Computational Studies of 1,3-Dipolar [3 + 2]-Cycloaddition Reactions of Fullerene-C60 with Nitrones

Over the past decades, the field of fullerene chemistry has developed remarkably, driven by the structural novelty and the intriguing properties of fullerenes that offer a wide variety of new possibilities in a diverse range of applications. Since the initial discovery of the fullerene C60 [1] and the development of a method for its preparation [2], fullerene-based complex molecular systems have received great attention [3-5]. Fullerene-C60 has many potential applications such as in synthetic chemistry, artificial photosynthesis, non-linear optics, surface coatings, superconductivity devices, and cosmetics to slow down the aging of the human skin. The high capability of C60 to act as an electron acceptor or even as electron accumulator has led to the synthesis of a large number of compounds in which the fullerene is covalently linked to photoactive groups serving as potential electron donors [6]. The size, hydrophobicity, three-dimensionality and electronic configurations of fullerenes make them an appealing subject in medicinal chemistry. For example, fullerene C60 has interesting photo, electrochemical and physical properties, which can be exploited in various medical fields. Fullerenes are able to fit inside the hydrophobic cavity of HIV-proteases, inhibiting access of substrates to the catalytic site of enzymes [7]. A series of fullerene-C60 derivatives displays a wide range of biological properties, including neuroprotective, enzymatic, antiapoptotic, antibacterial, DNA photocleaving [8], nitric oxide synthase inhibiting, and chemotactic activities. Moreover, C60 is able to efficiently generate cytotoxic singlet oxygen due to a practically unity value of intersystem crossing from the singlet excited state to the first excited triplet state [9]. It can be used as radical scavenger and antioxidant [10]. Watersoluble fullerenes have been investigated as neuroprotective agents, HIV protease inhibitors, MRI contrast agents, etc. [11]. It has been established that C60 can be used as a versatile building block for the construction of globular dendrimers [12]. Furthermore, an antibody or an antibody fragment can be linked to the fullerene molecule, based on which the C60 can be used as an efficient multiplier in modular drug delivery systems for a photodynamic therapy of tumors [13]. In such systems the antibody linked to the fullerene acts as a selective addressing unit. Special dye molecules which become cytotoxic after illumination with certain wavelength due to singlet oxygen generation which are attached to the C60 directly or via dendritic structure are used as photosensitizers [13,14]. Because fullerene-C60 has a unique spherical geometry, it constitutes a singular scenario in a variety of chemical reactions in which the highly reactive double bonds (30 for the most common C60) partake actively. Even though fullerenes have been among the most studied molecules in science over the last two decades since its preparation in multigram amounts, many important reactions in the arsenal of organic chemistry have not been extensively applied to fullerenes synthetically, despite the unprecedented chemical structures that could be formed.


