Macroscopic dielectric function within time-dependent density functional theory—Real time evolution versus the Casida approach

Abstract

Linear optical properties can be calculated by solving the time-dependent density functional theory equations. Linearization of the equation of motion around the ground state orbitals results in the so-called Casida equation, which is formally very similar to the Bethe-Salpeter equation. Alternatively one can determine the spectral functions by applying an infinitely short electric field in time and then following the evolution of the electron orbitals and the evolution of the dipole moments. The long wavelength response function is then given by the Fourier transformation of the evolution of the dipole moments in time. In this work, we compare the results and performance of these two approaches for the projector augmented wave method. To allow for large time steps and still rely on a simple difference scheme to solve the differential equation, we correct for the errors in the frequency domain, using a simple analytic equation. In general, we find that both approaches yield virtually indistinguishable results. For standard density functionals, the time evolution approach is, with respect to the computational performance, clearly superior compared to the solution of the Casida equation. However, for functionals including nonlocal exchange, the direct solution of the Casida equation is usually much more efficient, even though it scales less beneficial with the system size. We relate this to the large computational prefactors in evaluating the nonlocal exchange, which renders the time evolution algorithm fairly inefficient.

Kohn–Sham Decomposition in Real-Time Time-Dependent Density-Functional Theory: An Efficient Tool for Analyzing Plasmonic Excitations

“…75,77 The calculations are commonly performed by diagonalizing the Casida matrix directly or by solving the equivalent problem with different iterative subspace algorithms. [78][79][80][81] The real-time-propagation formulation of TDDFT (RT-TDDFT) 82,83 is a computationally efficient alternative to frequency-space approaches with favorable scaling with respect to system size, 84 and has the additional advantage of being also applicable to the non-linear regime. However, RT-TDDFT results are often limited to absorption spectra or to analyses of transition densities, apart from a few exceptions focusing on characterizing plasmonic [45][46][47]85 or other electronic excitations.…”

Impact of packing arrangement on the optical properties of C60 cluster aggregates

“…As extensively shown in the past, the former is particularly capable of dealing with bigger systems. 30…”

Plasmonic properties of nanohybrids made of metallic nanoring and benzene molecules

“…Nevertheless, recent quantum calculations using time dependent density functional theory (TDDFT) [33][34][35][36] reveals a different scenario when the metal NP size shrinks to the nanometer or subnanometer length scales [37][38][39][40][41]. TDDFT is implemented in both the frequency domain (lr-TDDFT: [42][43][44][45][46][47][48] in terms of the Casida matrix expressed in the Kohn-Sham electron-hole space) and time domain (rt-TDDFT: [49][50][51][52][53] based on the time evolution of the occupied Kohn-Sham orbitals). It is reported that rt-TDDFT is more computationally efficient technique than lr-TDDFT due to the favorable scaling with respect to system size [54][55][56][57][58][59][60].…”