Theoretical Study on the Chiroptical Optical Properties of Chiral

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Theoretical Study on the Chiroptical Optical Properties of Chiral Fullerene C60 Derivative Guochun Yang,† Yanling Si,‡ and Zhongmin Su*,† † ‡

Institute of Functional Material Chemistry, Faculty of Chemistry, Northeast Normal University, Changchun, 130024 Jilin, China College of Resource and Environmental Science Jilin Agricultural University, Changchun, 130118 Jilin, China

bS Supporting Information ABSTRACT: Time-dependent density functional theory (TDDFT) calculations have been used to investigate UV/ CD spectra and nonlinear optical (NLO) property of the C60-fullerene bisadduct (R,R,f,sA)-[CD(+)280] for the first time. The electron transition natures of the four main measured bands are analyzed, and their results are used to designate the excited states involved in an electron-transfer process of the studied compound. On a comparative scale, the predicted excitation energies and oscillator strengths are in reasonable agreement with the observed values, demonstrating the efficiency of TDDFT in predicting the localized and charge transfer transitions. The good agreement between the experimental and the simulated CD spectra shows that TDDFT calculations can be used to assign the absolute configurations (ACs) of chiral fullerene C60 derivatives with high confidence. The observed large dissymmetry ratio g (g = Δε/ε) at about 700 nm results from the orbital characters of the local fullerene excited state, which leads to large transition magnetic dipole moment and small transition electronic dipole moment. The different functionals and solvent effects on UV/CD spectra were also considered. The studied compound has a possibility to be an excellent second-order NLO material from the standpoint of transparency and large second-order polarizability value.

’ INTRODUCTION Fullerene chemistry has attracted the interest of a wide crosssection of scientists. From the standpoint of cost analysis, commercial applications of fullerenes and fullerene derivatives are initially envisioned in the areas of pharmaceuticals and optics.1 Chiral fullerenes are likely to play important roles in both areas. Moreover, a number of higher fullerenes2 as well as carbon nanotubes3 have been predicted to be chiral. The first chiral fullerene C76 was obtained after the isolation and structural characterization in 1991.2b Chiral fullerenes C78 and C84 were kinetically resolved by asymmetric osmylation in 1994.4 Subsequently, a considerable fraction of the fullerene derivatives isolated and characterized was found to be chiral even if the compounds have been prepared from the achiral parent fullerenes C60 and C70.5 Their structural novelty and interesting electronic properties have exhibited great promise for material and biomedical applications. For example, fullerene amino acid derivatives can be incorporated into a peptide sequence through solid phase peptide synthesis (SPPS)6 and acted as interesting pharmacophores in biologically active molecules.7 The fullerene amino acids also facilitate penetration of peptides through porcine skin.8 Recently, Thilgen et al. provided an overview of the different aspects of fullerene chirality that have been identified and investigated.9 Chiral fullerenes have been challenging molecules to synthesize with significant enantiomeric excess and to assign absolute r 2011 American Chemical Society

configurations (ACs).10 In recent years, electronic circular dichroism (CD) and optical rotation dispersion (ORD) spectroscopy, combined with the state-of-the-art time-dependent density functional theory (TDDFT) simulations has emerged as a powerful tool for investigation of chiral organic compounds, biomolecules, and metal complexes.11 However, only a few papers reported such tests for pure chiral fullerenes (C76, C80, and C84) at the TDDFT level. CD computations based on TDDFT method have provided support for the structural assignment of C84 and C80.12 Polavarapu et al. have tackled the C76 AC assignment by using the CD and ORD computations.13 A number of chiral fullerene C60 derivatives have been synthesized by the addition of chiral residues to an achiral fullerene C60. It has been recognized that CD spectra of inherently chiral fullerenes depend sensitively on the electronic structure.14 Moreover, the addition of substituents to C60 lowers the symmetry of the carbon framework and increases the topological complexity of the π-system.15 To the best of our knowledge, no structural determination using TDDFT calculations of CD spectra has been previously applied to chiral fullerene C60 derivatives. Thus, it is necessary to carry out systematic DFT calculations to explore the effects of different functionals and basis sets on CD spectra Received: May 25, 2011 Revised: October 13, 2011 Published: October 14, 2011 13356

dx.doi.org/10.1021/jp204860x | J. Phys. Chem. A 2011, 115, 13356–13363

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Figure 1. Optimized geometry of the studied C60-fullerene bisadduct (R,R,f,sA)-[CD(+)280] (1) at the B3LYP/6-31G* level of theory.

