Within mean field theories for electrons in solids, electrons and holes move independently of one another. However, in practice, electrons, holes, etc interact with one another and with collective excitations (plasmons, phonons). Manybody perturbation theory (MBPT) provides a means of incorporating these interaction effects and introduces new quantities such as the selfenergy, S(q,w), and various propagators. We have developed a code, 'EXCITON', for calculating electron and hole selfenergies and exciton binding energies in a Gaussian orbital basis. The main developers are Svjetlana GalamicMulaomerovic, Conor Hogan and Charles Patterson. EXCITON is linked to the CRYSTAL code and uses wave functions from CRYSTAL to perform the manybody calculations.

The code has been used to calculate the band structure of rare gas solids (Ne and Ar) and the excitonic optical absorption spectrum of Ne and Ar to a high degree of accuracy. The figure on the left shows the experimental optical absorption spectrum of solid Ar (green dots) and the result of a BetheSalpeter equation calculation on solid Ar using (S. GalamicMulaomerovic, PhD thesis 2004).

The B3LYP hybrid density functional is known to predict band gaps of oxides quite well. For example, we find a band gap of 3.4 eV for ZnO with B3LYP compared to an experimental value of 3.5 eV. What distinguishes hybrid functionals such as B3LYP from pure density functionals is that they contain a proportion of HartreeFock exchange; 20% in the case of B3LYP. From the GW approximation it is known that this exchange is screened to a large extent (of order of the inverse, electronic part of the static dielectric constant). The success of the B3LYP hybrid functional compared with experiment or GW may be because it imitates the screened exchange in GW, albeit without any energy or wave vector dependence. The panel on the right compares B3LYP and GW band structure calculations for the minority spins in NiO in a ferromagnetic spin state using EXCITON. Solid lines GW, dotted lines B3LYP.


