The moments method is used to calculate the density of states and optical-absorption spectra of large quantum systems. This method uses random wave functions to calculate 500 Chebyshev moments of the density of states (${500}^2$ for the optical-absorption spectra), and transforms these moments back to energy space. The results compare well with direct calculations on a large, 2048 Si-atom bulklike supercell system. To demonstrate its utility, the spectra of a realistic quantum dot with 1035 Si and 452 H atoms are calculated using an empirical pseudopotential Hamiltonian and a plane-wave basis of wave functions.

• Received 27 December 1993

DOI:https://doi.org/10.1103/PhysRevB.49.10154