In this paper, we propose to compute the electronic circular dichroism (ECD) spectra of chiral molecules using a real-time propagation of the time-dependent Schrodinger equation (TDSE) in the space of electronic field-free eigenstates, by coupling TDSE with a given treatment of the electronic structure of the target. The time-dependent induced magnetic moment is used to compute the ECD spectrum from an explicit electric perturbation. The full matrix representing the transition magnetic moment in the space of electronic states is generated from that among pairs of molecular orbitals. In the present work, we show the ECD spectra of methyloxirane, of several conformers of L-alanine, and of the lambda-Co(acac)(3) complex, computed from a singly excited ansatz of time-dependent density functional theory eigenstates. The time-domain ECD spectra properly reproduce the frequency-domain ones obtained in the linear-response regime and quantitatively agree with the available experimental data. Moreover, the time-domain approach to ECD allows us to naturally go beyond the ground-state rotationally averaged ECD spectrum, which is the standard outcome of the linear-response theory, e.g., by computing the ECD spectra from electronic excited states.
