Intersystem Crossing Rates of Isolated Fullerenes: Theoretical

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Intersystem Crossing Rates of Isolated Fullerenes: Theoretical Calculations Yuxiu Liu, Min-Song Lin, and Yi Zhao J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b12352 • Publication Date (Web): 18 Jan 2017 Downloaded from http://pubs.acs.org on January 24, 2017

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The Journal of Physical Chemistry

Intersystem Crossing Rates of Isolated Fullerenes: Theoretical Calculations Yuxiu Liu, Minsong Lin and Yi Zhao∗ State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, 361005, P. R. China

Abstract Although the triplet states of fullerenes have prosperous applications, it remains unclear how the structural parameters of singlet and triplet states control the intersystem crossing (ISC) rates. Here, electronic structure calculations (reorganization energy, driving force and spin orbit coupling) and a rate theory (Marcus formula) are employed to quantitatively predict the ISC rates of isolated fullerenes Cn (n=60∼110). The results demonstrate that the driving force is not an only factor to predict the ISC rates. For instance, although C80 , C82 and C110 have the favorable driving force, the ISC rates are close to zero because of small spin obit couplings, whereas small ISC rate of C96 and C100 results from quite small reorganization energies. Meanwhile, in addition to well-known C60 and C70 , C92 possesses good ISC property with obviously large ISC rate. C92 also has a higher triplet-state energy than singlet-state oxygen energy, it may thus have a good photoactive property.

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Introduction Since the discovery of C60 buckminsterfullerene in 1985, 1 the photophysical properties of

fullerenes have been becoming interesting along with extensive experimental researches. 2–13 Thereinto, the long-lived triplet states resulting from intersystem crossing (ISC) process of ∗

To whom correspondence should be addressed. E-mail: [email protected]

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excited singlet states has given rise to a significant attention due to their prosperous applications, such as, the generation of singlet oxygen for various organic reactions, 2,4,5,14,15 enhancing photoinduced electric conductivity as the excited triplet state of fullerene forms a charge separated state with doped molecules 16–18 and the close relevance with photochemical up-conversion and down-conversion processes in the applications of photovoltaics, photocatalysis, photoinduced charge separation, and molecular probes. 19–25 So far, the ISC processes for pristine fullerenes from C60 to C84 have been extensively studied experimentally with comprehensive elaborations of the ISC rates and ISC quantum yields over the past several years. 2,8,9,26–33 The measured ISC quantum yields for C60 , C70 , C76 , C78 and C84 are 0.93, 0.90, 0.05, 0.12 and 0.01, respectively 26,30,31,33 , decreasing with the increase of carbon number of fullerenes. For higher fullerenes Cn (n>84), experimental studies are lacking for ISC processes because of the difficult isolation from abundant isomers, such as C92 , C96 , C100 etc. Theoretically, the ISC processes are mainly investigated from the simulations of energies and structures of triplet states 34–38 . However, the obtained triplet-state energies of C60 to C84 are not monotonic decreasing. Thus the only triplet-state energies cannot be used to explain ISC processes. Several works have also calculated the triplet-state energies of higher fullerenes 37,38 because the larger fullerenes may possess variable cage geometries 39,40 and exhibit different ISC properties. But the relationship between ISC quantum yields and pristine fullerene structures remains unclear. It is well known that ISC process is energy transfer from singlet to triplet states, and the rate theory is required to reveal how the structure parameters control the ISC. In this paper, we start from the perturbation rate theory to calculate ISC rates from C60 to C110 . At a high temperature limitation, Marcus formula 41 for electron transfer can be safely used to the present energy transfer rate 42,43 . Based on Marcus formula, the ISC rate is heavily dependent on the three factors, namely driving force, reorganization energy and spin orbit coupling (SOC). The driving force of singlet to triplet states is defined by the difference between the adiabatic energies of singlet


