Density functional study on the electronic properties ... - NSFC-OR

Computational and Theoretical Chemistry 991 (2012) 154–160

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Density functional study on the electronic properties, polarizabilities, NICS values, and absorption spectra of fluorinated fullerene derivative C60F17CF3 Chunmei Tang ⇑, Weihua Zhu, Hua Zou, Aimei Zhang, Jiangfeng Gong, Chengjun Tao College of Science, Hohai University, Nanjing, Jiangsu 210098, China

a r t i c l e

i n f o

Article history: Received 18 December 2011 Received in revised form 12 April 2012 Accepted 12 April 2012 Available online 27 April 2012 Keywords: C60 C60F18 C60F17CF3 Fullerene Density functional

a b s t r a c t Electronic structures, polarizabilities, NICS values, and absorption spectra of the fluorinated fullerene derivative C60F17CF3 have been systematically studied by density functional theory. The large Eg (2.39 eV) between HOMO and LUMO and the strong aromatic character (with NICS 7.25 ppm) of C60F17CF3 indicate it posses high stability. Further investigations show that C60F17CF3 could be excellent electron acceptors for potential photonic/photovoltaic applications in consequence of its large VIP (8.78 eV). The density of states and frontier molecular orbitals are also calculated, which present that HOMOs and LUMOs are mainly distributed in the tortoise shell subunit of C60F17CF3, and the influence from F and CF3 is secondary. Our calculations shows that the absorption spectra of C60F17CF3 structure is distorted by the F and CF3 addition and the optical gaps of C60F17CF3 is red shifted relative to that of C60. The attached F and CF3 in C60F17CF3 greatly change the cage and disrupt aromatic rings, which lead to stronger aromatic character of itself than that of C60. In addition, the static linear polarizability a and first-order hyperpolarizability b0 for C60F17CF3 are significantly larger than those of C60 because of its lower symmetric structures and high delocalization of p electrons. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction In recent years, there has been a significant interest in fluorined derivatives of fullerenes, which exhibited specific characteristics, such as, good solubility, high reactivity toward nucleophiles and enhanced dienophilicity of the pristine part of the cage, and resulting from electron withdrawal by fluorine atoms [1]. Experimentally, C60F18 is one of the three fluorofullerenes that was obtained with high yield and purity, the other two relatively abundant fluoro-fullerenes are C60F36 [2] and C60F48 [3], are known for isomeric coexistence. Heating C60 with K2PtF6 at 500–600 K produces C60F18 molecule [4], which is readily separated by HPLC in quantities sufficient for structural characterization by means of X-ray diffraction [5]. C60F18 has a structure which contains half of the carbon cage retaining conjugated p system of the fullerene and half of the molecule with attached 18 F atoms forming an isolated benzene ring on the pole. Such a peculiar molecular structure originally was proposed on the basis of 19F NMR spectroscopy [4], and now is known with high precision from the single-crystal X-ray diffraction studies [5–7]. As a result, C60F18 has very different properties from other polyfluorinated C60 compounds. For example, the dipole moment of C60F36 is close to zero, while C60F18 is estimated to have a

⇑ Corresponding author. E-mail address: [email protected] (C. Tang). 2210-271X/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.comptc.2012.04.015

large dipole moment due to compact arrangement of fluorine atoms on one pole of the carbon sphere [5]. Due to high electron affinity and polarity, C60F18 has propensity for the formation of the stable charge transfer complexes with different organic molecules, such as forming C60F17CF3. Comparably, in view of the greater electron-withdrawing power of CF3 groups compared to F atom, and possibly lower susceptibility to nucleophilic substitution, these groups may prove to be particularly important [8]. Experimentally, Boltalina et al. [9] have isolated the stable fullerene derivative C60F17CF3, which is a good example of trifluorocarbon. Later on, Troshin et al. [10] have suggested two possible stable sites to locate CF3 in the cage, however, they did not explore which one was favored theoretically, and the detail research on other properties is still missing until now, such as, the electronic properties, polarizabilities, and NICS values. As indicated, C60F18 possess heavily deformed structures and substantial absorptions in the visible and near infrared ranges [11,12], which could be promising candidates for optoelectronics, molecular scale logic gates, and sensor design [13]. In view of the inherent delocalization of p electrons and the drastic structure changes stemming from the attached halogens, C60F17CF3 is also expected to possess these properties. It is well-known that the static linear polarizability and firstorder hyperpolarizability represents one of the most important observations to the understanding of the electronic and optical properties of molecules, since it is very sensitive to the delocalization of

C. Tang et al. / Computational and Theoretical Chemistry 991 (2012) 154–160

valence electrons, as well as the structure and shape [14]. In the literature, there are two common theoretical methods to calculate the static linear polarizability and first-order hyperpolarizability. One is sum-over-state (SOS) [15] and the other is finite-field (FF) approach [16]. For molecules with a considerable number of atoms, SOS treatment seems to be out of reach for ab initio methods in respect that it necessitates the calculations of many excited states. The FF method has been proven to be acceptable for large system calculations [17,18]. It has been verified that the FF approach based on density functional theory can produce reliable polarizability since even the local density approximation for exchange and correlation produces an accurate electron screening response to the application of an external field to the system [19]. In this paper, on the basis of density functional theory (DFT), we will study the electronic properties, NICS values, optical absorption spectra, static linear polarizability and first-order hyperpolarizability by means of FF approach of C60F17CF3. This paper is organized as follows. We describe our computational details in Section 2 and present the results and discussion in Section 3. Finally the conclusion is given in Section 4.

