Implementation of Orbital Functionals in the Context of Time-Dependent Density-Functional Theory
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Implementation of Orbital Functionals in the Context of Time-Dependent Density-Functional Theory ´ Flavia P. de Farias Guarezi1,2 · Daniel Vieira1 Received: 18 August 2020 / Accepted: 2 September 2020 / Published online: 8 October 2020 © Sociedade Brasileira de F´ısica 2020
Abstract The computational implementation of orbital functionals has become one of the great modern challenges for densityfunctional theory (DFT). In static cases, the exact procedure of implementing orbital functionals is the so-called optimized effective potential method (OEP). In situations involving temporal variations, in the context of the time-dependent densityfunctional theory (TDDFT), TDOEP becomes the correct approach. However, both OEP and TDOEP are known by their severe computational costs, and for this reason they are used in a very restricted set of situations. Therefore, the development of approximations is important. In this work, using one-dimensional model systems, we investigate strategies for the implementation of time-dependent orbital functionals, in order to circumvent or avoid the use of TDOEP. We have found that a local scaling approximation to the TDOEP yields encouraging results aiming the numerical implementation of orbital functionals within the TDDFT context. Keywords Time-dependent density-functional theory · Orbital functionals · Optimized effective potential method · Self-interaction correction
1 Introduction Since its formulation, with the publications in 1964 and 1965, density-functional theory (DFT) [1–7] has become one of the most used tools in electronic-structure calculations, with many applications in physics and chemistry. In 1984, E. Runge and E. K. U. Gross proved [8] that the DFT formalism can be also applied to timedependent many-body quantum systems, giving rise to the time-dependent density-functional theory (TDDFT). The same as in the Kohn-Sham (KS) approach, the timedependent many-body Schr¨odinger equation (TDSE) can be replaced by an equation of non-interacting particles subjected to an effective potential vKS (r, t), which, in principle, yields the same density distribution n(r, t) that would be obtained by means of the TDSE equation, as functions of position r and time t. However, as in the Daniel Vieira
[email protected] 1
Departamento de F´ısica, Universidade do Estado de Santa Catarina, Joinville, SC, Brazil
2
Present address: Escola de Educac¸a˜ o B´asica Dr. Tufi Dippe, Joinville, SC, Brazil
static case, approximations are necessary for the effective potential, particularly for the exchange-correlation (XC) contribution—which is not exactly known. TDDFT has emerged as one of the most successful computational methods for obtaining electronic excitation spectra. As example of applications we can mention the linear response, double excitations, second ionization thresholds, optical responses, and gaps in solids, as well as electronic transport in molecules [9, 10]. Within TDDFT, and the same as with DFT, the approximations for the XC functional may explicitly de
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