Relativistic real-time time-dependent density functional theory for molecular properties

We present the development and applications of relativistic real-time time-dependent density functional theory. The method is based on the four-component Dirac–Coulomb Hamiltonian in the basis of restricted kinetically balanced Gaussian functions exploiting the noncollinear Kramers unrestricted formalism. A quasirelativistic two-component X2C Hamiltonian obtained from the original four-component Hamiltonian by an algebraic decoupling transformation is also considered. The equation of motion is formulated for the one-electron density matrix and solved in a series of discrete time steps utilizing the second order Magnus propagator corrected by a self-consistent extrapolation-interpolation procedure. Induced dipole moments recorded during simulations are transformed to the frequency domain to yield molecular spectra. Presented methodology includes scalar and spin-orbit relativistic effects variationally. It is demonstrated for valence and core electron molecular spectroscopies such as electron absorption and circular dichroism.