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2 COMPUTATIONAL DETAILS

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and triplet states, and many experiments and theoretical calculations have been used to determine these values for C60 to C120 . 2,8,9,26–32,37,38 However, to the best of our knowledge, for the other two factors, reorganization energy and spin-orbit coupling have not been systematically quantified for these large fullerene systems. The reorganization energy reflects the rigidity of system arising from energy relaxation from the equilibrium configurations of primary state to the final state, and spin-orbit coupling impacts the interaction between the initial singlet state and final triplet state. Therefore, combining these three factors is of great significance to understand the ISC process for fullerene systems in detail. For the cage-structured fullerenes consisted of hexagon and pentagon rings, all carbon atoms are sp2 hybridized and the most stable structures comply with the isolated-pentagonrule (IPR) which is an empirical and geodesic rule proposed by Kroto in 1987 and has been verified by abundant experimental and theoretical results . 44 In this case, the pentagons are isolated from each other and embraced by five hexagons 45 to achieve the minimum steric strain and preferable π-electron delocalization. 46 In this work, we choose pristine fullerenes from C60 to C110 based on IPR 13,37,39,40,47–49 as model systems and calculate the intersystem crossing rates. The ISC properties are further analyzed based on the three factors and the structure-property correlations are discussed simultaneously.

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Computational details The ISC process is essentially a radiationless step of the photo-physical processes in a

fullerene molecule. After photoexcitation, the molecule is excited from the ground state S0 to singlet excited states Sn . The energy then relaxes from Sn to the lowest excited S1 . Succeedingly, the ISC may occur from S1 to triplet states Tn . Meanwhile, there are the other radiation and radiationless channels from S1 to S0 . Therefore, ISC competes with these relaxations to the ground state. To follow those photo-physical processes, we first calculate the electronic absorption spectra at the stable ground-state geometries of fullerenes. The stable ground states S0 are



3 RESULTS AND DISCUSSION 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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optimized by using the hybrid density functional theory (DFT) with Becke and Lee, Yang, and Parr (B3LYP) functional and the 6-31G* basis set, whose accuracy has been demonstrated in broad simulations of fullerene candidiates. 50–53 In the calculations of electronic absorption spectra, we use time-dependent DFT (TDDFT) with B3LYP/6-31G*. The other two functionals CAM-B3LYP, ωB97XD with more HF components are also adopted for the comparison. Comparing with available experimental data, we find B3LYP is obviously better than others in predicting excited states properties (see Fig. S1 in supporting information (SI)). Thus, the remaining calculations are performed at the B3LYP level. The solvent effect is mimicked by Polarizable Continuum Model (PCM) and all the above calculations are achieved in Gaussian09 program package. 54 In general, the energy relaxation process from high singlet states to low singlet states is much faster than the intersystem crossing one. Thus, the triplet states Tn may dominantly generated from the lowest singlet state, and Fermi-Golden rule is applicable to quantitatively predict the intersystem crossing rates. 42,55 In the semiclassical approximation, the intersystem crossing rate from a singlet state to a triplet state can be estimated from Marcus formula 41 kISC

1 2 = VSOC ~

√

π (λ + ∆G0 )2 exp[− ]. λkB T 4λkB T

(1)

Here, kB is the Boltzmann constant and T is the temperature. λ and ∆G represent the reorganization energy and the driving force. They can be calculated from conventional methods, and more detailed computational descriptions are given out in the section of results. VSOC is the SOC between the excited singlet state and triplet state, and it is calculated from ADF 4.0 program package 56–59 at the DFT/B3LYP/TZ2P level, in which TZ2P is a core double zeta, valence triple zeta, doubly polarized basis known as slater type orbits.

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Results and Discussion

3.1

Structures and singlet excited-state properties of fullerenes

There are too many isomer structures for a given cage-structured fullerene molecule, for


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3 RESULTS AND DISCUSSION

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instance, C60 has 12500 possible resonance structures. To catch the excited-state properties with respect to carbon number in fullerene molecules, we only consider the most stable isomer for a given fullerene. These stable structures are selected based on the IPR with use of CAGE program that is on account of a top-down divide and conquer method and are also extensive for other spherical structures. 60 For C60 , the only spherical appearance with Ih point group satisfies IPR among its isomers. 61 The same characteristic is endowed for C70 that the only structure shaped ovally with a D5h point group satisfies the IPR. 61 Fig. 1 displays the optimized structures and corresponding point groups of fullerene molecules investigated in this work. The results show that C78 and C82 with D3 and C2 symmetry, respectively, are peach-heart shaped, C80 and C110 have the same cylinder shapes with D5d , D5h symmetries, similar to the carbon nanotube, and the remaining fullerene molecules are nearly spherical.