and the degree of agreement that can be achieved, to investigate the electronic chiroptical properties of chiral fullerene C60 derivatives, and to find an easy, reliable and economic way to determine their ACs. Although chiral fullerene derivatives have been receiving much attention from chemists during past decades, the ACs for most of these compounds have not yet been clearly determined due to the difficulties in obtaining X-ray quality crystals. The C60-fullerene bisadduct (R,R,f,sA)-[CD(+)280] (1) was synthesized and characterized by X-ray crystallography, UV, and CD spectra, which is the first report successful in determining the AC of chiral C60fullerene bisadducts of the cis-3 type by X-ray crystallography (Figure 1).16 In (R,R,f,sA)-[CD(+)280], the parent part C60 of the bisadduct is rigid, the two branched chains COOEt on the (2R,3R)-tethers may rotate around the CC single bond to a certain degree both in the gas phase and in solution. Thus, (R,R,f,sA)[CD(+)280] might exhibit different conformers. Studies show that chiroptical properties are also highly sensitive to the conformers of chiral molecules. Thus, it might be a good model compound to evaluate how the CD spectra can be used to characterize the conformational isomerism and ACs of chiral fullerene C60 derivatives. For the studied compound, there might exhibit charge-transfer excitation between (2R,3R)-butane-2, 3-diyl diethyl dimalonate and C60 or locally excited states. We will evaluate how the efficiency of TDDFT in predicting the localized and the charge transfer transitions. Interestingly, C60fullerene bisadduct (R,R,f,sA)-[CD(+)280] shows large dissymmetry ratio g (g = Δε/ε) value at about 700 nm. Moreover, the general rule of its CD spectra was established. A positive Cotton effect in their CD spectra at around 280 nm has the f,sA configuration, whereas a negative Cotton effect has the f,sC configuration. The main aim of this investigation was (i) to assess the utility of TDDFT in predicting the excitation energies by comparing the calculated results with the experimental data, (ii) to provide the first significant evaluation of the reliability of the TDDFT technique in determining the ACs of chiral C60fullerene derivatives, (iii) to assign electron transition and chiroptical properties of the studied compound, and (iv) to investigate its NLO properties and find its potential application in material science field. Furthermore, different functionals and solvent effects on the UV/CD spectra were also studied.

