Effects of the Cage Unit Size and Number of Cage Units As Well As

Article pubs.acs.org/JPCA

Effects of the Cage Unit Size and Number of Cage Units As Well As Bridge Unit on the Second Order Nonlinear Optical Response in Multicage Electride Molecules Zhen-Bo Liu,†,‡ Yan-Chun Li,† Jia-Jun Wang,† Yang Bai,† Di Wu,† and Zhi-Ru Li*,† †

State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun, 130023, China. ‡ The Laboratory of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Yantai University, Yantai, 264005, China S Supporting Information *

ABSTRACT: Interesting effects of the cage unit size and number of cage units as well as bridge unit on the static first hyperpolarizabilities (β0) for novel multicage electrides are revealed. (1) The small cage unit C8 systems have larger β0 for cage unit size effect. (2) The β0 increases with increasing cage unit number. (3) The effect of the bridge between cage units on β0 is O > NH > CH2. Specially, a novel relationship between the excess electron cloud and β0 is revealed. Assembling the three effects, the constructed multicage electride structure with three small C8 cage units connected by the O-bridge (K···3C8(O)) is a electride salt K+[e@3C8(O)]− and has the considerable β0 value of 7.1 × 105 au, which is about 55 times larger than the 13 000 au of the single-cage electride molecule Na3O+(e@C20F20)−. The novel multicage strategy is effective to enhance nonlinear optical (NLO) response.

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previous researches43−48 show that the novel model systems with excess electron have large NLO responses. However, this type of NLO model system with excess electrons does not have a large stability because the excess electron is not protected inside the cage. Fortunately, an excess electron can be trapped inside a single molecular cage such as synthesized C60F60 and C20F20,49 forming a single molecular solvated electron e@CnFn (n = 20 and 60).50,51 Perfluorinated exohedral metallofullerenes52 are also reported. In 2012, the organic single-cage electride molecules M+(e@ C20F20)−, as the new nonlinear optical (NLO) molecules, were reported.45 The NLO molecules have improved stabilities due to the excess electron inside the single cage. The β0 values of single-cage structures are 600 (K+(e@C20F20)−) and 13 000 au (Na3O+(e@C20F20)−). How to enhance the β0 value for organic cage electride molecules with the excess electron inside the cage is a new challenge. New multicage electrides with the excess electron inside the multicage exhibiting large β0 is expected. The mechanism of forming the multicage organic electride molecule is unusual and shown in Scheme 1. Alkali metal atom K doping on the multicage, the multicage electride with the excess electron inside the cage, is formed due to a long-range electron transfer from K to multicage (see HOMO). In the lowenergy transition (from HOMO to LUMO) of the multicage

INTRODUCTION Unordinary electrides, a kind of multielectron many-cage solid salts with anions containing excess electrons inside the cages, have attracted significant interest in the past decades due to their potential applications.1−10 Several electrides have been synthesized by Dye and other groups.4−13 Owing to loosely bound excess electrons, electrides have broad or potential applications in chemical synthesis, catalysis, nanodevices, and functional materials.1−10,14 How to construct molecules of an organic electride with the excess electron inside the cage(s) is a challenge to chemists. The different kinds of organic electride molecules with excess electrons inside the cage(s) may become new molecular materials and electronic devices. For nonlinear optical (NLO) molecules and materials, in the last few decades, great efforts have been devoted to design various inorganic crystals15−18 that exhibit large NLO responses. For dendrimers,19 organic20,21 and metal−organic salts,22 large static first hyperpolarizabilities (β0) are obtained. Nanosystems including nanoparticle,23 nanotube,24 and nanocone25 for large NLO responses have been reported. New approaches including cation and external electric field have been used for strongly enhancing NLO response.26,27 For unusual ground electron state, NLO responses of open-shell singlet systems are fascinating.28,29 In metal-doping research, Champagne et al30−38 reported the dramatic effects of charging on the second hyperpolarizability by doping alkali atoms. Recently, some large β0 values have been reported for alkali metal doping nanotube and graphene systems.39−42 Our © 2013 American Chemical Society