2. Computational details The density functional theory (DFT) approach, due to its significant character of high accuracy and low cost, has become one of the most popular calculation routines for large systems [20]. It has been found that the generalized gradient approximation (GGA) is more accurate than the local density approximation (LDA) in the calculations of the bond length and binding energy [21]. Therefore, GGA [21] based on DFT [20] is adopted in this paper. We used the DMol3 package [22]. We chose the Becke–Lee– Yang–Parr (BLYP) correlation exchange function, a combination of the Becke exchange functional [23] coupled with the Lee– Yang–Parr (LYP) correlation potential [24] in the calculations. The basis sets used were double-numerical quality basis sets with polarization functions (DNP), comparable to Gaussian 6–31G sets, the real space cutoff of 5.5 were chosen. Electronic structure was obtained by solving the spin-polarized Kohn–Sham (KS) equations self-consistently, and the calculations were of all-electron type [25]. Mulliken population analysis was made to obtain the effective charges and net spin populations on each atom. Self-consistent field procedures were carried out with a convergence criterion of 106 a.u. on the energy and electron density. Geometry optimizations were performed using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm [26] with a convergence criterion of 103 a.u. on the displacement and 105 a.u. on the energy. To test the accuracy and reliability of the method we used, the bond lengths of the optimized structures of C60 are compared with the experimental values. In the optimized structure of C60, all 60 carbon atoms are chemically equivalent and only two different bonds, namely, the C–C single bond (the common bond of a hexagon and pentagon) and C=C double bond (the common bond of two hexagons). The Rc–c and Rc=c, according to our calculation, are 1.46 and 1.40 Å, respectively, comparable to the calculations of Kertesz and coworkers [27] (1.45 Å for Rc–c and 1.40 Å for Rc=c). These values are also in excellent agreement with the nuclear magnetic resonance (NMR) values (Rc–c = 1.450 ±0.015 Å and Rc=c = 1.400 ± 0.015 Å) [28] and the single-crystal X-ray diffraction data (the average values for Rc–c and Rc=c are 1.47 and 1.36 Å, respectively) [29]. Therefore, the method used is reliable to calculate the structure of C60F17CF3. The absorption spectra are calculated in the dipole approximation using the dipole transition between the ground state and excited state. The DMol3 assumes the ground state is a Slater determinant formed by the occupied Kohn–Sham orbitals, while the

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excited state is a Slater determinant obtained from the Slater determinant describing through eliminating one electron from an occupied Kohn–Sham orbital and placing it into an unoccupied Kohn–Sham orbital. The excitation of a single electron does not alter the spin of the electron, because the resulting matrix element would otherwise vanish. The intensity of the absorption, or the height of the absorption peak, is the square of the transition dipole moment associated with the transition energy. With this method, the optical absorption spectra of different Au32 isomers [30] and Sn12M (M = Ti, V, Cr, Mn, Fe, Co, Ni) clusters [31] have been successfully calculated and used to identify their geometric structures. The FF method was broadly applied to investigate coefficients of molecules. When a molecule is subjected electronic field (F), the energy (E) of molecule can in Taylor series as expressed in the equation [32]:

1 1 E ¼ Eð0Þ li F i aij F i F j bijk F i F j F K 2 6

ð1Þ

where E(0) is the energy of molecule in the absence of an electronic field, li is the components of the dipole moment vector, aij is the linear polarizability tensor, bijk is the first-order hyperpolarizability tensor, and i, j and k are designated different components x, y, and z. The molecular Hamiltonian includes a term (l0 FÞ describing the interaction between the external uniform static field and the molecule. l0 is the molecular total dipole moment. A set of equations is given through calculating the system energy with each electric field, and then the values of li, aij, and bijk can be obtained through simultaneous equations by altering E with respect to F. An appropriate electric field has significant effect on the polarizability and hyperpolarizability results, as that two different and opposite requirements governing the choice of electric field should be satisfied at the same time. First, the field must be large enough to ensure that the imprecision in the calculated dipole moments is small compared with the contribution to the dipole moment expansion. At the same time, the field must be small enough so that the error incurred by the truncation of the expansion is acceptable. In our calculations, an external electric field of 0.001 atomic units was added into the molecules containing coordinates along x, y, and z directions in a three dimensional Cartesian coordinate system. Apart from the tensor components of the dipole polarizability and first-order hyperpolarizability we considered also the mean (or average) static dipole polarizability hai, the anisotropy Da of the polarizability tensor which can be used as a measure of the anisotropy of the cluster’s electron density, and the first order hyperpolarizability (b0). These quantities are defined as[33,34]:

hai ¼ ½axx þ ayy þ azz =3

Da ¼

b0 ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ½ðaxx ayy Þ2 þ ðaxx azz Þ2 þ ðayy azz Þ2 =2

3 ðb l þ by ly þ bz lz Þ=l0 5 x x

where bi ¼ bixx þ biyy þ bizz ði ¼ x; y; zÞ

ð2Þ

ð3Þ

ð4Þ

ð5Þ

Our aim is not only to verify whether the described density functional theory provide an qualitative representation about the (hyper) polarizabilities of these systems but also to test their ability in offering utilizable hyperpolarizability results for successful quantitative predictions.

