Theoretical Study of Fulleropyrrolidines by Density Functional and

J. Phys. Chem. C 2007, 111, 14139-14149

14139

Theoretical Study of Fulleropyrrolidines by Density Functional and Time-Dependent Density Functional Theory Ioannis D. Petsalakis, Nikos Tagmatarchis, and Giannoula Theodorakopoulos* Theoretical and Physical Chemistry Institute, The National Hellenic Research Foundation, 48 Vassileos Constantinou AVe., Athens 116 35, Greece ReceiVed: June 6, 2007; In Final Form: July 13, 2007

Density functional theory (DFT) calculations have been employed in a study of various fulleropyrrolidines in order to determine their electronic structure and in particular the effect on the chemical properties of the pyrrolidine nitrogen atom of fullerene as well as of additional substituents. It is found that fullerene causes a large chemical shift in the calculated N 1s binding energy, while further substitution at N has smaller effect independent of the type of substituent. Time-dependent DFT calculations have been employed for the calculation of the energy of the lower-lying electronic states of fulleropyrrolidines, as well as on higher-lying states, in view of the intense interest related to photoinduced charge-transfer processes in these systems. The TDDFT calculations on the lower-lying states converge on the same lowest excitation energy for most of the substituted fulleropyrrolidines, favoring excitations from occupied orbitals localized on C60 even when the highest occupied molecular orbital (HOMO) is localized on the substituent groups. Good agreement is found with the experimental lowest excitation energy in fullerene and in the fulleropyrrolidine-porphyrin system. Finally, an excitation to a higher-lying state, related to the charge-transfer process, has been determined by TDDFT calculations on a porphyrin-fulleropyrrolidine system, where it is found that the absorption characteristics of the individual substituent are transferable to the combined system.

1. Introduction The discovery of C60 fullerene in 19851 has spurred a great deal of research on fullerenes and their derivatives, the properties of which make them interesting for different technological applications.2 Early Hu¨ckel molecular orbital theory calculations3 gave a good indication of the electronic structure of C60, where the well-known spherical shape consists of 20 sixmembered rings and 12 five-membered rings, in which all the carbon atoms are equivalent, but where two different C-C bond lengths are found.3,4 In particular, it was found that the lowest unoccupied molecular orbital is low in energy and triply degenerate, implying a capability for accepting six electrons upon reduction, and indeed the electrochemistry of C60 does show the existence of C60n- (for n ) 1-6), for a particular choice of solvent.5 Thus it is generally established that fullerenes are electron-attracting compounds, and therefore their chemistry involves mainly addition reactions.6,7 Current research interest on the spectroscopy and photochemistry of fullerene C60 is quite intense8-10 because it is considered to be an ideal candidate as the electron acceptor in systems suitable for photoinduced transfer of electrons and/or energy and thus of interest for organic solar cells. Light-harvesting systems are developed by dyads or triads of compounds involving moieties covalently bonded to C60. HOMO (highest occupied molecular orbital)LUMO (lowest unoccupied molecular orbital) arguments are usually employed to describe the photoinduced charge-/energytransfer process,8 since theoretical calculations on the excited states of these systems are scarce. Recently, time-dependent density functional theory (TDDFT) has been used to calculate the lowest excited levels of a number of hybrid systems, * Corresponding author. Telephone: + 30 2107273800. Fax: + 30 2107273794. E-mail: [email protected].

including fullerene-tetrathiafulvalene,11 and a porphyrinfullerene dyad.12 In general it is difficult to have one-to-one correspondence between the observed and calculated levels, as it was found that, depending on the particular functional used, different numbers of excitations are calculated in a given energy range.12 Of the great variety of organofullerene compounds, fulleropyrrolidines have been the object of a great deal of research effort,6,7,13 as they are easy to prepare and have many synthetic variations. Recently, the effect of the fullerene substituent as well as of the addition of further substituents on the pyrrolidine nitrogen atom has been studied by X-ray photoelectron spectroscopy, for neutral as well as positively charged compounds,13 in order to obtain information on the chemical bonding in the different systems from the observed chemical shifts in the binding energies of the atomic C and N 1s electrons. In the present work, density functional theory (DFT)14 calculations are employed to study the electronic structure of fulleropyrrolidines in the ground electronic state. In particular, chemical shifts in the calculated pyrrolidine N 1s binding energy are determined and the results are compared to available experimental data.13 Second, time-dependent density functional theory (TDDFT)15 calculations are employed on the above molecules in an effort to determine the excitation energies of the lower-lying excited states in these systems, beyond the orbital (HOMO-LUMO) description. Similarly, TDDFT calculations have been carried out on higher-lying excited states, in an effort to determine the excitation relevant to the photoinduced charge-transfer process. 2. Computational Methods In the present work the methods of calculations used are density functional theory14 and time-dependent density func-

