the doped systems e@AlNNT and M@N-AlNNT (M = Li, Na, K) with a small EH-L value in the range of 3.42–5.37 eV. The E H-L of e@AlNNT is 4.37 eV, smaller than that of the undoped AlNNT. The EH-L of M@N-AlNNT (M = Li, Na, K) decreases with the increase of the atomic number of alkali metal. The EH-L of Li@NAlNNT is 5.37 eV and it is further decreased to be 3.57 eV for Na@N-AlNNT and 3.42 eV for K@N-AlNNT. For a further study of the electronic properties, the frontier molecular orbitals (HOMO, HOMO-1, and LUMO) (in Fig. 2) and total density of states (TDOS) of the undoped AlNNT and all doped structures were plotted in Fig. 3. In TDOS analysis (Fig. 3), we can find the HOMO-LUMO energy gap (EH-L) of the doped structures to be obviously lower than that of the undoped AlNNT, especially the doping of Na and K atoms. From Fig. 2, the electron clouds of HOMO-1 in all doped structures are almost the same shape as the HOMO in the undoped AlNNT. Furthermore, the HOMO-1 s energies of M@N-AlNNT (M = Li, Na, K) (−9.13- −9.23 eV) are close to the HOMO energy of the undoped AlNNT (−9.23 eV). Compared with the old LUMO energy (0.212 eV), there is little change of M@N-AlNNT (M = Li, Na, K) (−0.288−0.212 eV). The case of e@AlNNT is a little bit out of the way, HOMO-1 and LUMO energies of e@AlNNT are −6.06 and 2.07 eV, larger than the old HOMO and LUMO energies, respectively. As shown in Fig. 2, doping an excess electron may introduce a new HOMO between HOMO and LUMO of the original AlNNT, while the original HOMO in AlNNT
e
Li
Na
K
serves as the HOMO-1 in the doped AlNNT. This explains why the EH-L of the doped structures is obviously decreased compared with the EH-L of the undoped AlNNT.
Static first hyperpolarizability A previous study [13] has shown that the existence of the diffuse excess electron can usually cause the large NLO response. It is because the doping excess electron can considerably change the polarizability and first hyperpolarizability of a system. Thus, the polarizability (α 0 ) and the first hyperpolarizability (β0) of AlNNT, e@AlNNT, and M@NAlNNT (M = Li, Na, K) were calculated by the HF method, and the corresponding results are listed in Table 3. The α0 of e@AlNNT is 415 a.u., which is larger than 355 a.u. in the undoped AlNNT. The α0 of Li@N-AlNNT is slightly larger than that of the undoped AlNNT (398 a.u. vs 355 a.u.). Moreover, the α0 of Na@N-AlNNT is 1353 a.u., and that of K@N-AlNNT is 1315 a.u. This proves that the doping of the alkali metal Na or K has a tremendous influence on the value of α0. The β0 of e@AlNNT is 646 a.u., which is larger than 130 a.u. of the undoped AlNNT. It can be inferred that the diffuse excess electron dramatically enhances the β0 value of AlNNT. The β0 of Li@N-AlNNT is 2606 a.u., which is 20 times larger than that of the undoped AlNNT. Amazingly, the β0 of Na@N-AlNNT and K@N-AlNNT is respectively 1.14 × 105 and 1.37 × 106 a.u., increased by 870 and 10,000 times. This indicates that the doping of the alkali metal Na and K considerably enhances the NLO of AlNNT. According to our results, the doping of the excess electron can enhance the β0 of AlNNTs effectively, and the enhanced effect of alkali metals is consistent with the atomic number. It is meaningful to compare the β0 values of alkali metals doping structures M@N-AlNNT (M = Li, Na, K) with previous works. The maximum β0 value of M@x-Al12N12 (M = Li, Na, and K; x = b66, b64, and r6) systems [46] is 8.89 × 105 a.u., and the
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β0 of B12N12–M (M = Li, Na, K) [48] is 1537–18,889 a.u. The β0 values of alkali metals doping structures M@N-AlNNT (M = Li, Na, K) in our study (K@N-AlNNT = 1.37 × 106 a.u.) are much larger and more meaningful. To have a deep understanding of this tremendous increase in the first hyperpolarizability due to the doping of excess electron in AlNNT, the following two-level expression [16, 59] is employed. β0 ∝βzzz ¼
9 Δμ f 0 ΔE 3
ð5Þ
where Δμ is the difference of the dipole moment between the ground state and the excited state, f0 is oscillator strength, and ΔE is the energy of crucial transition. The ΔE of the undoped AlNNT is as large as 4.49 eV. In contrast to the undoped AlNNT, the ΔE values of e@AlNNT, Li@N-AlNNT, Na@N-AlNNT, and K@N-AlNNT decrease to be 2.95, 3.21, 0.690, 0.657 eV, respectively. Clearly, the doping excess electron decreases ΔE. The ΔE of e@AlNNT and Li@N-AlNNT is 2.95 and 3.21 eV, and it decreases sharply to 0.690 and 0.657 eV for Na@N-AlNNT and K@NAlNNT, respectively. As can be seen from the two-level expression, the hyperpolarizability is inversely proportional to the third power of crucial transition energy, so ΔE is considered to be a decisive factor for the assessment of hyperpolarizability. This explains why the β0 of Na@N-AlNNT (1.14 × 105) and K@N-AlNNT (1.37 × 106 a.u.) is greater than that of e@NAlNNT and Li@N-AlNNT. According to Eq. (5), the order of 9Δμf0/ΔΕ3 values for the undoped AlNNT, e@AlNNT, and M@N-AlNNT (M = Li, Na, K) is consistent with the order of β0 values (see Fig. 4), showing that ΔΕ, f0, and Δμ may be controlling factors for β0.
AlNNT is attributed to the great decrease of ΔΕ. ΔΕ, f0, and Δμ may be controlling factors for β0. This work suggests that doped excess electron AlNNTs can be taken as potential members of the NLO nanomaterial family. Acknowledgments This work was supported by the Natural Science Foundation of Shandong Province (No. ZR2013BM016)
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Conclusions In this work, the electronic and nonlinear optical properties of the undoped AlNNT and the excess electron doped AlNNT (e@AlNNT, Li@N-AlNNT, Na@N-AlNNT, K@N-AlNNT) have been explored theoretically. The NBO charge population indicates that charge transfers from the alkali metal atom to the AlNNT. Doping the excess electron could remarkably decrease the EH-L value of the doped systems (3.42–5.37 eV) due to the appearance of a new energy level as the new HOMO with a higher energy than the original HOMO of AlNNT. It is important that doping the excess electron can increase the first hyperpolarizability (β0) considerably. Doping an excess electron induces the β0 to increase from 130 a.u. of the undoped AlNNT to 646 a.u. of e@AlNNT. Moreover, the β0 of Li@N-AlNNT, Na@N-AlNNT, K@NAlNNT is 2606, 1.14 × 105, and 1.37 × 106 a.u., respectively. The enormous increase of β0 for Na@N-AlNNT and K@N-
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