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3. Results and discussion 3.1. Geometric structure Fig. 1 shows (a) the schlegel diagram for C60F17CF3, where x, y, and z are three location sites respectively for CF3, and (b) the top view of C60F17CF3-x. Excepting for the two sites (x and y) suggested by Hübschle et al. [12], another site z symmetric to x is also considered to locate CF3, shown in Fig. 1a. The three formed isomers are respectively named as C60F17CF3x, C60F17CF3y, and C60F17CF3z. Commonly, the thermodynamic stability of a structure can be determined by its binding energy (BE) [35], defined as the difference between the energy sum of all free atoms constituting the molecule and the total energy of the molecule. The larger BE leads to the more stable structure. It is calculated that three isomers have the same BE of 501.27 eV. However, it has been reported that in a toluene/CDCl3 solution at room temperature, the C1 isomer of C60F36 rearranges into the C3 isomer over a period of four days, as a result of a unique 1,3-shift of fluorine [36]. In order to explore the stabilities of C60F17CF3x, C60F17CF3y, and C60F17CF3z three structures at the room temperature, the enthalpy S of them are also computed. The computed enthalpy S of these three isomers all are 216.06 cal/mol k. Therefore, addition sites, x, y, and z, for CF3 in the cage should be isoenergetic, demonstrating the correctness of the describing of Troshin et al. [11] that is, CF3 should not have three F neighbors that would restrict rotation. Thus, we take C60F17CF3x into deeper research. The C60F17CF3x is simplified as C60F17CF3 in the following text. Far away from the perfect sphericity of C60, C60F17CF3 is a ‘‘tortoise’’ – shaped structure, where the planar aromatic benzenoid ring is isolated from the residual p system by a belt composed of sp3 bybridized carbon atoms. The C(cage)-C(cage) bond lengths are equivalent in the planar aromatic benzene rings (Rc– c = Rc=c = 1.38 Å) owing to significant delocalization effect, which are in good agreement with the experimental values (Rc– c = Rc=c = 1.37 Å) for C60F18 [6], providing convincing evidence for the aromatic character. The lengths of those C(cage)–C(cage) bonds, bond to F or CF3 in C60F17CF3, are elongated significantly because of the transforming from sp2 to sp3 hybridization of carbon atom, whereas the other C(cage)–C(cage) bonds almost unaffected. The average values of C(cage)–C(cage), C(cage)–F, C(CF3)–F of C60F17CF3 are shorten as A[C(cage)–C(cage)], A[C(cage)–F], A[C(CF3)–F], and the bond length of C(cage)–C(CF3) are written as L[C(cage)–C(CF3)]. Consequently, the A[C(cage)–C(cage)] for C60F17CF3 is 1.48 Å, respectively 0.8 and 0.2 Å longer than that of RC=C and RC–C of C60, and a slightly longer relative to the experimental values of that of C60F18(1.46 Å) [6], indicating the F and CF3 draw the cage outward to some degree. The calculated A[C(cage)–F] of C60F17CF3 is 1.40 Å, slightly shorter relative to the experimental values of that of C60F18(1.38 Å) [6], and comparable to the 1.38 or 1.39 Å in CmFn molecules [37]. In addition, the

Fig. 1. (a) The schlegel diagram for C60F17CF3, where x, y and z are the location sites for CF3, (b) the top view of C60F17CF3x.

A[(CF3)–F] of C60F17CF3 is 1.36 Å, 0.4 Å smaller than that of A[C(cage)–F], while the L[C(cage)–C(CF3)] of it is 1.59 Å, about 0.11 Å longer than that of A[C(cage)–C(cage)]. In summary, the bond lengths of C60F17CF3 predicted at BLYP/DNP level in this paper are close to the theoretical and experimental values for C60F18, supporting that the theory method for geometry optimizations is qualitatively reliable.