10.1021/jp0743774 CCC: $37.00 © 2007 American Chemical Society Published on Web 09/01/2007

14140 J. Phys. Chem. C, Vol. 111, No. 38, 2007

Petsalakis et al.

Figure 1. Schematic drawing showing chemical structures of the fulleropyrrolidine molecules 1-11 calculated in the present work.

tional theory,15 provided within the computational package Gaussian 03.16 With such methods the results will depend on the choice of functional and basis set, as was shown by an analogous study on a porphyrin-fullerene system,12 where of the different functionals employed the B3LYP functionals17 were found to be the most appropriate to use. Accordingly, the B3LYP functionals have been employed in the present work, with a rather large basis set, namely the 6-31G(d,p) basis set of Gaussian 03. In addition, two other basis sets, differing in the number and type of polarization functions, have been employed

for one of the systems of interest, as will be described below, in order to get some information on the effect of such variations in the basis sets. Geometry optimizations have been carried out at the DFT level, with the aid of the default procedures of Gaussian 03. TDDFT calculations were subsequently carried out, at the optimum geometry, for the lowest three excitations to singlet states and three lowest excitations to triplet states. Additional TDDFT calculations have been carried out, requesting a large number (10-20) of excitations to singlet states, in an effort to

Theoretical Study on Fulleropyrrolidines

J. Phys. Chem. C, Vol. 111, No. 38, 2007 14141

TABLE 1: Binding Energies (∆Ε) of the Molecules in Figure 1, with Respect to the Separated Fragments, either C60 + R or C2H4 + R R

∆E (eV) (in C60-R)

∆E (eV) (in C2H4-R) 2.00

(H2C)2N-TEG-OC(CH3)3 (H2C)2N-TEG-pyrene (out) (H2C)2N-TEG-pyrene (in) (H2C)2N-TEG-TTF (out) (H2C)2N-TEG-TTF (in) (H2C)2N-TEG-fc- (out) (H2C)2N-TEG-fc- (in) (H2C)2N-TEG-porph- (out) (H2C)2N-TEG-porph- (in)

0.44 (over )C-C)) 1.30 (over -CdC-) 0.47 (over )C-C)) 1.33 (over -CdC-) 2.21 2.17 1.76 2.28 1.71 2.21 0.95 1.36 1.10

molecule (cf. Figure 1) 1

HN(CH2)2

2

H3CN(CH2)2

3 4 5 6 7 8 9 10 11 a

2.88 2.88 2.51 2.88 2.49 2.88 1.86 1.95 a

Calculation did not converge.

TABLE 2: Calculated Binding Energies of Bis-fulleropyrrolidine at the Eight Different Substitution Sites

a

2.04

geometrya

BE (eV) 2NC2H5

BE (eV) 2BOC-TEG-NC2H5

cis-1 cis-2 equatorial trans-4 cis-3 trans-2 trans-3 trans-1

2.637 2.635 2.761 2.718 2.600 2.739 2.769 2.716

4.198 4.110 4.254 4.207 4.084 4.219 4.252 4.202

Following the terminology of Figure 2.

