INTRODUCTION:

Fullerenes have attracted a great deal of interest because of their unique structure and properties. It was soon realized that C60, because of its high symmetry and stability, was also unique among the experimentally available fullerenes. Indeed moving from C60 to C70, the second most abundant fullerene, the symmetry decreases from Ih to D5h, and much lower symmetry characterizes most fullerene derivatives. Among the properties of fullerenes that can be related to their electronic structure and their symmetry, the optical properties are of particular relevance in view of the potential applications that might be based on them, such as the production of fullerene-based optical limiters [1-2]. In this contribution we review the optical properties of the two most abundant fullerenes, C60 and C70, by focusing on electronic spectroscopy studies carried out in solution, noble gas matrices or in the gas phase, in other words in conditions where the properties of approximately isolated molecules can be monitored. These spectroscopic studies represent an important source of information about the effect of intra-molecular couplings, although the interactions with the solvent will also cause significant perturbations that appear in the spectra.

On the other hand, these spectroscopic data are (the only data) directly comparable with the results of quantum-chemical computational studies carried out on isolated fullerene molecules. The two most abundant fullerenes C60 (a) and C70 (b) shown in fig.1.

Fig.1. The two most abundant fullerenes C60 (a) and C70 (b).

The bonds are shorter with more double-bond character and therefore a hexagon is often represented as a cyclohexatriene and a pentagon as a pentalene or radialene [3-6]. In other words, although the carbon atoms in fullerene are all conjugated the superstructure is not a super aromatic compound. The X-ray diffraction bond length values are 135.5 for the bond and 146.7 pm for the bond [7-8]. C₆₀ fullerene has 60 pi electrons but a closed shell configuration requires 72 electrons. Fullerenes tend to react as electrophiles. An additional driving force is relief of strain when double bonds become saturated. Key in this type of reaction is the level of functionalization i.e. monoaddition or multiple additions and in case of multiple additions their topological relationships (new substituent huddled together or evenly spaced). In conformity with IUPAC rules, the terms methanofullerenes are used to indicate the ring-closed derivatives, and fulleroid to ring-open structures.

The double bond is electron-deficient and usually forms metallic bonds with η = 2. Bonding modes such as η = 5 or η = 6 can be induced by modification of the coordination sphere. C₆₀ fullerene reacts with W (CO)₆ to the (η²-C₆₀)W(CO)₅ complex in a hexane solution in direct sunlight. A part of fullerene research is devoted to so-called open-cage fullerenes whereby one or more bonds are removed chemically exposing an orifice. In this way it is possible to insert into it small molecules such as hydrogen, helium or lithium. The first such open-cage fullerene was reported in 1995.

RESULT AND DISCUSSION:

After considerable work, Kroto, Smalley, and Curl determined that the structure of the C₆₀ buckyball was a combination of 12 pentagonal and 20 hexagonal rings, forming a spheroid shape with 60 vertices for the 60 carbons. The pentagonal rings sit at the vertices of an icosahedron such that no 2 pentagonal rings are next to each other Curl, Kroto, and Smalley received the Nobel Prize in 1996 for their work. The architect R. Buckminster Fuller designed a geodesic dome for the 1967 Montreal World Exhibition with the same structure; the scientists thus named the new molecule Buckminsterfullerene, which was shortened to fullerene when referring to the family of molecules. The bonding pattern of the C₆₀ fullerene is shown here, with yellow bonds representing double bonds and red bonds representing single bonds. The pentagonal rings contain only single bonds; double bonds have a shorter bond length and lead to instability in the pentagonal ring. The limitations on double bond locations lead to poor delocalization of electrons, increasing the molecule’s reactivity.

Electronic Structure of C60:

The C60 molecule contains 60 carbon atoms arranged in 20 six-membered and 12 five membered rings. The most stable of the 1812 possible isomers of C60, and the only one that is actually observed, follows the isolated pentagons rule that is, each of its fivemembered rings is completely surrounded by hexagons. Consequently, the only form of C60 that is observed belongs to the icosahedral (Ih) symmetry group. The CC bonds separating two hexagons are 1.40 Å and have a substantial double bond character while the pentagon CC bonds are 1.46 Å10 long and have a prevalent single bond character. In a simple quantum-chemical description of the electronic structure of C60, based on the molecular orbital approach, each carbon atom contributes with 4 valence orbital (2s, 2px, 2py, 2pz) and thus C60 has 120 occupied molecular orbitals (MOs) and 120 unoccupied or virtual MOs. With some approximations (C60 is not planar), 60 MOs (30 occupied and 30 virtual) can be considered of π type and the remaining 180 orbitals of σ type. In analogy with large aromatic compounds, the highest occupied MOs (HOMOs) and the lowest unoccupied MOs (LUMOs), which determine the lower electronically excited states, are of π type.