3.2. The electronic structure Fig. 2 shows the energy levels of C60F17CF3, as well as those for C60 and C60F18 for comparison. The black broken lines stand for the unoccupied orbitals, and black solid lines stand for the occupied orbitals. The molecular orbitals whose energies agree with each other within a difference of 0.05 eV are regarded as degenerate, and the length of the horizontal line shows the orbital degeneracy. As Fig. 2 shows, both the highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) of C60 10-fold degenerated, while, both HOMOs and LUMOs of C60F17CF3 sixfold degenerated, as same as that of C60F18. In comparison with those of C60, the HOMOs and LUMOs of C60F17CF3 shift down while presenting slight difference in energies, giving rise to the large energy gaps (Egs). We compare the Egs of all the considered structures, because they are often correlated with the kinetic stabilities [38]. The Eg of C60 is 1.66 eV, close to the 1.64 eV computed by Lu et al. [39]. While, C60F17CF3 has the Eg of 2.39 eV, which is almost as same as the calculated value of C60F18, 2.40 eV by us and 2.41 eV by Bakhtizin et al. [40]. Moreover, the Eg of C60F17CF3 is much larger than that of C60, so C60F17CF3 possess high kinetic stabilities, which may be useful to explain the reason why C60F17CF3 can be synthesized successfully [10]. In order to study the effects brought by CF3 addition to the energy levels of C60F18, the density of states (DOS) of them are discussed in the following. The total density of states (TDOSs), partial density of states (PDOSs), and frontier molecular orbitals (FMOs) can provide a convenient comprehensive view of the electronic structures and orbital populations of clusters and solids. Fig. 3 shows the TDOS of (A) C60, (B) C60F18 and (C) C60F17CF3, and PDOS of (D) F in C60F18, (E) F and (F) CF3 in C60F17CF3. The DOS are obtained by a Lorentzian extension of the discrete energy levels, with weights being the orbital populations in the levels, and a summation over them. The broadening width parameter is chosen to be 0.15 eV and the Fermi level (Ef) is taken as zero. It is clear from the Fig. 3 that the TDOS of C60F18 is very different from that of C60 near Ef, significantly due to the transforming from sp2 to sp3 hybridization of 18 Carbon atoms in the same hemisphere of fullerene core. Fig. 2 also presents the wave functions of HOMOs and LUMOs of both C60F18 and C60F17CF3 besides the orbitals, where the dark and light grays represent the negative and positive parts of the wave functions. It can be clearly observed from Fig. 2 that these 18 sp2 hybridized carbon atoms are dominated by the HOMO and LUMO in the C60 cage. However, there are almost no wavefunctions distribute on the fluorinated carbons. Therefore, the HOMO and LUMO dominantly come from the 2p orbitals of residual carbons with sp2 hybridization and mostly distribute around the tortoise shell. Moreover, the TDOS of C60F17CF3 is almost as same as that of C60F18, dominantly because of all the unaffected carbons in the cage after the substitution of CF3 for one F atom. We can find that the TDOS of a structure is the sum of the PDOS of all components. It is obvious that the peaks of the PDOS of F and CF3 are mainly distribute in the energy range between 12 to 2 eV and are almost zero near Ef, implying that the contribution of F and CF3 to the frontier orbitals can be ignored in C60F17CF3. We can notice that the Egs of C60F18 and C60F17CF3 are almost the same, which can be well explained from the zero PDOS of CF3 near HOMO and LUMO. This


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Fig. 2. The energy levels of C60, C60F18 and C60F17CF3.

Fig. 4. The computed absorption spectra of C60, C60F18, and C60F17CF3.

Fig. 3. The total density of states(TDOS) of (A) C60, (B) C60F18 and (C) C60F17CF3, and the partial density of states (PDOS) of (D) F in C60F18, (E) F and (F) CF3 in C60F17CF3.

scenario can be clearly seen from the wave functions of HOMOs and LUMOs of both C60F18 and C60F17CF3. The vertical ionization potentials (VIP) is the energy difference between the positively charged and neutral clusters, and the vertical electron affinities (VEA) is evaluated by adding one electron to the neutral cluster in its equilibrium geometry and taking the difference between their total energies. The VIP and VEA are 7.56 and 2.77 eV for C60, while the calculated VIP and VEA for C60F17CF3 are 8.78 and 3.33 eV, which are somewhat lager than those of C60, but similar to the calculated value for C60F18 [41]. It is known that halofullerenes C60Xn (X) F and Cl, are good electron-acceptors with possible photonic/ photovoltaic applications [43]. Like C60Xn, therefore, C60F17CF3 can serve as excellent acceptors with potential photonic/photovoltaic applications. 3.3. Optical absorption spectra Fig. 4 shows the computed absorption spectra of C60, C60F18, and C60F17CF3. The absorption spectra of exohedral fullerene derivatives are strongly sensitive to the substituent [8]. It is discovered that most of the absorption peaks locate in the visible and

near-UV range, similar to the computed scope of Popov et al. [42] and easily detected by further experimental measurements. The C60 cage shows four main peaks at 2.70, 2.89, 3.79, and 4.76 eV, respectively. For C60F18 and C60F17CF3 clusters, more absorption peaks are observed, and the spectra exhibit more or less similar peaks to the spectrum of C60. Especially, the distinct peaks near 2.89 eV are all found in the optical absorption spectra of the C60F18 and C60F17CF3. For C60F17CF3, there is a sharp peak at 2.78 eV. It is found from the calculated data that the absorption peak is formed by the electron transition from the energy level at 7.24 eV to that at 4.44 eV. To find out its origin, we observe the PDOS of CF3 and F of C60F17CF3 shown in Fig. 3. The figure shows that there are weak peaks at 7.44 eV for F and some peaks at 4.44 eV for both F and CF3 addicts. So the peak at 2.78 eV in the optical absorption spectrum of C60F17CF3 is derived from all atoms. Therefore, the absorption spectra of C60F17CF3 structure are distorted by the F and CF3 addition. It is well known that the optical gaps (OGs) for the compounds are corresponding to the lowest energy absorption feature in each spectrum [6]. The calculated OGs for C60, C60F18, and C60F17CF3 are 2.70, 2.40, and 2.40 eV. Hence, the lowest-energy absorptions of C60F18 and C60F17CF3 are both red shifted relative to that of C60, while, they have the same lowest-energy absorptions, indicating the OG is not sensitive to the substituting CF3 for F in C60F18.

