Efficient all-electron time-dependent density functional theory calculations using an enriched finite element basis

TL;DR

This paper introduces an efficient all-electron real-time TDDFT method using an enriched finite element basis that combines classical finite elements with atomic-centered functions, achieving significant speedups and accurate results.

Contribution

The authors develop a systematically convergent enriched finite element basis for all-electron TDDFT, incorporating atomic groundstate functions and demonstrating high efficiency and accuracy.

Findings

Achieves 50-100x speedup over classical finite element basis.

Demonstrates close to optimal convergence rates for dipole moments.

Shows good parallel scalability up to 1000 processors.

Abstract

We present an efficient and systematically convergent approach to all-electron real-time time-dependent density functional theory (TDDFT) calculations using a mixed basis, termed as enriched finite element (EFE) basis. The EFE basis augments the classical finite element basis (CFE) with compactly supported numerical atom centered basis, obtained from atomic groundstate DFT calculations. Particularly, we orthogonalize the enrichment functions with respect to the classical finite element basis to ensure good conditioning of the resultant basis. We employ the second-order Magnus propagator in conjunction with an adaptive Krylov subspace method for efficient time evolution of the Kohn-Sham orbitals. We rely on \textit{a priori} error estimates to guide our choice of an adaptive finite element mesh as well as the time-step to be used in the TDDFT calculations. We observe close to optimal rates of convergence of the dipole moment with respect to spatial and temporal discretization. Notably, we attain a $50-100\times$ speedup for the EFE basis over the CFE basis. We also demonstrate the efficacy of the EFE basis for both linear and nonlinear response by studying the absorption spectrum in sodium clusters, the linear to nonlinear response transition in green fluorescence protein chromophore, and the higher harmonic generation in magnesium dimer. Lastly, we attain good parallel scalability of our numerical implementation of the EFE basis for up to $\sim1000$ processors, using a benchmark system of 50-atom sodium nanocluster.