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

TL;DR

This paper extends imaginary-time TDDFT to periodic systems, demonstrating its effectiveness as an alternative to SCF methods for obtaining ground states in DFT calculations, with successful implementation in Quantum ESPRESSO.

Contribution

It implements and validates imaginary-time TDDFT for periodic systems within Quantum ESPRESSO, showing convergence to the SCF ground state and improved convergence strategies.

Findings

It-TDDFT converges to the SCF ground state in periodic systems.

Implementation is correct for DFT+U non-collinear and ultra-soft pseudo potentials.

Adaptive imaginary-time steps enhance convergence speed.

Abstract

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 for {\it periodic systems} by modifying the Quantum ESPRESSO package, which uses a plane-wave basis with multiple $\boldsymbol{k}$ points, 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 multiple $\boldsymbol{k}$ points 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 to reach the Kohn-Sham ground state. In addition, we demonstrate that rapid convergence can be achieved if we use adaptive-size imaginary-time-steps for different kinetic-energy plane-waves.