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Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Design of a Novel Series of Donor−Acceptor Frameworks via Superalkali−Superhalogen Assemblage to Improve the Nonlinear Optical Responses Akbar Omidvar* Department of Chemistry, College of Sciences, Shiraz University, Shiraz, Iran

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ABSTRACT: Presently, many researches are directed toward the design of novel superatoms with high nonlinear optical responses. Inspired by a fascinating finding of superatoms which were designed by bonding superhalogen (Al13 nanocluster) with superalkalis (M3O, M = Na and K), we suggest an effective strategy to form a series of typical donor−acceptor frameworks with high nonlinear optical responses via bonding the superalkalis M3O (Li3O, Na3O, K3O, Li2NaO, Li2KO, Na2LiO, Na2KO, K2LiO, K2NaO, and LiNaKO) with low ionization potential to the superhalogen Al13 with large electron affinity. The ionization potential, electronic spatial extent, electric field gradient tensors of 17O nuclei, and natural bond orbital charge values of the superalkalis M3O were also calculated. We found that the M ligands have the remarkable effect on the ionization potential as well as 17O nuclear quadrupole resonance parameters of the superalkalis M3O. Our results also represented that the bonding superalkalis can efficiently narrow wide HOMO−LUMO gap and considerably enhance first hyperpolarizability of the pristine Al13, due to electron transfer in this type of superatom. Also, the effect of oriented external electric fields on the nonlinear optical responses of the superatoms M3O−Al13 has been systematically explored. We found that the first hyperpolarizability of the superatom compounds can be gradually increased by increasing the imposed oriented external electric field from zero to the critical external electric field along the charge transfer direction (M3O → Al13). In this respect, this work reveals an effective approach to gradually enhance the nonlinear optical responses of the superatoms through applying oriented external electric fields.

1. INTRODUCTION Previously, Khanna and Jena1,2 have suggested that atomic clusters with appropriate building blocks could mimic the chemical properties of single atoms in the periodic table. Such interesting units are classified as superatoms and have attracted large attention. Two main groups of the superatoms are superhalogens and superalkalis which were initially presented by Gutsev et al.3,4 Superhalogens are species with large electron affinities (EAs) (>3.61 eV for Cl atom).5 However, the superalkalis are used to define species whose ionization potentials (IPs) are lower than that of Cs atom ( 0) was utilized for imposing positive electric field, whereas “Field = x − n” (n > 0) was utilized for imposing negative electric field on the M3O−Al13. The geometric configurations without imaginary frequency were optimized at M06/6-31+g(d) level. At the same level, the highest occupied molecular orbital−lowest unoccupied molecular orbital (HOMO−LUMO) gaps (EHL) were calculated, and the natural bond orbital (NBO)80 charges were estimated to analyze charge transfer. Also, nuclear quadrupole resonance (NQR) spectroscopy is performed to achieve valuable data about the nuclear charge distribution around the nucleus of interest. In the present study, the NQR spectroscopy can help as a suitable technique to explore the charge distribution around the oxygen nuclei of the considered superalkalis M3O. The quadrupole coupling constant (CQ) calculated from NQR is related to the charge on nuclei and gives information on the electron distribution in a molecule, whereas asymmetry

(1)

where F is an external electric field, E0, μ0, α0, and β0 are the system energy, dipole moment, polarizability, and the first hyperpolarizability under the zero-external field, respectively. The polarizability and the first hyperpolarizability are second and third order tensors, respectively. What we are mainly interested in are their magnitudes: α0 =

3 (β + βijj + βikk ); 5 iii

(2) (3) C

DOI: 10.1021/acs.inorgchem.8b01322 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry parameter (ηQ) supplies information on the chemical bonds.81 It has been proposed that more accurate estimation of the local distribution of the electron density around nuclei is feasible using CQ.82,83 In this respect, in order to examine the effects of the M ligands on the electronic futures of the superalkalis M3O, the 17O NQR parameters are calculated at M06/631+g(d) level. The principal components of the electric field gradient (EFG) tensors, qii, are calculated, with |qzz| ≥ |qyy| ≥ | qxx| and qxx + qyy + qzz = 0. These components relate to each other by means of ηQ = |(qyy − qxx)/qzz|, 0 ≤ ηQ ≤ 1, which defines the deviation of the EFG tensors from axial symmetry. The calculated qzz element of the EFG tensor is used to give the CQ: CQ (MHz) =

e 2Qqzz (5)