Figure 1: Fullerene structures and point groups Based on the geometries of those stable ground states, we calculate their electronic absorption spectra and display the results in Fig. 2 and the UV-VIS peak half-widths at half height are 0.15 eV for all fullerenes which is used to fit the experimental spectra of C60 and




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C70 . It is seen that the spectra of C60 has the well-known narrow absorption band around 4.30 eV. 62,63 The detailed analysis shows that this narrow band comes from S0 to S55 , S56 and S57 transitions with similar oscillator strengths of 0.29, consistent with a previous report. 64 With the increase of n in fullerene Cn , as expected, the maximal absorption peaks have red-shifts. Additionally, it is interesting that the absorptions to lower excited states appear. For instance, the low-energy peaks with 2.34 eV to 2.71 eV for C70 are mainly from the excitations of S25 , S26 , the low-energy absorptions of C80 come from the excitations to S11 , S12 , and the similar peak for C110 is from S9 excitation. Especially, those low-energy absorptions of C80 and C110 are obviously stronger than those of other candidates.

Figure 2: Absorption spectra of fullerenes The absorption spectra clearly demonstrate that the photo excitation of isolated fullerenes are mainly distributed in high excited states. According to the Kasha’s rule, however, before photoemission, such as fluorescence, these energies in high excited states should relax into S1 state. Therefore, the properties of S1 is important to understand the radiation channel and other radiationless channels. On account of present simulations, the S1 excited state mainly


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involves in the transition pattern of the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) for all fullerene candidates. 65,66 For simplification, Table 1 lists the energies of HOMO and LUMO and also the orbital degeneracies in parentheses. For C60 , the HOMO and LUMO are five-fold and three-fold degeneracies, respectively, and both the HOMO and LUMO for C70 are two-fold degeneracies. These properties are consistent with previous reports. 67,68 For the other fullerene molecules, the corresponding degeneracies of HOMO and LUMO are not found, however, the degeneracies are found for higher and lower molecular orbits. These LUMO degeneracies essentially represent the fullerene property as strong electron acceptors. Table 1: The HOMO and LUMO energies and their gaps of fullerenes (eV). The number in parentheses represents degeneracy. C60 C70 C76 C78 C80 C82 HOMO -5.95(5) -5.88(2) -5.39(1) -5.26(1) -4.88(1) -5.16(1) LUMO -3.18(3) -3.19(2) -3.42(1) -3.63(1) -3.84(1) -3.90(1) ∆Egap 2.77 2.69 1.98 1.62 1.03 1.25 C84 C92 C94 C96 C100 C110 HOMO -5.60(1) -5.51(1) -5.34(1) -5.42(1) -4.98(1) -4.74(1) LUMO -3.61(1) -3.63(1) -3.75(1) -3.81(1) -3.78(1) -3.70(1) ∆Egap 1.98 1.88 1.59 1.61 1.20 1.04

Consistent with reported results, 33,37,39,40,49,67 the energy gaps of HOMO and LUMO are oscillatory with respect to the number of carbon, and C80 and C110 possess the minimum energy gaps. Meanwhile, HOMO and LUMO distributions are displayed in Fig. 3 . Because of the high symmetry properties for all of the fullerene systems, the HOMO and LUMO distributions are almost on the whole fullerene cages. According to the previous report, 69 C80 and C110 have alternating bond-length chains distributed throughout the cylinder section, and every 30 carbons added to the cylinder can form new carbon nanotubes. It has been demonstrated that this alike single-walled carbon nanotube shape possesses the lower energy gap. It is thus expected that the geometric structures similar to nanotubes may cause the oscillation of energy gaps.




