# Imaginary-time time-dependent density functional theory and its application for robust convergence of electronic states

## TL;DR

This paper introduces an imaginary-time evolution method within density functional theory to achieve more reliable and robust convergence to electronic ground states, especially in challenging systems where traditional SCF methods struggle.

## Contribution

The paper presents a novel imaginary-time TDDFT approach that guarantees convergence to the ground state regardless of the exchange-correlation functional used, improving robustness over conventional methods.

## Key findings

- Successfully applied to systems with convergence issues
- Maintains self-consistency throughout the process
- Theoretically justified via the van Leeuwen theorem

## Abstract

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.