Singular Spectrum Analysis of Time-series Data from Time-dependent density-functional theory in Real-time

Abstract: This paper introduces a spectral analysis of time-seires data derived from real-time time-dependent density functional theory (TDDFT) using Singular Spectrum Analysis (SSA). TDDFT is a robust method for obtaining molecular excited states and optical spectra by tracking the time evolution of dynamical dipole moments. However, the spectral resolution can be compromised when Fourier transformation's total time duration is insufficient. SSA enabled the extraction of specific oscillation components from the time-series data, facilitating the generation of higher-precision spectra. Even with relatively short time-series dataset, the predictive extension of SSA yielded high-resolution spectra, demonstrating substantial agreement with results obtained through conventional methods. The efficacy of this approach was validated for several small molecules, including ethylene, benzene, and others. SSA's ability to conduct detailed spectral anasysis in specific energy regions enhance spectral resolution and facilitates the clarification of oscillation components within these regions. Real-time TDDFT combined with SSA provides a new analytical method for analyzing the optical properties of molecules, significantly improving the accuracy of the analysis of emission and absorption spectra analysis. This method is expected to have various applications.