Electronic Structures and Optical Properties of Phenyl C 71 Butyric Acid Methyl Esters

Phenyl C 71 butyric acid methyl ester (PC 71 BM) has been adopted as electron acceptor materials in bulk heterojunction solar cells with relatively higher power conversion efficiency. The understanding of the mechanism and performance for the devices based upon PC 71 BM requires the information of conformations, electronic structures, optical properties, and so forth. Here, the geometries, IR and Raman, electronic structures, polarizabilities, and hyperpolarizabilities of PC 71 BM isomers are studied by using density functional theory (DFT); the absorption and excitation properties are investigated via time-dependent DFT with B3LYP, PBE0, and CAM-B3LYP functionals. The calculated results show that [6,6]PC 71 BM is more stable than [5,6]PC 71 BM due to the lower total energy. The vibrational modes of the isomers at IR and Raman peaks are quite similar. As to absorption properties, CAM-B3LYP functional is the suitable functional for describing the excitations of PC 71 BM because the calculated results with CAM-B3LYP functional agree well with that of the experiment. The analysis of transition configurations and molecular orbitals demonstrated that the transitions at the absorption maxima in UV/Vis region are localized π-π transitions in fullerenes cages. Furthermore, the larger isotropic polarizability of PC 71 BM indicates that the response of PC 71 BM to applied external electric field is stronger than that of PC 61 BM, and therefore resulting into better nonlinear optical properties.


Introduction
The electronic devices based upon organic materials, such as organic radiofrequency identification, light emitting diode, memory devices, and solar cells, have attracted considerable attention in the past decade due to their potential to be lower-cost, light-weight, flexible, and large-area equipment.These devices usually contain heterojunction formed by electronic donor and acceptor materials.The properties of materials in these devices, including chemical structures [1], electronic structures [2], excited states [3], charge transfer, and charge transport [4], are of particular importance for their overall performance.To provide a better understanding toward the higher performance of device, it is necessary to investigate the electronic structures of the materials, as well as the energy level alignment at the heterojunction interface [5].The discovery of ultrafast photoinduced charge/energy transfer from a conjugated polymer to fullerene molecules and introducing bulk heterojunction (BHJ) stimulated the rapid development of organic photovoltaic (OPV) technology [4,[6][7][8][9][10][11].Also, some fullerene hybrids show good nonlinear optical properties [12].
Among the fullerene derivatives in OPV, [6,6]-phenyl-C 61 butyric acid methyl ester (PC 61 BM) as the soluble electron acceptor was widely used to fabricate efficient BHJ organic polymer solar cells (PSCs) [13].For instance, Svensson et al. reported the PSC with open circuit voltage ( oc ) 1 V based on alternating copolymer PFDTBT blended with PC 61 BM [14].Inganäs et al. performed a systematic study of PSCs and found the efficiency about 2-3% using four different fluorene copolymers through changing the length of the alkyl side chains and chemical structures [15].A series of highly soluble fullerene derivatives with varying acceptor strengths was applied in PSCs, and the  oc of the corresponding devices was found to correlate directly with the acceptor strength of the fullerenes [16].Unfortunately, PC 61 BM has very low absorption coefficients in UV/Vis region [17], which limits the light harvesting efficiency.
PC 71 BM has similar geometry to PC 61 BM, and the fullerene cage of PC 71 BM contains ten C atoms more than that of PC 61 BM, but the performances of them in PSCs are quite different.The better understanding of the mechanism and performance for the devices based upon PC 71 BM requires the information of conformations, electronic structures, optical properties, and so forth.In this work, taking into account two kinds of possible isomers of phenyl C 71 butyric acid methyl esters, the geometries, electronic structures, vibrational properties, polarizabilities, and hyperpolarizabilities are calculated using density functional theory (DFT), and the absorption properties which relate to the character of excited states are addressed with timedependent DFT (TDDFT) [28][29][30][31][32][33][34]; the comparative analyses for the isomers are also reported.

Computational Methods
The computations of the geometries and vibrational properties have been performed with Becke's three parameters gradient-corrected exchange potential and the Lee-Yang-Parr gradient-corrected correlation potential (B3LYP) [35][36][37][38], since the comparison with the MP2 geometries of several organic molecules confirmed the accuracy of B3LYP for the geometry optimizations [39].In order to get the reliable calculations of absorption spectra and excited states, the hybrid functionals B3LYP and PBE0 [40][41][42], as well as long-rangecorrected hybrid functional Coulomb attenuation method CAM-B3LYP [43], are adopted in TDDFT calculations.The comparison of absorption spectra between experiment and calculations demonstrates the better performance of CAM-B3LYP functional in describing the excited state properties of PC 71 BM.Thus, the electronic structures, polarizabilities, and hyperpolarizabilities are also analyzed using CAM-B3LYP functional.The nonequilibrium version of the polarizable continuum model (PCM) [44] is employed to take account of the solvent effects of toluene solution.The polarized splitvalence 6-31G(d,p) basis sets are sufficient for calculating the excitation of organic molecules [45], and introducing additional diffuse functions in basis sets generates negligible effects on the electron density and hence on the accuracy of DFT and TDDFT results [39].All calculations were performed with 6-31G(d,p) basis sets without any symmetry constraints using the Gaussian 09 package [46].

