Photoinduced Charge Separation in the Carbon Nano-Onion C60

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Photoinduced Charge Separation in the Carbon Nano-Onion C @C Alexander A. Voityuk, and Miquel Solà

J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b04127 • Publication Date (Web): 06 Jul 2016 Downloaded from http://pubs.acs.org on July 7, 2016

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The Journal of Physical Chemistry

Photoinduced Charge Separation in the Carbon Nano-Onion C60@C240 Alexander A. Voityuk1,2* and Miquel Solà2*

1

Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona 08010, Spain

2

Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química, Campus de Montilivi, 17003 Girona, Catalonia, Spain. E-mail: [email protected]; [email protected] Tel. 34 972418926 (AAV) and 34 972418912 (MS)

Abstract The double-shell fullerene C60@C240 formed by inclusion of C60 into C240 is the smallest stable carbon nano-onion. In the paper, we analyze in detail the character of 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 by 0.5 eV higher in energy than the CS states C60+@C240-. Unlike the situation observed in donor-acceptor systems, the energy of the CS states in C60@C240 does 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 states 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 multi-shell 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 in between 30-70 Å in diameter. Five years later, C60 was discovered by Kroto, Smalley, and Curl.5 In 1987, Iijima realized that the inner most shell of the CNOs he observed in 1980 has a diameter of 8 Å and, therefore, it could perfectly be C60.6 In 1992, Ugarte7 obtained CNOs by intense irradiation of carbon soot. Nowadays, there are several procedures that can be used to produce CNOs at 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 proved to offer a variety of potential applications. Among them, we can mention their application as electrode materials in capacitors,11 anode materials in lithium-ion batteries,8 catalyst support in fuel cells,12 solid lubrication,13 heterogeneous catalysis,14 or electrooptical devices.15 The first observation of double- and triple-shell CNOs was reported in 2000.16 The doubleshell C60@C240 and C240@C560 and triple-shell C60@C240@C560 fullerenes were found in the products of the 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 has been 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, the Ih structure depicted in Figure 1 being almost isoenergetic with the D5d one. Geometry relaxation of C60 and C240 in C60@C240 was found to be negligible,19 C60 being slightly expanded inside C240, while C240 somewhat shrunk.18 Moreover, because C60, C240, and C60@C240 are of the same symmetry (Ih), the electronic structure of these molecules is similar. In particular, their HOMO (highest occupied molecular orbital) is five-fold degenerated whereas the LUMO (lowest unoccupied molecular orbital) has threefold degeneracy. In fact, it was found computationally that C60@C240 shows an UV-Vis spectrum that is the overlap of the two 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 deformation of C60 and C240.18 When an external electric field is applied, the outer shell C240 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 structure, ionization potential and electron affinity have been recently reported for large fullerenes (up to C2160). 22


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From the information given above, it is clear that some properties of the fullerenes change significantly while others remain almost unchanged by the formation of two- and multishell structures. Being the smallest stable CNO,18 C60@C240 is a good computational model to study the structural and electronic properties of CNOs. Because of the size of the CNOs, not much is known about the nature of excited states of these species. In the paper, we will perform a detailed analysis of the excited states of C60@C240. Note that the excited states of both 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 may have a similar energy and significantly contribute to excited states of interest. In such CT states, no charge separation between the inner and outer spheres is observed (both fullerenes remain electroneutral like in LE states). Because of that, a special computational tool is required for 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 paper, 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 the light absorption with the aim to know whether C60@C240 can act as an effective chromophore in dye-sensitized solar cells. We also calculate electron transfer (ET) parameters for the photo-induced charge separation (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) charge separated states C60+@C240- lie 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 the 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, may be exploited in molecular electronics.



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Figure 1. C60@C240 complex is composed of two shells C60 and C240 with Ih symmetry

shown in the olive and gray color, respectively.

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 the 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 treatment of excited state properties of large organic systems including fullerene based materials.29-33 The advantages and limitations of INDO/S as well as its recent 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 accounted for in the configuration interaction scheme. To illustrate the performance of INDO/S, let us compare excitation energies and oscillator strengths computed for C60 by several methods with experimental data (Table 1). As seen, the INDO/S results are in better agreement with observed electronic spectra than the TDDFT data. A detailed comparison of experimental and computational data for several fullerenes may be found in Ref. 22. Also, the INDO/S scheme reproduces observed 4 ACS Paragon Plus Environment

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spectroscopic parameters of C240 better than the TD-DFT BLYP/TZP calculation.18 Because of that, we used the INDO/S to analyze the nature of excited states in C60@C240.

Table 1. Excitation Energies and Oscillator Strengths for Optically Allowed Transitions in C60 Method B3LYP/6-31G(d) B3LYP/6-311+G(d) CAM-B3LYP/6-311+G(d) INDO/S Experiment a a

hν, eV 3.510 3.484 4.320 3.214 3.04

f 0.0105 0.0103 0.247 0.011 0.015

hν, eV 3.954 3.902 4.691 3.846 3.78

f 0.156 0.170 0.101 0.386 0.37

Experimental data are taken from Refs. 18 and 36.