Received: May 11, 2013 Revised: June 25, 2013 Published: July 2, 2013 6678

dx.doi.org/10.1021/jp404671w | J. Phys. Chem. A 2013, 117, 6678−6686

The Journal of Physical Chemistry A

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In this work, the static first hyperpolarizabilities (β0) are evaluated by using the LC-BLYP method. It has been employed to calculate the first hyperpolarizabilities of large molecular structures.55 For some large molecules, the Hartree−Fock (HF) method may not give quantitatively correct results.56 However, since the works of Champagne et al., it is well-known that DFT calculations, using conventional functionals, fail to correctly predict the amplitude of NLO properties of long organic materials.57,58 For the calculations of hyperpolarizabilities, Nakano and co-workers pointed out that for a medium-size system, the BHandHLYP method can also reproduce the hyperpolarizability values from the more sophisticated CCSD(T) method.59,60 For charge transfer systems, it is reported that the results of the BHandHLYP and M06−2X methods are close to those of CAM-B3LYP.61 CAM-B3LYP has been proven to be the good option for calculating the first hyperpolarizability of π-conjugated systems compared with the other methods.62 To select the suitable method for β0 calculation, the appropriate method to calculate the first hyperpolarizabilies of our K doped systems, we have used the small analogue K···2C8(NH) as a multicage sample to compute the β0 values by six different methods: MP2, LC-BLYP, M06−2X, HF, CAM-B3LYP, and B3LYP with the 6-311+G(d) basis set. The results are 7.2 × 104 (MP2), 6.1 × 104 (LC-BLYP), 5.9 × 104 (M06−2X), 5.7 × 104 (HF), 3.4 × 104 (CAM-B3LYP), and 7.9 × 103 au (B3LYP). As the calculated β0 value at the LC-BLYP level is roughly close to that at the MP2 level, the LC-BLYP/6311+G(d) method was chosen for the calculations of the first hyperpolarizability, to show physical rules and specifically the order of β0. The transition energy ΔE and the difference in the dipole moment between the ground and the excited state Δμ are calculated at the TD-LC-BLYP/6-311+G(d) level. The magnitude of the applied electric field is chosen as 0.0010 au, due to the flat region of β0 values around 0.0010 au. All calculations were performed with use of the GAUSSIAN 09 program package.63 When a system is in a weak and stable applied electric field, its energy can be written as:

Scheme 1. The Unusual Mechanism of Forming the Multicage Electridea

a

Alkali metal atom K doping on the multicage, the multicage electride with the most excess electron inside the cage, is formed due to a longrange electron transfer from K to the multicage (see HOMO). In the low-energy transition (from HOMO to LUMO) of the multicage electride molecule, new long-range electron transfer from K to the second cage unit occurs. The multicage electride has a large first hyperpolarizability.

electride molecule, new long-range electron transfer from K to the second cage unit occurs. In this paper, our investigation aims at obtaining the structures of new multicage organic electride salt molecules, showing the localization of an excess electron inside the multicage of the electride salt molecules, exhibiting the effects of the cage unit size and number of cage units as well as bridge unit on the β0, and revealing the new relationship between the excess electron cloud and β0.The provided knowledge is significant for designing new NLO molecules, materials, and electronic devices with electrons inside the cages.

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COMPUTATIONAL DETAILS Very recently, the structures and properties of the guanine− cytosine base pair have been successfully calculated by the density functional theory (DFT) with use of the long-range correction (LC-BLYP) method.53 For multicage organic electride molecules with long-range interaction (about 3 Å of K···F) and relevant molecules, the optimized geometric structures of undoped and alkali metal doped multicages with all real frequencies were obtained by using the LC-BLYP method and the 6-31G(d) atomic basis set. MK (Merz− Kollman) charges54 are calculated at the LC-BLYP/6311+G(d) level, due to the NBO charge (2.793) of K in K···2C20(O) being too large (see Table 1).

