First-principles determination of the structural, vibrational and thermodynamic properties of diamond, graphite, and derivatives

The structural, dynamical, and thermodynamic properties of diamond, graphite and layered derivatives (graphene, rhombohedral graphite) are computed using a combination of density-functional theory total-energy calculations and density-functional perturbation theory lattice dynamics in the generalized gradient approximation. Overall, very good agreement is found for the structural properties and phonon dispersions, with the exception of the $c∕a$ ratio in graphite and the associated elastic constants and phonon dispersions. Both the ${C}_{33}$ elastic constant and the $\ensuremath{\Gamma}$ to $A$ phonon dispersions are brought to close agreement with available data once the experimental $c∕a$ is chosen for the…