TABLE 3: Chemical Shift of the Pyrrolidine N 1s Electron Binding Energya in the Different Molecules Calculated in the Present Work, with Respect to the Value in the Pyrrolidine Molecule

fragment R

N 1s chemical shift (eV) (in C60-R)

N 1s chemical shift (eV) (in C2H4-R)

HN(CH2)2 H3CN(CH2)2 (H2C)2N-TEG-OC(CH3)3 (H2C)2N-TEG-pyrene (out) (H2C)2N-TEG-pyrene (in) (H2C)2N-TEG-TTF (out) (H2C)2N-TEG-TTF (in) (H2C)2N-TEG-fc- (out) (H2C)2N-TEG-fc- (in) (H2C)2N-TEG-porph- (out) (H2C)2N-TEG-porph- (in)

0.85 0.96 0.88 0.51 0.94 0.88 1.16 0.84 0.91 0.82 1.06

(389.34)a 0.0 0.19 0.23 0.23 0.39 0.25 0.64 0.25 b 0.26 b

a With respect to the N 1s binding energy in pyrrolidine. b Calculation did not converge.

obtain information on the photoinduced charge-transfer process. These calculations, which are very demanding of computer time, do not always yield the required excited state in the different systems, as there exist many lower-lying states. 3. Results and Discussion 3.1. Effects of Functionalization in Fulleropyrrolidines on the N 1s Binding Energy (BE). Density functional theory (DFT) calculations, using the B3LYP functionals and the 6-31G(d,p) basis set of Gaussian 03, have been carried out on pyrrolidine and various fulleropyrrolidines. Schematic drawings showing the chemical structures of the molecules calculated are

given in Figure 1. Some of these systems are also found in the XPS study of Benne et al.13 in their study of the C and N 1s chemical shifts in different substituted fulleropyrrolidines. Structures 4-11 (see Figure 1) differ in the location of the substituent group, whether it is at the end of the connecting triethylene glycol (abbreviated as TEG) chain (out) or at the R-C atom of the pyrrolidine moiety (in). Geometry optimization was carried out for each molecule, and the binding energy of the molecule with respect to dissociation into fullerene plus the corresponding substituted pyrrolidine fragment was calculated. For example, the separated fragments for the simplest fulleropyrrolidine itself (1) are C60 + HN(CH2)2. The results are collected in Table 1, where for comparison the binding energies with respect to the fragments are given for pyrrolidine and substituted pyrrolidine itself. As shown, substantial binding energies are calculated for all the systems studied. For the first two systems, addition of pyrrolidine at two different types of sites at C60 was calculated, and as expected addition over a -CdC- (i.e., the side of 6,6-membered rings) leads to a more stable compound (see Table 1). Substitution at the pyrrolidine nitrogen atom with methyl does not change the binding significantly; however, substitution by the other groups (see Table 1) results in significantly larger binding energies. Furthermore, it might be noted that the out versions of substituted fulleropyrrolidines have much larger binding energies than the corresponding in structures. It is instructive to calculate optimum geometries and binding energies for higher adducts of fulleropyrrolidine derivatives. In particular, DFT calculations have been carried out for eight symmetry-distinct bis-fulleropyrrolidines (cf. Figure 2) as well as the corresponding structures with N-TEG-BOC-substitited pyrrolidine (where BOC stands for the tert-butoxycarbonyl protecting group). The resulting binding energies are collected in Table 2. As shown in Table 2, substantial binding is calculated, with the largest values found for the equatorial and trans-3 positions, with more than 2 times the BE value for single addition in the case of pyrrolidine and slightly less than 2 times the BE value for single addition in the case of substituted pyrrolidine. As in the single additions, increased binding energy is calculated for the N-substituted adducts. Chemical shifts in the electronic binding energies of an atom in different chemical environments can be used to derive information on the chemical bonding in the different environments. For fulleropyrrolidine and different derivatives,13 the C 1s binding energy and to a lesser extent the N 1s binding energy have been determined by XPS to show small chemical shifts between the different compounds.13 In the present calculations,


Figure 2. Schematic drawing showing the eight symmetry-distinct bisfulleropyrrolidines calculated in the present work.

it is possible to use the negative of the orbital energies as a measure of the electron binding energy, by analogy with Koopmans’ theorem for closed-shell Hartree-Fock wave functions.18 While the orbital energies themselves greatly overestimate the binding energies, especially for inner levels, the chemical shifts in the orbital energies can be useful. In Table 3, the chemical shifts of the N 1s binding energy in the different systems calculated are listed with respect to the N 1s binding energy in pyrrolidine (given in parentheses). As in Table 1, here too results are given for both pyrrolidine and fulleropyrrolidines 1-11 (see Figure 1) for comparison. As shown in Table 3, a large shift of 0.85 eV toward larger binding energy is calculated for N 1s in fulleropyrrolidines compared to pyrrolidine (first

