TIGHT-BINDING STUDY OF THE LATTICE-DYNAMICS OF GRAPHITE

The vibrational spectrum of a two-dimensional (2D) sheet of graphite is examined using a tight-binding total-energy formalism. Motivation for this work is provided by the poor transferability of classical valence-force models for sp2 carbon. A major problem with such models is the neglect of pi-electron polarizability. The full tight-binding formalism considered here includes both this effect and covalent sigma-bonding on the same footing. Atomic force constants of arbitrary range are calculated quantum mechanically using a Green's-function approach. Long-range interactions, resulting from delocalized pi-bonding, are shown to be important for in-plane vibrations. The restoring forces for out-of-plane vibrations are dominated by sigma-pi mixing. The resulting phonon spectrum for 2D graphite is accurate only to within 30%. This is considerably worse than previous tight-binding results for sp3 solids. Some possible reasons for this are discussed. The difficulties encountered here may well impede our ability to understand the vibrational properties of more complicated pi-bonded solids, particularly amorphous carbons and fullerenes.