Efficient All-Electron Time-Dependent Density Functional Theory Calculations Using an Enriched Finite Element Basis

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 a compactly supported numerical atom-centered basis, obtained from atomic ground-state 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 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 discretizations. 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 responses by studying the absorption spectra in sodium clusters, the linear to nonlinear response transition in the green fluorescence protein chromophore, and the higher harmonic generation in the magnesium dimer. Lastly, we attain good parallel scalability of our numerical implementation of the EFE basis for up to ∼1000 processors, using a benchmark system of a 50-atom sodium nanocluster.

MISTER-T: An Open-Source Software Package for Quantum Optimal Control of Multi-Electron Systems on Arbitrary Geometries

“…Later, Kanungo et al [40] proposed an a priori mesh adaption technique by minimizing the semi-discrete and full-discrete error estimates on higher-order finite elements. More recently, a mixed basis was presented to carry out all-electron, real-time TDDFT calculations by augmenting a finite element basis with numerical atomic functions [41]. The MISTER-T code is written in the MATLAB programming environment in a class-oriented fashion to aid in its readability, reusability, and general accessibility to both users and practitioners.…”