Introduction
Over the past decades, the field of fullerene chemistry has developed remarkably, driven by the structural novelty and the intriguing properties of fullerenes that offer a wide variety of new possibilities in a diverse range of applications. Since the initial discovery of the fullerene C 60 [1] and the development of a method for its preparation [2], fullerene-based complex molecular systems have received great attention [3][4][5]. Fullerene-C 60 has many potential applications such as in synthetic chemistry, artificial photosynthesis, non-linear optics, surface coatings, superconductivity devices, and cosmetics to slow down the aging of the human skin. The high capability of C 60 to act as an electron acceptor or even as electron accumulator has led to the synthesis of a large number of compounds in which the fullerene is covalently linked to photoactive groups serving as potential electron donors [6]. The size, hydrophobicity, three-dimensionality and electronic configurations of fullerenes make them an appealing subject in medicinal chemistry. For example, fullerene C 60 has interesting photo, electrochemical and physical properties, which can be exploited in various medical fields. Fullerenes are able to fit inside the hydrophobic cavity of HIV-proteases, inhibiting access of substrates to the catalytic site of enzymes [7]. A series of fullerene-C 60 derivatives displays a wide range of biological properties, including neuroprotective, enzymatic, antiapoptotic, antibacterial, DNA photocleaving [8], nitric oxide synthase inhibiting, and chemotactic activities. Moreover, C 60 is able to efficiently generate cytotoxic singlet oxygen due to a practically unity value of intersystem crossing from the singlet excited state to the first excited triplet state [9]. It can be used as radical scavenger and antioxidant [10]. Watersoluble fullerenes have been investigated as neuroprotective agents, HIV protease inhibitors, MRI contrast agents, etc. [11]. It has been established that C 60 can be used as a versatile building block for the construction of globular dendrimers [12]. Furthermore, an antibody or an antibody fragment can be linked to the fullerene molecule, based on which the C 60 can be used as an efficient multiplier in modular drug delivery systems for a photodynamic therapy of tumors [13]. In such systems the antibody linked to the fullerene acts as a selective addressing unit. Special dye molecules which become cytotoxic after illumination with certain wavelength due to singlet oxygen generation which are attached to the C 60 directly or via dendritic structure are used as photosensitizers [13,14]. Because fullerene-C 60 has a unique spherical geometry, it constitutes a singular scenario in a variety of chemical reactions in which the highly reactive double bonds (30 for the most common C 60 ) partake actively. Even though fullerenes have been among the most studied molecules in science over the last two decades since its preparation in multigram amounts, many important reactions in the arsenal of organic chemistry have not been extensively applied to fullerenes synthetically, despite the unprecedented chemical structures that could be formed.
The structure of C 60 includes two different types of bonds, those at the junction of two hexagons and those at the junction of a pentagon and a hexagon (Scheme 1). A pentagon in C 60 is surrounded by five hexagons thereby forming [5,6] C-C junctions and also [6,6] C-C junctions between the neighbouring hexagons. The mean [5,6] C-C Abstract Solubility of fullerene-C 60 improves with functionalization. 1,3-dipolar [3+2]-cycloaddition reactions of fullerene-C 60 with substituted nitrones, a versatile method for fullerene functionalization, were investigated at the MO6/6-31G*//PM3 level of theory to elucidate the effect of electron-releasing (-CH 3 , -CH 2 CH 3 , -CH 2 CH 2 CH 3 , C 6 H 5 CH 2 ) substituents and electronwithdrawing substituents (-F, -Cl, -Br, -NC, and -NO 2 ) on the energetics of the reaction; the regio-and stereo-selectivity of the mono-and bis-addition of nitrones; and global reactivity descriptors of the molecular systems to rationalize and predict their chemical reactivity and site selectivity. The results show that electron-withdrawing groups on the nitrones increase the activation barrier of the reaction whereas electron-donating groups decrease the activation barriers. However, electron-withdrawing groups on the nitrones result in more stable products compared to the electron-donating groups. It was found that the reactions with electron-donating substituents on the nitrone are normal electron demand reactions, with C 60 as the dipolarophile and the substituted nitrones as the dipoles while the reactions with electron-withdrawing substituents on the nitrones are inverse electron demand reactions. The chemical hardness values show greater positive values for adducts with electron-withdrawing substituents on the nitrone and smaller negative values