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Although the oscillation property of energy gaps, the calculated oscillator strengths between S0 and S1 are close to zero for most fullerenes. The energy on S1 state should be lost by radiationless channels. Among the channels, the intersystem crossing is an important one because of interesting property of triplet states, such as the generation of singlet oxygen, photochemical up-conversion and down-conversion processes in photovoltaics, photocatalysis, photoinduced charge separation, and molecular probes. In the next section, we focus on the simulations and discussions of intersystem crossing rates involving the factors of reorganization energy, driving force and SOC.

Figure 3: Molecular orbital distributions

3.2

Intersystem crossing rates

Reorganization energy To determine the ISC rate, as discussed in details of computation, we need to know the reorganization energy, the driving force and SOC. Here, we first consider the reorganization energy which will be also used in the estimation of driving force. There are several ways 55,70 to get the reorganization energy between two states for energy transfer. Here, we calculate


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the total reorganization energy from mode-specific reorganization energies λ=

1∑ 2 ω ∆Q2i , 2 i i

(2)

where ωi and ∆Qi are the vibrational frequency of the ith mode and corresponding coordinate shift between two states. In numerical calculations, we first optimize one of states and calculate the mass-weighted Hessian matrix H. The frequencies are then obtained from the diagonalization of H by LT HL = ω 2 . Under the vertical gradient approximation, 71 demonstrated to be reasonable for absorption, antiresonance and resonance Raman spectra, 71 ∑ ∂V )Lji , where V is the potential energy of second state and xj is we get ∆Qi = j (ωi )−2 ( ∂x j atomic Cartesian coordinate. In the present work, the reorganization energies of the two photophysical processes S0 → S1 and S1 → T1 are calculated by taking S0 and T1 as initial states, respectively. The calculated results, listed in Table 2, show that the reorganization energies from S0 →S1 are much larger than those from S1 →T1 , manifesting that the geometries of S1 and T1 are more similar to each other than those of S0 and S1 . Interestingly, the S1 →T1 reorganization energies of C60 , C78 and C110 are even smaller than 3 cm−1 .

C60

C70

Table 2: Reorganization energy (eV) C76 C78 C80 C82

S0 to S1 S1 to T1

0.0845 0.0293 0.1635 0.0003 0.0188 0.0397 C84 C92 C94

0.1599 0.0003 C96

0.2114 0.0581 C100

0.1721 0.0023 C110

S0 to S1 S1 to T1

0.0932 0.1209 0.1133 0.0026 0.0875 0.0151

0.1286 0.0008

0.1034 0.0009

0.1247 0.0002

Driving force The driving force of S1 to T1 is defined by the difference between the adiabatic energies of S1 and T1 . Instead of the optimization of S1 structures, the adiabatic energy of S1 can be alternatively estimated by the vertical excited energy at the ground state structure subtracting reorganization energy of S0 to S1 . The T1 structures are optimized to acquire




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the adiabatic energies of T1 . The results are displayed in Table 3. It is found that the experimental driving force for C60 , C70 and C84 are 0.31, 0.29 and 0.16 eV 32,72 respectively which are agreed with the calculated 0.37, 0.39, 0.14 eV manifesting that the excited-state potential energy surfaces can be approximated by harmonic oscillators. Meanwhile, the change of S1 energies with respect to fullerene molecules is consistent with that of LUMOHOMO gaps because S1 mainly corresponds to the transition from HOMO to LUMO. From the optimized geometries of T1 , we find that the molecular structures are close to those of S0 , and except C60 , the trivial alteration of structures do not impact the symmetry as well as the orbital distribution (see figure 2S for the distributions of SOMO (single occupied molecular orbital) and SOMO-1 in SI). For T1 of C60 , the Ih symmetry of S0 is switched into D5d . The spin densities of T1 for fullerenes are shown in Fig. 4 , where the blue areas represent the alpha electron distributions. Similar to the distributions of SOMO and SOMO1, the spin distributions are also delocalized in all fullerene candidates, manifesting that the net spin is mainly concentrating on these orbits. Similar to the energies of S1 , the ET1 of C80 , C82 , C100 and C110 are extremely small comparing with those of other fullerenes which are also consistent with the small energy gaps of LUMO and HOMO because T1 states are mainly constructed by the electron transition from HOMO to LUMO with a spin flip. At the same time, we calculate the radiative rates kr of T1 states, which is given by 73,74 Cω 2 f with C=

