Understanding the Exohedral Functionalization of Endohedral Metallofullerenes

Abstract

The endohedral metallofullerenes (EMFs) and their exohedral functionalized derivatives present an increasing attention due to their potential applications in materials science and medicine. However, the current understanding of the reactivity of endohedral metallofullerenes is still very incomplete. In this chapter, we present a thorough study of the Diels-Alder (DA) reactivity of D _3h -C ₇₈ , Sc₃N@D _3h -C ₇₈ , Y₃N@D _3h -C ₇₈ , Ti₂C₂@D _3h -C _78, Sc₃N@D _5h -C ₈₀ , Lu₃N@D _5h -C ₈₀ , Gd₃N@D _5h -C ₈₀ , Sc₃N@I _h -C ₈₀ , Lu₃N@I _h -C ₈₀ -C₈₀, Gd₃N@I _h -C ₈₀ , Y₃N@I _h -C ₈₀ , La₂@I _h -C ₈₀ , Y₃@I _h -C ₈₀ , Sc₃C₂@I _h -C ₈₀ , Sc₄C₂@I _h -C ₈₀ , Sc₃CH@I _h -C ₈₀ , Sc₃NC@I _h -C ₈₀ , Sc₄O₂@I _h -C ₈₀ , Sc₄O₃@I _h -C ₈₀ , and La@C _2v -C _82. We have studied both the thermodynamic and the kinetic regioselectivity , taking into account when it was required the free rotation of the metallic cluster inside the fullerene. This systematic investigation was possible only because we use the Frozen Cage Model , which is a low-cost approach to determine the EMF exohedral regioselectivity. Our study has allowed the correction of two wrong experimental assignations of DA adducts, highlighting the key role of computational studies to achieve a deep understanding of exohedral reactivity of the EMFs. The incarceration of the metallic cluster reduces the reactivity of the EMFs respect to the hollow fullerenes. Our results also show that bond distances, pyramidalization angles , LUMOs shape, charge transfer , and cluster volume are the key factors that determine the DA regioselectivity of the fullerenes and EMFs. However, none of them can be used alone to predict which bond will be attacked. Finally, we focus our attention on the essential role of the dispersion interactions to reproduce the experimental results of the exohedral cycloaddition on EMFs.

Appendix: Computational Details

All Density Functional Theory (DFT ) calculations were performed with the Amsterdam Density Functional (ADF) program (Baerends et al. 2010). The molecular orbitals (MOs) were expanded in an uncontracted set of Slater type orbitals (STOs) of double-ζ (DZP) and triple-ζ (TZP) quality containing diffuse functions and one set of polarization functions. In order to reduce the computational time needed to carry out the calculations, the frozen core approximation has been used (te Velde et al. 2001). In this approximation, the core density is obtained and included explicitly, albeit with core orbitals that are kept frozen during the SCF procedure. It was shown that the frozen core approximation has a negligible effect on the optimized equilibrium geometries (Swart and Snijders 2003). Scalar relativistic corrections have been included self-consistently using the Zeroth Order Regular Approximation (ZORA) (van Lenthe et al. 1993). An auxiliary set of s, p, d, f, and g STOs was used to fit the molecular density and to represent the Coulomb and exchange potentials accurately for each SCF cycle (Baerends et al. 1973). Energies and gradients were calculated using the local density approximation (Slater exchange) with non-local corrections for exchange (Becke88) (Becke 1988) and correlation (Lee-Yang-Parr) (Lee et al. 1988) included self-consistently (i.e. the BLYP functional). In some cases, energies and gradients were calculated using the local density approximation (Slater exchange and VWN correlation) (Vosko et al. 1980) with non-local corrections for exchange (Becke 1988) and correlation (Perdew 1986) included self-consistently (i.e. the BP86 functional). Also in some studies, we performed single point energy calculations at the B3LYP-D₂/TZP level of theory (Becke 1993; Lee et al. 1988; Stephens et al. 1994) (i.e., B3LYP-D₂/TZP//BLYP-D₂/DZP). Open-shell systems were treated with the unrestricted formalism.

Moreover, energy dispersion corrections were introduced using Grimme’s methodology (Grimme 2006; Grimme et al. 2010) (D₂/D₃) implemented in ADF 2010.01 version (Baerends et al. 2010). All the structures were fully optimized using these corrections in each optimization step. It was shown that dispersion corrections are essential for a correct description of the thermodynamics and kinetics of fullerene and nanotube reactions (Osuna et al. 2010; Garcia-Borràs et al. 2012a).

The actual geometry optimizations and transition state (TS) searches were performed with the QUILD (Swart and Bickelhaupt 2008) (QUantum-regions Interconnected by Local Descriptions) program, which functions as a wrapper around the ADF program. The QUILD program constructs all input files for ADF, runs ADF, and collects all data; ADF is used only for the generation of the energy and gradients. Furthermore, the QUILD program uses improved geometry optimization techniques, such as adapted delocalized coordinates (Swart and Bickelhaupt 2006) and specially constructed model Hessians with the appropriate number of eigenvalues (Swart and Bickelhaupt 2006). The latter is particularly useful for TS searches. All TSs were characterized by computing the analytical (Wolff 2005) vibrational frequencies, to have one and only one imaginary frequency corresponding to the approach of the reacting carbons. In selected DA attacks, analytical Hessians were computed for all stationary points along the reaction coordinate to calculate unscaled zero-point energies (ZPEs) as well as thermal corrections and entropy effects using the standard statistical-mechanics relationships for an ideal gas (Atkins and De Paula 2006). These two latter terms were computed at 298.15 K and 1 atm to provide the reported relative Gibbs energies (ΔG₂₉₈). Pyramidalization angles , introduced by Haddon (Haddon 2001; Haddon and Chow 1998) as a measure of the local curvature in polycyclic aromatic hydrocarbons, were calculated using the POAV3 program (Haddon 1988).

In the case of the first study including dispersion corrections, full geometry optimizations were carried out with the hybrid B3LYP (Becke 1993; Lee et al. 1988; Stephens et al. 1994) density functional with the standard 6-31G(d) basis set (Hehre et al. 1972; Hariharan and Pople 1973). The two-layered ONIOM approach (ONIOM2) (Svensson et al. 1996; Dapprich et al. 1999; Vreven et al. 2006) were employed to perform geometry optimizations using a combination of the SVWN method (Slater 1974; Vosko et al. 1980) together with the standard STO-3G basis set (Hehre et al. 1969) for the low level calculations and the B3LYP methods with the standard 6-31G(d) basis set (Hehre et al. 1972; Hariharan and Pople 1973) for the high level part. In both cases, we performed the study including dispersion corrections following the Grimme’s approach (B3LYP-D and ONIOM2-D) (Grimme 2004, 2006; Grimme et al. 2010). In selected cases, we carried out calculations with the M06-2X functional (Zhao and Truhlar 2008). Frequency calculations indicated that we obtained the correct stationary points, characterized by the number of imaginary eigenvalues of their analytic Hessian matrix. Solvent effects were estimated in some particular cases with single point calculations on the gas phase optimized structures using the polarizable continuous solvation model (PCM) and considering toluene as the solvent (Tomasi and Persico 1994). All calculations including Grimme’s dispersion corrections (Grimme 2004, 2006) were performed using a locally modified version of the Gaussian 09 (revision A.02) program (“IOP(3/124 = 3)” for including the dispersion correction; the S₆ value for B3LYP was set to 1.05). Apart from that, we adapted the program to allow the inclusion of dispersion effects within the ONIOM approach (the S₆ value is set to 1.05 for the high level B3LYP-D and 1.0 for the low level SVWN-D).