h

where e and h are the charges of the electron and the Planck’s constant,84 respectively. In eq 5, the standard value of Q reported by Pyykko85 is employed (Q (17O) = 25.58 mb). In addition, to get transition energy (ΔE), oscillator strength (f), and difference of dipole moment between the ground state and excited state (Δμ), the time-dependent density functional theory (TD-DFT) calculation was performed at M06/631+g(d). Moreover, the calculated binding energy per atom (Ebin) given by E bin

ij = jjjjEsuperatom − j k

yz ∑ Enzzzzz/N n=1 {

Figure 2. Optimized geometry of pristine icosahedral (i-Al13) and decahedral (d-Al13) isomers of Al13 cluster and the corresponding M3O−Al13 composite systems. The binding energy and structural parameters of the considered systems are also given.

the M3O units. Inconsistent with the recent study,57 the EHL values decrease monotonically as one of the M ligands is substituted by a larger one. Also, as shown in Figure S2, the HOMO and LUMO of the considered M3O are distributed uniformly on the M3O surface and localized on the alkali atoms, respectively. In addition, all the HOMOs are half-filled and represent the s-type state, which is similar to the alkali metals. Consistent with the charge distributions (Figure S1), in the superalkalis with the pure ligands, the corresponding HOMOs exhibit spherically symmetric s character, which is nonsymmetric for those species with mixed ligands. 3.1.2. Vertical Ionization Potential. It is well-known that the first IP is the minimum amount of energy required to convert an atom into a cation and a free electron.87 The calculated IP and binding energy per atom (Ebin) of the considered superalkalis are reported in Table S2. As shown in this table, the binding energies decrease in the order Li3O > Li2NaO > Li2KO > Na2LiO > LiNaKO > K2LiO > Na3O > Na2KO > K2NaO > K3O. As results show, the superalkalis with the larger size of the M ligand show higher Ebin values. Also, it is found that Li3O, Na3O, and K3O can represent the significantly low IPs of 3.54, 3.06, and 2.49 eV, respectively, much lower than the corresponding alkali metals Li (5.39 eV), Na (5.14 eV), and K (4.34 eV).18 This observation offers that the studied superalkalis possess great ability to donate the outer electron and can be considered as excellent candidates of electron-donors. From Table S2, the IPs of the considered superalkalis calculated at the MP2 and CCSD(T) methods are also reported. Clearly, an excellent agreement between these results and our DFT measured IPs confirms the reliability of computational level that was used for this study. From Figure S1, the O atom in the M3O units carries −1.773e to −2.058e NBO charges, representing electron transfer from M ligands to the oxygen atom. From the HOMOs of the M3O (Figure S2), the electron clouds are repulsed by the O anion and protrude against O atom, which leads to enhancing the diffusion degree of the electron cloud. This observation can be measured by

N

(6)

For evaluating the stability of the superatoms M3O−Al13 quantitatively, we also calculated the interaction energies (EInt) using the following equation: E Int = [E(M3O−Al13) − E(Al13) − E(M3O)]

(7)

3. RESULTS AND DISCUSSION 3.1. Superalkalis. 3.1.1. Structural, NBO, and Energetic Analyses. The optimized geometrical structures of the pristine superalkalis M3O with pure and mixed ligands together with the NBO charges are represented in Figure S1. The corresponding geometrical parameters, symmetries, and the real lowest vibrational frequencies of the considered species are also listed in Table S1. From Figure S1 and Table S1, 10 planar structures of the M3O were obtained at the M06/6-31+g(d) level. In agreement with the previous study, our results show that Li2NaO, Li2KO, Na2LiO, Na2KO, K2LiO, and K2NaO possess C2v symmetry, while LiNaKO exhibits a minor deviation in the planar structure from C2v to Cs during the optimization. The Li3O, Na3O, and K3O otherwise have the trigonal shape (D3h symmetry) representing the characteristics of the strong s−p σ-type interactions. The largest and shortest Li−O bond length is found for Li3O (1.69 Å) and Na2LiO (LiNaKO) (1.66 Å), respectively. These results are in good agreement with Li−O bond length measured from gas-phase electron diffraction, is 1.60 Å.86 The negative charge on the O atoms (−1.773e to −2.058e) in each M3O is close to −2, and the positive charge on the alkali atoms range from +0.304e to +0.926e (Figure S1). The chemical reactivity and structural stability of the superalkalis can be estimated by the energy difference between the HOMO and LUMO. Here the calculated EHL are represented in Figure S2. As shown in this figure, the EHL values are in the range of 0.71−1.17 eV for D