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Although the OGs of C60F18 and C60F17CF3 are equal to the Egs of them respectively, it should be noticed that the optical gap of a system has no relation to its energy gap, such as M@Sn12 Chen et al. [43]. 3.4. Aromatic character Aromaticity is often discussed in terms of various criteria such as energetics, magnetics, and geometry. As a measure of aromaticity, the nucleus-independent chemical shift (NICS) proposed by Schleyer et al. [46] is based on magnetic shieldings. NICS values are computed at selected points inside or around a molecule. For fullerenes, the computed NICS values at the center agree well with the endohedral 3He NMR chemical shifts measured [44], and thus it is an effective way to evaluate aromaticity. According to the socalled NICS characterization, the aromaticity is characterized by a negative NICS value, antiaromaticity by a positive NICS, and nonaromaticity by a value close to zero. The NICS value of C60 calculated by us, using gauge-including atomic obital (GIAO) method, is 0.10 ppm, suggesting that C60 is nonaomatic, which suggests C60 is nonaromatic, the same conclusion gotten by Shabtai et al. using the experimental method [45], whereas the C60F18 and C60F17CF3 molecules show larger NICS values with 5.84 and 7.25 ppm at the cage center respectively, indicating the efficient well delocalization of electron density. Meanwhile, considering that the magnetic field in fullerene subunits is practically uniform throughout the interior cavity in C60F17CF3, we also calculated the NICS values at different sites, moving from the center of the planar aromatic benzenoid ring toward the middle points of hexagons along the direction of z axis. For comparison purpose, the NICS values of C60 and C60F18 between the central points of two hexagons face to face in the cage are evaluated in the same direction. As depicted in Fig. 5, alien from C60, C60F18 and C60F17CF3 become much more shielded in the consequence of drastic structure changes and aromatic ring disruptions of fullerene subunits in the whole distance interval, which are as evidenced by the more negative NICS values. For C60, The NICS curves are symmetric because of the two hexagons in the C60 cage are symmetric. The NICS value becomes more negative gradually when the NICS index (Bq atom) moves from the cage center toward the middle points of hexagon and then reaches the maxima NICS value of 16.14 ppm at the hexagon center. In the case of C60F17CF3, the evolutional tendencies of NICS values are looked

Fig. 5. The NICS variation with distance from the molecule center through the middle points of hexagon in C60, C60F18, and C60F17CF3 along the negative direction of z axis.

identical to that of C60F18 except for a difference in the distance from the molecular center. The smallest NICS values are 21.07 ppm at 1.2 Å distance to the benzenoid ring for C60F18 and 20.72 ppm at 1.4 Å far from the benzenoid ring for C60F17CF3. After these smallest knee points, the NICS values become slightly less negative as the Bq atom moves toward the surface hexagon center until react to the sites, 1.2 Å to the hexagon center both for C60F18 and C60F17CF3, then, the NICS values of them become dramatically decreased when shift to the hexagon center. By comparison of C60, the NICS values of C60F18 and C60F17CF3 that point further away to the centers of hexagon become much more shielded so that the NICS values at the surface hexagon center are 13.76 and 12.87 ppm, respectively, showing strong aromatic character. To sum up, the attached F and CF3 in C60F17CF3 greatly change the cage structure and disrupt aromatic rings, which lead to strong aromatic character. 3.5. The static linear polarizability and first-Order hyperpolarizability In order to check the reliability of our method as well as to get the results of pure C60 for comparison, we first calculate the mean static linear polarizability hai of C60. Our value and the others are listed in Table 1. It can be found that our average value of a (77.4 Å3) is almost the same as most other calculations with the same basis set. For example, Yang et al. [46] got the values of 77.6 and 76.1 Å3 using the same DNP basis sets but with the Perdew–Burke–Ernzerhof (PBE) function at the GGA level and the Vosko–Wilk–Nusair (VWN) function at the LDA level, respectively. Weiss et al. [47], using the random phase approximation (RPA) and the basis set of 6–31G+sd, got a value of 78.8 Å3. It is worth noting that these results are in good agreement with the experimental value of 76.5 ± 8.0 Å3 obtained by Antoine et al. [48] using the molecular beam deflection (MBD) method. Therefore both our calculation approach and the basis sets are reliable. Table 2 displays the calculated results of a tensors, hai, Da, hbi, and b0 of C60F17CF3 as well as those of C60 and C60F18 for comparison. The static dipole polarizability measures the ability of the valence electrons to find an equilibrium configuration which screens a static external field [49]. Hence, molecules with many delocalized valence electrons should display large values of static dipole polarizabilities. Obviously, because the electron distribution for C60, as discussed before, is isotropic in the x, y, and z directions, there is no difference between z and x (or y) components of the polarizabilities a and the polarizability ellipsoid becomes a sphere, which indicate the strong isotropy, as evidenced by the zero value of Da. However, as to C60F18 and C60F17CF3, the isotropy is destroyed in consequence of the structure changes deriving from the F and CF3 attachments. The values of the components of a are different in the x, y, and z directions (axx, ayy, azz) resulting in the hai values of 11.7 and 25.6 Å3, respectively. As we know, the former C3v symmetry is completely destroyed to the C1 symmetry upon the substituting CF3 for F in C60F18, so the static linear polarizabily is indeed very sensitive to the molecule structure, as Zagorodniy et al. stated [50]. The calculated tensor components of C60F18 and C60F17CF3 are larger than those of C60, resulting in the stronger response of external field. Actually, this is expected since the sp structure for them is rich of p bonds delocalized along the entire body of the system [49]. As known, the static first hyperpolarizability is an estimate for the intrinsic molecular hyperpolarizability in the absence of any resonance effect. The first-order hyperpolarizability b0 of C60 is calculated and found to be zero, the same as that calculated by Xie et al. [51] This is actually expected since they display inversion symmetries. Consequently, it is convinced from normalized b0 values that C60F18 and C60F17CF3 have large b0 values in contrast to C60. The decrease of b0 value for C60F17CF3 amounts to 34% related

