Article pubs.acs.org/JPCA
Photoinduced Charge Separation in the Carbon Nano-Onion C60@C240 Alexander A. Voityuk*,†,‡ and Miquel Solà*,‡ †
Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona 08010, Spain Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química, University of Girona, Campus de Montilivi, 17003 Girona, Catalonia, Spain
‡
ABSTRACT: The double-shell fullerene C60@C240 formed by inclusion of C60 into C240 is the smallest stable carbon nano-onion. In this article, we analyze in detail the character of the excited states of C60@C240 in terms of exciton localization and charge transfer between the inner and outer shells. The unique structure of the buckyonion leads to a large electrostatic stabilization of charge-separated (CS) states in the C60@ C240. As a result, the CS states C60+@C240− lie in the same region of the electronic spectrum (2.4−2.6 eV) as strongly absorbing locally excited states and, therefore, can be effectively populated. The CS states C60−@C240+ are found to be 0.5 eV higher in energy than the CS states C60+@C240−. Unlike the situation observed in donor−acceptor systems, the energies of the CS states in C60@C240 do not practically depend on the environment polarity. This leads to exceptionally small reorganization energies for electron transfer between the shells. Electronic couplings for photoinduced charge-separation and charge-recombination processes are calculated. The absolute rate of the formation of the CS state C60+@C240− is estimated at ∼4 ps−1. The electronic features found in C60@C240 are likely to be shared by other carbon nano-onions.
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INTRODUCTION Carbon nano-onions (CNOs), also known as multishell fullerenes, hyperfullerenes, or buckyonions, are formed by several concentric shells of carbon atoms in a structure resembling a nesting Russian doll.1−3 From vacuum-deposited amorphous carbon films, Iijima observed CNOs for the first time in 1980.4 He presented electron micrographs of small spherical particles of graphitized carbon whose sizes varied between 30 and 70 Å in diameter. Five years later, C60 was discovered by Smalley and co-workers.5 In 1987, Iijima realized that the innermost shell of the CNOs he observed in 1980 had a diameter of 8 Å, and therefore, it could be C60.6 In 1992, Ugarte7 obtained CNOs by intense irradiation of carbon soot. Currently, there are several procedures that can be used to produce CNOs at a relatively large scale.1,3,8,9 A number of various functionalization reactions of CNOs have been developed. In fact, the first covalent functionalized CNO was obtained by a 1,3-dipolar addition of azomethine ylide in 2003.10 CNOs have already been found to offer a variety of potential applications. Among them, we can mention their applications as electrode materials in capacitors,11 anode materials in lithium-ion batteries,8 catalyst supports in fuel cells,12 solid lubricants,13 heterogeneous catalysts,14 an electrooptical devices.15 The first observation of double- and triple-shell CNOs was reported in 2000.16 The double-shell C60@C240 and C240@C560 and triple-shell C60@C240@C560 fullerenes were found in the products of high-temperature laser pyrolysis. Because of its relatively small size, C60@C240 has been studied theoretically by several groups. At the density functional theory (DFT) level, it © 2016 American Chemical Society
was found that the van der Waals interaction energy between C60 and C240 in C60@C240 is about −150 to −185 kcal/ mol.17−19 The global minimum of C60@C240 has D5d symmetry, although rotation of C60 inside C240 is almost free, with energy barriers of about 1 kcal/mol, so that the Ih structure depicted in Figure 1 is almost isoenergetic with the D5d one. Geometry relaxation of C60 and C240 in C60@C240 was found to be negligible,19 with C60 being slightly expanded inside C240 and C240 being somewhat shrunk.18 Moreover, because C60, C240, and C60@C240 are of the same symmetry (Ih), the electronic structures of these molecules are similar. In particular, their highest occupied molecular orbitals (HOMOs) are 5-folddegenerate, whereas their lowest unoccupied molecular orbitals (LUMOs) have 3-fold degeneracy. In fact, it was found computationally that C60@C240 exhibits a UV−vis spectrum that is the overlap of the spectra of C60 and C240.18 The vibrational modes of C60 and C240 in C60@C240 are clearly recognizable, with small shifts that reflect the small geometrical deformations of C60 and C240.18 When an external electric field is applied, the outer C240 shell of the onion essentially shields the inner C60 cage (the reduction in the C60 polarizability after inclusion in C240 was found to be about 75%), which makes C60@C240 a near-perfect Faraday cage.20,21 DFT estimates of the structures, ionization potentials, and electron affinities were recently reported for large fullerenes (up to C2160).22 Received: April 25, 2016 Revised: June 11, 2016 Published: July 6, 2016 5798
DOI: 10.1021/acs.jpca.6b04127 J. Phys. Chem. A 2016, 120, 5798−5804
Article
The Journal of Physical Chemistry A
in the same region of the electronic spectrum (2.4−2.6 eV) as locally excited (LE) states responsible for strong light absorption, and therefore, they can be effectively populated; (ii) unlike the situation commonly observed for donor− acceptor systems, the energy of the CS states in C60@C240 is practically independent of the environment polarity (because of its concentric structure), resulting in exceptionally small reorganization energies for electron transfer between the shells; and (iii) C60@C240 is able to absorb sun energy much more efficiently than free C60 or C240 molecules. We hope that the unique electronic features of C60@C240, which are most likely shared by other CNOs, can be exploited in molecular electronics.