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Inorganic Chemistry

Table 4. Calculated Interaction Energies (Eint), NBO Charges on the M3O Units, HOMO Energies (EHOMO), Fermi Energies (EF), LUMO Energies (ELUMO), and EHL for the M3O−Al13 Complexes species

Eint (kcal mol−1)

NBO charges on M3O |e|

EHOMO (eV)

EF (eV)

ELUMO (eV)

|EHL| (eV)

A113 Li3O−A113 Na3O−A113 K3O−A113 Li2NaO−A113 Li2KO−A113 Na2LiO−A113 Na2KO−A113 K2LiO−A113 K2NaO−A113 LiNaKO−A113

−109.56 −136.05 −151.84 −118.47 −124.52 −127.03 −140.74 −137.79 −146.11 −132.23

0.852 1.016 1.129 0.889 0.909 0.965 1.049 1.029 1.089 0.959

−5.57 −4.44 −4.10 −3.71 −4.31 −4.18 −4.21 −3.97 −3.94 −3.83 −4.06

−4.16 −3.29 −3.03 −2.84 −3.22 −3.21 −3.10 −2.99 −2.99 −2.91 −3.09

−2.76 −2.15 −1.96 −1.97 −2.13 −2.25 −2.00 −2.02 −2.05 −1.99 −2.13

2.81 2.29 2.14 1.74 2.18 1.93 2.21 1.95 1.89 1.84 1.93

Figure 3. Total and partial DOS (TDOS-PDOS) of the pristine Al13 and the M3O−Al13 complexes. HOMO and LUMO orbitals are also shown as insets. The dashed line shows Fermi energy of the considered systems.

electronic spatial extent (⟨R2⟩), a scale related to dispersion of electron cloud (Table S2). As shown in Table S2, the M3O units with much larger IP show higher ⟨R2⟩ values. Hence, the more diffuse HOMOs enable the valence electron to easily escape from the M3O. Consequently, the superalkalis M3O are apt to ionize and exhibit low IP values in comparison to the alkali metals. 3.1.3. NQR Analysis. Now, the magnetic properties of the considered superalkalis are studied by use of NQR analysis.

The 17O EFG tensors and related NQR parameters (CQ and ηQ) of the studied superalkalis are listed in Table 2. Since homonuclear diatomic molecules (such as O2) have axial symmetry, the EFG tensors for these molecules are qxx = qyy = −qzz/2, so ηQ = 0. As ηQ values show (Table 2), the charge distributions around the O atom for the superalkalies with mixed ligands (Li2NaO, Li2KO, Na2LiO, Na2KO, K2LiO, K2NaO, and LiNaKO) remarkably deviate from cylindrical symmetry (ranging from 0.117 to 0.994). However, the ηQ for E


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Inorganic Chemistry

Table 5. Mean Polarizability (α0), First Hyperpolarizability (β0), Transition Energy (ΔE), Oscillator Strength ( f), Difference of Dipole Moment between Ground State and Excited State (Δμ), Estimated β0 under the Two-Level Model (Δμ f/ΔE3), and Main Compositions of Crucial Transition State of the M3O−Al13 Compoundsa species

α0 (a.u.)

β0 × 104 (a.u.)

f 0 (a.u.)

Δμ (a.u.)

ΔE (a.u.)

Δμ f/ΔE3 (a.u.)

A113 Li3O−A113 Na3O−A113 K3O−A113 Li2NaO−A113 Li2KO−A113 Na2LiO−A113 Na2KO−A113 K2LiO−A113 K2NaO−A113 LiNaKO−A113

512.20 610.31 631.82 656.20 596.77 611.14 602.63 633.11 621.43 644.10 620.11

0.00 1.04 1.29 1.55 0.99 1.06 1.04 1.30 1.25 1.35 1.15

0.0455 0.0684 0.0939 0.1147 0.0573 0.0730 0.0584 0.0928 0.0729 0.1005 0.0768

0.0000 1.0290 1.4363 1.7388 0.8594 1.1357 0.8859 1.4296 1.1454 1.5273 1.1675

0.1017 0.0998 0.0981 0.0990 0.1000 0.0964 0.0989 0.0974 0.0955 0.0987 0.0986

0.00 70.89 143.06 205.76 49.26 92.68 53.43 143.51 95.83 159.51 93.43

crucial transitiona H H H H H H H H H H

→ → → → → → → → → →

L(71%) L(92%) L(78%) L (77%) L(61%) L(80%) L(82%) L(87%) L(92%) L(77%)

a

The H and L denote HOMO and LUMO, respectively.