The molecular orbitals of C60 can be classified according to the Ih irreducible representations. In Table 1 we list the character table for the I point group from which the characters of the Ih point group, Ih = I × i, are easily derived. Furthermore, if we consider the icosahedral symmetry as a perturbed spherical symmetry, we can classify approximately the C60 MOs according to the angular momentum quantum number l of the spherical harmonics. The degeneracy of Ih orbitals are 1 (age, au), 3 (t1u, t1g, t2u, t2g), 4 (go, gag) and 5 (hg, hub). The degeneracy of spherical harmonics are 1 (s), 3 (p), 5 (d), 7 (f ), 9 (g), 11 (h), 13 (i) and so on. In the Ih symmetry, s, p and d orbitals transform as ag, t1u and hg, respectively. However, f, g, h and i orbitals, with degeneracy higher than 5, split in gu + t2u (f ), hg + gg (g), hu + t1u + t2u (h) and ag + t1g + gg + hg (i), respectively.

The energies of MOs can be obtained by the Hartree–Fock approach and by proper experiments. The energies of occupied MOs were determined by the photoelectron spectroscopy (PES) technique, while the energy of the LUMO was obtained by the PES of the anion [5] and the energies of virtual orbitals were estimated from near-edge X-ray absorption fine structure (NEXAFS) [9]. The experimental energies of the MOs relevant to the visible and near UV electronic transitions are reported in Table 2. The negative energies of the t1u LUMO account for the large electron affinity shown by this molecule which can be reduced to the hexa-anion form in solution and can exist in the gas phase as the dianion [10].

Table 1. Character table of the I point group (Ih = I × i)

Irreducible Representation	I	12C₅	12C₅²	20C₃	15C₂
A	1	1	1	1	1
T₁	3	(1 _ 5½)/2	(1 _ 5½)/2	0	1
T₂	3	(1 _ 5½)/2	(1 _ 5½)/2	0	1
G	4	1	1	1	0
H	5	10	10	1	1

Table 2. C60 molecular orbitals energies (in eV), Ih symmetry labeling and angular

Momentum quantum number l.

Symmetry	Energy	Type	l-shell
gu, t2g	0.6/1.0 [a]	π*	7-k, 8-l
Gg	-0.2/0.0 [a]	π*	6-i
hu, hg, t2u	0.7/-1.2 [a]	π*	7-k, 6- i, 5-h
t1g	2.3 [a]	π*	6-i
t1u	2.69 [b]	π*	5-h	LUMO
Hu	8.74 [c]	π	5-h	HOMO
gg, hg	10.14 [c]	π	4-g
gu, t2u,	10.74/11.94[ c]	π	3-f
hu, hg	10.74/11.94[ c]	σ	9-m, 10- n

a From ref.[ 4]. b From ref. [5]. c From ref.[6]

Electronic Structure of C70:

The second, most abundant fullerene is C70. Although very similar in size to C60, C70 shows rather different spectroscopic features, most of which can be rationalized in terms of its lower symmetry. In this sense, the effect of symmetry lowering manifested in C70 spectroscopy can be considered as a reference starting point for what can be expected for larger, and generally less symmetric, fullerenes and fullerene-derivatives. Indeed, a fundamental difference, compared to C60, appears clearly by considering the results of simple molecular orbital calculations: regardless of the energy order, the symmetries of the lowest two unoccupied MOs (e1’ and a1’) and highest two occupied MOs (e1’ and a2’) indicate that low energy one electron excitations in C70 give rise to dipole-allowed excited states of E1’ symmetry.