Petsalakis et al. row of Table 3). This is the largest effect calculated for this property as the addition of further substituents, in general, does not produce large shifts. Generally “in” substitutions lead to greater chemical shifts, indicating a more “electron-withdrawing” environment for the N atom. The “out” geometries do not add significantly to the chemical shift caused by the presence of fullerene. Among the systems studied by Benne et al.,13 the N 1s binding energy was reported for only two systems with a neutral fulleropyrrolidine nitrogen, namely N-methylfulleropyrrolidine and one similar to our compound 9, but with an ammonium end functional group,13 and it was found that within their experimental error limits the two compounds have the same N 1s binding energy. This is also reflected in the calculated chemical shifts of Table 3, at 0.96 and 0.91 eV, respectively; cf. second and third from the last rows. Thus the present calculations support the conclusions of Benne et al.13 that there is no observable difference in the charge redistribution caused by a methyl group or by an alkyl chain. Of the other systems calculated, the tetrathiafulvalene (abbreviated as TTF) substituent in the “in” position causes the largest chemical shift in the N 1s binding energy, while the pyrene substituent in the “out” position seems to compensate to some degree for the electronwithdrawing effect of the fullerene cage. 3.2. Energy Levels of the Three Lowest Singlet and Triplet Excited States of Fulleropyrrolidines. Energy levels of the three lowest singlet and triplet excited electronic states have been calculated for the systems of interest in the present work, using TDDFT calculations at the ground-state DFT-optimized geometry (cf. previous section). It is common practice to describe the excited states of polyatomic systems in terms of excitations from the occupied to the unoccupied orbitals and, in particular, to make use of the HOMO-LUMO picture.8,19 Increased use of TDDFT calculations of the lower-lying states

Figure 3. Electron density plots of the orbitals associated with the lower excitations in fulleropyrrolidine (1) and TEG-TTF (in) substituted fulleropyrrolidine (7).



Figure 4. Electron density plots of the orbitals associated with the lower excitations in N-TEG-porphyrin (out) substituted fulleropyrrolidine (10), and intermediate orbitals.

of hybrid molecules was found recently,12 where in addition to optical transitions rates of resonant energy transfer have been also addressed.20 In the present work, the TDDFT calculations as the DFT of the previous section have been performed using B3LYP functionals and 6-31g(d,p) basis set, of Gaussian 03, with the default option of three singlet and three triplet states. The results are listed in Table 4, where the excitation energies and the dominant excitations (where “H” stands for HOMO and “L” for LUMO in Table 4) are given. Several points might be noted: in unsubstituted fullerene, the above approach leads to three slightly different excitation energies for the three lowest singlet states, while they are virtually identical in the triplets. The orbital energies yield a single value, at 2.76 eV, as the

HOMO is 5-fold degenerate and the LUMO is 3-fold degenerate in fullerene. The calculated TDDFT excitation energy is very close to the experimental value for the lowest excitation in fullerene, at 1.941 eV.21 It should be noted that in fullerene, as well as in the other systems calculated here, the transitions listed in Table 4 correspond to weakly allowed transitions at the lowenergy edge of the electronic spectra of these systems, while the significant maxima occur at much higher energies (or shorter wavelengths). In fulleropyrolidine, N-methylfulleropyrrolidine (compounds 1 and 2 of Figure 1), and compound 3 of Figure 1, which is characterized by the BOC substituent, nearly identical excitation energies are calculated, with the same excitation pattern, HOMO f LUMO, HOMO f LUMO + 1,

TABLE 4: Transition Energies at the DFT Optimum Ground-State Geometry Calculated by TDDFT

e

molecule

S1, S2, S3 (eV)

T1, T2, T3 (eV)

C60a 1 (fulleropyrrolidine) 2 (N-methyl-fp)b 3 (BOC)b 4 (pyrene-out) 5 (pyrene-in)

