Classical versus ab initio structural relaxation: electronic excitations and optical properties of Ge nanocrystals embedded in a SiC matrix

We discuss and test a combined method to efficiently perform ground- and excited-state calculations for relaxed structures using both a quantum first-principles approach and a classical molecular-dynamics scheme. We apply this method to calculate the ground state, the optical properties, and the electronic excitations of Ge nanoparticles embedded in a cubic SiC matrix. Classical molecular dynamics is used to relax the large-supercell system. First-principles quantum techniques are then used to calculate the electronic structure and, in turn, the electronic excitation and optical properties. The proposed procedure is tested with data resulting from a full first-principles scheme. The agreement is quantitatively discussed between the results after the two computational paths with respect to the structure, the optical properties, and the electronic excitations. The combined method is shown to be applicable to embedded nanocrystals in large simulation cells for which the first-principle treatment of the ionic relaxation is presently out of reach, whereas the electronic, optical and excitation properties can already be obtained ab initio. The errors incurred from the relaxed structure are found to be non-negligible but controllable.