for adducts with electron-donating substituents on the nitrone, confirming the trend that larger activation barriers accompany reactions with electron-withdrawing substituents on the nitrone while electron-donating substituents lower activation barriers. The activation barriers of the second nitrone addition (bisadduct formation) were found to be lower than the barriers for the first nitrone addition (monoadduct formation). Stereo-chemically, syn-bisaddition was found to be thermodynamically and kinetically stable favoured over anti-bisaddition. Electron donating and electron-withdrawing substituents have a marked effect on the energetics of the reaction. and [6,6] C-C bond distances are 1.458 Å and 1.401 Å respectively [15] C 60 is not a "superarene" or superaromatic as it was previously thought, but rather a weakly conjugated, very strained, and electron-deficient polyene [16,17]. The major drawback of fullerenes is their low solubility in organic solvents, which decreases substantially their processibility and hence their applicability [18]. The solubility of C 60 has been studied in a wide variety of solvents [19]. The solvation of C 60 requires the disruption of many solvent-solvent interactions, which are not adequately compensated by the interactions between solvent and C 60 due to the rigid geometry of the latter and the lack of permanent dipole moment. In fact, C 60 is almost completely insoluble in protic or dipolar aprotic solvents like MeOH, MeCN, tetrahydrofuran (THF), and Dimethylsulfoxide (DMSO). It is scarcely soluble in alkanes, with the solubility increasing from pentane to decane. Solubility of fullerene-C 60 improves with functionalization. Many reactions have been developed for the functionalization of C 60 , the main ones being cycloadditions and nucleophilic additions [20]. [3+2] cycloaddition between C 60 and an azomethine ylide (the Prato reaction) stand out as the most frequently applied reaction in the preparation of C 60 derivatives [21]. The azomethine ylide is generally formed in situ from the reaction between an aldehyde or ketone and an amino acid derivative and allows up to five alkyl groups to be introduced to C 60 in a one-step reaction. A related reaction that has been frequently used to prepare C 60 derivatives is the Bingel reaction [22] in which a haloester or ketone is first deprotonated by a base and subsequently added to one of the double bonds in C 60 resulting in an anionic intermediate that reacts further into a cyclopropanated C 60 derivative. The electron affinity of C 60 decreases somewhat upon functionalization as a result of disturbing the conjugated network when converting sp2 carbons into sp3, an effect that is more pronounced in higher C 60 adducts. Although a large number of fullerene derivatives containing nitrogen and oxygen atoms in the organic addend have been prepared, for example, the C 60based dyads formed with the well-known electron-donating addends [23] fullerene derivatives in which the carbon sphere is directly or otherwise linked to nitrogen and oxygen atoms are among the less studied modified fullerenes and the mechanism of addition is less understood. One of the important goals in physical organic chemistry is to have an appropriate description of the chemical substituents in the reactivity patterns of molecules. Parr et al. [24,25] have proposed the global electrophilicity index, ω of a molecule in terms of its chemical potential and chemical hardness as, ω ≈ μ 2 /2η where μ ≈ -(I + A)/2 = [E(HOMO + LUMO)/2] and η = (I -A)/2 = [E(LUMO-HOMO)/2] are the electronic chemical potential and chemical hardness of the ground state of atoms and molecules respectively, approximated in terms of the vertical ionization potential (I) and electron affinity (A) using Koopmans' theorem. ω describes the electrophilic power of a ligand and also its propensity to soak up electrons. This index measures the stabilization in energy when the system acquires an additional electronic charge from the environment. By definition, it encompasses both the ability of an electrophile to acquire additional electronic charge and the resistance of the system to exchange electronic charge with the environment. Global electrophilicity, chemical hardness and chemical potential are very important global reactivity descriptors for studying the chemical reactivity and site selectivity of various molecular systems [26][27][28]. In view of the above, this work aims at exploring (1) mono-and bis-1,3-dipolar cycloaddition of nitrone and its substituted derivatives to fullerene C 60 (Scheme 2); (2) the effect of electron-releasing (CH 3 , CH 2 CH 3 , CH 2 CH 2 CH 3 , C 6 H 5 CH 2 ) substituents and electron-withdrawing substituents (F, Cl, Br, NC, and NO 2 -) on the energetics of the reaction; (3) the regio-and stereo-selectivity of the mono-and bis-addition and (4) global reactivity descriptors of the molecular systems to rationalize and predict their chemical reactivity and site selectivity.

