Structural, Electronic, and Nonlinear Optical Properties of C66H4 and C70Cl6 Encapsulating Li and F Atoms.

Recently, nonclassical fullerene derivatives C66H4 and C70Cl6, which both contain two negatively curved moieties of heptagons, have been successfully synthesized. Inspired by these experimental achievements, the structural and electronic properties of C66H4, C70Cl6, Li@C66H4, F@C66H4, Li@C70Cl6, and F@C70Cl6 were systematical studied through density functional theory calculations in this work. Our results show that the reduction of the front molecular orbital gap of fullerene derivatives occurs with the introduction of Li and F atoms. After quantitative analysis of back-donations of charge between an encapsulated atom and an external carbon cage, it is found that C66H4 and C70Cl6 prefer to act as electron acceptors. It is interesting to note that the strong covalent nature of the interactions between a F atom and a carbon cage is observed, whereas the weak covalent and strong ionic interactions occur between a Li atom and a carbon cage. On the other hand, according to the first hyperpolarizability results, the encapsulation of the Li atom enhances the nonlinear optical response of fullerene derivatives. This work provides a strategy to improve nonlinear optical properties of C66H4 and C70Cl6, reveals the internal mechanism of the contribution from Li and F atoms to endohedral fullerene derivatives, and will contribute to the designation of endohedral fullerene derivative devices.

Introduction

Since the discovery of the first fullerene C60 by Kroto et al.[1] in the experiment of laser gasification of graphite in 1985, fullerenes have attracted extensive attention due to their unique physical and chemical properties.[2−8] Later, structural characterization confirmed that C60 is a closed cage structure composed of 20 hexagons and 12 nonadjacent pentagons, where the 60 carbon atoms are completely equivalent, adding a new allotrope to the elemental carbon family. Nowadays, fullerenes have been defined as closed cage-like carbon cluster molecules composed of carbon atoms, in which the carbon atoms are sp2 hybridized and three-fold coordinated. The distinctive cavity structure of fullerenes allows them to trap atoms or clusters and form the so-called endohedral fullerenes.[9] The first macroscopic quantity of endohedral fullerene La@C82 was synthesized by Smalley et al.[10] in 1991, and since then, a wide variety of endohedral fullerenes have been developed.[11−16] Compared with parent fullerenes, endohedral fullerenes have been found to have better performance due to the charge transfer between trapped atoms and the external carbon cage, which make them important in various fields such as organic electronics,[17] biomedicine,[18,19] cosmetics,[20] nonlinear optics,[21,22] etc.

Fullerenes following the well-known isolated-pentagon rule (IPR) only containing pentagons and hexagons are “classical fullerenes”.[23] Outside of this rule, the so-called “nonclassical” fullerenes containing quadrilaterals or heptagons have been found.[24,25] Recently, researchers have synthesized two nonclassical fullerene chloride- and hydride-containing heptagons, C70Cl6 and C66H4.[26,27] In previous experiments, all of the synthesized C70 isomers had a positive curvature. C70Cl6 is the first nonclassical C70 fullerene derivative that possesses two negatively curved heptagons captured in situ from a chlorine-containing carbon arc. On the other hand, C66H4 is the first nonclassical fullerene containing two heptagons and features with its smallest size among synthesized fullerenes with two heptagons currently. Interestingly, for both C70Cl6 and C66H4, two pairs of double-fused pentagons can be observed, which are exactly fused to two concave heptagons. Theoretical calculation results discover that the strain in the fused pentagons is released by the adjacent heptagon, the modified chlorine, and hydrogen atoms. Meanwhile, the sp2-hybridized carbon atoms connected with chlorine and hydrogen atoms are converted into sp3-hybridized atoms.

Considering that Li and F are the elements with low first ionization energy and high electron affinity,[28] respectively, we suppose that introducing these elements into the nonclassical C70Cl6 and C66H4 will exert a distinctive influence on their electronic properties, and thus on their application performance. At present, the scale of previous studies on encapsulating Li and F atoms into fullerenes is limited, and nonetheless, their results favor that Li- and F-encapsulated endohedral fullerenes have novel properties.[29−32] It is, therefore, valuable to investigate the interactions between the internal Li and F atoms and the C66H4 and C70Cl6 carbon cages for fullerene designation and its property improvement. In this work, we have systematically studied the geometries and electronic properties of C66H4 and C70Cl6 with encapsulating Li and F atoms based on density functional theory calculations. Despite fundamental physical chemistry properties, we also focus on the influences of Li atoms on nonlinear optical properties of C66H4 and C70Cl6 that directly reflect the application value of these nonclassical endohedral fullerenes.