E = E 0 − μα Fα −

a

structure

K···F

K···BAa

d

qK

3C8(NH) K···2C14(O) K···2C10(O) K···2C20(O) K···1C8 K···3C8(CH2) K···3C8(NH) K···2C8(O) K···3C8(O)

face face face face edge edge edge edge

2.555 2.551 2.724 2.813 2.783 2.774 2.749 2.735

7.433 6.221 7.663

3.868 2.996 4.333 2.727 2.730 2.730 2.729 2.729

0.891(0.899) 0.892(0.894) 0.877(2.793) 0.859(0.846) 0.001(0.056) 0.087(0.100) 0.636(0.540) 0.635(0.533)

5.903 5.711 5.715 5.714

(1)

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:

Table 1. The Distances (Å), Cage Unit Diameter (d in Å), Charges (qK) of Merz−Kollman, and NBO (in parentheses) for Alkali Metal Atom K at the LC-BLYP/6-311+G(d) Level doping mode

1 1 ααβFαFβ − βαβγFαFβFγ ... 2 6

μ0 = (μx 2 + μy 2 + μz 2 )1/2

(2)

1 (αxx + αyy + αzz) 3

(3)

α0 =

The static first hyperpolarizability is noted as: β0 = (βx 2 + βy 2 + βz 2)1/2

(4)

where βx =

The bridge atom BA = O, N for NH and C for CH2. 6679

3 (β + βxyy + βxzz ) 5 xxx dx.doi.org/10.1021/jp404671w | J. Phys. Chem. A 2013, 117, 6678−6686


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βy =

3 (β + βyxx + βyzz ) 5 yyy

βz =

3 (β + βzxx + βzyy) 5 zzz

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2) > 2.735 Å (n = 3) for K···nC8(O) (n = 1, 2, and 3). The cage unit number effect of the K···F distances shows that the K···F distance decreases and interaction between K and cage increases with the increasing unit number. From Table1, it is exhibited that K···BA distance (between K and bridge atom BA) relates to the doping mode. For the K···1C8 electride molecule without the bridge, the face doping mode is adopted. Electride molecules with the bridge unit, K···2C10(O), K···2C14(O), and K···2C20(O), have a large cage unit diameter d = 2.996−4.333 Å leading to large K···BA distances of 6.221−7.663 Å, so the structures with large cage unit adopt the face doping mode (see Figure 1). For structures with small cage C8 unit(s), the small d of about 2.73 Å relates to small K···BA distances of 5.715−5.903 Å, so the edge doping mode is formed due to obvious attraction between the K atom and near bridge atom. This cage unit size effect brings not only different doping modes but also the change of β0 values. Multicage Electride Molecules. From Figure 2, the highest occupied molecular orbitals (HOMOs) exhibit the

RESULTS AND DISCUSSION Optimized Structures. To gain large NLO response, the connected fluorinated carbon cage CnFn−2(4) (marked Cn and n = 8, 10, 14, and 20) units by bridge units (CH2, NH, O) as the multicage electron trappers and the alkali metal atom K as the source of the electron were used. The optimized geometric structures of doped and undoped multicage (cage unit number, n = 1, 2, 3) electride molecules (in Figure 1) with all real frequencies were obtained at a density functional theory (DFT) with the long-range correction, the LC-BLYP/6-31G(d) level.

Figure 1. The optimized geometries for multicages doped by alkali metal K.