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’ COMPUTATIONAL DETAILS Geometrical optimization of the studied compound 1 without any symmetry constraint was carried out with the B3LYP17 combinations of density functional theory (DFT) in the Gaussian 09 computational chemistry program.18 The B3LYP functional is a combination of Becke’s three-parameter hybrid exchange functional17 and the LeeYangParr19 correlation functional. Basis sets of 6-31G* for C, O, and H atoms were applied. The electronic excitation energies, oscillator strengths, and rotational strengths of the studied compounds have been calculated at the TDB3LYP/6-31G* level of theory. Rotational strengths were calculated using both length and velocity representations, and only the velocity-gauge representation of the dipole operator is gauge origin independent. In comparison of the calculated CD spectra with experimental spectra, Gaussian bandshapes20 with a bandwidth of 0.2 eV (two thousand wavenumbers) were used to simulate the UV/CD spectra, which appear to be suitable in most cases.21 To evaluate the solvent effect of ClCH2CH2Cl, the integral equation formalism (IEF)22 version of the PCM23 as implemented in Gaussian 09 was utilized. In PCM, the problem was divided into a solute part lying inside a cavity and a solvent part represented as an isotropic continuum, characterized by its macroscopic properties (dielectric constant, radius, density, and molecular volume). The solvent ClCH2CH2Cl was treated as a continuum dielectric environment with a dielectric constant of 10.7. ’ RESULTS AND DISCUSSION The molecular structure of the C60-fullerene bisadduct (R,R,f,sA)[CD(+)280] (1) is shown in Figure 1. To the studied compound, the C60-fullerene part is conformationally rigid; however, the two branched chains (COOEt) on the (2R,3R)-tethers may rotate around the CC single bond in certain degree both in the gas phase and in solution. Thus, the studied compound might exhibit two conformers. One conformer has the C1 symmetry; the other has the C2 symmetry. The two structures of the studied compound 1 were optimized and their optimized structures are shown in Figure S1 (Supporting Information). Their calculated relative total energies ΔE, and the normalized Boltzmann factors Bf at 298.15 K based on the relative total energy are listed in Table S1 (Supporting Information). The most stable conformer with the C2 symmetry accounts for 78.51% of the population. In general, the theoretical structural parameters could be compared to the X-ray crystal structure. However, the DFT-optimized geometry is not as strongly distorted as the experimental crystal structure, possibly due to the lack of the crystal packing effect. As far as we know, no systematic theoretical investigation has been reported to the studied compound. To find appropriate DFT functionals and basis sets to explain the properties of electron transition, accurately simulate UVvis and CD spectra, and assign the AC, a series of TDDFT calculations was performed upon varying functionals and basis sets, and the solvent effect has also been considered. In general, basis sets have to be chosen with due care for the calculation of response properties, especially in CD calculation.24 To study the relationship between the oscillatory and rotatory strengths and basis sets, five different basis sets (6-31G, 6-31G*, 6-31+G*, 6-311+G*, 6-311++G**) including diffuse functions and polarization functions were used. We carried out this study by using the B3LYP functional, which has been proved to be quite efficient in CD studies. Figure 2 shows the computed oscillatory and rotatory strengths for the 13357

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Figure 2. Calculated oscillatory (f) and rotatory strengths (R) for the first three excited states (j = 1, 2, 3) of compound 1 as a function of basis set.

first three excited states of compound 1, and how they change with increasing the size of basis sets. For the numerical values corresponding to the data shown in Figure 2, the reader should refer to Table S2 (Supporting Information). It is rather evident that whereas oscillatory strengths already converge at 6-31G* level, rotatory strengths need the 6-31+G* basis sets. It should be noted that the sign of rotatory strengths does not change with increasing the size of basis sets. Although the rotatory strengths of individual transitions can deviate slightly, the shape of the entire spectra is rather insensitive on basis set size (Figure S2, Supporting Information). Moreover, extensive studies have shown that 6-31G* basis set can properly describe the electronic properties for the C, O, and H atoms.25 Considering the computational cost, we used the 6-31G* basis set in the following calculation. Studies show that dichroic properties may depend substantially on the choice of the density functional.26 BHandHLYP shows good performance in predicting the CD spectra of C76.17 In addition, new developed functionals have shown to improve the accuracy of excitation energies and charge transfer bands both in the gas phase and in solution, such as M05-2X27 and CAM-B3LYP.28 Cramariuc et al. systematically studied photoabsorption and electron transfer in a covalently bonded porphyrinfullerene dyad by using the different exchangecorrelation functionals (PBE, B3LYP, and PBE1PBE).29 Toivonen et al. reported the good performance of TDDFT with hybrid B3LYP functional in predicting electron transition energies of a covalently linked porphyrinfullerene dyad.30 A good match between simulated and measured spectra that cover several well separated excitations can normally be used for a confidential assignment of the AC.12b To get the reliable results and simulate the experimental UV and CD spectra of the studied compound 1, the excitation energies, oscillator strengths, and rotational strengths of the 150 lowest energy electronic excitations for the most stable conformers have been calculated used six different functionals, which covers the range of experimental measurement (Table S3, available as Supporting Information). The calculated UV absorption energies and oscillator strengths of the six functionals are given in Table S4 (Supporting Information), and their simulated UV/CD spectra are shown in Figure 3 and Figure S3 (Supporting Information). Compared with the experimental results (Table S4, Supporting Information), the excitation energies of the four considered transitions obtained from the PBE functional are considerably