Electronic transitions from the ground state to states belonging to the E1’ irreducible representations are dipole-allowed in D5h symmetry. The presence of low lying allowed excited states in C70 is expected to add complexity to the electronic spectroscopy of this fullerene. Indeed, the absorption spectrum of C70 shows a much stronger intensity in the low energy region as compared to C60 [11]. To unravel the order and the nature of the lowest excited states of C70, both of singlet and triplet multiplicity, the availability of well resolved electronic spectra (absorption fluorescence, phosphorescence) was of fundamental importance. However, nicely resolved spectra have become available only relatively recently. This, combined with the computational difficulties in predicting the exact order of the lowest excited states of C70 with a precision of few tens of cm_1, resulted in a delay in the assignment of its lowest excited singlet states which was accomplished with satisfactory accuracy only recently [12]. C70 molecule structure consists of twelve pentagons and fourteen hexagons. Five inequivalent atomic sites (a-e) and eight kinds of bonds (r1- r8) are marked where r 1 = r 3 = r 5 = r6= 1.46Å , r 2 = r4 = 1.40 Å , r 7 = r 8 = 1.42 Å. We know that the electrons of each carbon atom are in four valence states 2s, 2px, 2py, 2pz. Each pz state is perpendicular to the surface. Let tij denotes the hopping matrix element of electron between I and j sites which are nearest neighbors and t the hopping between 2pz states of nearest. To display the effect of the bond lengths, we use the approximation radiation. D5h symmetry of fullerene C70 shown in fig. 2.

Figure 2. D5h symmetry of fullerene C70

Energy States:

The electronic ground state of C60 is a closed shell and has Ag symmetry. The five lowest excited configurations and the corresponding state symmetries are

HOMO ---> LUMO h_u ---> t_1u T_1gT_2gG_gH_g

HOMO -1 ---> LUMO h_g--->t_1uT_1u T_2u G_u H_u

HOMO ---> LUMO +1 h_u ---> t_1gT_1u T_2u G_u H_u

HOMO -1 ---> LUMO +1 h_g ---> t_1g T_1gT_2gG_gH_g

HOMO -2 ---> LUMO g_g--->t_1uT_2u G_u H_u

The electronic states in the visible and near UV can be both of singlet and triplet spin multiplicity.

Singlet electronic states:

A large molecule like C60 has an enormous number of electronic excited states. Even a calculation based only on singly excited electronic configurations from 120 occupied and 120 unoccupied MOs leads to 14400 states. Calculations of energies and oscillator strengths of the lower excited states have been performed by several authors but in all of them some approximations had to be made because of the size of the molecule. The results obtained by two different calculations, are quite similar: this exemplifies the fact that the electronic state calculations provide a consistent picture of singlet excited states of C60. The picture that emerges fits with the experimental results and can be summarized as the lowest electronic states are the four T1g, T2g, Gg and Hg states, which have also very similar energies. Actually, the lowest three T1g, T2g and Gg states, which are predicted at 2.3 eV, are found to be practically degenerate, within 0.05 eV (400 cm_1) of one another, while the Hg state is predicted to be 0.3 eV above Gg. Slightly above, at 2.77 eV, a T2u state is computed. For all these states the electric dipole moment transition to the ground state is zero by symmetry.

The lowest T1u state is calculated at 3.4 eV, that is, ca. 1 eV above the lowest excited singlets. The T1u excited states with larger oscillator strengths are found at 4.3, 5.2 and 5.7 eV. The large energy gap between the lowest energy singlet states and the intensity lending T1u states allows one to describe the intensity borrowing by means of the HT perturbation approach, despite the high density of electronic states. In fullerenes of lower symmetry, like C70, forbidden and allowed states will be closer in energy and the interpretation of vibronic spectra is more complicated.

Transition between the states:

The discussion on the prediction of electronic excited states of C70 makes evident, in analogy with C60, an important intrinsic limit of molecular quantum chemical calculations, which is difficult to overcome: when several electronic states are predicted to be quasi-degenerate, as is the case for C60 and C70, their energy order can be affected by changing the parameters employed in the calculations (geometrical structure, CI dimension, etc.). In this case the identification of the ‘true’ lowest excited state is critical and must be based on the simulation of its properties, among which, of crucial importance are the spectroscopic characteristics. Thus, for C70, the relevant result of CISD calculations shows that in the region of S1 there is a congestion of electronic states, composed of several dipole-forbidden states and a dipole allowed E1’ state. In order to assign the ‘true’ lowest singlet state, the vibronic activity was simulated for each of the low lying excited states of C70 and compared with the observed spectra. In particular, three states were considered as possible candidates for S1. Beside the 1A2’state, namely the 2A2’ and 2A1’ states whose excitation energy is considerably lowered by inclusion of double excitations. Conversely, the predicted 1E1’ state was considered to be the only state responsible for the S2 S0 emission.

