We have investigated polyyne and cumulene prototypes based on the density-functional theory. Our independent-particle spectra show that the various carbynes can be distinguished by optical properties comparing the low-energy spectral structure as wel
l as using very general considerations. The latter conclusion is supported by results based on the random-phase approximation including local-field effects.
The calculation of self-energy corrections to the electron bands of a metal requires the evaluation of the intraband contribution to the polarizability in the small-q limit. When neglected, as in standard GW codes for semiconductors and insulators, a
spurious gap opens at the Fermi energy. Systematic methods to include intraband contributions to the polarizability exist, but require a computationally intensive Fermi-surface integration. We propose a numerically cheap and stable method, based on a fit of the power expansion of the polarizability in the small-q region. We test it on the homogeneous electron gas and on real metals such as sodium and aluminum.