Results and Discussion

Optimized geometries of C66H4, C70Cl6, Li@C66H4, F@C66H4, Li@C70Cl6, and F@C70Cl6 are presented in Figure . The detailed bond lengths, radii that coordinate the carbon cage center along X, Y, and Z directions, and encapsulation energies of fullerene derivatives are given in Table . As shown in Table , compared with C66H4 and C70Cl6, slightly changes in the bond lengths of C5–5 and C5–7 are observed on Li@C66H4, F@C66H4, Li@C70Cl6, and F@C70Cl6. Moreover, their radii in the X, Y, and Z directions are almost equal to the corresponding values in C66H4 and C70Cl6 too. Therefore, the encapsulation of F and Li atoms has a limited effect on the deformation of the total cage framework. However, it is noted that F atoms cause the collapse of the local C atoms in the carbon cage. This phenomenon is due to the strong covalent interaction between the F atom and the carbon cage. In addition, F@C66H4 and F@C70Cl6 have larger encapsulation energies (64.07 and 64.81 kcal/mol) than the Li encapsulation cases, reflecting that the encapsulation of F atoms in the fullerene cages is easier than that of Li atoms.

Figure 1

Optimized geometries of C66H4, C70Cl6, F@C66H4, F@C70Cl6, Li@C66H4, and Li@C70Cl6. Cyan, white, green, pink, and mauve balls denote C, H, Cl, F, and Li atoms, respectively.

Table 1

Bond Lengths for C5–5 (Pentagon–Pentagon, d5–5, Å) and C5–7 (Pentagon–Heptagon, d5–7, Å), Encapsulation Energies (Een, kcal/mol) of X@C66H4 and X@C70Cl6 (X = F and Li), and Their Radii along the r, r, and r (Å) Directions

molecule	d5–5	d5–7	Een	rX	rY	rZ
F@C66H4	1.59–1.59	1.53–1.54	64.07	3.84	3.26	3.96
Li@C66H4	1.59–1.60	1.54–1.54	42.38	3.84	3.28	3.95
F@C70Cl6	1.61–1.62	1.52–1.53	64.81	3.49	3.74	4.78
Li@C70Cl6	1.62–1.62	1.52–1.52	39.53	3.48	3.74	4.77
C66H4	1.59	1.54		3.85	3.28	3.94
C70Cl6	1.62	1.52		3.46	3.75	4.80

Infrared spectroscopy of endohedral fullerenes is an effective method to elucidate the cage structure.[33] In this study, infrared spectra of X@C66H4 and X@C70Cl6 (X = F and Li) are simulated and are shown in Figure . It can be observed that some weak absorption peaks are distributed under 200 cm–1, which are caused by the vibration of Li and F atoms. The absorption peaks in 200–1000 cm–1 correspond to the “breathing” mode of the carbon cage, while the absorption peaks above 1000 cm–1 originate from the C–C stretching mode of the carbon cage. For X@C66H4 (X = F and Li), the absorption peak at 2900–3000 cm–1 corresponds to the C–H tensile vibration. In addition, the intensity of the absorption peaks of Li@C66H4 and Li@C70Cl6 is stronger than their parent cage, while the intensity of the absorption peaks of F@C66H4 and F@C70Cl6 is weaker than their parent cage. This is because the doping of Li and F atoms introduces the change of charge distribution and the dipole moment, which further results in a change in the intensity of the absorption peaks. We, thus, performed static polarizability and dipole moment calculations, and the results are given in Table . Compared with F@C66H4 and F@C70Cl6, Li@C66H4 and Li@C70Cl6 have higher dipole moments and polarities, so their corresponding intensities of absorption peaks are stronger.

Figure 2

Simulated infrared spectra of C66H4, C70Cl6, F@C66H4, F@C70Cl6, Li@C66H4, and Li@C70Cl6.

