基于实时含时密度泛函理论的时间序列数据的奇异谱分析
Singular Spectrum Analysis of Time-series Data from Time-dependent density-functional theory in Real-time
AI总结：
针对实时TDDFT光谱分析中傅里叶变换时长不足导致分辨率低的问题，提出结合奇异谱分析（SSA）提取振荡分量并预测扩展短时序数据，在小分子上验证可得高精度高分辨率光谱，为分子光学性质分析提供新方法。
摘要：
本文介绍了利用奇异谱分析（Singular Spectrum Analysis，SSA）对实时含时密度泛函理论（time-dependent density functional theory，TDDFT）得到的时间序列数据进行谱分析的方法。TDDFT是通过追踪动态偶极矩的时间演化来获取分子激发态和光谱的可靠方法，但当傅里叶变换的总时长不足时，光谱分辨率会受到影响。SSA能够从时间序列数据中提取特定振荡分量，有助于生成精度更高的光谱。即使时间序列数据集相对较短，SSA的预测扩展也能得到高分辨率光谱，与传统方法得到的结果高度一致。该方法的有效性已在乙烯、苯等多种小分子上得到验证。SSA在特定能量区域进行详细谱分析的能力提升了光谱分辨率，有助于厘清这些区域内的振荡分量。实时TDDFT与SSA相结合，为分析分子光学性质提供了一种新的分析方法，显著提高了发射光谱和吸收光谱分析的准确性，预计该方法将有多种应用场景。
英文摘要：
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.
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