Finding Stationary States in Density Functional Theory Using Imaginary Time Propagation

Density functional theory (DFT) is widely successful for determining electronic and structural properties of materials and molecules. In order to perform a DFT calculation, the Kohn-Sham nonlinear equations must be solved self-consistently, which often proves to be a frustrating task. Conventionally, the KS equations are solved iteratively using the self-consistent field (SCF) approach whose effectiveness is increased by introducing density mixing schemes. However, for some metallic and large systems, convergence is still difficult, and some guesswork is required to choose mixing parameters that coax the system towards the ground state. We found that propagating the electronic system in imaginary time using the time-dependent DFT framework can be useful in these problematic systems, owing to the continuous change in density which follows a trajectory with monotonically decreasing energy. Furthermore, the “charge sloshing” phenomenon often responsible for SCF non-convergence does not occur in imaginary time propagation. We present a few sample systems where this method outperforms standard SCF procedures.