Imaginary-time time-dependent density functional theory for periodic systems

Imaginary-time time-dependent density functional theory (it-TDDFT) has been proposed as an alternative method for obtaining the ground state within density functional theory (DFT) which avoids some of the difficulties with convergence encountered by the self-consistent-field (SCF) iterative method. It-TDDFT was previously applied to clusters of atoms where it was demonstrated to converge in select cases where SCF had difficulty with convergence. In the present work we implement it-TDDFT propagation forperiodic systemsby modifying the Quantum ESPRESSO (QE) package, which uses a plane-wave basis with multiplepoints, and has the options of non-collinear and DFT + U calculations using ultra-soft or norm-conserving pseudo potentials. We demonstrate that our implementation of it-TDDFT propagation with multiplepoints is correct for DFT + U non-collinear calculations and for DFT + U calculations with ultra-soft pseudo potentials. Our implementation of it-TDDFT propagation converges to the exact SCF energy (up to the decimal guaranteed by double precision) in all but one case where it converged to a slightly lower value than SCF, suggesting a useful alternative for systems where SCF has difficulty reaching the Kohn-Sham (KS) ground state. In addition, we demonstrate that more rapid convergence can be achieved if we use adaptive-size imaginary-time-steps for different kinetic-energy plane-waves.