Driving Force of Photoinduced Charge Separation in Metal- Cluster Encapsulated Triphenylamine-[80]fullerenes

Understanding of photoinduced charge separation in fullerene-based dye-sensitized solar cells is crucial for the development of photovoltaic devices. In this work, we explore how the driving force of the charge separation process in conjugates of M@C80 (M = Sc3N, Sc3CH, Sc3NC, Sc4O2, and Sc4O3) with triphenylamine (TPA) depends on the nature of the metal cluster. Both singlet and triplet excited state electron transfer reactions are considered. Our results based on TD-DFT calculations demonstrate that the driving force of charge separation in TPA-M@C80 can be well tuned by varying the structure of the metal cluster encapsulated inside the fullerene cage.


Introduction
The present energetic, environmental, and economic crisis has stimulated the interest in developing inexpensive renewable energy sources. Among these sources, solar energy is expected to play a critical role in helping us to meet the current and future global energy demands. In this framework, the dye-sensitized solar cell (DSSC), a photovoltaic cell with potential commercial applications that could compete with existing photovoltaic devices, has strongly transformed the photovoltaic landscape. DSSCs are usually 10-µm-thick, optically transparent film of titanium dioxide particles of a few nm in size, coated with a monolayer of a charge transfer dye to sensitize the film for light harvesting. DSSCs exhibit large current densities (greater than 12 mA/cm 2 ) and exceptional stability as well. [1] Fullerenes and derivatives have emerged as promising materials for the design of efficient DSSCs. [2][3][4][5][6][7][8][9][10][11][12][13] The reason can be attributed to the fact that fullerene-based materials are a low-cost alternative for silicon-based solar cells and they are associated to profitable manufacturing and negligible toxicity. [14][15][16][17][18][19] Two different types of DSSCs are usually distinguished: bulk heterojunctions [20] (BHJs) where the donor and acceptor (D/A) moieties are not covalently connected, and molecular heterojunctions [21] (mHJs) with covalently linked donor-acceptor (D-A) fragments. Several experimental and theoretical studies have been focused on the blends of poly(3-hexylthiophene) (P3HT) and [6,6]-phenyl-C61butyric acid methyl ester (PCBM); [17,[22][23][24][25][26][27][28][29][30] however, detailed information of charge transfer (CT) processes can be also extracted from mHJs since a better structural control and charge mobility tuning can be achieved within this approach. Endohedral metallofullerenes (EMFs) have been used in mHJs as electron acceptor groups because they possess larger absorption coefficients than C60 in the visible region. This property together with the low reorganization energy [13,31] make them suitable candidates for mHJs. Most studies involving EMFs employ Sc3N@Ih-C80 because it is the most abundant EMF. [32] In fact, Sc3N@C80 has been studied in D-A dyads linked to ferrocene, phthalocyanine, tetrathialfulvalene, and triphenylamine (TPA). [33][34][35][36] In the particular case of TPA as the donor moiety, Echegoyen et al. performed electrochemical and photophysical studies in mHJs constituted by TPA (the electron donor) and fullerene cages (C60 and Sc3N@C80, the electron acceptors) from which they revealed valuable information for the understanding of the CT processes occurring in fullerene DSSCs. [36] Indeed, Echegoyen et al. found that TPA-Sc3N@C80 generates longer-lived CT states than does TPA-C60; consequently, the charge recombination (CR) reaction in the former is slower and the driving force was attributed to be the key factor determining the rate of the reaction. [36] TPA and derivatives have been used as photoactive molecules during several decades and their applicability in the construction of DSSCs is also of technological interest. [37][38][39][40][41][42] Moreover, TPA and derivatives can retain cationic charge and hamper aggregation between molecules, which induce self-quenching and reduce the electron injection efficiency thus promoting a longer separation of charge. [39,41] On the other hand, EMFs are excellent electron acceptors [33,36,[43][44][45][46] that react with a variety of chemical agents. [47][48][49][50][51][52][53][54] Consequently, the covalent junctions between TPA and fullerene cages result in interesting assemblies due to: (i) they show, after photoinduction, ultrafast charge separation (CS) reactions in which the lowest-energy excited state entirely localized at the (endohedral)fullerene cage, D-A*, can be efficiently dissociated to form an excited state with strong CT character (i.e., D-A* → D 1+ -A 1-); (ii) the variation of the distance between the D-A interface has an impact in the rate of CT reactions: the shorter the D-A distance, the faster the CT reaction; (iii) nonpolar solvents bring about lack of CT activity since D-A* → D 1+ -A 1becomes an uphill process; on the contrary, more polar solvents diminish the rate of CR reaction thus delaying the recovery of the ground state (i.e., the rate decreases for D 1+ -A 1-→ D-A).
In this contribution, we aim to characterize excited states and explore the effect of the driving force on photoinduced CS reactions in a series of D-A conjugates constituted by TPA and the EMF M@C80 with a scandium-based cluster encapsulated inside the cage (see Figure 1; M = Sc3N, Sc3CH, Sc3NC, Sc4O2, and Sc4O3). It should be noted that for systems containing transition metals the rate constant for intersystem crossing can be much larger (by factor of 10 6 ) as compared with related organic molecules. [55,56] In view of that, CS reactions in TPA-M@C80 are analyzed by considering both singlet and triplet excited states. For the C80 cage encapsulating the metal clusters, we have considered the one having icosahedral symmetry (Ih-C80) throughout this work. We anticipate here that we have found that the nature of the cluster plays an essential role in the charge separation processes. Figure 1 TPA-M@C80 structures under study. All these M@C80 cages have been experimentally detected. [12,[57][58][59][60][61]