underestimated. However, the excitation energies obtained from the PBE1PBE, BHandHLYP, M05-2X, and CAM-B3LYP functionals are considerably overestimated. Moreover, the simulated CD spectra of these functions do not capture the relative intensity and sign of the experimental ones. The results obtained from the B3LYP functional are most close to the experimental ones not only in band position but also relative intensity. Our calculated results also show that the HF exchange fraction has certain influence on electronic properties of our studied compound (Table S5, Supporting Information). On the basis of the results of Table S3 (Supporting Information), we found that the differences between the rotational strengths calculated using the length- and velocity-gauge representation of the electric dipole operator are quite small, confirming again the suitability of B3LYP/6-31G* for the CD calculations. The effect of different conformers on the UV and CD spectra was examined. The calculated UV and CD spectra of the two most stable conformers were shown in Figure S4 (Supporting Information). The differences of the simulated spectra of the two most stable conformers are quite small, which means that the effect of different conformers on the UV and CD spectra is negligible (Figure S4, Supporting Information). In other words, the electron transition properties of the studied compound are insenstivie to the orientation of the two branched chains COOEt. It is due to no distribution of electron density on the two branched chains COOEt (Figure 3 and Figure S5, Supporting Information). Thus, the results obtained from the most stable conformer with the C2 symmetry are used in the following discussion. In Table 1, we summarized the UV absorption energies, oscillator strengths, and major contribution for compound 1, as compared to experimental data. This result shows an intense absorption band at 245 nm, a moderately intense absorption band at 384 nm, and two very weak absorption bands at 664 and 676 nm, respectively. This indicates that there are significantly different relative intensities of the oscillator strengths in these four bands. What does lead to the different oscillator strengths of these four bands? Molecular orbitals (MO) involved in the main electron transitions of compound 1 were shown in Figure 4. On the basis of the distribution of MO coefficients in Figure 4, the transition predicted at 245 nm is of charge transfer from (2R,3R)butane-2,3-diyl diethyl dimalonate to C60 and vice versa, which has finite charge transfer character. Moreover, the delocalization of LUMO+6 orbital over the entire compound relaxes the symmetry constraints. These features could gain oscillator strength.31 13358



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Figure 3. Calculated UV (left) and CD (right) spectra of compound 1 using three different functionals.

Table 1. Calculated Absorption Energies (nm), Oscillator Strengths (f), Major Contribution at the TDB3LYP/6-31G* Level of Theory, and Experimental Data of Compound 1 absorption energies experiment

theory

254

245

f main contribution 0.1855

HOMO2 f LUMO+14 HOMO17 f LUMO+2

316

310

0.1021

HOMO1 f LUMO+6 HOMO13 f LUMO+1

643 706

664 676

0.0021 0.0014

HOMO f LUMO+1 HOMO f LUMO

The calculated oscillator strengths of the two very weak absorption bands at 664 and 676 nm are very close to the observed oscillator strength (0.004) of C60.32 A crucial feature of the two electron transitions is that these orbitals involved are mainly localized on C60 with π f π* character, which has the feature of the local fullerene excited state and leads to the smaller oscillator strength.30 The transition nature of the band at 310 nm involves charge transfer not only between (2R,3R)-butane-2,3-diyl diethyl dimalonate and C60 but also the local fullerene excited state. Thus, this band exhibits moderately intense. Overall, the calculated excitation energies and oscillator strengths of the four main bands are in agreement with the experimental ones, which indicate that the

B3LYP functional can well describe the localized and the charge transfer transitions. UV/CD spectra were simulated by using a Gaussian band shape with a bandwidth of σ = 0.2 eV and were shown in Figure 5. In the simulated CD spectra, a negative Cotton effect is observed around 250 nm and a couple of positive Cotton bands around 300 nm. From 400 to 800 nm, there are a few weak Cotton bands. Comparison of the experimental and simulated spectra shows that the calculated gas phase CD spectra capture not only the band positions but also the relative intensity of the experimental spectra, which allows us to assign the ACs of chiral fullerene C60 derivatives with high confidence. But, it is noted that there is a small positive band at ∼230 nm, which cannot be seen in the experimental spectra. The results show that the B3LYP functional can be used to assign the ACs of chiral C60-fullerene derivatives. It should be noted that unique phenomena in the UV/CD spectra of compound 1 at about 700 nm were observed. It exhibits a very weak UV band and an intense negative CD band at this region. Namely, there is large dissymmetry ratio g (g = Δε/ε) value. Although the argument about these phenomena was given in ref 16, these phenomena were verified computationally here. The experimental g value is 0.110, and the calculated g value is 0.079. The main contribution to this band is the second excited state (664 nm). In terms of the same transition, the intensity of the UV band is proportional to the transition electronic dipole moment, whereas the intensity of CD band is proportional to the product of the transition electronic dipole moment and 13359



