Using a first-principles method based on density functional theory, we have carried out a study of static properties and vibration frequencies at the $\Gamma$ point of cubic and hexagonal diamonds. The bulk modulus and bond length are found to be slightly larger in hexagonal diamond than in cubic diamond. At the $\Gamma$ point, there are five Raman active modes with three different frequencies but no IR active mode of hexagonal diamond is found. The Raman active modes of hexagonal diamond contain one nondegenerate mode $A_{1g}$ and two doubly degenerate modes $E_{1g}$ and $E_{2g}.$ The calculated frequency of the triply degenerate Raman active mode (1334 ${\mathrm{cm}}^{-1})$ of cubic diamond agrees very well with the experimental value (1333 ${\mathrm{cm}}^{-1})$.

• Received 10 November 1997

DOI:https://doi.org/10.1103/PhysRevB.57.13355