1.94, 1.95, 1.98 1.89, 1.91, 1.91 1.89, 1.91, 1.91 1.89, 1.91, 1.91 1.89, 1.91, 1.92 1.89, 1.91, 1.92c 1.87, 1.88, 1.89d 1.88, 1.89, 1.91

1.59, 1.59, 1.59 1.53, 1.64, 1.67 1.53, 1.64, 1.67 1.53, 1.64, 1.67 1.53, 1.64, 1.67 1.53, 1.64, 1.67c 1.51, 1.62, 1.65d 1.53, 1.64, 1.67

6 (TTF-out) 7 (TTF-in) 8 (Fc-out) 9 (Fc-in)e

1.69, 1.78, 1.78 1.21, 1.32, 1.58 1.88, 1.91, 1.92 1.87, 1.88, 1.88

1.53, 1.67, 1.67 1.20, 1.30, 1.54 1.53, 1.64, 1.67 1.53, 1.64, 1.66

10 (porphyrin-out)f 11 (porphyrin-in)

1.68, 1.88, 1.90 1.67, 1.68, 1.81

1.36,1.53, 1.67 1.37, 1.53, 1.64

main orbital excitations (for the lowest three levels) H (5-degenerate) f L (3-degenerate) H f L (68%), H f L (64%) + 1, H - 1 f L (67%) H f L (68%), HL + 1 (64%), H - 1 f L (67%) H f L, H f L + 1, H - 1 f L H - 1 f L (68%), H - 1 f L + 1 (65%), H - 2 f L(67%) H - 1 f L (65%), H f L (55%) and H - 2 f L (36%), H - 1 f L + 1 (66%) H f L (71%), H f L + 1 (71%), H - 1 f L (66%) H f L (71%), H f L + 1 (71%), H f L + 2 (71%) H - 2 f L (68%), H - 2 f L + 1 (64%), H - 3 f L (67%) H f L (65%) and H - 2 f L (25%), H - 2 f L (57%) and H f L (25%), H - 1 f L (27%) and H - 2 f L (638%) H - 2 f L (64%), H - 2 f L + 1 (64%), H - 3 f L (67%) H f L (68%), H - 2 f L (64%), H f L + 1 (68%)

a Experimental value is 1.94 eV.21 b Experimental value for 2 is 1.78 eV22 and for 3 is 1.76 eV.23 Experimental value is 1.76 eV.23 f Experimental value is 1.7 eV.12

c,d

Basis sets 6-31g(2d,p) and 6-31g(dfp).


Petsalakis et al.

Figure 5. Electron density plots of orbitals associated with the lower excitations in TEG-porphyrin (in) substituted fulleropyrrolidine (11), and intermediate orbitals.

Figure 6. Electron density plots for frontier orbitals calculated for the individual substituents: 1, TTF; 2, ferrocene, 3; pyrene.

HOMO - 1 f LUMO, for the three lowest singlet states. This similarity is also shown in the density plots of the relevant molecular orbitals, where in all three cases the HOMO is localized on C60 and the bond with the two C atoms of pyrrolidine attached to C60. Orbital HOMO - 1 is localized on C60 as are the LUMO and the next highest, LUMO + 1 orbital, as may be noted in the electron density plots of the

relevant molecular orbitals of fulleropyrrolidine, shown in the upper part of Figure 3. The lowest transition energy calculated for these systems is lower than the corresponding value in unsubstituted fullerene, see Table 4, while an even lower value is indicated by the experimental excitation energy of 1.78 eV22 for compound 2 and 1.76 eV23 for compound 3.



Figure 7. Frontier orbitals calculated for substituted fulleropyrrolidines, localized on the substituent moiety.

