Propagation of maximally localized Wannier functions in real-time TDDFT*

Real-time, time-dependent density functional theory (RT-TDDFT) has attracted much attention in recent years as an approach to study a variety of excited state phenomena ranging from optical excitations to electronic stopping. Many applications of RT-TDDFT involve the inclusion of a time-dependent applied electric field to perturb the system. In the length gauge representation, one can apply a scalar electric field to localized orbitals, such as maximally localized Wannier functions (MLWFs). We have implemented a method in the QB@LL plane-wave pseudopotential RT-TDDFT code to transform the time-dependent Kohn-Sham (TDKS) states into MLWFs, allowing for simulations with time-dependent electric fields and for the calculation of absorption spectra and nonlinear optical responses for both isolated and periodic systems. The propagation of MLWFs in RT-TDDFT gives access to dynamic polarization and quantities such as the MLWF spread, allowing for detailed analysis of a wide range of excitation phenomena.