Table 2

Dipole Moment (μ, Debye) and Static Polarizability (α, au) of X@C66H4 and X@C70Cl6 (X = F and Li), and Natural Population Analysis (NPA) Charges (e) of Encapsulated Atoms

molecules	μ	α	atom	charge
F@C66H4	4.24	631.00	F	–0.43
Li@C66H4	4.72	652.86	Li	+0.88
F@C70Cl6	3.32	772.86	F	–0.42
Li@C70Cl6	4.20	814.47	Li	+0.89
C66H4	4.38	621.98
C70Cl6	3.48	770.45

Frontier molecular orbitals of X@C66H4 and X@C70Cl6 (X = F and Li) were calculated to analyze their electronic properties and stabilities. Figure shows their highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO), and HOMO–LUMO gap, which includes the frontier molecular orbitals of empty C66H4 and C70Cl6 for comparison. For empty C66H4, the HOMO level is −6.92 eV, while the LUMO level is −2.90 eV, and hence the HOMO–LUMO gap equals to 4.02 eV. For empty C70Cl6, the corresponding values are −7.54, −3.30, and 4.24 eV, respectively. As presented in Figure , compared with C66H4 and C70Cl6, the HOMO–LUMO gaps of X@C66H4 and X@C70Cl6 (X = F and Li) are all declined. This result is mainly attributed to the introduction of additional Li and F energy levels, which thereby reduce the HOMO–LUMO gap. The stability of thermally dynamically favored fullerene can also be judged with HOMO–LUMO gaps. Generally, fullerenes with a smaller HOMO–LUMO gap possess lower dynamic stability and higher reactivity.[34] According to Figure , the HOMO–LUMO gaps of F@C66H4 and F@C70Cl6 are larger than those of Li@C66H4 and Li@C70Cl6, indicating the better stability of fullerene derivatives encapsulating a F atom. The charge distributions are also shown in Figure . For Li@C66H4 and Li@C70Cl6, the electron density distribution around Li atoms is poor in both HOMO and LUMO. Such charge distributions are induced by the electron transfer from the internal Li atoms to the carbon cage, forming a strong ionic interaction and a weak covalent interaction between them, which also leads to lower encapsulation energies. On the other hand, the LUMO of F@C66H4 and F@C70Cl6 is mainly contributed by the C atoms close to the F atom. According to our static polarizability calculations, the static polarizability of fullerene derivatives increases after encapsulating Li atoms and F atoms, providing evidence of the charge transfer between the encapsulated atoms and the carbon cage.

Figure 3

(a) HOMO and LUMO diagrams of C66H4, F@C66H4, and Li@C66H4. (b) HOMO and LUMO diagrams of C70Cl6, F@C70Cl6, and Li@C70Cl6. The values of the red lines, the black lines, and the red font represent the LUMO, HOMO, and HOMO–LUMO gap values, respectively. Cyan, white, green, pink, and mauve balls denote C, H, Cl, F, and Li atoms, respectively.

Thus, natural bond orbital (NBO) population analysis was performed to quantitatively investigate the electron transfer behavior of X@C66H4 and X@C70Cl6 (X = F and Li). As the first ionization energy of a Li atom is low and the electron affinity of a F atom is strong, the valence electron of the inner Li atom transfers to the carbon cage, and similarly, the external carbon cage transfers electrons to the F atom. Referring to the ground-state electronic configurations of Li and F ([Xe] 2s1 and [Xe] 2s22p5), the number of transferred electrons is supposed to be one in both cases. Counterintuitively, NBO results in Table show that charges on the Li and F atoms of Li@C66H4, Li@C70Cl6, F@C66H4, and F@C70Cl6 are +0.88 e, +0.89 e, −0.43 e, and −0.42 e, respectively, none of which reaches 1 e. From theoretical perspective, this phenomenon is the consequence of the back-donation of the charge between the encapsulated atoms and the carbon cage. In other words, there is the back-donation of 0.12 e from the C66H4 cage to the Li atom in Li@C66H4, reducing the charge of the Li atom to +0.88 e. In the same way, there is the back-donation of 0.57 electrons from the F atom to the C66H4 cage in F@C66H4, reducing the charge of the F atom to −0.43 e. It is then identified that the back-donation of charge between the F atom and the carbon cage is stronger. Now, that the electron transfer toward the carbon cage is less hindered, it can be inferred that C66H4 and C70Cl6 are better electron acceptors than electron donors.

Previous research studies have reported that the back-donation of charge indicates the covalent interactions between the inner atoms and the carbon cage.[35,36] Herein, we first performed localized orbital locator (LOL) analysis on X@C66H4 and X@C70Cl6 (X = F and Li) to study such interactions. As shown in Figure , the LOL function between Li atoms and carbon atoms is sparsely distributed, while a highly localized region occurs between F atoms and carbon atoms. This indicates that Li atoms and carbon atoms are mainly bound by electrostatic force and the covalent interaction is very weak, whereas F atoms interact strongly with carbon atoms through covalent bonds, consistent with the abovementioned NBO analysis. Focusing on the strong covalent interaction between F and C in F@C66H4 and F@C70Cl6, we further performed bond critical point (BCP) and Mayer bond order (MBO) calculations. The critical points of F@C66H4 and F@C70Cl6 are shown in Figure , where the BCPs between a F atom and carbon atoms are emphasized with a red circle mark. Typical bond descriptors of BCPs and the MBO results are given in Table . For both structures, the values of ρBCP > 0, HBCP < 0, |VBCP|/GBCP > 2 and MBO > 0.8 can be observed, indicating the strong covalent interaction between the F atom and carbon atoms. Besides, the bond between F and C in F@C70Cl6 possesses larger values of ρBCP, |VBCP|/GBCP and MBOs, thus proving that the covalent interaction between F and C70Cl6 is stronger than that between F and C66H4.