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METHODS Quantum-mechanical calculations were performed with the Gaussian program.27 The ground-state geometries of neutral fullerenes C60 and C240 and their radical cation and radical anion species were optimized using the B3LYP/6-31G(d) scheme. The geometries of the radicals are needed to estimate the reorganization energy of ET between C60 and C240. For comparison, excited states of C60 were calculated using both time-dependent density functional theory (TD-DFT) [B3LYP and CAM-B3LYP with B3LYP with 6-31G(d) and 6-311+G(d) basis sets] and the semiempirical INDO/S approach.28 The INDO/S method was successfully applied for the treatment of excited-state properties of large organic systems including fullerene-based materials.29−33 The advantages and limitations of INDO/S and its applications were recently considered.34 Moreover, INDO/S is the only semiempirical scheme that provides reasonable values for ET couplings.35 INDO/S calculations of 300 low-energy excited states of C60@C240 were performed using Gaussian. All possible singly excited configurations (360000) were considered in the configuration interaction scheme. To illustrate the performance of INDO/S, we compare the excitation energies and oscillator strengths computed for C60 by several methods with experimental data in Table 1. As can be seen, the INDO/S results are in better
Figure 1. C60@C240 complex composed of two shells of C60 and C240, shown in the olive and gray, respectively, with Ih symmetry.
From the preceding information, it is clear that some properties of the fullerenes change significantly whereas others remain almost unchanged upon the formation of two- and multishell structures. Because it is the smallest stable CNO,18 C60@C240 is a good computational model for studying the structural and electronic properties of CNOs. Because of the sizes of the CNOs, not much is known about the nature of the excited states of these species. In this work, we perform a detailed analysis of the excited states of C60@C240. Note that the excited states of the two fullerenes have similar energies, and just a small electronic interaction (coupling) of the states leads to exciton delocalization and to mixing of the locally excited (LE) and charge-transfer (CT) states. Then, the dipole moment of all electronic states including charge-transfer (CT) configurations C60+@C240− and C60−@C240+ is equal to zero and cannot be used to identify such states. Moreover, the CT configurations can have similar energies and contribute significantly to excited states of interest. In such CT states, no charge separation between the inner and outer spheres is observed (both fullerenes remain electroneutral as in LE states). Consequently, a special computational tool is required for the quantitative analysis of excited states in C60@C240. Our analysis is based on the treatment of the transition electronic density developed in several recent works23−25 and used to describe electronic excitations in a number of molecular systems. In this article, excited states of the C60@C240 complex are characterized in terms of exciton localization and CT between the inner and outer spheres. In particular, we consider the nature of states responsible for light absorption with the aim of determining whether C60@C240 can act as an effective chromophore in dye-sensitized solar cells. We also calculate electron-transfer (ET) parameters for the photoinduced chargeseparation (CS) and charge-recombination (CR) reactions. Marcus theory26 is applied to determine the absolute rate for ET between the inner and outer fullerenes. Our results (vide infra) show that (i) the charge-separated states C60+@C240− lie
Table 1. Excitation Energies and Oscillator Strengths for Optically Allowed Transitions in C60
a
method
hν (eV)
f
hν (eV)
f
B3LYP/6-31G(d) B3LYP/6-311+G(d) CAM-B3LYP/6-311+G(d) INDO/S experimenta
3.510 3.484 4.320 3.214 3.04
0.0105 0.0103 0.247 0.011 0.015
3.954 3.902 4.691 3.846 3.78
0.156 0.170 0.101 0.386 0.37
Experimental data taken from refs 18 and 36.