M3O increase by increasing the natural charges on the related O and M atoms. For example, the K2LiO and K2NaO with the largest values of ηQ and CQ show higher natural charges on the O atom and M ligands. Since the magnitude and orientation of the CQ are basically sensitive to the condition around the nuclei, this parameter along with the ηQ seems to be a useful index to determine the M−O position in the superalkalis. 3.1.4. Dissociation Pathways. To explore the thermodynamic stability of the considered superalkalis, the dissociation energies (Edis) of the various fragmentation pathways were investigated. The computed Edis values of the superalkalis in various pathways are reported in Table 3, which gives a scale of their stabilities relative to plausible fragments. The large Edis represent that these superalkalis are more stable. Earlier calculations17 give Edis of 1.99 eV for Li3O and 1.74 eV for Na3O. Also, the experimental Edis for Na3O is 1.96 eV.88 The lowest Edis is seen for Li2KO with Li2KO → Li2O + K dissociation pathway (1.20 eV). Among the other superalkalis, the highest stability against dissociation is obtained for Li3O → O + Li3 (11.96 eV), Li2NaO → O + Li2 + Na (11.21 eV), Li2KO → O + Li2 + K (11.12 eV), Na2LiO → O + Li + Na2 (10.40 eV), LiNaKO → O + Li + Na + K (10.29 eV), and K2LiO → O + Li + K2 (10.13 eV) pathways. These results are in good agreement with the Ebin of the superalkalis reported in Table S2. As results show, the end Li atoms are possessing loosely the excess electron in the neighboring atom, contributing therein to stabilize the superalkalis. In this respect, we can realize that the favored dissociation pathway is the release of the Li atoms. The enthalpy changes (ΔH) of various fragmentation pathways were also calculated (at T = 298 K and P = 1 atm), as obtained from the frequency calculations. Consistent with the large Edis value, the more negative ΔH value (−11.89 eV) also indicates that the highest stability against dissociation for Li3O → O + Li3. 3.2. Superalkali−Superhalogen Donor−Acceptor Frameworks. 3.2.1. Structural, NBO, and Energetic Analyses. As pointed out earlier, the electronic structure and stability of metal clusters can be determined within jellium model.89 In the jellium model, the electronic structure of a system is described by one electron levels 1s, 1p, 1d, 2s, 1f, and 2p. For example, Al13 with 39 valence electrons corresponds to the electronic structure of 1s21p61d102s21f142p5 missing one electron in the HOMO, which represents a state similar to halogen atoms. Also, theoretical (EA = 3.57 eV)90 and

Figure 4. Correlation between the exactly computed β0 (blue curve) and that investigated by the two-level model (red curve) of the M3O− Al13.

Figure 5. Cartesian axis and the direction of the positive and negative electric fields (F, in 10−4 a.u.) in the superatoms M3O−Al13.

the superalkalis with pure ligands (Li3O, Na3O, and K3O) are negligible (ranging from 0.028 to 0.054). Also, the results show that the M ligands with the larger atomic numbers generally caused the charge distribution around the central O atom in the superalkalis M3O deviate significantly from axial symmetry. These results can be ascribed to the effect of chemical bonds or the electric field of the neighboring nucleus on the charge distribution in the considered superalkalis. To further describe the considered electronic properties of the superalkalis, NBO analysis (Figure S1) was performed to verify the 17O NQR parameters. Analyses of the results in Table 2 and Figure S1 demonstrate that the ηQ and CQ of the considered superalkalis F


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Inorganic Chemistry Table 6. First Hyperpolarizability (β0, in ×103 a.u.) with the OEEF (in ×10−4 a.u.) for the M3O−Al13 OEEF

Li3O

Na3O

K3O

Li2NaO

Li2KO

Na2LiO

Na2KO

K2LiO

K2NaO

LiNaKO

−70 −60 −50 −40 −30 −20 −10 0 10 20 30 40 50 60 70

1.36 2.15 3.67 3.82 5.49 7.07 7.65 10.42 14.44 19.34 25.21 35.50 45.91 66.14 179.68

0.31 1.89 2.62 4.15 6.01 6.57 8.03 12.91 14.97 18.42 21.85 38.72 66.59 153.93 780.74

0.31 2.79 4.37 7.74 8.03 11.34 11.35 15.45 21.44 31.90 51.95 101.56 1536.89 9824.38 76326.13

0.52 1.96 2.06 3.48 4.59 4.93 9.36 9.54 9.94 12.58 14.52 20.22 27.37 52.30 98.68

1.95 2.50 4.24 4.79 6.01 8.03 9.30 10.57 14.06 19.03 26.78 40.76 204.49 963.65 1870.59