Results and Discussion
3.1.Geometrical Structures.C 70 fullerene is composed of 12 five-C rings and 25 six-C rings with  5ℎ symmetry.However, when the C atom in the side chain of butyric acid methyl ester connects to C 70 cage, two possible isomers can be formed since the C atom can connect to not only the most "polar" carbon-carbon double bonds in C 70 (the adjacent edge of six-C rings), but also the carbon-carbon single bond in C 70 (the adjacent edge between five-C rings and six-C rings), and these two structures were denoted as [6,6]PC 71 BM and [5,6]PC 71 BM, respectively.The isomerization is similar to other fullerene derivatives [47].
The optimized geometries of [6,6]PC 71 BM and [5,6]PC 71 BM at the B3LYP/6-31G(d,p) level in gas phase are shown in Figure 1.The calculated total energy of [6,6]PC 71 BM is about 0.54 eV lower than that of [5,6]PC 71 BM.The NMR spectrum confirmed the stability of [6,6]PC 71 BM isomer [17].The selected bond lengths, bond angles, and dihedral angles are listed in Tables s1 and s2 in Supplementary Material available online at http://dx.doi.org/10.1155/2013/612153.The calculated average bond lengths of single and double bonds in fullerene cage of PC 71 BM isomers are about 0.145 and 0.141 nm, respectively, which are very close to the corresponding values (0.145 and 0.140 nm) of C 70 fullerene obtained from the same level of theoretical calculation.The bond character of C5-C15 was changed from double bond (0.140 nm) in pure C 70 fullerene to single bond (0.163 nm) in [6,6]PC 71 BM due to forming a carbon trigon (C5-C15-C71) through the changes of orbital hybridization, and the change of C5-C15 bond length is similar to the cases of C 60 -TPA [48] and N-methyl-3,4-fulleropyrrolidine [49], while, in [5,6]PC 71 BM, the atomic distance between C14 and C15 is about 0.213 nm, which far exceeds the typical C-C single bond length (0.154 nm).Therefore, the single bond of C14-C15 is broken in the isomer.This is the main difference between the two isomers and it may affect electronic and optical properties.The other corresponding geometrical parameters of these isomers are very similar because of the localized character of chemical bonds.

IR and Raman.
In order to investigate the IR and Raman properties of PC 71 BM, the vibrational analyses are performed based upon the optimized structures of isomers.The IR and Raman spectra of [6,6]PC 71 BM and [5,6]PC 71 BM are shown in Figure 2. The calculated vibrational data indicates that there are no imaginary frequencies.This means that the optimized isomer structures are the minima of potential energy surface indeed.
The vibrational frequency ranges of [6,6]PC 71 BM and [5,6]PC 71 BM are 10∼3210 cm −1 and 13∼3209 cm −1 , respectively.For [6,6]PC 71 BM, the strongest IR peaks at about 1219 and 1203 cm −1 correspond to the C-H bond-bending vibrational modes in butyric acid methyl ester group, while the IR peak at about 1826 cm −1 comes from stretch mode of C-O bond in carbonyl group.As to [5,6]PC 71 BM, the vibrational modes of the strongest peaks at about 1222 and 1826 cm −1 are very similar to those of [6,6]PC 71 BM, whereas to Raman, for [6,6]PC 71 BM, the peak at about 1609 cm −1 comes from the stretching mode of C-C bonds in the fullerene cage, and the peak at about 3210 cm −1 relates to the stretching mode of C-H bonds in phenyl group.Again, the vibrational modes of peaks at about 1608 and 3209 cm −1 for [5,6]PC 71 BM are very similar to those of [6,6]PC 71 BM.Furthermore, the strengths of IR and Raman at the strongest peaks of [6,6]PC 71 BM are slightly larger than those of [5,6]PC 71 BM due to its larger dipole moment.The vibrational modes at the IR and Raman peaks of PC 71 BM are very similar to those of PC 61 BM [50] due to the same moiety and the similarity of fullerene cages.