Figure 4. Molecular orbital isosurfaces involved in the main electron transitions of compound 1 at the TDB3LYP/6-31G* level of theory.

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the transition magnetic dipole moment. The calculated transition electronic and magnetic dipole moments of this excited state are 0.21 and 2.06 au, respectively, which means that the magnitude of transition magnetic dipole moment is 10 times larger than transition electronic dipole moment. The main contribution of this transition corresponds to the promotion of one electron from HOMO to LUMO+1 (Table 1 and Figure 4). These orbitals are mainly localized on C60. The occupied π electron molecular orbitals are spherical, as they reflect the shape of the fullerene, which might increase the probability of magnetic dipole transition and the strength of corresponding chiroptical effects. Moreover, the transition properties of the main observed CD bands were assigned as Supporting Information (Figure S5). Studies show that the CD spectra are very sensitive to external factors such as the nature of the solvent.33 Moreover, we found that the implicit continuum polarization model (PCM) results of the bicyclo[3.1.0]hexane derivative calculations are closer to the experimental ones than from the gas phase calculations.34 To account for the effect of the ClCH2CH2Cl solvent, we employed the PCM model. The geometries of the two most stable conformers have been reoptimized under the solution phase PCM condition. Their calculated relative total energies ΔE, and the normalized Boltzmann factors Bf at 298.15 K based on the relative total energy are listed in Table S1 (Supporting Information). The C1 conformer in the solution phase becomes more stable than in the gas phase. This means that the relative

Figure 5. Calculated UV (left) and CD (right) spectra in both gas and solution phases of compound 1 at the TDB3LYP/6-31G* level of theory along with experimental UV and CD (red line). Data to prepare the experimental CD spectra were taken from ref 16. 13360



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Table 2. Predicted ORD Values (Specific Optical Rotation/ deg dm1 g1 mL1) at Five Wavelengths Using Linear Response Theory compound

589 nm

578 nm

546 nm

C1 conformer 27461.05 20006.44 7540.09

436 nm

365 nm

10829.04 35681.15

C2 conformer 24321.30 15937.23 14853.51 10448.80 29396.50

a

ligand

14.02

14.49

15.93

21.69

22.37

C76a

55143

17875

12829

59655

8032

From ref 14.