Figure 4

Localized orbital locator (LOL) map of F@C66H4, Li@C66H4, F@C70Cl6, and Li@C70Cl6. The plane is defined by the encapsulated atom and two carbon atoms.

Figure 5

Critical points (CPs) of F@C66H4 and F@C70Cl6. Each purple, orange, yellow, and green ball represents a critical point of (3, −3), (3, −1), (3, +1), and (3, +3), respectively. BCPs between a F atom and carbon atoms are marked in red circles.

Table 3

Density of All Electrons (ρBCP), Energy Density (HBCP), and Ratios of Potential Energy Density to Lagrangian Kinetic Energy (|VBCP|/GBCP) of BCPs in F@C66H4 and F@C70Cl6, and the Bond Length (d) and MBO Values between a F Atom and Carbon Atoms

molecules	bond	ρBCP	HBCP	|VBCP|/GBCP	d	MBO
F@C66H4	C43–F71	0.191	–0.205	2.330	1.497	0.844
F@C70Cl6	C21–F77	0.199	–0.223	2.359	1.482	0.908

One of the benefits of the considerable charge transfer from the internal atoms is the improvement of the redox properties of C66H4 and C70Cl6. We then applied vertical ionization potential (VIP) and vertical electron affinity (VEA) of X@C66H4 and X@C70Cl6 (X = F and Li) to interpret such effects. Table shows our calculation results. Compared with C66H4 and C70Cl6, the fullerenes encapsulating F and Li atoms exhibit lower VIP and higher VEA values so that they are not only easier to lose electrons but also easier to accept electrons. In a word, the presence of inner atoms improves the redox properties of C66H4 and C70Cl6. On the other hand, compared with Li@C66H4 and Li@C70Cl6, the fullerene derivatives encapsulating F atoms have higher VIP and VEA values, indicating that their reducibility and antioxygenic properties are better.

Table 4

Vertical Ionization Potential (VIP, eV), Vertical Electron Affinity (VEA, eV), and First Hyperpolarizability (β, au) of F@C66H4, Li@C66H4, F@C70Cl6, Li@C70Cl6, C66H4, and C70Cl6

molecule	VIP	VEA	β
F@C66H4	7.01	3.33	673.16
Li@C66H4	5.67	2.61	4810.42
F@C70Cl6	7.66	3.57	619.72
Li@C70Cl6	5.97	3.00	7848.96
C66H4	7.39	2.40	608.55
C70Cl6	7.98	2.78	770.45

In application, fullerenes are famous for their good nonlinear optical properties due to the three-dimensional (3D) delocalized π-electron conjugated system. In recent years, it has been discovered that the presence of metal atoms can further improve the nonlinear optical properties of fullerenes.[37,38] As we introduced Li atoms to C66H4 and C70Cl6, the first hyperpolarizability (β) was calculated to reveal the influence of Li atoms on the nonlinear optical properties of C66H4 and C70Cl6. The hyperpolarizability β is defined as:where β is tensorial components of the first hyperpolarizability. The β values of C66H4 and C70Cl6 are 608.55 and 770.45 au, respectively. The encapsulation of Li atoms in C66H4 and C70Cl6 cages strongly impacts nonlinear optical responses of C66H4 and C70Cl6, resulting in a steep increase in the β values of Li@C66H4 and Li@C70Cl6, which are 7.90 times of original C66H4 and 10.19 times of original C70Cl6, which creates favorable conditions for their applications in advanced electronic devices. A Li atom significantly improves the nonlinear optical properties of fullerenes, which makes us suspect whether a F atom also has this ability. Therefore, we calculated the first hyperpolarizabilities of F@C66H4 and F@C70Cl6. The result is disappointing that the encapsulation of the F atom into C66H4 can marginally increase the first hyperpolarizability. Moreover, when the F atom is encapsulated into C70Cl6, the first hyperpolarizability decreases rather than increases. The comparison between the two results reflects that the halogen F atom is indeed inferior to the metal Li atom in improving the nonlinear optics of fullerenes. The reason why metal atoms can increase the first hyperpolarizability of fullerenes has been proposed as the reason for the electron transfer from the metal atom to the external carbon cage and the symmetry reduction after metal atom encapsulation.[39] The abovementioned NBO population analysis shows that the inner Li atoms transfer 0.88 and 0.89 electrons to the carbon cages of C66H4 and C70Cl6, respectively. Moreover, the symmetry of the parent cages of C66H4 and C70Cl6 are C2v and Cs, respectively. The symmetry of Li@C66H4 is reduced to Cs and the symmetry of Li@C70Cl6 remains unchanged. Therefore, the phenomenon of improving the nonlinear optical properties with encapsulating Li atoms can be well explained.