0.32 1.34 3.05 3.28 5.05 6.48 6.92 10.39 12.59 15.77 21.39 29.75 52.07 106.45 375.60

1.05 2.81 3.59 5.25 7.05 7.38 9.87 13.00 15.11 20.24 30.13 47.03 231.37 1429.75 3467.00

0.62 2.45 2.96 4.63 6.76 7.38 9.26 12.45 13.45 23.03 33.00 54.22 147.68 300.90 1892.11

0.64 2.92 3.39 5.24 7.54 8.95 10.23 13.54 18.48 26.28 41.12 78.87 789.42 3527.16 6046.81

0.52 2.19 2.91 4.64 5.95 6.61 8.61 11.51 13.23 16.34 23.98 45.24 983.61 4513.85 9956.88

experimental (EA = 3.62 ± 0.06 eV)91 studies demonstrate that Al13 cluster has a high EA in comparison to 3.46 eV for Br atom and 3.61 eV for Cl atom. To examine the various DFT methods to reproduce the experimental EA of Al13 cluster, we tested considered XC functionals. The accuracy of the results has been explored by computing the vertical electron affinity (VEA) of Al13 and comparing the theoretical EAs with the experimental value (3.62 ± 0.06 eV).91 The calculated EAs of Al13 are given in Table S3. As results show, the M06 significantly outperforms other functionals, and its result for the EA (3.45 eV) is in better agreement with the experimental value (|Δ| = 5%). Now, the interesting question is to explore what kind of properties92 can obtain by linking the superalkalis M3O to the superhalogen Al13. Therefore, we begin with a discussion of the M3O−Al13 complexes. As Al13 needs only one electron to fill its valence shell, we examine only one superalkali M3O linked on the surface of Al13 cluster. A superalkali M3O was attached on top, bridge, or hollow site above Al13, and the geometry was fully optimized without any symmetry constraints. Figure 2 shows the optimized geometry of the pristine icosahedral (i-Al13), decahedral (d-Al13) and M3O−Al13 systems. It should be noted that we studied both the icosahedral and decahedral isomers of Al13. Our results show that the icosahedral isomer lies lower in energy (Ebin= −58.51 kcal mol−1) than does the corresponding decahedral isomer (Ebin=-57.79 kcal mol−1). In fact, in the case of the pristine Al13 cluster, an icosahedral is more stable than the decahedral isomer. This is in agreement with the previous study where a significant stability of the icosahedral isomer has been revealed.93 Accordingly, in the present work, we study icosahedral isomer of Al13 cluster as the building block for designing superalkali−superhalogen complexes. As shown in Figure 2, in the ground state, the oxygen atom of the superalkalis attach an on-top site above Al atom of Al13 cluster. Pristine Al13 has a point group of Ih, with Ci as one of its subgroups; thus, Al13 has centrosymmetry. The centrosymmetry of Al13 can be destroyed by linking it with a superalkali. The M3O−Al13 complexes were revealed to have point group of Cs. In pristine icosahedral Al13 cluster, the nearest-neighbor Al−Al distances range between 2.61 and 2.91 Å. This is in agreement with the previous study on Al13 cluster.94 Introduction of the superalkalis obviously lengthens the Al−Al bonds near the linked site. When linking the superalkali M3O to Al13, the Al− Al distance near the linked site can be lengthened from 2.61 Å

