Using imaginary-time time-dependent density functional theory for robust convergence of ground states

We transform the time-dependent density functional theory equations to imaginary time and use imaginary-time evolution as a reliable alternative to the self-consistent field (SCF) procedure for determining the Kohn-Sham (KS) ground state. We discuss the technical and theoretical aspects of this approach and show that the ground state of the Kohn-Sham system should be expected to be the long-imaginary-time output of the evolution, independent of chosen functional or level of theory used to simulate the system. By maintaining self-consistency between the single-particle wavefunctions and electronic density throughout the determination of the stationary state, our method avoids some of the difficulties encountered in SCF such as charge sloshing and other unproductive occupancy rearrangements. To demonstrate dependability, we successfully apply our method to selected systems which struggle to converge when standard SCF is employed. Given its minimal required inputs and robust convergence, our method should be a useful tool in applications of density functional theory. Additionally, through the van Leeuwen theorem we affirm the physical meaningfulness of imaginary time in density functional theory, justifying the use of DFT in quantum statistical mechanics such as in computing imaginary time path integrals.