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C. Tang et al. / Computational and Theoretical Chemistry 991 (2012) 154–160 Table 1 The calculated and experimental average values of the static linear polarizability hai for C60 with the unit in Å3. Methods

BLYP/DNP

PBE/DNP [45]

VWN/DNP [45]

PRA/6–31G+sd [46]

MBD [47]

hai

77.4

77.6

76.1

78.8

76.5 ± 8.0

Table 2 Static linear polarizability hai (in Å3), polarizability Anisotropy Da (in Å3), and firstOrder hyperpolarizability b0 (in 1030 esu) for C60, C60F18, and C60F17CF3.

axx ayy azz hai Da b0

C60

C60F18

C60F17CF3

71.32 71.32 71.32 71.32 0.00 0

101.49 99.42 94.47 98.46 8.84 2.55

100.96 100.88 93.78 98.54 10.11 1.68

to C60F18. The relatively large geometric variations of C60F17CF3 compared to C60F18 are responsible for the large decrease. 4. Conclusion Systematic calculations based on the DFT have been performed for electronic structure, polarizabilities, NICS values, and absorption spectra of the fluorinated fullerene derivative C60F17CF3. The C60F17CF3 has large Eg of 2.39 eV, suggesting its highly kinetic stabilities. Bonding-specific F and CF3 to C60 produce a remarkable enhancement of the VIP of C60F17CF3 (8.78 eV). Hence, C60F17CF3 should be good electron acceptors with potential photonic/photovoltaic applications. The DOS and FMOs analyses show that the HOMOs and LUMOs are mostly distributed in the tortoise shell subunit of C60F17CF3, and the influence from the attached halogen atoms is secondary. Our calculations shows that the absorption spectra of C60F17CF3 structure is distorted by the F and CF3 addition and the optical gaps of C60F17CF3 is red shifted relative to that of C60. The attached F and CF3 in C60F17CF3 greatly change the cage and disrupt aromatic rings, which lead to stronger aromatic character of itself than that of C60. In addition, the static linear polarizability a and first-order hyperpolarizability b0 for C60F17CF3 are significantly larger than those of C60 because of its lower symmetric structures and high delocalization of p electrons. Acknowledgments Project supported by the Special Foundation of National Natural Science (Grant Nos. 11104062, 10947132, 11004047), the China Postdoctoral Science Foundation funded Project (Grant No. 20100471307), Jiangsu Planned Projects for Postdostoral Research Funds (Grant No. 1001001C), the Research Starting Foundation of Hohai University (Grant No. 2084/40801130), the Excellent Innovation Personal Support Plan of Hohai University, and the Fundamental Research Funds for the Central Universities (Grant No. 2012B12914). References [1] R. Taylor, Why fluorinate fullerenes, J. Fluorine Chem. 125 (2004) 359–368. [2] Z. Slanina, F. Uhlík, Energy-entropy interplay of C60F36 isomers, Chem. Phys. Lett. 374 (2003) 100–103. [3] J. Cioslowski, N. Rao, A. Szarecka, K. Pernal, Theoretical thermochemistry of the C60F18, C60F36, and C60F48 fluorofullerenes, Mole. Phys. 99 (2001) 1229–1232. [4] O.V. Boltalina, V.Y. Markov, R. Taylor, M.P. Waugh, Preparation and characterisation of C60F18, Chem. Commun. (1996) 2549–2550. [5] I.S. Neretin, K.A. Lyssenko, M.Y. Antipin, Y.L. Slovokhotov, O.V. Boltalina, P.A. Troshin, A.Y. Lukonin, L.N. Sidorow, R. Taylor, C60F18, a flattened fullerene: alias a hexa-substituted benzene, Angew. Chem. Int. Ed. 39 (2000) 3273–3276.