in pristine Al13 to 2.78 Å in Li3O−Al13, 2.82 Å in Na3O−Al13, and 2.87 Å in the K3O−Al13, respectively. Also, Al−O is an important bond in the studied M3O−Al13, as it has a charge transfer path role in the M3O−Al13 complexes to form a D-A framework. The geometrical parameters of the M3O−Al13 complexes are also represented in Figure 2. From this figure, the Al−O bond length decreases in the order Li3O−Al13 (1.79 Å) > Li2NaO−Al13 = Li2KO−Al13 (1.77 Å) > Na2LiO−Al13 (1.76 Å) > Na3O−Al13 = K2LiO−Al13 = LiNaKO−Al13 (1.75 Å) > Na2KO−Al13 (1.74 Å) > K3O−Al13 = K2NaO−Al13 (1.73 Å). To explore the stability of the M3O−Al13 complexes, we calculated interaction energy (Eint) values. As reported in Table 4, the Eint of Li3O−Al13 is −109.56 kcal mol−1, which is the lowest among the 10. With the increasing atomic number of the alkali ligand in the superalkalis, the Eint values increase, causing the interaction between the M3O and Al13 to become stronger; this could be realized as a companion effect of the shrinking of the Al−O bond length. The smaller distance of Al−O is expected to be more suitable for charge transfer and thus leads to superior NLO responses. We also found that the NBO charge on the M3O linked to Al13 increases with raising the atomic number of the M ligand, among which Li3O has the lowest charge (0.852e) while the K3O has the highest charge (1.129e) (Table 4). To gain deeper insight into the properties of the M3O−Al13 complexes, the EHL values have been calculated (Table 4). As seen in Table 4, the EHL of the pristine Al13 is 2.81 eV, which is a large value, offering Al13 itself should present semiconductor nature. The results also show that the EHL of Al13 can be significantly reduced by linking a superalkali onto its surface. Li3O−Al13, Na3O−Al13, and K3O−Al13 have the EHL of 2.29, 2.14, and 1.74 eV, respectively. It is obvious that the K3O lowered the EHL of Al13 by more than 38% and converted it to an n-type semiconductor. Also, the Fermi level locates at 1.40 eV below the LUMO for the pristine Al13. After linking the superalkalis to Al13, the Fermi level approaches the LUMO region (Table 4). This shift to higher energies leads to n-type semiconducting behavior in the M3O−Al13 complexes. To verify the effect of the M3O-linked superalkalis on the electronic properties of Al13 cluster, the corresponding density of states (DOSs) are plotted and represented in Figure 3, the corresponding frontier molecular orbitals (HOMO and LUMO) are also presented as subgraphs. The large EHL of the pristine Al13 can be clearly observed in the DOS plot, while G


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Inorganic Chemistry

Figure 6. Dependence of the β0 on the OEEFs (in 10−4 a.u.) for the superatoms M3O−Al13.

the situation is totally different for the M3O−Al13 complexes. As shown in Figure 3, there is a newly formed HOMO located between the original HOMO and LUMO. As a consequence, the original HOMO becomes HOMO−1, and the EHL becomes much smaller than the pure Al13. Also, the PDOSs show that for all the M3O−Al13 complexes Al13 unit contributes large majority to the HOMOs of DOS. Superalkalis M3O also have a minor contribution to the LUMOs, and we found the value consistently increases with rising the atomic number of the M ligands. Above analyses demonstrate that the linking with superalkali is an effective method of creating a new HOMO with higher energy than before so that the EHL could be decreased. Moreover, the EHL

of the M3O−Al13 can be tuned using mixed alkali ligands. For example, K2NaO−Al13 (EHL = 1.84 eV), K2LiO−Al13 (EHL= 1.89 eV), Li2KO−Al13LiNaKO−Al13 (EHL= 1.93 eV), and Na2KO−Al13 (EHL = 1.95 eV) lowered the EHL of Al13 by more than 35, 33, 32, and 30%, respectively. 3.2.2. Nonlinear Optical Responses. The NLO responses of the superatom M3O−Al13 compounds have been investigated by calculating the mean polarizability (α0) and first-order static hyperpolarizability (β0) as given in Table 5. The β0 is an important NLO response property we paid extensive attention to. Lack of the centrosymmetry is a prerequisite of nonvanishing β0. Obviously, the β0 of the pristine Al13 must be zero due to its centrosymmetry. After H


