Time-dependent Orbital-free Density Functional Theory: Background and Pauli kernel approximations

TL;DR

This paper develops a time-dependent orbital-free DFT method by deriving a frequency-dependent Pauli kernel, enabling more efficient and potentially more accurate simulations of large-scale quantum systems out of equilibrium.

Contribution

It formalizes time-dependent orbital-free DFT using a bosonic mapping and derives an approximate nonlocal Pauli kernel based on the uniform electron gas model.

Findings

The proposed kernel shows promising performance in pilot calculations.

Nonlocality is essential for accurate Pauli kernel modeling.

Second order expansion captures key nonlocal features.

Abstract

Time-dependent orbital-free DFT is an efficient method for calculating the dynamic properties of large scale quantum systems due to the low computational cost compared to standard time-dependent DFT. We formalize this method by mapping the real system of interacting fermions onto a fictitious system of non-interacting bosons. The dynamic Pauli potential and associated kernel emerge as key ingredients of time-tependent orbital-free DFT. Using the uniform electron gas as a model system, we derive an approximate frequency-dependent Pauli kernel. Pilot calculations suggest that space nonlocality is a key feature for this kernel. Nonlocal terms arise already in the second order expansion with respect to unitless frequency and reciprocal space variable ($\frac{\omega}{q\, k_F}$ and $\frac{q}{2\, k_F}$, respectively). Given the encouraging performance of the proposed kernel, we expect it will lead to more accurate orbital-free DFT simulations of nanoscale systems out of equilibrium. Additionally, the proposed path to formulate nonadiabatic Pauli kernels presents several avenues for further improvements which can be exploited in future works to improve the results.