Methods
The ground-state geometry for each structure TPA-M@C80 was optimized using the Gaussian 09 program [62] at the CAM-B3LYP [63] /6-31G*~SDD [64,65] level of theory in implicit solvent (COSMO [66] :benzonitrile). The SDD pseudopotentials were used only for the Sc atom. The geometry of the metallic clusters corresponds to that experimentally observed in the isolated M@C80 cage. [12,[57][58][59][60][61] The orientation of the metallic cluster with respect to the pyrrolidine ring corresponds to the most stable orientation determined for Diels-Alder adducts. [67] We assumed that this orientation is the same for these 1,3-dipolar adducts (see Table S1), which was confirmed for the complex TPA-Sc3N@C80. It is worth noting that in TPA-M@C80 the rotation of the metal cluster M is partially hindered. [67] Moreover, in the case of the Zn tetraphenyl porphyrin Sc3N@C80 conjugate, Baruah et al. observed that the cluster orientation has a negligible effect on the excitation energies of charge-separated (CS) states. [68] Table S2 shows that the geometry of TPA-Sc3CH@C80, for instance, optimized in the gas phase is almost the same as the solvated one with a calculated root-mean-square deviation (RMSD) of 0.27 Å (in Table S2 the superposition between these geometries is also schematized). Moreover, B3LYP [69,70] and CAM-B3LYP geometries are found to be nearly identical. Our previous study of excited states for several thermally-accessible conformations of TPA-C60 revealed that the structural variability of these TPA-fullerene interfaces does not significantly affect the electronic properties of excited states. [71] It has been also postulated that CS reactions in organic photovoltaic interfaces are mostly purely electronic processes. [72] Thus our analysis of TPA-M@C80 appears to remain valid even though the effect of the structural fluctuations is not included. [73,74] The lowest-in-energy one hundred singlet excited states and sixty triplet excited states for each complex were calculated using the CAM-B3LYP/6-31G* scheme in the framework of the time dependent density functional theory (TD-DFT) formalism. The quantitative analysis of exciton delocalization and charge separation in the donor-acceptor complexes was carried out using a tool suggested recently by Plasser et al. [75] A key quantity is the parameter Ω: where S is the overlap matrix and P 0i the transition density matrix for a 0  i excitation. The equilibrium solvation energy eq S E in medium with the dielectric constant  was estimated using a COSMO-like polarizable continuum model (C-PCM) in monopole approximation: [76] eq where f() is the dielectric scaling factor, , Q the vector of n atomic 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 -1 B, where the m x m matrix A describes electrostatic interactions 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. The GEPOL93 scheme was used to construct the molecular boundary surface. [77] The non-equilibrium solvation energy for excited state i can be estimated as: [78] neq In Eq. (3), n 2 (the squared refraction index) is the optical dielectric constant of the medium and the vector  describes the change of atomic charges in the molecule by excitation.
Changes in electronic energy, ΔEct, for CT reactions are assumed to be nearly equal to changes in Gibbs energy, ΔGct, (the entropic term for all compounds is expected to be very similar). In a previous study, we noted that the relaxed geometry of a charged state, D + -A -, does not involve significant geometrical changes as compared to the equilibrium geometry of the ground state. [79] 3