The molecular symbol 3C8(NH) for an undoped system represents three fluorinated C8 cage units connected by NH bridge units. The different cage unit sizes (n = 8, 10, 14, and 20) are also selected, such as K···2C8(O), K···2C10(O), K···2C14(O), and K···2C20(O) for K doped systems. In addition, the selected bridge units between the cage units are CH2, NH, and O, such as K···3C8(CH2), K···3C8(NH), and K···3C8(O). Specially, the cage unit numbers (1, 2, and 3) of the multicage electrides are investigated for K···1C 8 , K···2C8(O), and K···3C8(O). For the alkali metal atom K doping mode types, Figure 1 shows that the structures with face doping mode (alkali metal atom doping on the face of F atoms) include K···2C20(O), K···2C10(O), K···2C14(O), and K···1C8, while edge doping mode structures (K atom doping on the edge formed by two F atoms) include K···3C8(B) (B = CH2, NH, and O). Table 1 shows that the range of large K···F distances is from 2.456 to 2.813 Å, which exhibits that the doped molecules are longrange interaction systems. For the K···F distances of K···2Cn(O) (n = 8, 10, 14, and 20), the polyhedron character effect of the different size cage unit is obvious. The structures with regular polyhedron units have larger K···F distances (2.749 for n = 8 and 2.724 for n = 20), but the structures with nonregular polyhedron units have shorter K···F distances (2.551 for n = 10 and 2.555 Å for n = 14). For the bridge unit effect, the K···F distances are 2.783 (B = CH2) > 2.774 (B = NH) > 2.735 Å (B = O) for K···3C8(B) (B = CH2, NH, and O). The order of K···F distances is 2.813 (n = 1) > 2.749 (n =

Figure 2. The HOMOs. For face doping modes, excess electron clouds locate mainly inside the multicages; for the edge doping modes with non-O bridge units, K•••3C8(B) (B = CH2 and NH), excess electron clouds locate near the K atom, and the edge doping modes with O bridge units, not only the most excess electron cloud inside the multicage but also a small portion of the dispersive electron cloud still near K. The electron cloud distribution relates to the first hyperpolarizability.

formation and location of the anion of excess electron for doped systems. Interestingly, the location of excess electron depends on the cage unit (in the middle between K and a bridge atom) size and the bridge unit property. For large cage unit size (n > 8) systems with bridge and without obvious interaction between K and bridge atom due to the long K···BA distances, the face doping mode is adopted and excess electron clouds of the systems are almost inside the large cage unit with large inner attractive potential. For the small single-cage K···1C8 electride molecule, the face doping mode is also adopted and excess electron cloud is almost inside the small cage due to no bridge. For small cage unit size (n = 8) systems with a bridge, the K···BA distance is not large and the bridge atom pulls the K atom away from the face doping mode, which forms the edge 6680



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It is shown that α0 relates to the electronegativity of the bridge atom. We focus on the structure effects on the hyperpolarizability. The large static first hyperpolarizabilities (β0) at the LC-BLYP/ 6-311+G(d) level are exhibited for multicage electrides (see Table 2 and Figure 3). The order of the β0 values in Table 2 is

doping mode. Considering the effect of bridge on excess electron cloud for small cage unit size (n = 8) systems, the large electronegative O bridge connects the C8 cages, most excess electron cloud is inside the C8 cage unit with larger inner attractive potential and a small portion of the excess electron cloud is near K, while in the C8 cage systems with CH2, NH bridge, most excess electron cloud is still near the K atom due to the short attractive potential of the C8 cage connected to the bridge atom of small electronegativity. This indicates that long-range electron transfer from the K atom to the multicage occurs in face doping mode systems and edge doping mode with O bridge systems. Table 1 shows that MK charges of 0.859−0.892 for the K atom for face doping modes and 0.635−0.636 for edge doping modes with O bridge units are roughly close to 1, while the charges of −0.635 to −0.892 are close roughly to −1 for the multicages. These indicate that the multicaged organic electride salt molecules with the excess electron anion inside the multicage are formed for the structures of face dopeing modes and edge doping modes with an O bridge. The electron wrapped inside its electron hole multicage is an unusual electron−hole (multicage) pair that is different from the spatially separated electron−hole pair in usual cases. For the edge doping modes with non-O bridge, K···3C8(B) (B = CH2 and NH), excess electron clouds locate near the K atom, so the K atom has a small charge (below 0.088). For these electride molecules, the excess electron does not reach inside the multicage. Static First Hyperpolarizabilities and Relative Properties. To exhibit the first hyperpolarizabilities and relative properties of multicage electride molecules, the ground-state dipole moments (μ0), static polarizabilities (α0), and first hyperpolarizabilities (β0) at the LC-BLYP/6-311+G(d) level for optimized structures are listed in Table 2.