For system 4, with a pyrene substituent in the out geometry, in addition to the 6-31g(d,p) calculations, two larger sets were used, 6-31g(2d,p) and 6-31g(dfp), involving larger sets of polarization functions. The calculated excitation energies are also listed in Table 4. As shown, the effect of the inclusion of the second set of d functions is not significant, while the addition of f polarization functions makes a small difference in the lowest excitation energy and somewhat larger on the higher values (see Table 4, values with superscript d). Some small differences are found in the calculated excitation energies of the out and the in (compounds 4 and 5, respectively), as well as in the excitation patterns. In terms of the calculated lowest excitation energy, compounds 4 and 5 are very similar to compounds 1-3. However, the lowest excitations in 4 and 5 correspond to excitations HOMO - 1 f LUMO, unlike the previous systems. For the pyrene-substituted systems, 4 and 5 of Figure 1, the HOMO (or “H” in Table 4) orbital is localized on the pyrene part, while HOMO - 1 in 5 resembles the HOMO in systems 1-3, and HOMO - 2 in 5 resembles HOMO - 1 in 1-3; see above. In 4, both HOMO - 1 and HOMO - 2 are localized on C60. Thus even though there is a higher-energy HOMO in 4 and 5, which might lead to a lower excitation energy, based on a HOMO-LUMO type of excitation, the present TDDFT calculations converge on the excitations from HOMO - 1 in these systems (see Table 4). For the next two systems in Table 4, compounds 6 and 7, involving TTF substituent in the out and in geometries, respectively, the TDDFT calculations for this case converge on the lowest excitation energy characterized by the HOMO f LUMO excitation, and consequently the calculated excitation energies are significantly lower than those of 4 and 5 above. Electron density plots for the molecular orbitals of the in structure of the TTF-substituted system (7), relevant

for the three lowest excited singlet states, are shown in the lower part of Figure 3. The calculations on the out and in ferrocene-substituted compounds, compounds 8 and 9, respectively, converge on energies characterized by HOMO - 2 f LUMO for the lowest energy transition in the out system and a combination of HOMO f LUMO and HOMO - 2 f LUMO in the in system. As in 6 and 7, the HOMO is localized on the substituent, in this case ferrocene, but here also HOMO - 1 is localized on the substituent and HOMO - 2 is localized on C60. Thus in these systems, too, the TDDFT calculations find the lowest energy transition to correspond to excitations from an occupied orbital localized on C60. An experimental λmax value for a system very similar to 9 corresponds to 1.76 eV excitation energy.23 Presumably, a HOMO f LUMO type excitation might have led to a lower excitation energy for these systems as found for systems 6 and 7, and perhaps better agreement with experiment, but the present TDDFT calculations converged on the states as indicated in Table 4. It is not clear whether this is as it should be or whether it is a result of properties inherent in the TDDFT method and the local density approximation, where a similarity of the excited and the ground states is favored.15 Here it seems to be a similarity between the orbitals involved in the excitation that is favored, in some of the systems calculated. The last two systems listed in Table 4 involve porphyrin substituents in the out and in geometries respectively (10 and 11 of Figure 1), and the localization of the highest occupied and lowest unoccupied orbitals are as in the ferrocene-substituted compounds, 8 and 9. In this case, the patterns of the dominant excitations are different in the two systems, out and in, where for the in system the TDDFT calculations converge to a HOMO


Petsalakis et al.

Figure 8. Electron density plots of frontier orbitals calculated for the in structures of substituted fulleropyrrolidine, for pyrene and for TTF substituents.

Figure 9. Electron density plots of frontier orbitals calculated for the porphyrin substituent molecule.



Figure 10. Electron density plots of frontier orbitals of the out combined fulleropyrrolidine-porphyrin system, relevant to the strong absorption in porphyrin.

f LUMO excitation, finding an additional low root to the HOMO - 2 f LUMO one found in both out and in systems (see Table 4). Electron density plots for the frontier molecular orbitals in systems 10 and 11 are shown in Figures 4 and 5, respectively. An experimental value for the lowest excitation energy in a fullerene-porphyrin dyad system (but with a different connecting group from the present work), is reported at 1.7 eV,12 which is close to the present calculated value. Finally, the calculated excitation energies to the lowest three triplet states, listed in Table 4, under “T1, T2, T3,” are smaller than the corresponding values for the singlets, but generally follow the variations found in the singlets, with the lowest triplet calculated identical to that in fulleropyrrolidine, for all systems except the TTF-in (7), porphyrin-out (10), and porphyrin-in (11). Comparison of the present results with corresponding experimental and previous theoretical results for the substituted fulleropyrrolidine systems studied here is possible to the extent already discussed (see also experimental quantities in Table 4). However, experimental and theoretical work exists on the spectra of the substituents alone, and it is instructive to consider those data as well. The synthesis and structure of the porphyrin substituent (in our compounds 10 and 11) have been published recently,24 with λmax corresponding to transition energies of 2.96, 2.41, 2.26, 2.10, and 1.92 eV, with recent related theoretical values in the same range.25-27 In the present work, the lowest energy transition calculated for the above porphyrin substituent is 2.03 eV, while as mentioned above our calculated value for porphyrin-substituted fulleropyrrolidine (10) is 1.68 eV with an experimental transition energy for a similar system at 1.7 eV.12 The reduction in the lowest transition energy (cf. 1.7 eV vs 1.92 eV) in the combined system as compared to the free