agreement with the observed electronic spectra than the TDDFT data. A detailed comparison of experimental and computational data for several fullerenes can be found in ref 22. Also, the INDO/S scheme reproduces observed spectroscopic parameters of C240 better than the TD-DFT BLYP/TZP calculation.18 Consequently, we used INDO/S to analyze the nature of the excited states of C60@C240. Analysis of Excited States. The energetic similarities of electronic excitations in C60 and C240 make it difficult to describe, even qualitatively, the excited states of C60@C240. The quantitative analysis of exciton delocalization and charge separation was carried out in terms of transition density.24,25 Because the INDO/S scheme employs an orthogonal basis set 5799
DOI: 10.1021/acs.jpca.6b04127 J. Phys. Chem. A 2016, 120, 5798−5804
Article
The Journal of Physical Chemistry A (so that the overlap matrix is diagonal), the key quantity Ω(L,M) is used in the analysis of the density distribution between molecules L and M; it is defined as Ω(L, M) =
1 2
In C60@C240, there are many degenerate and nearly degenerate states. Consequently, a two-state model that takes into account only one state per site cannot be used to properly describe electronic coupling in the system, and several combinations of initial and final states should be considered. The fragment charge difference (FCD)35,40 method was employed to calculate the electronic couplings in this work. The reorganization energy is usually divided into two parts, λ = λi + λs, including the internal and solvent terms, respectively. Often, the term λs is treated classically, whereas the internal component is calculated with a quantum-chemical approach.26 The internal reorganization energy λi was calculated at the B3LYP/6-31G(d) level. Two types of CT states, C60+@C240− and C60−@C240+, were considered. For the radical cation and radical anion states, the unrestricted Kohn−Sham method was applied. To estimate λi for ET between the sites L and M, LM → L+M−, the following terms were computed: (1) the energies of neutral species L and M at the optimized geometries, E0(L) and E0(M); (2) the energies of the corresponding radical cation and anion at the optimized geometries, E+(L+) and E−(M−); (3) the energies of neutral L and M calculated at the geometries of L+ and M−, E+(L) and E−(M); and (4) the energies of the radical ions at the neutral geometries, E0(L+) and E0(M−). Then, λi is the sum of the reorganization energies of sites L and M, λi = λi(L) + λi(M), where
P0αβi P0αβi
∑ α ∈ L, β ∈ M
X(L) = Ω(L, L) X(M) = Ω(M, M) Δq = Ω(L, M) − Ω(M, L)
(1)
where P is the transition density matrix for the ψ0 → ψi excitation. The extents of exciton localization on sites L and M are denoted X(L) and X(M), respectively; the weights of electron-transfer configurations L → M and M → L are represented by Ω(L,M) and Ω(M,L), respectively. The total CT weight in the excited state ψi is Ω(L,M) + Ω(M,L), whereas the charge separation between these sites is determined by the difference Δq = Ω(L,M) − Ω(M,L). Solvent Effects. The equilibrium solvation energy Eeq S in a medium with dielectric constant ε was estimated using a COSMO-like polarizable continuum model (C-PCM) in the monopole approximation28,37 0i
1 −ESeq (Q, ε) = − f (ε)Q+DQ 2
(2)
λ i(L) =
ε−1 ; ε
where f(ε) is the dielectric scaling factor, f (ε) = Q is the vector of n atomic charges in the molecular system; and D is the n × n symmetric matrix determined by the shape of the boundary surface between solute and solvent: D = B+A−1B, where the m × m matrix A describes the electrostatic interaction between m surface charges and the m × n B matrix describes the interaction of the surface charges with n atomic charges of the solute.37 The GEPOL93 scheme38 was used to construct the molecular boundary surface. The charge on atom X in the excited state ψi, qiX, was calculated as qXi
qX0
=
+
ΔiX ,
ΔiX
1 = 2
0i (P0αβi Pαβ
∑ ∑
−
λ i(M) =
λS = ESneq (Qi, Δ, ε , n2) − ESeq (Qf , ε)
(3)
i
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where is the atomic charge on A in the ground state (the reference state) and ΔiA is its change upon ψ0 → ψi excitation. The nonequilibrium solvation energy for excited state ψi can be estimated as37,39