Figure 3. The β0 value mainly increases with the decreasing of ΔE. Specially, edge doping modes have larger β0 than face doping modes.

5.0 (3C8(NH)) < 9.8 × 102 (K···2C14(O)) < 1.4 × 103 (K···2C10(O)) < 1.9 × 103 (K···2C20(O)) < 5.4 × 103 (K···1C 8 ) < 1.2 × 10 5 (K···3C 8 (CH 2 )) < 1.9 × 10 5 (K···3C8(NH)) < 5.4 × 105 (K···2C8(O)) < 7.1 × 105 au (K···3C8(O)). Analyzing structure characters and the β0 values, for the doped systems, some interesting effects of the cage unit size and number of cage units as well as bridge atom on the β0 are revealed. (1) For the size effect of the cage unit, the small cage unit brings large β0. For example, β0 values are 5.4 × 105 (K···2C8(O) with the small cage unit) ≫ 9.8 × 102 au (K···2C14(O) with the large cage unit). (2) The cage unit number effect is great for the multicage electride molecules. For K···nC8(O) (n = 1, 2, and 3), the order of the β0 values is 5.4 × 103 (K···1C8) < 5.4 × 105 (K···2C8(O)) < 7.1 × 105 au (K···3C8(O)). (3) The effect of the bridge between cage units on β0 also shows that O > NH > CH2 for the K···3C8(B) (B = O, NH, and CH2). To find some clues for understanding these effects, we will consider the sum over states method of the two-level model:64

Table 2. The Ground-State Dipole Moment μ0 (au), the Polarizability α0 (au), the First Hyperpolarizability β0 (au) at the LC-BLYP/6-311+G(d) Level, and the Transition Energy ΔE (eV) at the TD-LC-BLYP/6-311+G(d) Level structure 3C8(NH) K···2C14(O) K···2C10(O) K···2C20(O) K···1C8 K···3C8(CH2) K···3C8(NH) K···2C8(O) K···3C8(O)

doping mode

μ0

α0

face face face face edge edge edge edge

0.528 5.118 4.746 5.459 4.177 0.153 0.280 4.528 4.768

239 296 220 412 130 765 841 715 902

5.0 9.8 1.4 1.9 5.4 1.2 1.9 5.4 7.1

β0

ΔE

× × × × × × × ×

4.944 2.720 2.973 2.457 3.081 0.982 0.850 0.725 0.680

102 103 103 103 105 105 105 105

β0 ∝ Δμf0 /ΔE3

where ΔE, f0, and Δμ are the transition energy, oscillator strength, and the difference of the dipole moment between the ground state and the crucial excited state, respectively. In the two-level expression, the third power of the ΔE is inversely proportional to the β0 value, Δμ and f 0 are proportional to the β0 value. These physical quantities describing electron transition properties are useful to understand the β0 value changing with the structure. For finite field theory, electron density distribution ρ(r) can also be expanded in a Taylor series in the electric field65

For the dipole moments, it is found that the μ0 values (4.528−5.459 au) for the systems with an O bridge unit are larger than those (0.153−0.811 au) for the systems with a nonO bridge unit in the alkali metal doped systems (face doping modes and edge doping modes), which is the effect of the bridge unit on dipole moment and relates to the K atom charge (see Tables 2 and 1). For the cage unit number effect on the polarizability (α0), the α0 increases naturally with the increase of cage unit number, 130 (K···1C8) < 715 (K···2C8(O)) < 902 au (K···3C8(O)). The bridge unit (B) effect on α0 shows that 902 au (O) > 841 au (NH) > 765 CH2) for K···3C8(B) (B = O, NH, and CH2).

ρ(r ) = ρ(r )0 + Aj (r )Fj + Bjk (r )FjFk + ...