substituent is of course a consequence of the fact that in the hybrid system the lowest energy transition involves excitations to orbitals (LUMO) localized on fullerene (see Figures 4 and 5), which are lower in energy than the LUMO of the substituent. A similar observation has been made for the HOMO-LUMO gap in a theoretical study of a fullerene-ferrocene hybrid.28 Similarly, the experimental lowest level for TTF (in cyclohexane) is at 2.13 eV29 with a slightly higher theoretical value,30 while the present value for fulleropyrrolidine-TTF (6) is 1.69 eV (cf. Table 4). In pyrene the lowest energy transition is observed at 3.36 eV,31 with a corresponding theoretical value at 3.57 eV,32 while for the combined fulleropyrrolidine-pyrene system (4), the TDDFT value is 1.89 eV (see Table 4). In all these systems, the lowest-lying unoccupied orbitals are localized on fullerene. 3.3. Excitation Energies and Frontier Orbitals Relevant to the Absorption Step of the Photoinduced Charge-Transfer Process. As mentioned in the Introduction, one of the interesting aspects of these hybrid systems, calculated in the present work, is their photoinduced charge-transfer activity and potential use in solar cells. The process involves absorption by a substituent group and subsequent transfer of energy or electron toward the fullerene cage. Of the systems calculated in the present work, systems 4-11 of Figure 1 are of interest for such a process. Accordingly, TDDFT calculations have been carried out on the separate substituents, i.e., pyrene, ferrocene, TTF, and porphyrin, to obtain a theoretical value for one of the strong absorption peaks in each case. Also, the combined system was examined, both in terms of the orbital pictures and by TDDFT calculations, where possible. As will be described below, the required excitations, involving orbitals localized on the substituent, appear


Petsalakis et al.

Figure 11. Electron density plots of frontier orbitals of the in combined fulleropyrrolidine-porphyrin system, relevant to the strong absorption in porphyrin.

to lie above a rather large number of lower-lying states, and as a result for most systems calculated it was not possible to reach the desired state, even with a TDDFT calculation involving 50 excited states. Only for the fulleropyrrolidine-porphyrin system was it possible in the present work to calculate the required transition by TDDFT. It is instructive to note that, in most cases, and especially for the out type of structures, the orbital picture yields a basically well-separated type of charge distribution, with localization of charge either on the fullerene cage or on the substituent, and it is possible to identify in the combined systems transitions involving the separate substituents. For example, in Figure 6, plots of the HOMO and LUMO of the individual substituents TTF, ferrocene, and pyrene are given, along with the excitation energy for the transition HOMO f LUMO in each case, calculated from the orbital energies. The corresponding plots for the combined systems are given in Figure 7, where it is shown that basically the same charge distribution and excitation energies are found as in the substituents alone. However for the in structures, the clear separation between the cage and the substituent frontier orbitals is not always found, as shown for example in Figure 7, for the pyrene-substituted in structure, although it persists in some cases as for the in TTF structure, also shown in Figure 8. For the case of the porphyrin, TDDFT calculations obtain the transition observed at 2.92 eV,24 as corresponding to a combination of different one-electron excitations, the most important of which involve the molecular orbitals shown in Figure 9, with a TDDFT excitation energy of 3.02 eV and oscillator strength (f-value) of 0.96. When TDDFT calculations

