Maximum entropy method for time-series data obtained from real-time evolution of time dependent density functional theory

The maximum entropy method is one of the key techniques for spectral analysis. The main feature is to describe spectra in low frequency with short time-series data. We adopted the maximum entropy method to analyze the spectrum from the dipole moment obtained by the time-dependent density functional theory calculation in real time, which is intensively studied and applied to computing optical properties. In the maximum entropy method analysis, we proposed that we use the concatenated data set made from several-times repeated raw data together with the phase. We have applied this technique to spectral analysis of the dynamic dipole moment obtained from time-dependent density functional theory dipole moment of several molecules such as oligo-fluorene with $n = 8$. As a result, the higher resolution can be obtained without any peak shift due to the phase jump. The peak position is in good agreement to that of FT with just raw data. This paper presents the efficiency and characteristic features of this technique.