Atomic structure and phonons in the π-bonded chain of the clean diamond (111) surface

Abstract

Detailed atomic structure and phonon frequencies for the clean diamond (111) surface are studied based on the density-functional theory within the generalized-gradient approximation (GGA) as well as the local-density approximation (LDA). The \ensuremath{\pi}-bonded chain structure with a $2\ifmmode\times\else\texttimes\fi{}1$ unit cell is found to be the most stable, while the recently proposed \ensuremath{\pi}-bonded trimer structure with a $2\ifmmode\times\else\texttimes\fi{}2$ unit cell is found to be highly unstable. Both the LDA and GGA calculations indicate that the \ensuremath{\pi}-bonded chain is undimerized and unbuckled, i.e., the Peierls transition does not occur. Yet considerable softening of the \ensuremath{\pi}-bond stretching mode at the \ensuremath{\Gamma} point is found instead of the Peierls transition. Detection of this softening is expected to be a clear evidence of the \ensuremath{\pi}-bonded chain structure without both buckling and dimerization.