are carried out on the combined porphyrin-fulleropyrrolidine system (10), two transitions are found that would be candidates corresponding to the above transition in porphyrin, where both involve orbitals localized on the porphyrin moiety, but they are found at different transition energies and with different f-values. The one with the larger f-value, of 0.83, involves excitations between the orbitals shown in Figure 10 (out) structure and Figure 11(in), with a charge density pattern very similar to that of the porphyrin moiety alone (Figure 9), and calculated excitation energies at 3.15 and 3.16 eV, for the out and in structures, respectively. The other calculated transition has a much smaller excitation energy at 2.13 eV and oscillator strength of 0.0428, so it is considered to correspond to the absorption in free porphyrin at 2.10 eV,24 which was calculated here by TDDFT at 2.10 eV with an f-value of 0.063. In general, the above results show that more than one single-electron excitation needs to be considered for these absorptions, requiring at least a TDDFT approach. Also, it is found that the information on the absorption process in the separate substituent moiety, to a very large extent, is transferable to the absorption process in the combined system, where, in general, it may be difficult to determine the required excited states. 4. Conclusions In the present work DFT and TDDFT calculations are presented on various fulleropyrrolidines in order to obtain information on the ground-state electronic structure as well as on their lowest-lying excited states. Increased binding is calculated for N-substituted fulleropyrrolidines, while for bisfulleropyrrolidine roughly twice the binding energy of single

Theoretical Study on Fulleropyrrolidines addition is calculated. The chemical shift in the N 1s orbital energy is related to the chemical environment, and in agreement with experimental work, fullerene as an electron-withdrawing substituent causes a large shift in the N1s binding energy of pyrrolidine. Further substitution at the pyrrolidine nitrogen generally has little effect, while introduction of substituent groups in the in position, i.e., at the R-C atom of the pyrrolidine moiety, results in an additional but small chemical shift in the N 1s binding energy. The results of TDDFT calculations on a number of substituted fulleropyrrolidine systems show that the calculations for the lowest-lying states tend to converge, mostly, to energies characterized by excitations from occupied molecular orbitals localized on the C60 part of the molecule, even when they are not the highest energy occupied orbitals (HOMOs). It is difficult to establish whether the calculated excitation energies are indeed the lowest, for all the cases considered, or the results are a consequence of the present TDDFT calculations favoring electron excitations between orbitals with the same type of charge localization, which appears to be the case in pyrene-, Fc-out-, and porphyrin-out-substituted fulleropyrrolidine. Comparison of calculated excitation energies with experimental data yields good agreement for fullerene itself, and for the porphyrinsubstituted system, and less good agreement for the BOCsubstituted and the ferrocene-substituted systems. It must be kept in mind that the theoretical calculations involve isolated molecules, while the experimental work is in solutions, and also that, for the systems considered here, the particular transitions correspond to very low bumps at the low-energy edge of the electronic spectra, which have very strong and distinct features at higher energies. Thus it is difficult to have corresponding experimental information for all the systems considered in the present work. Finally, TDDFT calculations on higher-lying states of the systems of interest for photoinduced charge transfer show that in general the state of interest for the absorption lies above a large number of lower-lying excited states and thus is difficult to determine in the combined system. In the present work, it was possible to reach it by TDDFT only in the porphyrinsubstituted fulleropyrrolidine. However, information on the excitation process in the systems of interest here may be derived from calculations on the substituent moieties alone, as the relevant excitations retain their characteristics to a very large extent, in the combined system. Acknowledgment. This work, conducted as part of the award (“Functionalization of Carbon Nanotubes Encapsulating Novel Carbon-based Nanostructured Materials”) made under the European Heads of Research Councils and European Science Foundation EURYI (European Young Investigator) Awards scheme, was supported by funds from the Participating Organizations of EURYI and the EC Sixth Framework Programme. Supporting Information Available: Calculated orbital energies are given for the four highest energy occupied molecular orbitals and the 10 lowest energy unoccupied molecular orbitals, for substituted fulleropyrrolidines and pyrene, TTF, ferrocene, and porphyrin substituents, calculated in the present work. In addition, a figure is included, showing electron density plots of the orbitals involved in the predicted weak absorption peak of porphyrin in the combined fulleropyrrolidine-porphyrin system. This material is available free of charge via the Internet at http://pubs.acs.org.

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Theoretical Study of Fulleropyrrolidines by Density Functional and

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