Results and Discussion
First, we discuss ground-state properties and compare main energetic, electronic, and structural parameters of the TPA-M@C80 structures. Then, a classification of excited states is provided. Finally, the driving force is examined to determine the most exergonic and endergonic processes.

Properties in the ground state
The ground-state geometries and electronic properties of the TPA-M@C80 structures are quite similar. For M = Sc3N, Sc3CH, Sc3NC, Sc4O2, and Sc4O3, the charge on C80 ranges from -2.0 to -1.7 whereas the corresponding charge on the metallic cluster changes from +1.9 to +1.6, respectively. The charge on TPA is +0.1. The molecular dipole moment is found in the range from 5.0 to 6.6 D. The solvation energies, ∆Gsol, range from -0.74 to -0.71 eV. In Table S3, we separately compare the isolated structures of TPA and C80 with those in the complexes. The small values of RMSD suggest that both the TPA fragment and the fullerene cage do not show significant geometrical differences. Also, the shortest distance between the nitrogen atom in TPA and a carbon atom in C80 ranges from 7.6 to 7.9 Å. This difference is expected to have a negligible effect on the electronic properties of excited states (Table S4 summarizes the electronic and structural characteristics of the TPA-M@C80 structures in the ground state).

Characterization of excited states
The nature of excited states is studied within a two-fragment model. Most electronic transitions occur at the M@C80 acceptor since many frontier molecular orbitals are mainly localized at this fragment (for instance, see Figure 2 for the case of TPA-Sc3N@C80). There are a few excited states with significant contribution of CS configurations; that is, excited states resulting from an electronic transition where the main orbital contribution is a HOMO-X (located at TPA) to LUMO+Y (situated at M@C80). In Table 1, the HOMO-to-LUMO transitions in the gas phase are reported for the lowest locally excited (LE1) and charge-separated (CS1) states, as well as the excitation energy, oscillator strength, and dipole moment associated to such states.
In all cases, singlet LE1 is formed from a HOMO→LUMO excitation with an energy cost ranging from 1.2 to 1.7 eV. Moreover, the dipole moment in LE1 remains similar to the dipole moment in the ground state for every TPA-M@C80 structure, ~6.0 D, with the largest deviation for TPA-Sc4O3@C80. On the other hand, an excited state generated from a HOMO-X→LUMO (X = 1, 2, or 3) transition corresponds to singlet CS1. These states are characterized by a dipole moment larger than 50.0 D. However, TPA-Sc4O2@C80 does not show any pure CS state and for our purposes we use an ME state with the largest contribution of CS, ∆q=0.8 (see Table S6 for complete details. Besides, this state shows a dipole moment below 50.0 D). Nonetheless, the electronic transitions leading to LE1 and CS1 are orbitally forbidden. We note that CS states, [TPA] --[M@C80] + , [35,80,81] where an electron is transferred from M@C80 to TPA are considerably higher in energy than [TPA] + -[M@C80] -, and thus they are not considered here. a For this EMF, the H→L transition leads to the second lowest-in-energy LE. b Only in these two cases, an ME state was used with the largest contribution of CS, ∆q=0.8.
Triplet LE1 and CS1 keep almost the same characteristics as the respective singlet states. One exception is for TPA-Sc3NC@C80, where a HOMO→LUMO excitation leads to the second triplet LE. Another difference is the dipole moment lower than 50.0 D for the triplet CS1 in TPA-Sc3CH@C80 and singlet CS1 in TPA-Sc4O2@C80. As mentioned before, these triplet and singlet CS states are indeed ME states with a large contribution of CS, ∆q = 0.8.

