Extended random phase approximation method for atomic excitation energies from correlated and variationally optimized second-order density matrices

► We consider the problem of computing molecular excitation spectra from ground state density matrices. ► A generalized RPA method extracts excitation energies from a correlated ground state second order density matrix. ► We apply this method to exact and variationally optimized second order density matrices. ► The inclusion of correlation gives better excitation energies than the RPA, which uses uncorrelated ground states. ► Ensemble density matrices lead to poor and qualitatively incorrect spectra.