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Linear scaling time-dependent density-functional tight-binding method for absorption spectra of large systems

机译：大型系统吸收光谱的线性尺度随时间变化的密度泛函紧结合方法

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摘要

A time-dependent density-functional tight-binding method in real time domain is developed to calculate the absorption spectra of very large systems. The time-dependent first-order response of the density matrix due to an external perturbation is solved using Chebyshev method with high efficiency and accuracy. Linear scaling of CPU time and memory usage with the system size is achieved by exploring the sparsity of the involving matrices as well as by introduction of a cutoff for the first-order density matrix. The compressed sparse row scheme is used to store the matrices, and sparsekit is employed for sparse matrix multiplication. The absorption spectra of three-dimensional water clusters (H_2O)_(216), (H_2O)_(432), (H_2O)_(648), and (H_2O)_(864) are calculated using the present approach. The error due to the cutoff of density matrix is negligible. It is shown from these calculations that the presented method is very efficient and capable of calculating the absorption spectra for very large three-dimensional systems.
机译：建立了实时域中随时间变化的密度泛函紧密结合方法，以计算非常大系统的吸收光谱。使用Chebyshev方法可以高效且准确地解决由于外部扰动引起的密度矩阵随时间变化的一阶响应。通过探索相关矩阵的稀疏性以及引入一阶密度矩阵的截止值，可以实现CPU时间和内存使用量随系统大小的线性缩放。压缩的稀疏行方案用于存储矩阵，而sparsekit用于稀疏矩阵乘法。使用本方法计算三维水团簇（H_2O）_（216），（H_2O）_（432），（H_2O）_（648）和（H_2O）_（864）的吸收光谱。由密度矩阵的截止引起的误差可以忽略不计。从这些计算表明，所提出的方法非常有效并且能够计算非常大的三维系统的吸收光谱。

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