Small endohedral metallofullerenes: exploration of the structure and growth mechanism in the Ti@C2 n (2 n = 26-50) family

Abstract

The formation of the smallest fullerene, C₂₈, was recently reported using gas phase experiments combined with high-resolution FT-ICR mass spectrometry. An internally located group IV metal stabilizes the highly strained non-IPR C₂₈ cage by charge transfer (IPR = isolated pentagon rule). Ti@C₄₄ also appeared as a prominent peak in the mass spectra, and U@C₂₈ was demonstrated to form by a bottom-up growth mechanism. We report here a computational analysis using standard DFT calculations and Car-Parrinello MD simulations for the family of the titled compounds, aiming to identify the optimal cage for each endohedral fullerene and to unravel key aspects of the intriguing growth mechanisms of fullerenes. We show that all the optimal isomers from C₂₆ to C₅₀ are linked by a simple C₂ insertion, with the exception of a few carbon cages that require an additional C₂ rearrangement. The ingestion of a C₂ unit is always an exergonic/exothermic process that can occur through a rather simple mechanism, with the most energetically demanding step corresponding to the closure of the carbon cage. The large formation abundance observed in mass spectra for Ti@C₂₈ and Ti@C₄₄ can be explained by the special electronic properties of these cages and their higher relative stabilities with respect to C₂ reactivity. We further verify that extrusion of C atoms from an already closed fullerene is much more energetically demanding than forming the fullerene by a bottom-up mechanism. Independent of the formation mechanism, the present investigations strongly support that, among all the possible isomers, the most stable, smaller non-IPR carbon cages are formed, a conclusion that is also valid for medium and large cages.

Fig. 1. Molecular orbital diagrams for T _d(2)–C₂₈, C ₂(5)–C₃₄ and D ₂(89)–C₄₄. The four electrons formally transfer from the Ti atom to the carbon cage.

Fig. 2. Ball and stick representations showing the displacement of the Ti atom from the centre of the cage for (a) Ti@T _d(2)–C₂₈, (b) Ti@C _2v(3)–C₃₀, (c) Ti@D ₃(6)–C₃₂, and (d) Ti@C ₂(5)–C₃₄. The Ti atom is represented as an orange sphere, the carbon cages as grey sticks and the centre of each cage as a small blue point. The [5,5,5] junctions nearest to the Ti atom are highlighted in blue.

Fig. 3. Ball and stick representations for the lowest-energy Ti@C_2n (2n = 36–50): (a) D _2d(14)–C₃₆, (b) C ₂(10)–C₃₈, (c) C _s(24)–C₄₀, (d) C ₁(33)–C₄₂, (e) D ₂(89)–C₄₄, (f) C ₂(116)–C₄₆, (g) C _s(197)–C₄₈, and (h) C _s(266)–C₅₀. Same colour codes as in Fig. 2.

Fig. 4. Variation of the distance between the center of the cage and the titanium atom (in Å) along 14 ps Car–Parrinello MD trajectories for Ti@T _d–C₂₈(2), Ti@D ₃–C₃₂(6), Ti@D ₂–C₄₄(89) and Ti@C ₁–C₄₈(196).

Fig. 5. Representation of the molar fraction (x _i) for the competitive isomers of the C₃₆, C₄₀, C₄₂, C₄₆ and C₄₈ families using the RRHO approximation.

Fig. 6. Schlegel representations of D _3h–C₂₆(1) and T _d–C₂₈(2) showing that the latter can be obtained from the former by ingestion of a C₂ unit (red) as proposed originally by Endo and Kroto. Insertion does not take place in a single step, but through several intermediates (see text and Fig. 7).

Fig. 7. Gibbs free energy profile at 1000 K (in kcal mol^–1) for the formation of Ti@C₂₈ from Ti@C₂₆ and C₂ ingestion.

Fig. 8. Free energy profiles at 1000 K (in kcal mol^–1) for the formation of Ti@C₂₈ from Ti@C₂₆. The profiles for the C₂ and the two successive C atom insertion mechanisms are represented with blue and grey lines, respectively.

Fig. 9. Schlegel diagrams connecting the most abundant isomers of each Ti@C_2n family. The hexagons where C₂ inserts are highlighted in yellow, the formed C–C bonds are in red and the bonds that rearrange (Stone–Wales) are in green. Most of the lowest-energy isomers are linked through a C₂ insertion and only a few of them are related by Stone–Wales transformations (cages C₃₆ and C₄₂). Minimization of pentagon adjacencies is not the sole criterion for EMF growth because for larger carbon cages the stabilization due to charge transfer can reverse the relative stabilities seen in neutral fullerenes.

Fig. 10. Energy per atom (in eV) for the lowest-energy C_2n ^4– isomers (2n = 26–50), black dots; and their fit to an exponential function, blue line. The energies for the T _d–C₂₈(2) and D ₂–C₄₄(89) tetraanions are shown as red dots. The insets show the extra stability of these two isomers.

Fig. 11. Collision kinetic energies involved in (i) the closure of I2 Ti@C₂₈ (right); and (ii) the shrinkage of Ti@C₃₀ by successive removal of two C atoms (left). Closure of the endohedral metallofullerene requires kinetic energies above 13 eV, whereas the extrusion of single C atoms from the cage was always found to take place at much higher kinetic energies. These results correspond to simulations using initial structures optimized at 0 K. When initial distorted structures from MD at 2000 K were used, the kinetic energies needed to observe successful events were smaller (see the text).