Absorption Spectra and Electronic Structures.
The UV/Vis absorption of PC 71 BM was measured in toluene solution, and the absorption peaks locate at about 462 and 372 nm, respectively [17].Also, the experiment demonstrated that the absorption coefficient of PC 71 BM is significantly higher than that of PC 61 BM in the visible region [17].The better absorption properties of PC 71 BM are favorable for improving light harvesting efficiency in OPV.In order to select a suitable functional for the excitations of PC 71 BM, the B3LYP, PBE0, and CAM-B3LYP functionals are adopted in computing the absorption spectra of the isomers in toluene solution.
The simulated absorption spectra for the two isomers of PC 71 BM are presented in Figure 3. Apparently, the excitation energies calculated with CAM-B3LYP are larger than the corresponding values calculated with PBE0 and B3LYP functionals due to the different methods for dealing with exchange and correlation energies.Comparing with the experimental results, we found that the CAM-B3LYP functional results agree well with the experimental data.
The excitation properties for the first excited state S 1 and the excited states at absorption peaks in UV-Vis region for [6,6]PC 71 BM and [5,6]PC 71 BM in toluene are listed in Table 1, which includes the excitation energies (eV), wavelength (nm), oscillator strengths () and the transition configurations with coefficients larger than 10%.The results indicate that the excitation energies at the absorption maxima for the isomers are very close, and the excited states include several transition configurations.To understand the transition character, the molecular orbitals involved transitions in Table 1 are presented in Figure 4.The HOMOs are  orbitals between C-C bonds in fullerene cage, while the LUMOs are  * orbitals in fullerene.Thus, the transitions in Table 1 are localized - * transitions in fullerenes cages.This is different from that of PC 61 BM, which has several intramolecular charge transfer transitions [50].
The exciton binding energy (EBE), an important quantity for the efficiency of excitonic solar cells, determines the charge separation in solar cells [51].The EBE can be calculated as the difference between the electronic and optical band gap energies [52].The electronic band gap is calculated as the energy difference between the HOMO and LUMO levels, while the first excitation energy is adopted as the optical gap [51,53].The molecular orbital energy levels and HOMO-LUMO gaps of PC 71 BM isomers are shown in Figure 5.The HOMO-LUMO gap of [6,6]PC 71 BM is about 4.34 eV, which is about 0.09 eV smaller than that of [5,6]PC 71 BM.The calculated EBE for [6,6]PC 71 BM and [5,6]PC 71 BM are 2.08 Table 1: The excitation energies (eV), wavelength (nm), oscillator strengths (), and the transition configurations with coefficients larger than 10% for the first excited state S 1 and the excited states at absorption peaks in UV/Vis region for [6,6]PC 71 BM and [5,6]PC 71 BM in toluene.

Polarizabilities and Hyperpolarizabilities.
Polarizabilities and hyperpolarizabilities characterize the response of a system in an applied electric field in some extent [54], such as the strength of molecular interactions, the cross sections of scattering, collision processes, and the nonlinear optical properties of the system [55,56].The definition for the isotropic polarizability is the polarizability anisotropy invariant is and the average hyperpolarizability is

Conclusions
In this work, the geometries, IR and Raman, electronic structures, polarizabilities, and hyperpolarizabilities of PC 71 BM isomers are studied by using DFT; the absorption and excitation properties are addressed via TDDFT with B3LYP, PBE0, and CAM-B3LYP functionals.Based upon the calculated results, we found the following: the lower total energy of [6,6]PC 71 BM suggests that [6,6]PC 71 BM is more stable than [5,6]PC 71 BM.The geometrical characters reveal that the C-C bond at the edge of six-C rings is changed from double bond in pure C 70 fullerene to single bond in [6,6]PC 71 BM, while the C-C bond at the edge between five-C and six-C rings is broken in [5,6]PC 71 BM.The wave numbers of strongest IR peaks of [6,6]PC 71 BM and [5,6]PC 71 BM are 1219 and 1222 cm −1 , respectively.The Raman peaks of [6,6]PC 71 BM and [5,6]PC 71 BM locate at about 1609 and 1608 cm −1 , respectively.The vibrational modes of [6,6]PC 71 BM and [5,6]PC 71 BM at IR and Raman peaks are quite similar and also very similar to that of PC 61 BM.Compared with the experimental absorption properties, it can be found that the CAM-B3LYP functional is the most suitable functional for describing excitations of PC 71 BM.The analysis of transition configurations and MOs demonstrated that the transitions at the absorption maxima in UV/Vis region are localized - * transitions in fullerenes cages.The calculated EBE for [6,6]PC 71 BM and [5,6]PC 71 BM are 2.08 and 2.11 eV, respectively.The smaller EBE of [6,6]PC 71 BM is favorable for exciton dissociation in heterojunction.Furthermore, the larger isotropic polarizability of PC 71 BM indicates that the response of PC 71 BM to applied external electric field is stronger than that of PC 61 BM, and therefore resulting into better nonlinear optical properties.

Figure 2 :
Figure2: The IR and Raman spectra of[6,6]PC 71 BM and[5,6]PC 71 BM.The top panel is IR spectra, while the bottom panel is Raman spectra.

Figure 3 :
Figure3: The simulated absorption spectra for[6,6]PC 71 BM and[5,6]PC 71 BM based upon TD-DFT results calculated with different functionals.The 0.15 eV of half-width at half-maximum was applied for simulating absorption spectra.