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Inorganic Chemistry

to the lower IP and the induced greater degree of charge transfer, it is very expected that linking Na3O and K3O to Al13 cluster can attain the higher β0 value. Indeed, our calculated β0 show that when replacing Li3O with Na3O and K3O, the β0 value of complex can be increased from 1.04 × 104 to 1.29 × 104 a.u. and to 1.55 × 104 a.u., respectively (Table 5). This can be chiefly due to the case that the attaching of K3O and Na3O can reduce the ΔE value (from 0.1017 to 0.0981 a.u.) and remarkably enhance the Δμ and f 0 values (from 1.0290 to 1.7388 a.u.) and (from 0.0684 to 0.1147 a.u), respectively. Evidently, linking the superalkali unit with the larger atomic number can more increase the α0 and β0 values of the M3O− Al13 complexes with the D-A framework. According to this exciting finding, we have further attached the mixed M3O to Al13 cluster in order to estimate whether replacing the alkali ligands of the M3O can more increase the α0 and β0 of considered systems. Our calculated results (Table 5) present that compared with Li3O−Al13 (α0 = 610.3 a.u. and β0 = 1.04 × 104 a.u.) and Na3O−Al13 (α0 = 631.8 a.u. and β0 = 1.29 × 104 a.u.), bonding superalkalis K2NaO and Na2KO can enhance the β0 value up to 1.35 × 104 and 1.30× 104 a.u., respectively. Now, we put all the parameters together in eq 8, to obtain the trend of the β0 value using the two-level formula Δμ f/ΔE3 (Figure 4). Accordingly, as shown in Table 5 and Figure 4, the observed trend of the β0 values approximately investigated by the twolevel model matches nicely with that exactly calculated values. In this respect, attaching the superalkalis can be an effective approach to increase the β0 of Al13 cluster via forming a typical D-A framework, where the atomic number of the alkali ligand in the superalkalis can play a very important role in enhancing the β0 value. 3.2.3. Effect of OEEFs on the NLO Responses. To reveal how the OEEFs affect the NLO responses, the considered superatoms M3O−Al13 have been optimized under the influence of OEEFs. Our calculations represent that the critical positive electric field for the M3O−Al13 is 70 × 10−4 a.u. (1 a.u. = 5.142 × 109 V cm−1) because a larger positive electric field will destroy their geometric structure. In this respect, the superatoms M3O−Al13 have been optimized under the influence of OEEFs with strengths ranging from −70 × 10−4 to 70 × 10−4 a.u. All the external electric fields have been imposed parallel to the charge transfer direction (M3O → Al13) in both directions, that is, positive fields (F > 0) with the direction of the M3O → Al13 and negative fields (F < 0) with the direction of the M3O ← Al13 (Figure 5). Our results show that the superatoms M3O−Al13 present relatively large NLO response without any OEEF (Table 5). However, one interesting question emerges: Can the NLO responses of the superatoms M3O−Al13 be increased by applying the appropriate OEEFs? Therefore, the β0 values of the M3O−Al13 under the chosen OEEFs have been calculated and listed in Table 6. To better represent the results, the correlation of the β0 values of the M3O−Al13 with the electric fields is exhibited in Figure 6. As shown in Table 6 and Figure 6, the β0 values of the superatoms M3O−Al13 gradually increase along with the applied OEEF changing from −70 × 10−4 to 70 × 10−4 a.u., revealing that the NLO response of the superatoms M3O−Al13 can be modulated by changing the strength and direction of an imposed OEEF. To be specific, the field-free β0 values of Li3O−Al13, Na3O− Al13, K3O−Al13, Li2NaO−Al13, Li2KO−Al13, Na2LiO−Al13, Na2KO−Al13, K2LiO−Al13, K2NaO−Al13, and LiNaKO−Al13

bonding the superalkalis, the centrosymmetry of Al13 is destroyed. β0 is no longer zero, and its magnitude mainly evaluated by electron donating capability of the superalkalis. It is extremely expected that this kind of the M3O−Al13 systems can represent the remarkable NLO responses because the linking of the superalkalis can not only break the centrosymmetry of Al13 cluster but also leads to the obvious charge transfer between the M3O and Al13 units. We calculated the α0 and β0 for the case of Al13 bonded with the M3O species (Table 5). Once Li3O is attached to Al13, the push−pull scheme of the electron creates between the two units and the valence electrons of the superalkali transfer to Al13 unit; these are the origin of the 1.04 × 104 a.u. of β0 of Li3O−Al13. When Na3O instead of Li3O is bonded, β0 was enhanced by more than 24%, chiefly because Na has a larger electropositivity than that of Li and hence has a higher ability to donate the electrons that to be transferred. Also, when K3O is bonded to Al13, a significantly large β0 (1.55 × 104 a.u.) can be obtained, which is as large as 50% more than that of the Li3O bonded case. As Table 5 shows, β0 decreases in the order K3O−Al13 > K2NaO− Al13 > Na2KO−Al13 > Na3O−Al13 > K2LiO−Al13 > LiNaKO− Al13 > Li2KO−Al13 > Li3O−Al13 = Na2LiO−Al13 > Li2NaO− Al13. It should be noted that the α0 and β0 of the M3O−Al13 vary in a similar fashion, which reduces along the same sets. Obviously, bonding the M3O superalkalis with the larger atomic number (K3O, K2NaO, Na2KO, Na3O, and K2LiO) can considerably increase the β0 of Al13 cluster. In fact, the β0 increases as the atomic number of the M ligand increases, which has recently been shown in Li+(calix (4) pyrrole) M− alkalides.95 The two-level model, which may explain the mechanism on how the β0 of the M3O−Al13 are affected, can be defined as96,97 β0 ∝