The ßijk is also obtained easily from the second-order polarization density coefficient Bjk(r) 6681


The Journal of Physical Chemistry A βijk =

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unit, due to the electronegativity of O closing to the F atom, the cage units still have larger electron inner attraction potential to form the multicage electride molecules with not only the most excess electron cloud inside the multicage but also a small portion of the electron cloud with large dispersiveness near the K atom. This large-area dispersive electron cloud accompanies the small ΔE (0.725 and 0.68 eV), which brings large β0 values (5.4 × 105 and 7.1 × 105 au). From above, the relationship between the β0 value and the excess electron cloud is summarized. The electron cloud is almost captured inside the cage unit(s) (see the first line in Figure 2), the system has a small β0 value (in the large cage systems with face doping mode). The electron cloud is near the K atom and not captured inside the cage unit (see the last line in Figure 2), the system has a larger β0 value (in the small cage connected non-O bridge systems with edge doping mode). Most electron cloud is wrapped inside the cage unit(s) and a small portion of the cloud with large dispersiveness is near the K atom (see the middle line in Figure 2, except the K···1C8 case), the system with the large-area dispersive electron cloud has a large β0 value for the small C8 cage O bridge systems with edge doping mode. For the multicage effect, in the case of fixed cage and bridge units, the cage unit number effect is great for the multicage electrides. From Table 4 and Figure 5, the order of the β0

∫ rBi jk (r) dr 2

This formula shows the correlation between the molecular electron density distribution (electron cloud) and β0 value through ßijk. In the molecular electron cloud, the excess electron cloud in HOMO may be the most sensitive to the action of an electric field, so the excess electron cloud should be relevant with the β0 value. For the two-level model (considering electron transition properties), the electron clouds of designated frontier orbitals in crucial transitions are needed for understanding the relationship between structural characteristics and β0. We consider the effects of the cage unit size and number of cage units as well as the bridge atom on β0 (see Figure3). For the cage unit size effect on β0 (see Table 3 and Figure 4), the Table 3. The Cage Unit Size Effect of β0: β0 (au), ΔE (eV), and Charge qK (MK) in the Electrides at the LC-BLYP/6311+G(d) Level structure

β0

K···2C14(O) K···2C10(O) K···2C20(O) K···2C8(O)

× × × ×

9.8 1.4 1.9 5.4

ΔE 2

10 103 103 105

2.720 2.973 2.457 0.725

transition H H H H

→ → → →

L+6 L L+2 L

qK(MK) 0.891 0.892 0.877 0.636

Table 4. Effect of the Cage Unit Number on β0: β0 (au), ΔE (eV), and the HOMO-LUMO(+8) Gap Δε (eV) at the LCBLYP/6-311+G(d) Level structure

β0

Δε

ΔE

transition

K···1C8 K···2C8(O) K···3C8(O)

5.4 × 103 5.4 × 105 7.1 × 105

9.139 3.563 3.509

3.081 0.725 0.680

H→L+8 H→L H→L

Figure 4. The change of β0 values with cage unit size and ΔE as well as electron cloud.

large cage unit (n > 8) systems (the K···BA distance is long and interaction between the K atom and the bridge atom is weak due to the isolation of large cage unit) and small 1C8 cage without bridge atom system, the K atom adopts the face doping mode. From Figure2, the excess electron cloud (in HOMO) almost completely is captured inside the cage units accompanying the larger transition energy (2.457−3.081 eV), which leads to the smaller β0 (about 103 au). For the small cage unit C8 systems, the K atom is near the bridge atom and attracted by the near bridge atom forming the edge doping mode. For the systems with non-O bridges, owing to the smaller electronegativities of the bridge (NH and CH2) atoms, the C8 cage unit does not have enough inner attractive potential to pull the excess electron inside the small C8 cage unit, so the excess electron cloud with dispersiveness is near the K atom accompanying the smaller transition energy ΔE (0.850 and 0.982 eV), which brings larger β0 values (1.2 × 105 and 1.9 × 105 au). For the small C8 cage unit systems with the O bridge

