Molecular structure of the fullerene C₇₀ at 825°C: quantum-chemical molecular dynamics simulations

Molecular dynamics simulations on semi-empirical AM1 and PM3 potential energy surfaces have been performed for C₇₀ at the temperature of a recent electron diffraction experiment (825°C). Compared with the equilibrium structure, the average CC bond lengths are increased uniformly by ca. 0.01 Å at 825°C. Due to the lack of specific temperature effects, the simulations do not support the interpretation of the electron diffraction data in terms of exceptionally long equatorial bonds. Recently [1], the structure of the free C₇₀ molecule was derived from gas-phase electron diffraction (GED) experiments carried out at 810–835°C. The radial distribution curve calculated from the scattered intensity could be fit equally well by six different models (D_5h symmetry, 12 independent geometrical parameters). A best model was chosen by considering the relative energies of these structures (from density functional theory, DFT) and by comparing the theoretical ab initio ¹³C NMR chemical shifts with those from experiment. The selected model [1]is in good agreement with solid-state structures determined by neutron diffraction (C₇₀) [2]and X-ray diffraction (adduct C₇₀S₄₈) [3], except that the equatorial bond is about 0.06 Å longer. Table 1 lists the experimentally derived bond lengths 1, 2 and 3(without the less accurate values from solid-state electron diffraction [4]; see also Fig. 1). Many theoretical geometries of C₇₀ are available [5]. As representative examples, Table 1 includes optimized bond lengths from ab initio Hartree–Fock (RHF/dzp) [6], density functional (BP86/TZP) [7], and semi-empirical (AM1, PM3) calculations. The theoretical bond lengths reproduce the values from neutron [2]and X-ray [3]diffraction very well and often lie within the quoted experimental uncertainties. Relative to the neutron diffraction data [2], the mean absolute deviations are 0.010 Å for RHF/dzp and BP86/TZP, 0.009 Å for AM1, and 0.007 Å for PM3. In fact, all theoretical and experimental values in Table 1 show a striking internal consistency, with the sole exception of the equatorial bond which is exceptionally long in the high-temperature GED structure (see above). This has tentatively been ascribed [1]to the possibility that there may be “large-amplitude vibrational motions, such as combinations of boat–chair bends of the equatorial hexagons”, which at high temperature “might lead to substantial lengthening of the equatorial bonds without having much effect on the others”. This hypothesis can be checked theoretically by performing molecular dynamics (MD) simulations at the temperature of the experiment. Previous MD studies of C₇₀ have employed the nonempirical Car–Parrinello scheme (using the local density approximation of DFT) [8]as well as empirical tight-binding potential models 9 and 10. The former [8]extracted vibrational frequencies and zero-point motion effects from short MD runs (