e2 , 2πϵ0 c3 me ~2

where ω is the energy gap between state T1 and S0 at the optimized geometry

of T1 state, f is the oscillator strength under the SOC involved, and ϵ0 is the permittivity of vacuum. The obtained rates are listed in Table 3. Although C92 has a maximal radiation rate of 2.12 × 10−2 s−1 , the value is still quite small comparing with conventional phosphorescence emission rates ( 106 s−1 ). This behaviour manifests that the efficiencies of phosphorescence emissions in the fullerenes are very low, and it is also the reason why the conventional experiments do not observe phosphorescence unless suppressing radiationless channels with ultralow temperature condition. 75 Finally, it is noted that although the energies of S1 and T1 have an oscillatory property


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with C80 and C110 having minimal energies, the driving forces do not follow similar property. Except C60 and C70 with relatively large driving forces, the driving forces for other fullerenes are small and their values are less than 0.20 eV. Table 3: The energies of S1 and T1 (eV), Driving force (eV), radiative rates kr of T1 (s−1 ) C60 C70 C76 C78 C80 C82 S1 T1 ∆GS1 −T1 kr

2.01 1.64 0.37 1.18×10−7 C84

2.02 1.63 0.39 6.43×10−3 C92

1.24 1.08 0.16 3.54×10−3 C94

0.88 0.75 0.13 1.69×10−3 C96

0.24 0.11 0.13 5.81×10−17 C100

0.52 0.37 0.15 8.74×10−9 C110

S1 T1 ∆GS1 −T1 kr

1.33 1.19 0.14 1.04×10−2

1.22 1.15 0.07 2.12×10−2

0.96 0.77 0.19 8.87×10−3

0.94 0.83 0.11 5.74×10−4

0.61 0.45 0.17 8.85×10−4

0.36 0.25 0.11 1.39×10−13

Figure 4: Spin density of fullerenes

Spin orbit coupling The SOC represents the intersystem crossing interaction, and its value is calculated with ADF program package, 56 where the 2-component zero-order regular approximation (ZORA)



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is employed for the solution of the 4-component Dirac-Kohn-Sham equation. The SOC is given by ES.O ≈< ΨSi |b hSO |ΨTj >, where ΨSi and ΨTj are the wave functions of excited single state and excited triplet state, respectively, and b hSO is SOC operator within ZORA. In the calculations of SOC, the 20-20 lowest singlet-singlet and singlet-triplet transitions are taken into account. Table 4 lists the SOC between S1 and T1 . It is seen that the SOC values are quite small. To prove the reasonability, we calculate the SOC of S1 →T1 for C70 by using the PBE functional. The result is 1.32×10−3 cm−1 , close to that from B3LYP functional. Table 4: Spin orbit coupling (cm−1 ) C70 C76 C78

C60

C80

C82

S1 →T1

-2.00×10−4 C84

1.80×10−3 C92

-6.00×10−4 C94

-1.60×10−5 C96

4.89×10−6 C100

1.01×10−5 C110

S1 →T1

-8.01×10−5

-8.86×10−2

-1.68×10−1

2.03×10−4

-3.76×10−3

-3.97×10−4

Intersystem crossing rate Generally, the intersystem crossing rates can be obtained from the Marcus semiclassical formula on account of VSOC , λ and ∆G0 . We thus calculate the intersystem crossing rates from S1 to T1 . However, the only C70 and C92 have large enough rates (> 107 s−1 ) for intersystem crossing to occur. It is noticed that the C60 and C70 are demonstrated experimentally to have similar efficiency for triplet state generation. Therefore, it may not be enough to only consider the transition between S1 and T1 . Indeed, there are degeneracies for S1 and T1 and those degenerate states may also have the contribution to intersystem crossing. To involve in the degenerate or multiple-electronic-state effect, we calculate the total rate by ∑ ∑ kij , where i is the initial singlet state, Pi represents the BoltzPi ki with ki = kISC = i

j

mann distribution on the i-th state, and j denotes the triplet states. In this case, we need additional data of VSOC , λ and ∆G0 between the initial i-th singlet state and the final j-th triplet state to calculate the rate kij . The energies of higher excited singlet and triplet states are estimated on account of vertical excited energies based upon the equilibrium structures of S0 and T1 , respectively, in