Figure 5. Cage unit number dependence of β0.

values is 5.4 × 103 (K···1C8) < 5.4 × 105 (K···2C8(O)) < 7.1 × 105 au (K···3C8(O)) for K···nC8(O) (n = 1, 2, 3). From HOMOs of Figure 6, the single-cage system (K···1C8) with face doping mode, the excess electron cloud is trapped inside the single cage tightly. For the edge doping systems with cage unit number n = 2 and 3, most electron cloud is wrapped inside the cage unit and a small portion of the cloud with large dispersiveness is near the K atom. For the portion of the cloud with large dispersiveness near the K atom, the system with 3 cage units is larger than the system with 2 cage units. So that the portion of the loosely bound electron cloud near the K atom increases with cage unit number (n) and the portion of the electron cloud inside the cage C8 unit decreases with n, 6682



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Figure 6. The transitions. In HOMOs, the portion of the electron cloud near the K atom increases with cage unit number (n) and the portion of electron cloud inside cage C8 decreases with n, which accompanies the decrease of ΔE and increase of β0. Figure 7. The bridge effect on β0 relates to ΔE and Δμ.

which accompanies the decrease of ΔE with n. Therefore, it is exhibited that β0 increases with the increase of cage unit number. The cage unit number is an important factor for manipulating β0. Considering the effect of the bridge unit on β0, based on cage unit size and number effects, the systems with a small size cage unit and three cage units K···3C8(B) (B = O, NH, CH2) are selected. From Table 5, the order of β0 values is 7.1 × 105 (O) > 1.9 × 105 (NH) >1.2 × 105 au (CH2). The effect of the bridge unit on β0 is O > NH > CH2. The bridge effect on the β0 value relates to two electron structure factors of ΔE and Δμ (see Figure 7). In Figure 8, the excess electron cloud is in a large spatial range from near K to inside the cage for the system with the O bridge, the cloud is near K and a small portion inside the first cage unit for the system with the NH bridge, and almost all of the electron cloud is near K for the system with the CH2 bridge. The decrease of electron cloud dispersiveness accompanies the increase of ΔE and the decrease of β0 for B = O, NH, and CH2. Considering the charge transfers in the assigned transitions (from HOMO to LUMO) in Figure 8, the main long-range charge transfers from K to the second cage for the O bridge, the electron transitions from K to the first cage (entering most electron cloud) and the second cage (entering small electron cloud) for the NH bridge, and the electron transitions from K to the first cage (see the LUMO) for the CH2 bridge. Obviously, in these transitions for B = O, NH, and CH2 the charge transfer degree decreases, which relates to the decrease of Δμ and decrease of β0. On the basis of the changes of electron clouds in HOMO and the charge transfer degree in transitions, it is easily understand that the effect of the bridge unit on β0 is O > NH > CH2. Integrating the above three effects, the multicage electride molecule with considerable β0 is constructed. For the K-doped structure of the edge mode, considering size and number effects of the cage unit, three small C8 cage units is adopted; considering the bridge effect, the O-bridge is used. In this work,

Figure 8. HOMO electron clouds. The cloud locates on a large area near K and inside the cage for the system with the O bridge, it is near K for the system and very slightly inside the first cage unit for the system with the NH bridge, and it is near K for the system with the CH2 bridge.

the constructed K···3C8(O) molecule is a salt K+[e@3C8(O)]− and has the largest β0 value of 7.1 × 105 au, which is about 55 times larger than 13 000 au for Na3O+(e@C20F20)− with the C20F20 single-cage and superalkali effect.45 It is explored that constructing the multicage electride molecule with incomplete excess electron cloud inside the multicage is a new strategy to enhance the nonlinear optical response. Comparing to the molecule 3C8(NH), the K···3C8(NH) structure increases the β0 value by about 40 000 times due to the doping effect. This enhancement is much higher than that in previous work. In previous work on alkali metal atom doping effect, the β0 value increased by about 20 times from 390 (calix[4]pyrrole) to 7326 au (Li@calix[4]pyrrole).46 Another doping effect brings only a 687 times increase from 112 (H− (CF2−CH2)3−H) to 76 978 au (Li2−H−(CF2−CH2)3−H).48 It has been reported that the β0 value increases by about 340 times from 68 (B10H14) to 2.3 × 104 au (Li@B10H14).66 Recently the β0 value increases by about 2700 times from 2.9 × 102 (UD) to 7.8 × 105 au (HF--LF) due to the edge-type push− pull electronic effect from alkali metal doping.67 Obviously,

