Identifying Electronic Modes by Fourier Transform from δ‑Kick Time-Evolution TDDFT Calculations

• Published in: Journal of chemical theory and computation 2018-12, Vol.14 (12), p.6417-6426
• Main Authors: Sinha-Roy, Rajarshi, García-González, Pablo, López Lozano, Xóchitl, Whetten, Robert L, Weissker, Hans-Christian
• Format: Article
• Language: English
• Subjects: Chemical Sciences; Complex systems; Computational Physics; Coordination compounds; Density functional theory; Electron states; Evolution; Excitation; Feasibility studies; Fourier transforms; Mathematical analysis; Noble metals; or physical chemistry; Physics; Reliability analysis; Theoretical and; Time dependence
• ISSN: 1549-9618; 1549-9626
• DOI: 10.1021/acs.jctc.8b00750

Time-dependent density-functional theory (TDDFT) is widely used for calculating electron excitations in clusters and large molecules. For optical excitations, TDDFT is customarily applied in two distinct approaches: transition-based linear-response TDDFT (LR-TDDFT) and the real-time formalism (RT-TDDFT). The former directly provides the energies and transition densities of the excitations, but it requires the calculation of a large number of empty electron states, which makes it cumbersome for large systems. By contrast, RT-TDDFT circumvents the evaluation of empty orbitals, which is especially advantageous when dealing with large systems. A drawback of the procedure is that information about the nature of individual spectral features is not automatically obtained, although it is of course contained in the time-dependent induced density. Fourier transform of the induced density has been used in some simple cases, but the method is, surprisingly, not widely used to complement the RT-TDDFT calculations; although the reliability of RT-TDDFT spectra is now widely accepted, a critical assessment for the corresponding transition densities and a demonstration of the technical feasibility of the Fourier-transform evaluation for general cases is still lacking. In the present work, we show that the transition densities of the optically allowed excitations can be efficiently extracted from a single δ-kick time-evolution calculation even in complex systems like noble metals. We assess the results by comparison with the corresponding LR-TDDFT ones and also with the induced densities arising from RT-TDDFT simulations of the excitation process.