Details of Calculation
All calculations were carried out with the Spartan '10 V1.1.0 Molecular Modeling program (Wavefunction, 2010) at the MO6/6-31G*//PM3 level of theory. Due to the large size of the systems under study the geometries could not be fully optimized at higher levels of theory [29]. The starting geometries of the molecular systems were constructed using Spartan's graphical model builder and minimized interactively using the SYBYL force field [30]. Geometry optimizations were carried out without symmetry restrictions. A normal mode analysis was performed to verify the nature of the stationary points. Equilibrium geometries were characterized by the absence of imaginary frequencies. Transition state structures were located by a series of constrained geometry optimizations in which the forming bonds are fixed at various lengths whiles the remaining internal coordinates were optimized. The approximate stationary points located from such a procedure were then fully optimized using the standard transition state optimization procedure in Spartan. All the critical points were further characterized by analytical computation of vibrational frequencies.
The transition state structures were found to have only one negative eigenvalue with the corresponding eigenvector involving the formation of the newly created C-C and C-O bonds. All reported thermodynamic and kinetic parameters of interest include thermal corrections at 298.15 K and 1 atmosphere pressure in the gas phase. Only closed-shell singlet states were considered.

Results and Discussion
Fullerene-C 60 , a polyolefin reacts with a typical 1,3-dipole such as nitrones to yield fullerenoisoxazolidines and substituted derivatives. As established by Kavitha and Venuvanalignam (2005) in a theoretical study at the B3LYP/6-31G (d,p)//AM1 level, dipolar cycloaddition to fullerene -C 60 can occur at the 6,6 and 6,5 C-C junctions and can form both open and closed adducts, namely closed 6-6, open 6-6, closed 6-5 and open 6-5 adducts but among these, the closed 6-6 is the most favoured. Preliminary calculations in this work to ascertain this assertion has shown that the closed 6-6 is the most preferred. Therefore, all the calculations reported herein are restricted to closed-shell singlet states at the 6,6 C-C bonds [31].

Substituent effects on the energetics of the reaction
The two types of substituents used are the electron-donating (nucleophilic) and electron-withdrawing (electrophilic) substituents. These substituents are characterized by the presence or absence of electron density in their molecular orbitals. The presence of the electron-donating (ED) and electron-withdrawing (EW) groups defines the direction of flow of electrons between any two or more reacting systems. In the course of a chemical interaction, EW substituents and ED substituents on either the dipole or the dipolarophile affects the transfer of electrons from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) of the reacting species according to frontier molecular orbital (FMO) approximation. The possible substituent positions on the nitrone considered in this work are shown below as R 1 , R 2 and R 3 . R 1 is on the nitrogen whereas R 2 and R 3 are both on the carbon atom. The reactions involving the various permutations of substituents R 1 , R 2 , and R 3 are indicated by serial numbers (SN) as given in (Tables 1 and 2).

The effect of electron-donating groups on the energetics
The electron-donating groups considered in this work are H, methyl (CH 3 ), ethyl (CH 3 CH 2 ), propyl (CH 3 CH 2 CH 2 ), pentyl (CH 3 CH 2 CH 2 CH 2 CH 2 ), benzyl (C 6 H 5 CH 2 ), and 1-naphthyl (C 10 H 7 ) groups. In each reaction, different combination of R 1 , R 2 and R 3 are considered. The most feasible [3+2] concerted addition pathway (lowest activation energy) was observed for SN 8 in which R 1 is a propyl group and the other substituents are H atoms, with activation energy of 19.5 kcal/mol. This reaction has an enthalpy of formation of -34.2 kcal/mol. The C-C and C-O forming bonds of the transition state of this reaction are 2.10 Å and 2.10 Å compared to 1.53 Å and 1.41 Å respectively in the product. The reaction with the highest activation barrier (37.4 kcal/mol) has a naphthyl group on R 1 and benzyl groups on R 2 and R 3 . The heat of formation of this reaction is -8.9 kcal/mol. The results (Table 1) show that generally, for electron-donating groups increasing the size of the substituent increases the activation energy and decreases the enthalpy of formation, probably due to steric effects.