stability of individual conformers is sensitive to solvent. Subsequently, excitation energies, oscillator strengths, and rotational strengths based on the solution phase optimized structure (Table S6, Supporting Information) were calculated and their CD spectra were given in Figure S6 (Supporting Information). The oscillator and rotational strengths in solution phase are considerably higher than those in gas phase (Table S3 and S6, Supporting Information).35 Although solvent influences the relative stability of individual conformers, the shape of the entire spectra is rather insensitive to solvent. Overall, the inclusion of solvent effects does not improve the agreement between measured and calculated spectra. Subsequently, we investigated the optical rotation (OR) property of the two conformers of compound 1. The specific OR values calculated using hybrid-DFT are sensitive to basis sets. In general, aug-cc-pVDZ can reproduce both the sign and the magnitude of the experimental values.34,36 Calculations with aug-cc-pVDZ basis set have been attempted, but the 2048 basis functions involved in this basis set resulted in linear dependencies and convergence problems that made it difficult to pursue these calculations. Polavarapu et al. used the 6-31G* basis set to predict optical rotatory dispersion (ORD) curves of C76 and found that the diffuse functions would be less important for a compact molecule such as C76, because the basis functions on the neighboring atoms will act as diffuse polarizing functions.13 Thus, we tested the relationship between the basis sets and the calculated OR values of (2R,3R)-butane-2,3-diyl diethyl dimalonate (Table S7, Supporting Information). The results show that the OR values obtained from 6 to 31++G* basis set at five different wavelengths are close to those from aug-cc-pVDZ. In terms of computational cost and accuracy, the 6-31++G* basis set was used here. The calculated OR values at five different wavelengths of compound 1 and (2R,3R)-butane-2,3-diyl diethyl dimalonate (ligand) were given in Table 2. The calculated OR values of compound 1 are of the same order of magnitude of C76 and are thousand times than lager these of (2R,3R)-butane-2, 3-diyl diethyl dimalonate, which means that the main contribution to the OR values might come from the C60. The specific reason has been addressed in the Supporting Information (Table S8). Comparison of the OR values of the two most stable conformers, the difference between them is quite large. Thus, the OR values of the studied compound are more sensitive to the conformers than UV/CD. Organic molecules with delocalized electron systems are of particular interest because of their potentially large nonlinear optical (NLO) response. The Buckminster fullerene C60 has exhibited excellent NLO properties.37 The introduction of chiral elements within the conjugated system might prove beneficial in obtaining noncentrosymmetrical crystals, which is very important to the second-order NLO material. Moreover, in view of the

energy of the UV spectra, compound 1 satisfies high transparency in the visible light area according to Gomper’s research.38 This transparency of the nonlinear optical materials is worthy of remarks in considering practical applications. On the basis of analysis of the electron transition, compound 1 could take place with larger intramolecular charge transfer under the external electronic field. We anticipate that this compound offers some interesting new opportunities to second-order NLO material. In general, there is a close relationship between the measured NLO response and concentration.39 It is noted that monomolecular NLO property was considered in this study. The static secondorder polarizability is termed the zero-frequency hyperpolarizability and is an estimate of the intrinsic molecular hyperpolarizability in the absence of resonance effect. The static second-order polarizability was calculated by using the finite-field (FF) method as implemented in the Gaussian program at the B3LYP/6-31+G* level. Suponitsky et al. found that the 6-31+G* basis set is enough to our studied compound.40 In the case of plane-polarized incident light and observation made perpendicular to the propagation plane without polarization analysis of the scattered beam, the second-order NLO response that can be extracted from HRS data41 can be described as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi βHRS ð2ω; ω, ωÞ ¼ fÆβZZZ 2 æ þ ÆβXZZ 2 æg ð1Þ ÆβZZZ2æ and ÆβXZZ2æ correspond to the orientational average of the β tensor without assuming Kleinman’s conditions.42 All the second-order polarizability values are consistent with convention B of ref 43. The calculated static hyper-Rayleigh scattering (HRS) value is 3738.98 1033 esu, which is about 20 times larger than the average second-order polarizability of the organic urea molecule.44 It indicates that the studied compound has excellent second-order nonlinear optical response. Moreover, time-dependent density-functional theory combined with sum-over-states method (TDDFT-SOS)45 was used to test the reliability of our calculated result. The HRS value based on TDDFT-SOS method is 3687.62 1033 esu, which is in agreement with FF result. To consider the influence of solvent effects on the second-order polarizability, we employed the PCM model to calculate the HRS value. The calculated HRS value by considering solvent effects is 9178.80 1033 esu, which is larger than that of gas phase. Other studies have also shown that solvent effects have greatly influenced on the second-order NLO response.41a,46

’ CONCLUSION The major goal of the present research is assessing the utility of TDDFT in predicting the excitation energies and providing the first detailed evaluation of the reliability of the TDDFT technique in determining the ACs of chiral C60-fullerene derivatives. On a comparative scale, the predicted excitation energies and oscillator strengths, and the simulated UV/CD spectra were in reasonable agreement with the observed values. The relative oscillator strengths of the four main bands are mainly determined by the extent of intramolecular charge transfer. The observed large dissymmetry ratio g (g = Δε/ε) at about 700 nm results from the orbital characters of the local fullerene excited state, which might enhance the transition magnetic dipole moment. The different functionals and solvent effects on UV/CD spectra were also considered. The work shows that DFT calculation complemented with the CD spectroscopy is a powerful and reliable method for the assignment of the molecular absolute 13361


The Journal of Physical Chemistry A configurations of chiral fullerene C60 derivatives. The studied compound has a possibility to be excellent second-order NLO material from the standpoint of transparency and large secondorder polarizability value.

