First-Principles Calculation of the Optical Absorption in Diamond

A nonempirical first-principles energy-band calculation for diamond has been used to calculate the optical absorption expressed as the imaginary part of the complex dielectric function ${\epsilon }_2\left(\omega \right)$ in the random-phase approximation. The use of $\overrightarrow{\mathrm{k}}$-dependent transition-probability matrix elements calculated from the Bloch linear-combination-of-atomic-orbitals wave functions is found to significantly improve agreement of the calculated ${\epsilon }_2\left(\omega \right)$ with experiment, as compared to the results obtained with averaged matrix elements. Within the statistical exchange one-electron band model Hamiltonian and the random-phase approximation to the dielectric function, we find good agreement with experiment for the magnitude and position of the main peak and general shape of ${\epsilon }_2\left(\omega \right)$ over a large energy range without any empirical adjustment of the calculation. There is structure in the low-energy region which is not reproduced by our treatment, suggesting inherent deficiencies of the band model and/or limitations of the theoretical expression for ${\epsilon }_2\left(\omega \right)$.