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consideration of the difficulty to obtain the optimized structures for higher excited states. The SOCs are calculated at the optimized geometries of T1 . The corresponding results are listed in Table S1 to S10 in SI. The reorganization energies are approximately set to that for S1 to T1 in view of almost the same equilibrium structures for T1 and higher excited triplet states. According to the Boltzmann distribution, the population on Si is negligibly small once the energy of Si is 0.1 eV higher than S1 at a room temperature. Meanwhile, ten excited triplet states are found to be abundant for the convergent calculations. In Table 5, we display the individual rate ki from initial Si to all triplet states T as well as the total rate kISC . The fullerenes which do not appear in the Table 5 have neglectful intersystem crossing rates, manifesting that the triplet states of those fullerenes are hardly produced from the low excited singlet states. The simulated ISC rates also show that the process from S1 to T in C60 and C84 are not dominant for the contribution of the total rates, whereas the higher excited singlet states contribute much larger rates. An experimental work 13 has measured the quantum yields of the intersystem crossing processes, and they are 1.0, 0.9, 0.05, 0.01, 0.01 for C60 , C70 , C76 , C82 , C84 , respectively. The present simulated rates are quite well consistent with those measurements. More importantly, we find that C60 , C70 and C92 possess about 107 times greater rates than other systems. Together with the triplet state energy of C92 , it is expected that C92 may be another good candidate of photoactive system.

C60 S1 -Tn S2 -Tn S3 -Tn S4 -Tn Total

6.49×101 3.42×107 1.81×107 1.31×106 1.34×107

Table 5: Intersystem crossing rate(s−1 ) C70 C76 C84 C92

C94

1.79×108 2.28×108

1.78×101

8.73×10−8 5.23

1.01×107 6.87×106

2.23×10−1

2.04×108

1.78×101

1.65

1.01×107

2.23×10−1



4 CONCLUDING REMARKS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Concluding Remarks The photophysical processes, specifically, the ISC properties of twelve cage-structured

fullerenes have been theoretically investigated, including the simulations of driving force, reorganization energy and spin orbit coupling for the excited singlet states and triplet states. The results demonstrate that the experimental observation that the quantum yields of triplet states via ISC decrease with increasing of fullerene size are only limited to the fullerenes whose size is smaller than C84 because C92 has a large ISC rate of 1.01×107 s−1 , very close to those of C60 and C70 . Meanwhile, C92 has a higher triplet energy than the energy of singlet oxygen, and it may be a good candidate for the photoactive system. Although C78 , C80 , C82 and C110 have the energy gaps of singlet and triplet states favorable for ISC, the ISC rates are close to zeros because of quite small spin-orbit coupling. The homologous phenomenon for the similar systems C80 and C110 may be used to recognize the poor ISC property for carbon nanotube systems. For the C96 and C100 , the reorganization energies for ISC are smaller than 8 cm−1 , manifesting that the geometries of excited states are similar to those of triplet states and ISC rates are quite low due to the property of Marcus inverted region. In all, one has to consider three factors to determine the ISC rate. For the prospective applications of fullerenes and their various derivatives, the photophysical properties involving ISC can be improved with the tuning of these three factors for different fullerene systems, such as the functional group substituted and metal doped fullerene derivatives.

Supporting Information The computational spectra from different density functional methods and experimental spectra for C60 , C70 , cis-bisPC71 BM, trans-bisPC71 BM. The energies of Sn for fullerenes. The energies of Tn for fullerenes. The involving spin orbit coupling values for fullerenes. The density of states (DOS) for fullerenes. The involving reorganization energies for all fullerenes.


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4 CONCLUDING REMARKS

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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The distribution of SOMO and SOMO-1 of T1 states for fullerenes. This material is available free of charge via the Internet at http://pubs.acs.org.

Acknowledgments The authors thank the financial supports from the National Science Foundation of China (Grant Nos. 91333101, 21133007 and 21573175).


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