’ ASSOCIATED CONTENT

bS

Supporting Information. Optimized molecular structures of the two most stable conformers; the simulated UV spectra (left) and CD spectra (right) of the two most stable conformers; the calculated excitation energies, oscillator and rotational strengths of the 150 lowest energy electronic excitations in gas and solution phase; optical rotation values at the five different wavelengths. This material is available free of charge via the Internet at http://pubs. acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT We gratefully acknowledge the financial support from the National Natural Science Foundation of China (Project No. 20903020), the Science and Technology Development Project Foundation of Jilin Province (20090146; 201101116), the Training Fund of NENU’s Scientific Innovation Project (NENUSTC08005), and The Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, Science Foundation for Young Teachers of Jilin Agricultural University (201018). ’ REFERENCES (1) (a) Kroto, H. W.; Fischer, J. E.; Cox, D. E. The Fullerenes; Pergamon Press: Oxford, U.K., 1993. (b) Koruga, D.; Hameroff, S.; Withers, J.; Loutfy, R.; Sundareshan, M. Fullerene C60; Elsevier Press: Amsterdam, 1993. (c) Billups, W. E.; Ciufolini, M. A. Buckminsterfullerenes; VCH Publishers Press: New York, 1993. (2) (a) Akasaka, T.; Wudl, F.; Nagase, S. Chemistry of Nanocarbons, Chapter 5. Higher Fullerenes: Chirality and Covalent Adducts; John Wiley & Sons, Ltd Press: Chichester, U.K., 2011; DOI: 10.1002/9780470660188. ch5. (b) Ettl, R.; Chao, I.; Diedefich, F.; Whetten, R. L. Nature 1991, 353, 149–153. (c) Diederich, F.; Whetten, R. L.; Ettl, R.; Chao, I.; Alvarez, M. M. Science 1991, 254, 1768–1770. (d) Diederich, F.; Whetten, R. L. Acc. Chem. Res. 1992, 25, 119–126. (e) Wilson, S. R.; Lu, Q. Y.; Cao, J. R.; Wu, Y. H.; Welch, C. J.; Schuster, D. Tetrahedron 1996, 52, 5131–5142. (3) Iijima, S. Nature 1991, 354, 56–58. (4) Hawkins, J. M.; Nambu, M.; Meyer, A. J. Am. Chem. Soc. 1994, 116, 7642–7645. (5) (a) Thilgen, C.; Gosse, I.; Diederich, F. Top. Stereochem. 2003, 23, 1–124. (b) Diederich, F.; Thilgen, C.; Herrmann, A. Nachr. Chem. Tech. Lab. 1996, 44, 9–16. (c) Thilgen, C.; Diederich, F. Top. Curr. Chem. 1999, 199, 135–171. (d) Thilgen, C.; Sergeyev, S.; Diederich, F. Top. Curr. Chem. 2004, 248, 1–61. (6) Yang, J.; Alemany, L.; Driver, B. J.; Hartgerink, J. D.; Barron, A. R. Chem.—Eur. J. 2007, 13, 2530–2545. (7) (a) DaRos, T.; Prato, M. Chem. Commun. 1999, 663–669. (b) Tagmatarchis, N.; Shinohara, H. Mini-Rev. Med. Chem. 2001, 1, 339–348. (8) (a) Rouse, J. G.; Yang, J.; Ryman-Rasmussen, J. P.; Barron, A. R.; Monteiro-Riviere, N. A. Nano Lett. 2007, 7, 155–160. (b) Strom, T. A.; Barron, A. R. Chem. Commun. 2010, 46, 4764–4766. (9) Thilgen, C.; Diederich, F. Chem. Rev. 2006, 106, 5049–5135.

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Theoretical Study on the Chiroptical Optical Properties of Chiral

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