Singular Spectrum Analysis for Time Series Data of real- time TDDFT

Abstract

Optical spectrum prediction based on first principles calculations is important for the development of optical materials. In particular, real-time Dependent Density Functional Theory (TDDFT) is one of the most widely used computational methods. The output of a real-time TDDFT calculation is the dipole moment, which is Fourier transformed (FT) and converted to polarizability. From this polarizability, an optical spectrum is obtained. However, if the time series data are not sufficient, the FT results are ambiguous. To solve this problem, we introduced Singular Spectral Analysis (SSA), which decomposes time-series data into several fundamental oscillations. Only the major components are extracted, and the essential time-series data are reproduced. During this process, high-frequency oscillations that are perceived as noise are removed. We applied this technique to ethylene TDDFT time-series data. By focusing on the fundamental vibrations that constitute the band edges, which are important for understanding their optical properties, we were able to clarify the signal. Furthermore, because the fundamental vibrations can be separated, it was found that the time series data can be extended and supplemented when the time series data is inadequate.