Conclusions

In summary, we conducted a systematic study on the structures and electronic properties of X@C66H4 and X@C70Cl6 (X = F and Li) through density functional theory calculations. It was found that the encapsulation of F and Li atoms has a slight effect on the deformation of the total cage frame of C66H4 and C70Cl6, but the strong covalent interaction between a F atom and a carbon cage results in the collapse of the local C atoms in the cage. In addition, the encapsulation of F atoms in fullerene derivatives is easier. Frontier molecular orbitals analysis shows that the encapsulation of F and Li atoms leads to the reduction of the HOMO–LUMO gap, which is mainly due to the additional energy levels introduced by the encapsulated atoms. According to NBO results, compared with electron donors, C66H4 and C70Cl6 are better electron-acceptor materials. Moreover, there is a back-donation of charge between the inner atoms and the carbon cage, which indicates covalent interactions between the inner atoms and the carbon cage. Through the analyses of LOL, AIM, and MBO, we found that due to the weak back-donation of charge between a Li atom and a carbon cage, strong ionic and weak covalent interactions occur between the Li atom and the carbon cage, while a strong covalent interaction occurs between the F atom and the carbon cage. The presence of inner F and Li atoms improves the redox properties and polarizabilities of X@C66H4 and X@C70Cl6. We also found that the presence of Li atoms can significantly improve the nonlinear optical properties of C66H4 and C70Cl6, while halogen F atoms can only slightly increase or even decrease the first hyperpolarizability. The work in this paper may help to understand the different effects of F and Li atoms on the electronic properties of fullerenes and promote the potential applications of X@C66H4 and X@C70Cl6 in the field of nanoelectronics.

Computational Method

The structural optimization, vibration frequency, and electronic structure calculations of C66H4, C70Cl6, F@C66H4, F@C70Cl6, Li@C66H4, and Li@C70Cl6 were performed using the hybrid density functional theory B3LYP exchange–correlation functional[40−42] with the def2-SVP basis set[43] as implemented in the Turbomole 7.4 package.[44] The Li and F atoms were encapsulated into the cavity of optimized C66H4 and C70Cl6. We designed encapsulation structures with different internal atom positions to screen out the most stable configurations, based on which frequency calculations were conducted to remove the metastable configurations. The electronic structures of C66H4, C70Cl6, F@C66H4, F@C70Cl6, Li@C66H4, and Li@C70Cl6 were calculated with finer precision on the M06-2X[45]-D3[46]/def2-TZVP[43] basis set. Subsequently, the dipole moment and polarizability were calculated with B3LYP/ma-def2-SVP[47,48] and the first hyperpolarizability was calculated with BHandHLYP[49]/ma-def2-SVP. The interactions between inner atoms and external carbon cages were studied via the Mayer bond order (MBO) analysis,[50] localized orbital locator (LOL) analysis,[51] and atoms in molecules (AIM)[52] theory analysis in Multiwfn 3.8.[53] Meanwhile, infrared spectra of Li@C66H4, F@C66H4, Li@C70Cl6, and F@C70Cl6 were simulated with B3LYP/def2-SVP. Due to the systematical errors and the use of resonance approximation, we corrected the frequency with the correction factor of 0.9671.[54] To explore the difficulty level of the encapsulating atom into a carbon cage, the encapsulation energies (Een) of endohedral fullerene derivatives, X@C66H4 and X@C70Cl6, were calculated using the following equations with the basis set superposition error (BSSE) corrections considered:where E(X@C66H4), E(X@C70Cl6), E(C66H4), E(C70Cl6), and E(X) are the electronic energies correspondingly. The atom X represents a Li atom and a F atom, respectively.