Table 5. The Bridge Unit Dependence of β0: β0 (au), Δμ (au), ΔE (eV), the HOMO-LUMO Gap Δε (eV), and the Shortest K···F (Å) structure

bridge

β0

Δμ

ΔE

Δε

transition

K···F

K···3C8(CH2) K···3C8(NH) K···3C8(O)

CH2 NH O

1.2 × 105 1.9 × 105 7.1 × 105

4.75 4.86 6.97

0.982 0.850 0.680

4.023 3.870 3.492

H→L H→L H→L

2.783 2.774 2.736

6683



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ACKNOWLEDGMENTS This work was financially supported by the National Natural Science Foundation of China (Nos. 21173098, 21173095, 21103065, and 21043003), and the Fund for Doctor of Yantai University (No. HY12B26).

doping alkali metal atom on the multicage is a new effective strategy to enhance the β0 value. It is well-known that many important papers on enhancing the NLO response have been published. Recently, the zwitterionic systems and charged species have exhibited exceptional hyperpolarizabilities.30,36,68−73 For these molecules with the β0 of about 105 au, a donor−acceptor polyene compound (1.7 × 105),74 an organometallic system (8.6 × 104),75,76 a pyridinium hexafluorophosphate (3.35 × 105),71 and tubiform multilithium salts (1.47 × 105)42 are reported. For these systems with the β0 of about 106 au, a benzothiazolium salt (1.93 × 106 au, 16664 × 10−30 esu)20 and a Li6@ pentacence (4.50 × 106)41 are interesting. The β0 value of 7.1 × 105 au of our K···3C8(O) structure with excess electron protected inside the cage is close to those large β0 values.

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CONCLUSIONS To obtain large NLO response, different multicage electride molecules with an excess electron are constructed. New effects of the cage unit size and number of cage units as well as bridge unit on the β0 are revealed. (1) For the small cage unit C8 systems, the K atom is attracted by the near bridge atom and adopts the edge doping mode, which brings larger β0, due to the dispersive electron cloud incompletely captured inside the cage units or electron cloud still near K, accompanying the smaller transition energy. (2) The effect of increasing cage unit number is great in enhancing β0, due to the increased excess electron dispersive space in the multicage electrides. (3) The effect of the bridge between cage units on β0 is O > NH > CH2, which relates to the evolution of the excess electron cloud accompanying the increase of transition energy and decrease of the dipole moment difference between the ground state and the crucial excited state. A new relationship between the excess electron cloud in HOMO and β0 is revealed. The excess electron cloud almost captured inside the multicage corresponds to small β0 and the electron cloud near K and far away from the multicage corresponds to larger β0, while for not only the most excess electron cloud inside the multicage but also a small portion of dispersive electron cloud still near K, the large-area and nonuniform electron cloud corresponds to large β0. On the basis of the three effects, the constructed multicage electride structure of three small C8 cage units connected by the O-bridge (K···3C8(O)) is a salt K+[e@3C8(O)]− and has the considerable β0 value of 7.1 × 105 au, which is about 55 times larger than the 13 000 au of the single-cage electride molecule Na3O+(e@C20F20)−. The novel multicage strategy is effective to enhance nonlinear optical (NLO) response. ASSOCIATED CONTENT

S Supporting Information *

The complete author lists of references with more than 10 authors. This material is available free of charge via the Internet at http://pubs.acs.org.

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Effects of the Cage Unit Size and Number of Cage Units As Well As

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