Ab initio calculations of optical absorption spectra: Solution of the Bethe-Salpeter equation within density matrix perturbation theory

We present an approach to compute optical absorption spectra from first principles, which is suitable for the study of large systems and gives access to spectra within a wide energy range. In this approach, the quantum Liouville equation is solved iteratively within first order perturbation theory, with a Hamiltonian containing a static self-energy operator [1]. This is equivalent to solving the Bethe-Salpeter equation. Explicit calculations of single particle excited states and inversion of dielectric matrices are avoided using techniques based on Density Functional Perturbation Theory [1,2]. The calculation and inclusion of GW quasi-particle corrections within this framework are discussed. The efficiency and accuracy of our approach are demonstrated by computing optical spectra of solids, nanostructures and dipeptide molecules exhibiting charge transfer excitations. \\[4pt] [1] D.Rocca, D.Lu and G.Galli, J. Chem. Phys. 133, 164109 (2010). \\[0pt] [2] H. Wilson, F. Gygi and G. Galli, Phys. Rev. B , 78, 113303, (2008).