The small energy difference among these states and the presence of a dipole-allowed excited state separated from them by a few hundred cm_1 makes impossible the use of the weak-coupling approach employed to investigate C60 singlet spectroscopy. A suitable model, in this case, must take into account electronic along with vibrational contributions to the energy gaps which separate vibronically coupled states. Thus, a perturbative approach that makes use of vibronic wave functions was adopted in this case to model the fluorescence spectrum of C70. This approach was employed successfully to simulate the vibronic structure in the electronic and ZEKE spectra of naphthalene and details on the method can be found in refs. [13]. Emission from the dipole-forbidden states of C70 occurs through the HT mechanism of intensity borrowing while emission from the E1’ state can be due to a combination of HT along with FC mechanisms.

Thus the two possible mechanisms, depicted in Figure 4.2 have to be considered. In the figure, for simplicity, we label with S1 each of the three possible candidates for the lowest emitting state of C70. In summary, the simulations show that the emission from the 2A2’ state accounts for most of the observed S1 S0 vibronic activity [14-18]. The emission predicted for the remaining two dipole forbidden states agrees with the observed emission only in selected frequency regions. Nevertheless, the role of the 2A1’ state is more intriguing, since it is predicted to be very close to the 2A2’ state and its simulated emission shows some vibronic features very similar to the emission of the 2A2’ state and, consequently, very close to the observed vibronic structure. This is especially true in the lowest frequency region.

Mechanisms of intensity borrowing for the S0↔Sn transition of C70:

Electronic levels are indicated by horizontal solid lines; allowed (forbidden) transitions are represented by vertical solid (dashed) lines; vibronic interactions V(sym) mediated by vibrations of ‘sym’ symmetry, are represented by dotted vertical lines [19]. Mechanism 1 for emission from the 1A2’, 2A2’ and 2A1’ states. Intensity is stolen from S0 E1’ transitions. Mechanism 2 for emission from the 1E1’ state. In this chapter we have reviewed some of the most important spectroscopic work aimed at clarifying the properties of the lowest excited states of C60 and C70 In the case of C60, the three lowest excited singlet states, of gerade symmetry species, namely T1g, T2g and Gg, are quasidegerate within 100 cm.

CONCLUSION:

The perturbation of any matrix environment and this is reflected in vibrational structure changes of the fluorescence measured in different matrices. The high resolution excitation spectra, through an educated analysis guided by theory and computational results, reveal the size of the energy gaps existing between the lowest excited states. Moving from C60 to C70, the molecular symmetry is lowered and the degeneracy of electronic states decreases. This fact leads to an increase in the density of electronic states and in the relative number of states with allowed spectroscopic transitions. As a consequence, for C70 both, symmetry forbidden and allowed states are found among the lowest singlet states. In particular, the S1 state is forbidden, while S2, only 170 cm above, is allowed. This leads to the observation of multiple emissions, which is rather unusual for organic molecules. A detailed analysis of the vibronic structure of the excitation spectrum of C70 becomes very complicated and has not been obtained so far. The complications encountered in the spectral analysis of C70 are expected also for the many other fullerenes that do not possess the high symmetry of C60. The lowest triplet state T1 is well separated from T2 both in C60 and C70. Correspondingly, the phosphorescence spectra of both fullerenes have been assigned in detail. However, the rationalization of the different triplet lifetimes of the two fullerenes is still an open problem. In summary, the combination of high resolution spectroscopic data along with the modeling of vibronic interactions and intensities has led to a good understanding of the vibronic structure associated with the lowest electronic states of C60 and, although to a lesser extent of C70.

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Received on 19.04.2013 Modified on 25.05.2013

Asian J. Research Chem. 6(8): August 2013; Page 722-726