Analysis of excited states The energetic similarities of electronic excitations in C60 and C240 make it difficult to describe even qualitatively the excited state 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 (it means that the overlap matrix is diagonal), a key quantity Ω (L,M) used in the analysis of the density distribution between molecules L and M, is defined as: Ω (L, M) =

1 ∑ Pαβ0i Pαβ0i 2 α∈L, β∈M

X(L) = Ω (L, L) X(M) = Ω (M, M)

(1)

∆ q = Ω (L, M) − Ω (M, L)

where P0i is the transition density matrix for the ψ0 →ψi excitation. The extent of exciton localization on the sites L and M is termed X(L) and X(M), respectively; the weight of electron transfer configurations L→M and M→L represented by Ω(L,M) and Ω(M,L). 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 ∆q=Ω(L,M)-Ω(M,L). Solvent effects. The equilibrium solvation energy E Seq in medium with the dielectric constant ε was estimated using a COSMO-like polarizable continuum model (C-PCM) in monopole approximation:28, 37 – E Seq (Q, ε ) = −

1 f ( ε )Q + DQ , 2


(2)


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ε −1 , Q -the vector of n atomic ε charges in the molecular system, D is the n x n symmetric matrix determined by the shape of the boundary surface between solute and solvent; D=B+A-1B, where the m x m matrix A describes electrostatic interaction between m surface charges and the m x 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.

where the f(ε) is the dielectric scaling factor, f ( ε ) =

The charge on atom X in the excited state ψi, q iX , was calculated as: q iX = q 0X + ∆ iX ,

∆ iX =

1 ∑ 2 Y≠X

∑

0i 0i 0i 0i (Pαβ Pαβ − Pβα Pβα ) ,

(3)

α∈X, β∈Y

where q 0X is the atomic charge on A in the ground state (the reference state) and ∆ iA is its change upon ψ0 →ψi excitation. The non-equilibrium solvation energy for excited state ψi can be estimated as:37, 39 E Sneq (Q0 , ∆ , ε, n 2 ) = f ( ε )∆ + DQ0 −

1 f (n 2 )∆ + D∆ , 2

(4)

In Eq. (4), n2 (the refraction index squared) is the optical dielectric constant of the medium and the vector ∆ 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 (electronic coupling Vij between the initial and final states, the reorganization energy λ, and the Gibbs energy of the reaction ∆G0) and can be estimated using Marcus equation:26  ( λ + ∆G 0 )2  2π 2 1  kct = Vij exp  −  h 4 λ k BT  4πλ k BT  

(5)

In C60@C240, there are many degenerate and nearly-degenerate states. Consequently, a twostate model that takes into account only one state per each 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.


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The reorganization energy is usually divided into two parts, λ = λi + λ s , 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. To 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) energies of neutral species L and M at the optimized geometries, E0 (L) and E0 (M) , (2) energies of the corresponding radical cation and anion at the optimized geometries, E+ (L+ ) and

E− (M − ) , (3) 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 a sum of the reorganization energies of the site L and M,

λi = λi (L) + λi (M) : λ i (L) =

1  E + (L) − E+ (L+ ) + E0 (L+ ) − E0 (L)  2

(6a)

λ i (M) =

1  E − (M) − E− (M − ) + E0 (M − ) − E0 (M)  2

(6b)

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 non-equilibrium and equilibrium solvation energies: λ S = E Sneq (Q i , ∆ , ε, n 2 ) − E Seq (Q f , ε )

(7)

where ∆ = Q f − Q i , see Eqs (2)-(4). Very small values were found also for λs. For the both types of the CS processes λs is estimated at 0.05 eV. Thus the total reorganization energy derived from our calculation is 0.17 eV.

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 charge on C60 and C240 to be 0.049 and +0.049, respectively. The same character of charge separation, C60-δ@C240+δ with δ=0.144, is given by INDO/S. Figure 2 shows the overall character of lowest-energy excited states in C60@C240 computed with INDO/S. Let us consider the states in terms of excitonic and CT contributions. The quantities X(C240) and X(C60) describe the weight of 7 ACS Paragon Plus Environment


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excited configuration 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, CT ~1 and both X(C240) and X(C60) approach to zero in charge transfer states. Mixed states include both LE and CT contributions. In C60@C240, where both fullerenes can donate and except an electron, there are two types of CT states, C60+@C240- and C60-@C240+. We consider all excited states lying in the region 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 seen from Fig. 2, the lowest excited states of C60@C240 at 1.8-2.1 eV are localized on C240. The highest occupied level 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 HOMO (hu) and LUMO (t1u) levels are symmetry forbidden (the parity rule). Thus, the oscillator strength is zero for all transitions from the ground state 1Ag to the lowest excited states T1g, T2g, Hg, and Gg stemming from to HOMO-LUMO excitations (hu⊗t1u =t1g+t2g+gg+hg). Symmetry allowed transitions from 11Ag to excited T1u states correspond to excitations HOMO-1→LUMO, HOMO→LUMO+1, HOMO→LUMO+2, etc. The highly absorbing states at 2.54 eV (see Fig. 2) include HOMO→LUMO+1 and HOMO-3→LUMO+1 excitations. The lowest CT excited states lie 0.5 eV higher than the lowest LE states (Fig. 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 lie in the same energy region as highly absorbing LE states may be populated even when the interaction between the LE and CT states is quite weak.


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Figure 2. Character of excited states in C60@C240: oscillator strength f (upper panel), contribution of excited configurations localized on the outer and inner fullerenes, X(C240) and X(C60) (middle panels) and CT configurations (lower panel).

Since 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 1 ψ − give similar contributions to an excited state e.g. Ψ1,2 = no + ±ψ C60 + @ C240− 2 C60 @ C240 +

(

)

charge separation occurs in the CT states Ψ1 and Ψ 2 . Figure 3 shows the 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.



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Figure 3. Photoinduced charge separated states in C60@C240: C60+@C240- and C60 @C240+ states are shown in the lower and upper panels, respectively. -

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 strength

Photoinduced Charge Separation in the Carbon Nano-Onion C60

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