Effect of electron-withdrawing substituents on energetics
Electron-withdrawing (EW) substituents F, Br, Cl, NC-, and NO 2 -were placed one after the other at the R 2 position of the nitrone while keeping CH3 on the R 1 and R 3 positions. The results ( Table 2) show that the EW substituents increase the activation barriers for the formation of the products significantly as compared to their ED counterparts for both the concerted (R 2 =Cl, O 2 N) and stepwise (R 2 =F, Br, NC) pathways. In the stepwise reactions, the activation barriers for the first step are significantly higher than for the second step. The exothermicity of the reactions involving the EW substituents was observed to increase steadily as compared to ED substituents. Analyses of all the stepwise pathways in both cases involving ED substituents and EW substituents show that addition through C-O bond formation first followed by the C-C bond formation is more kinetically favourable than the reverse. Energetics for EW substituents is listed in the ( Table 2).  ) and Activation Barriers (E a ) of the cycloaddition reactions with the various electron-donating substituents on the nitrones a a Reactions 9, 10, and 11 are stepwise reactions while the rest are concerted b Barriers of first step in a stepwise mechanism. c Barrier of second step in a stepwise reaction. All energies are calculated relative to the separated reactants (fullerene+nitrone). with ED substituents and other global and local properties such as global electrophilicity index (ω). From the calculated energy gaps it is observed that the reactions with electron-donating substituents on the nitrone are normal electron demand (NED) reactions. Considering the two reactants, C 60 and substituted nitrones, calculations are done with regards to both as dipole and dipolarophile and vice versa. It is thence deduced from these calculations that C 60 is the dipolarophile and the substituted nitrone is the dipole since NED values are smaller than inverse electron demand (IED) values. This means that electron density is drawn from the nitrone to the C 60 moiety when the substituents involved are electron-rich. Conversely an inverse electron demand (IED) is observed for reactions with EW substituents ie. F, Br, Cl, NC-, and NO 2 -at the R 2 position on the nitrone. Table 4 lists the properties of adducts with EW substituents in comparison with the properties of ED substituents. In the case of adducts with EW substituents, there is an electron transfer from the HOMO of the dipolarophile (C 60 ) to the LUMO of the dipole (nitrone). This order best explains the fact that EW substituent pulls electron density to itself in the course of a chemical reaction. The order of decreasing global electrophilicilty is: Cl>Br>F>NC->NO 2 ->>>methyl>ethyl>propyl>benzyl. Calculated parameters show that higher electrophilicity is most experienced with EW substituents since their global electrophilicity indices are far  greater than those for the ED substituents. It is also noteworthy that as the chain of the ED substituents increases, its electrophilic character decreases accordingly. The chemical hardness values (Table 4) show greater positive values for adducts with EW substituents and smaller negative values for adducts with ED substituent. This implies that as the system evolves toward a state of greater hardness, its stability increases. The adduct with the greatest chemical hardness will be the most stable hence least reactive. This conforms perfectly with the activation energies obtained from calculation for both EW and ED systems. Larger activation barriers accompanied EW substituents whereas ED substituents lower the activation barrier.

Geometrical parameters of transition states and mechanistic pathways
An analyses of the geometries of the transition states associated with these 1,3-dipolar cycloadditions for the various substituents show that most of the concerted reactions follow a synchronous pathway as shown in (Table 5).

Further addition of nitrone to monoadduct (bis-addition)
The addition of nitrone to the cis-1 position of the monoadduct of C 60 has two possibilities depending on the orientation of the incoming nitrone. It can be oriented syn or anti to the first nitrone on the buckyball. It is observed that both the syn and anti-additions follow stepwise mechanistic pathways. The syn-addition pathway was found to be kinetically and thermodynamically favoured over the anti-additon pathway. For the syn-pathway, the activation barrier for the first step is 8.3 kcal/mol and that for the second step is 4.2 kcal/mol. The enthalpy of formation of the syn-product is found to be -29.7 kcal/mol as compared to -14.9 kcal/mol for the anti-product which has an activation barrier of 24.2 kcal/mol for the first step and 15.6 kcal/mol for the second step ( Figure 1). C-O bond formation in the first steps of both additions is observed to be favoured over the C-C bond formation. The kinetics reveal that formation of the C-O bonds in the first step is about 13.0 kcal/mol favored over the formation of C-C bonds so in both the mono and bis-additions, the C-O is formed in the first step [32].

Conclusions
The following deductions were made from the results obtained from this work:      and smaller negative values for adducts with electron-donating substituents on the nitrone, confirming the trend that larger activation barriers accompany reactions with electron-withdrawing substituents on the nitrone while electron-donating substituents lower activation barriers.
4. Generally, the activation barriers of the second nitrone addition (bisadduct formation) were found to be less than barriers for the first nitrone addition (monoadduct formation).
6. The C-O bond formation is favored kinetically over the C-O bond at the saddle point in both the concerted and stepwise mechanistic pathways for all the reactions considered.