Δμ f ΔE3

(8)

where ΔE, f, and Δμ are transition energy, oscillator strength, and the difference of dipole moment between the ground state and excited state, respectively. The excited state we reported here is the lowest-lying one with high oscillator strength and is normally ascribed to the crucial state.98 For all the M3O−Al13 complexes, the first excited state can be considered the crucial state. Vividly, the crucial transitions of all the M3O−Al13 complexes represent charge transfer from the M3O to Al13, rationalizing the creation of the D-A framework. Here, to get ΔE, f 0, Δμ, and the molecular orbitals included in the corresponding crucial transition, the TD-DFT calculation was performed, as reported in Table 5. TD-DFT calculation presents that Al13 cluster has a large ΔE of 0.1017 a.u., which offers its valence electron is hard to be excited to higher-energy states. Also, from Table 5, the main reason leading to the vanishing β0 of Al13 is the zero value of Δμ due to the centrosymmetry. Compared with the pristine Al13 cluster, we can find that linking Li3O can considerably lower the ΔE value to as small as 0.0998 a.u. Meanwhile, the attaching of Li3O can bring a remarkable Δμ value (1.0290 a.u.) in the modified Al13 cluster. In this respect, the large decreased ΔE value and increased Δμ value should be the main reason for the significantly larger β0 value of Li3O−Al13 complex. Thus, bonding the superalkalis on Al13 cluster to form the typical D-A combination can considerably increase the β0 of Al13-based superatoms. Next, we calculate the β0 value of the N3O− and K3O−Al13 to explore the effect of the atomic number of the alkali ligand on the β0 of the M3O−Al13 complexes. According I


Article

Inorganic Chemistry are extremely enhanced to 179.68 × 103 a.u. (17-fold increase), 780.74 × 103 a.u. (60-fold increase), 76326.13 × 103 a.u. (4938-fold increase), 98.68 × 103 a.u. (24-fold increase), 1870.59 × 103 a.u. (176-fold increase), 375.60 × 103 a.u. (36fold increase), 3467.00 × 103 a.u. (266-fold increase), 1892.11 × 103 a.u. (151-fold increase), 6046.81 × 103 a.u. (466-fold increase), and 9956.88 × 103 a.u. (864-fold increase), respectively, via imposing an OEEF of 70 × 10−4 a.u. along the charge transfer direction, whereas they are decreased under OEEF of −70 × 10−4 a.u. against the charge transfer direction. We also found that under positive electric fields the β0 values of the superatoms M3O−Al13 are slowly enhanced in the range of low fields, but these are suddenly increased in the range of high fields, revealing that the enhanced influences of positive fields on the β0 are more clear for the larger electric fields. In this respect, the β0 of the M3O−Al13 are quickly enhanced when the applied OEEF is changed from 40 × 10−4 a.u. to the critical electric field (70 × 10−4 a.u.).

ORCID

Akbar Omidvar: 0000-0003-4691-4564 Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge support of the Shiraz University Research Council.

4. CONCLUDING REMARKS In this work, we provide theoretical evidence for the possibility of using the superatoms Al13 and M3O as building blocks to form materials with high NLO responses. DFT calculations show that the bonding superalkalis M3O to the superhalogen Al13 gives the combination, wherein the superatoms M3O−Al13 represent the significant NLO responses. Our results reveal that the electropositivity of the alkali ligands plays a crucial role in the IP values of the superalkalis. It was found that the ηQ values of the 17O nuclei considerably enhance with substituting the pure ligands with mixed ligands in the superalkalis M3O. Furthermore, it was shown that the CQ values of the 17O nuclei are sensitive to the corresponding intramolecular M−O bonds. In addition, the M3O units show high thermodynamic stability with respect to loss of small fragments, including Li atoms. It is worth mentioning that the superalkali linking leads to significant charge transfer from the M3O unit to Al13 cluster. Meantime, the EHL and β0 values of Al13 considerably decrease and extremely increase, respectively. Moreover, we show that the OEEF has the significant effect on the NLO responses of the superatoms M3O−Al13. Especially, the β0 can be considerably increased by increasing the OEEF strength from zero to the critical external electric field along the charge transfer direction. This represents that the applying an increasing OEEF, along with the charge transfer direction of the superalkali−superhalogen assemblage, is an effective strategy for significant enhancement of their NLO responses.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b01322. The NBO analysis, illustrations of HOMO and LUMO orbitals, structural properties, IP values, binding energies, and electronic spatial extent values of the pristine superalkalis M3O, as well as the EA values of Al13 cluster (PDF)

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REFERENCES

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