[6] I.V. Goldt, O.V. Boltalina, L.N. Sidorov, E. Kemnitz, S.I. Troyanov, Preparation and crystal structure of solvent free C60F18, Solid State Sci. 4 (2002) 1395– 1401. [7] S.I. Troyanov, O.V. Boltalina, I.V. Kouvytchko, P.A. Troshin, E. Kemnitz, P.B. Hitchcock, R. Taylor, Molecular and crystal structure of the adducts of C60F18 with aromatic hydrocarbons, Fullerenes Nanotubes Carbon Nanostruct. 10 (2002) 243–259. [8] A.G. Avent, O.V. Boltalina, A. Goryunkov, A.D. Darwish, V.Y. Markov, R. Taylor, Isolation and characterization of C60(CF3)2, Fullerenes Nanotubes Carbon Nanostruct. 10 (2002) 235–241. [9] O.V. Boltalina, P.B. Hitchcock, P.A. Troshin, J.M. Street, R. Taylor, Isolation and spectroscopic characterisation of C60F17CF2CF3 and isomers of C60F17CF3; insertion of CF2 into fluorofullerene C–F bonds, J. Chem. Soc. Perkin. Trans. 2 (2000) 2410–2414. [10] P.A. Troshin, A.G. Avent, A.D. Darwish, N. Martsinovich, A.K. Abdul-Sada, J.M. Street, R. Taylor, Isolation of two seven-membered ring C58 fullerene derivatives: C58F17CF3 and C58F18, Science 309 (2005) 278–281. [11] T. Canteenwala, P.A. Padmawar, L.Y. Chiang, Intense near-infrared optical absorbing emerald green [60]fullerenes, J. Am. Chem. Soc. 127 (2005) 26– 27. [12] C.B. Hübschle, S. Scheins, M. Weber, P. Luger, A. Wagner, T. Koritsánszky, S.I. Troyanov, O.V. Boltalina, I.V. Goldt, Bond orders and atomic properties of the highly deformed halogenated fullerenes C60F18 and C60Cl30 derived from their charge densities, Chem. Eur. J. 13 (2007) 1910–1920. [13] G.A. Burley, A.G. Avent, I.V. Gol’dt, P.B. Hitchcock, H. Al-Matar, D. Paolucci, F. Paolucci, P.W. Fowler, A. Soncini, J.M. Street, R. Taylor, Design and synthesis of multi-component 18p annulenic fluorofullerene ensembles suitable for donor–acceptor applications, Org. Biomol. Chem. 2 (2004) 319–329. [14] T. Wakahara, H. Nikawa, T. Kikuchi, T. Nakahodo, G.M.A. Rahman, T. Tsuchiya, Y. Maeda, T. Akasaka, K. Yoza, E. Horn, K. Yamamoto, N. Mizorogi, Z. Slanina, S. Nagase, La@C72 having a non-IPR carbon cage, J. Am. Chem. Soc. 128 (2006) 14228. [15] B.J. Orr, J.F. Ward, Perturbation theory of the non-linear optical polarization of an isolated system, Mol. Phys. 20 (1971) 513–526. [16] H.D. Cohen, C.C.J. Roothaan, Electric dipole polarizability of atoms by the Hartree—Fock Method. I. Theory for closed-shell systems, J. Chem. Phys. 43 (1965) S34–S40. [17] B.H. Cardelino, C.E. Moore, D.O. Frazier, Calculation of static third-order polarizabilities of large organic molecules, J. Phys. Chem. A 101 (1997) 2207– 2214. [18] P. Calaminici, K. Jug, A.M. Köster, Density functional calculations of molecular polarizabilities and hyperpolarizabilities, J. Chem. Phys. 109 (1998) 7756– 7763. [19] E. Westin, A. Rosén, G.T. Velde, E.J. Baerends, Analysis of the polarizability and optical properties of C60, J. Phys. B 29 (1996) 5087–5091. [20] C.G. Ding, J.L. Yang, Q.X. Li, K.L. Wang, F. Toigo, Electronic structure and magnetism of Y13 clusters, Phys. Lett. A 256 (1998) 417–421. [21] E. Artacho, D. Sánchez-Portal, P. Ordejón, A. García, J.M. Soler, Linear-scaling ab-initio calculations for large and complex systems, Phys. Status Solidi (b) 215 (1999) 809–817. [22] B. Delley, An all-electron numerical method for solving the local density functional for polyatomic molecules, J. Chem. Phys. 92 (1990) 508–517. [23] A.D. Becke, Correlation energy of an inhomogeneous electron gas: a coordinate-space model, J. Chem. Phys. 88 (1988) 1053–1062. [24] J.P. Perdew, Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B 45 (1992) 13244–13249. [25] P. Hohenberg, W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136 (1964) B864–B871. [26] R. Fletcher, Practical Methods of Optimization, Wiley, New York, 1980 (vol. 1). [27] C.H. Choi, M. Kertesz, L. Mihaly, Vibrational assignment of All 46 fundamentals of C60 and C606-: scaled quantum mechanical results performed in redundant internal coordinates and compared to experiments, J. Phys. Chem. A 104 (2000) 102–112. [28] C.S. Yannoni, P.P. Bernier, D.S. Bethune, G. Meijer, J.R. Salem, NMR determination of the bond lengths in C60, J. Am. Chem. Soc. 113 (1991) 3190–3192. [29] S.Z. Liu, Y.J. Lu, M.M. Kappes, J.A. Ibers, The structure of the C60 molecule: XRay crystal structure determination of a twin at 110 K, Science 254 (1991) 408–410. [30] W. Fa, J. Zhou, C.F. Luo, J.M. Dong, Cagelike Au32 detected in relativistic density-functional calculations of optical spectroscopy, Phys. Rev. B 73 (2006) 085405. 2 2 [31] E.N. Esenturk, J. Fettinger, B. Eichhorn, The Pb12 and Pb10 zintl ions and the 2 2 M@Pb12 and M@Pb10 cluster series where M = Ni, Pd, Pt, J. Am. Chem. Soc. 128 (2006) 9178–9186.

