Looking for $$sp^2$$ carbon atoms in diamond: a quantum mechanical study of interacting vacancies

This paper reports the calculated relaxed lattice configurations and corresponding electronic and magnetic structures, and Raman frequencies of two divacancies in diamond, \(V_2\) and VC=CV, in which the vacancies are first and third neighbours, respectively. The calculations are formulated within a supercell approach to local defects in crystalline solids, here 64- and 128-atom unit cells and based largely on the B3LYP one-electron approximation constructed from an all-electron Gaussian basis set. Three important findings are first, that, of the four possible spin states, \(S_z=\) 0, 1, 2, 3, the singlet is predicted to be lowest in energy for both divacancies; second, that the singlet state of \(V_2\) is \(\sim\)1.7 eV lower in energy than that in VC=CV; and third, that the Raman peak at 1628 cm\(^{-1}\) in defective diamond can be ascribed to the presence of a C=C double bond, as in the singlet state of VC=CV.