RESULTS AND DISCUSSION In the electronic ground state of C60@C240, the internal and external fullerene shells are almost electroneutral. The B3LYP scheme predicts the net charges on C60 and C240 to be −0.049 and +0.049, respectively. The same character of charge separation, C60δ−@C240δ+, with δ = 0.144, is given by INDO/ S. Figure 2 shows the overall character of the lowest-energy excited states in C60@C240 computed with INDO/S. Now, consider the states in terms of excitonic and CT contributions. The quantities X(C240) and X(C60) describe the weights of excited configurations localized on the outer and inner fullerenes, respectively, whereas the CT index characterizes the weight of charge-transfer configurations. By definition, X(C240) + X(C60) + CT = 1. Thus, excited states with X(C240) close to 1 are strongly localized on the outer fullerene, excitation of the inner fullerene occurs when X(C60) ≈ 1, and CT ≈ 1 and both X(C240) and X(C60) approach zero in chargetransfer states. Mixed states include both LE and CT contributions. In C60@C240, where both fullerenes can donate
(4)
2
where n (the refraction index squared) is the optical dielectric constant of the medium and the vector Δ describes the change of electronic density in the molecule by excitation in terms of atomic charges (see eq 3). Electron-Transfer Parameters. The rate of nonadiabatic electron transfer at the temperature T is controlled by three parameters, namely, the electronic coupling Vij between the initial and final states, the reorganization energy λ, and the Gibbs energy of the reaction ΔG0, and can be estimated using the Marcus equation26 ⎡ (λ + ΔG°)2 ⎤ 2π 2 1 Vij exp⎢ − ⎥ 4λkBT ⎦ ℏ ⎣ 4πλkBT
(7)
where Δ = Q − Q ; see eqs 2−4. Very small values were found also for λs. For both types of CS processes, λs was estimated at 0.05 eV. Thus, the total reorganization energy derived from our calculations is 0.17 eV. f
q0X
kct =
1 [E−(M) − E−(M−) + E0(M−) − E0(M)] 2
Our B3LYP calculations predict that the internal reorganization energy is 0.13 eV for ET from C60 to C240 (formation of C60+@C240−) and 0.10 eV for ET from C240 to C60. The solvent term λs is determined by the difference of the nonequilibrium and equilibrium solvation energies
P0βαi P0βαi )
1 2 + f (n )Δ DΔ 2
(6a)
(6b)
Y ≠ X α ∈ X, β ∈ Y
ESneq (Q0, Δ, ε , n2) = f (ε)Δ+DQ0 −
1 [E+(L) − E+(L+) + E0(L+) − E0(L)] 2
(5) 5800
DOI: 10.1021/acs.jpca.6b04127 J. Phys. Chem. A 2016, 120, 5798−5804
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The Journal of Physical Chemistry A
HOMO → LUMO + 1 and HOMO − 3 → LUMO + 1 excitations. The lowest CT excited states lie 0.5 eV higher than the lowest LE states (Figure 2, Table 2). In large systems, CT states cannot be directly excited by light absorption because of their weak oscillator strength but can be populated because of their coupling to strongly absorbing LE states. In C60@C240, CT states that lie in the same energy range as highly absorbing LE states can be populated even when the interaction between the LE and CT states is quite weak. Because the electronic properties of C240 and C60 are similar, the CS configurations C60+@C240− and C60−@C240+ have comparable energies and can mix. If these configurations give similar contributions to an excited state, for example, 1 Ψ1,2 = 2 [ψC − @C +( ±ψC + @C −)], no charge separation 60 240 60 240 occurs in the CT states Ψ1 and Ψ2. Figure 3 shows the
Figure 2. Characters of excited states in C60@C240: (upper panel) oscillator strength f, (middle panels) contributions of excited configurations localized on the outer and inner fullerenes, X(C240) and X(C60), respectively; and (lower panel) CT configurations.
and accept an electron, there are two types of CT states: C60+@ C240− and C60−@C240+. We consider all excited states lying in the range of 1.8−3.6 eV (700−350 nm). The oscillator strength of electronic transitions up to 2.5 eV is negligibly small (the transitions are dipole-forbidden). As can be seen in Figure 2, the lowest excited states of C60@C240 at 1.8−2.1 eV are localized on C240. The highest occupied level is hu, followed by lower-energy levels hg, gg, and gu. The lowest unoccupied level t1u is followed by t2g, hg, and hu levels. In the electric dipole approximation, transitions between the HOMO (hu) and LUMO (t1u) levels are symmetry-forbidden (parity rule). Thus, the oscillator strength is zero for all transitions from the 1Ag ground state to the lowest excited states T1g, T2g, Hg, and Gg stemming from HOMO−LUMO excitations (hu ⊗ t1u = t1g + t2g + gg + hg). Symmetry-allowed transitions from 11Ag to excited T1u states correspond to excitations of the types HOMO − 1 → LUMO, HOMO → LUMO + 1, HOMO → LUMO + 2, and so on. The highly absorbing states at 2.54 eV (see Figure 2) include
Figure 3. Photoinduced charge-separated states in C60@C240: (top) C60+@C240− and (bottom) C60−@C240+.
character of CT states in the system. The states C60+@C240− have lower energies (2.4−2.6 eV) than the C60−@C240+ states (2.8−3.3 eV). Several CT states at 3.1 eV have comparable contributions of both C60+@C240− and C60−@C240+ and only small charges on the fullerene subunits. The electronic properties of the excited states in the range of 1.79−3.00 eV are listed in Table 2. The lowest 22 states have very weak oscillator strengths (