160


[32] A.D. Mclean, M. Yoshimine, Study of energy transfer from Sb3+, Bi3+, Ce3+ to Sm3+, Eu3+, Tb3+, Dy3+, J. Chem. Phys. 47 (1967) 1927–1936. [33] R.J. Li, Z.R. Li, D. Wu, X.Y. Hao, Y. Li, B.Q. Wang, F.M. Tao, C.C. Sun, Density functional study of structures and interaction hyperpolarizabilities of NH3– HCl–(H2O)n (n=0–4) clusters, Chem. Phys. Lett. 372 (2003) 893–898. [34] L. Xiang, Y.G. Liu, A.G. Jiang, D.Y. Huang, Theoretical investigation of s-triazine derivatives as novel second-order nonlinear optical chromophores, Chem. Phys. Lett. 338 (2001) 167–172. [35] C.M. Tang, Y.B. Yuan, K.M. Deng, Y.Z. Liu, X.Y. Li, J.L. Yang, X. Wang, Geometric and electronic properties of endohedral Si@C74, J. Chem. Phys. 125 (2006) 104307. [36] A.G. Avent, R. Taylor, Fluorine takes a hike: remarkable room-temperature rearrangement of the C1 isomer of C60F36 into the C3 isomer via a 1,3-fluorine shift, Chem. Commun. (2002) 2726–2727. [37] R. Taylor, Fluorinated fullerenes, Chem. Eur. J. 7 (2001) 4074–4084. [38] J.I. Aihara, Kinetic stability of carbon cages in non-classical metallofullerenes, Chem. Phys. Lett. 343 (2001) 465–469. [39] G.L. Lu, K.M. Deng, H.P. Wu, J.L. Yang, X. Wang, Geometric and electronic structures of metal-substitutional fullerene C59Sm and metal-exohedral fullerenes C60Sm, J. Chem. Phys. 124 (2006) 054305. [40] R.Z. Bakhtizin, A.I. Oreshkin, P. Murugan, J. Vijay Kumar, T. Sadowski, Y. Fujikawa, Y. Kawazoe, T. Sakurai, Adsorption and electronic structure of single C60F18 molecule on Si(1 1 1)-7 7 surface. Fullerenes Nanotubes Carbon Nanostruct. 18 (2010) 369–375. [41] D.M. Guldi, Fullerenes: three dimensional electron acceptor materials, Chem. Commun. (2000) 321–327. [42] A.A. Popov, V.M. Senyavin, V.I. Korepanov, I.V. Goldt, A.M. Lebedev, V.G. Stankevich, K.A. Menshikov, N.Yu. Svechnikov, O.V. Boltalina, I.E. Kareev, S. Kimura, O. Sidorova, K. Kanno, I. Akimoto, Vibrational, electronic, and vibronic excitations of polar C60F18 molecules: experimental and theoretical study, Phys. Rev. B 79 (2009) 045413.

[43] X. Chen, K.M. Deng, Y.Z. Liu, C.M. Tang, Y.B. Yuan, W.S. Tan, X. Wang, The geometric, optical, and magnetic properties of the endohedral stannaspherenes M@Sn12 (M = Ti, V, Cr, Mn, Fe, Co., Ni), J. Chem. Phys. 129 (2008) 094301. [44] P.V.R. Schleyer, C. Maerker, A. Dransfeld, H. Jiao, N. J. R. v. E. Hommes, Nucleusindependent chemical shifts: a simple and efficient aromaticity probe, J. Am. Chem. Soc. 118 (1996) 6317–6318. [45] E. Shabtai, A. Weitz, R.C. Haddon, R.E. Hoffman, M. Rabinovitz, A. Khong, R.J. Cross, M. Saunders, P.C. Cheng, L.T. Scott, 3He NMR of He@C606 and He@C706. New Records for the Most Shielded and the Most Deshielded 3He Inside a Fullerene1, J. Am. Chem. Soc. 120 (1998) 6389–6393. [46] Y. Yang, F.H. Wang, Y.S. Zhou, L.F. Yuan, J.L. Yang, Density functional calculations of the polarizability and second-order hyperpolarizability of C50Cl10, Phys. Rev. A 71 (2005) 013202. [47] H. Weiss, R. Ahlrichs, M. Häser, A direct algorithm for self-consistent-field linear response theory and application to C60: excitation energies, oscillator strengths, and frequency-dependent polarizabilities, J. Chem. Phys. 99 (1993) 1262–1271. [48] R. Antoine, P. Dugourd, D. Rayane, E. Benichou, M. Broyer, F. Chandezon, C. Guet, Direct measurement of the electric polarizability of isolated C60 molecules, J. Chem. Phys. 110 (1999) 9771–9772. [49] M. Bianchetti, P.F. Buonsante, F. Ginelli, H.E. Roman, R.A. Broglia, F. Alasia, Abinitio study of the electromagnetic response and polarizability properties of carbon chains, Phys. Rep. 357 (2002) 459–513. [50] K. Zagorodniy, M. Taut, H. Hermann, Contribution of nuclear displacements to the static polarizability of molecules in an external electric field: application to fluorinated fullerenes C60Fn, Phys. Rev. A 73 (2006) 054501. [51] R.H. Xie, G.W. Bryant, V.H. Smith, Electronic, vibrational and magnetic properties of a novel C48N12 aza-fullerene, Chem. Phys. Lett. 368 (2003) 486–494.