Photoinduced charge transfer in TPA-M@C80
After light absorption (Eq. (4)) by the complex in the ground state, an LE state XM@C80 is generated. Then, very fast internal conversion leads to LE1. This state may be involved in the CS process (Eq. (5)) forming CS1. In turn, this state decays to the ground state (Eq. (6)) leading to charge recombination: [ Below we consider these processes in more detail.
The driving force of CS reactions is estimated as the energy difference between LE1 and CS1. The comparison between excitation energies computed in the gas phase and benzonitrile indicates that there are no significant changes in the position of LE states (the shifts are smaller than 0.1 eV. Complete details for all the transition energies for every TPA-M@C80 structure are provided in Table  S7). In contrast, CS states are strongly stabilized due to the solvent (from 1.0 to 1.8 eV). In the case of TPA-Sc3N@C80, in benzonitrile the energy of CS1 decreases by 1.64 eV. Then, LE1 and CS1 are found at 1.64 and 1.54 eV above the ground state. These estimates are in good agreement with the experimental energies of 1.50 and 1.45 eV, respectively. [36,79] LE1 and CS1 levels in the solvated complexes are depicted in Figure 3.
In the case of singlet excited states (Figure 3a), the CS driving forces are 0.10, 0.08, -0.25, -1.19, and -0.06 eV for TPA-M@C80 with M being Sc3N, Sc3CH, Sc3NC, Sc4O2, and Sc4O3, respectively. CS reactions may occur effectively in the structures containing Sc3N and Sc3CH inside the C80 cage because these processes are exergonic; unlike the endergonic CS occurring in the systems involving Sc3CN and Sc4O2. The CS process in TPA-Sc4O3@C80 is only slightly endergonic, G = 0.06 eV, therefore it can also occur. In the case of triplet excited states (Figure 3b), we assume that the metal cluster generates the formation of triplet states by intersystem crossing from singlet LE1 to triplet LE1. Then, the CS driving forces forming triplet CS1 are -0.18, -0.82, -0.42, -1.40, and -0.22 eV for TPA-M@C80 with M being Sc3N, Sc3CH, Sc3NC, Sc4O2, and Sc4O3, respectively. Accordingly, CS reactions certainly does not occur following a triplet reaction pathway because they are endergonic processes. Furthermore, the CS reaction from singlet LE1 to triplet CS1 is an uphill process in every TPA-M@C80 structure excepting TPA-Sc3N@C80, in which such a process is slightly favored by 0.07 eV. Nevertheless, the singlet-to-triplet spin-crossing from a neutral to a charged state is expected to be not allowed due to the small spin-coupling.
Even though there are no experimental evidence for the CS reaction in TPA-M@C80 (except for M = Sc3N), available electrochemical data can be used to approximate the value of CS1 (see Eq. 6) in the following way: [82] 1 = + @ 80 + where Eox/red are the redox potentials of TPA and M@C80, respectively, and the term C describes the solvent effects that are expected to be very similar in the considered TPA-M@C80 structures. Equation (7) suggests that the difference between CS1 in TPA-M@C80 and CS1 in TPA-Sc3N@C80 is determined by the difference of the reduction potentials; 1 − @ 80 − 1 − 3 @ 80 = @ 80 − 3 @ 80 . The reduction potentials for M@C80 are experimentally known. [58,[83][84][85] We noticed that the difference of the CS1 values calculated in this report is concomitant with the experimental data (the largest deviation is found for TPA-Sc4O2@C80) and thus supports our predictions (see Table S8 for details).

Conclusions
In our study, we examined the driving force of charge separation (CS) in TPA-M@C80 species with M = Sc3N, Sc3CH, Sc3NC, Sc4O2, and Sc4O3. Since CS is one of the most important processes occurring in dye-sensitized solar cells, we expect that our study can provide valuable information for the development of more efficient dye-sensitized solar cells containing endohedral metallofullerenes.
On the basis of TD CAM-B3LYP calculations we have found that: In benzonitrile, the systems containing Sc3N, Sc3CH, and Sc4O3 have been found to facilitate the formation of CS states. In contrast, no efficient electron transfer is expected for structures containing Sc3NC and Sc4O2. (iv) Even though the formation of triplet states is promoted by the metal cluster through intersystem crossing, the decay of these states through electron transfer does not efficiently occur. Triplet CS states are more likely generated in the species containing Sc3N and Sc4O3 inside C80.