  Reliable and robust convergence to the electronic ground state within density
functional theory (DFT) Kohn-Sham (KS) calculations remains a thorny issue in
many systems of interest. In such cases, charge sloshing can delay or
completely hinder the convergence. Here, we use an approach based on
transforming the time-dependent DFT equations to imaginary time, followed by
imaginary-time evolution, as a reliable alternative to the self-consistent
field (SCF) procedure for determining the KS ground state. We discuss the
theoretical and technical aspects of this approach and show that the KS ground
state should be expected to be the long-imaginary-time output of the evolution,
independent of the exchange-correlation functional or the level of theory used
to simulate the system. By maintaining self-consistency between the
single-particle wavefunctions and the electronic density throughout the
determination of the stationary state, our method avoids the typical
difficulties encountered in SCF. To demonstrate dependability of our approach,
we apply it to selected systems which struggle to converge with SCF schemes. In
addition, through the van Leeuwen theorem, we affirm the physical
meaningfulness of imaginary time TDDFT, justifying its use in certain topics of
statistical mechanics such as in computing imaginary time path integrals.
