Critical Assessment of Time-Dependent Density Functional Theory for Excited States of Open-Shell Systems: II. Doublet-Quartet Transitions
Critical Assessment of Time-Dependent Density Functional Theory for Excited States of Open-Shell Systems: II. Doublet-Quartet Transitions
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DOI：
10.1021/acs.jctc.5b01219
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发表时间：
2016-06-01
影响因子：
5.5
通讯作者：
Liu, Wenjian
中科院分区：
文献类型：
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作者：
Li, Zhendong;Liu, Wenjian
与闭壳系统相比，开壳系统对电子激发态的含时密度泛函理论(TD-DFT)提出了三个额外的挑战：(A)自旋污染问题是一个严重的问题；(B)交换关联(XC)核可能在数值上是不稳定的；(C)开壳基态的单行列式描述很容易变得能量不稳定。如果采用非共线的XC核，自旋翻转TD-DFT(SF-TD-DFT)形式可以在很大程度上避免自旋污染问题。至于与这种核有关的数值不稳定性，到目前为止只提出了一种特别的方案，即ALDA0核，它相当于将发散分量(由密度梯度和动能密度引起)简单地设置为零。将Tamm-Dancoff近似(TDA)引入到TD-DFT中，可以有效地避免基态不稳定性问题。因此，到目前为止，SF-TDA/ALDA0 Anatz是TD-DFT框架内唯一有希望用于开壳系统翻转单激发的方法。为了系统地评估SF-TDA/ALDA0的性能，在11个小自由基的基准集合中，总共61个低位四重态激发态[J.理论计算。2016，12,238]用各种XC泛函进行了研究。结果表明，SF-TDA/ALDA0与SAOP(模型轨道势的统计平均)、全局杂化和距离分离杂化泛函的平均绝对误差在0.20.4 eV以内。这不仅符合TD-DFT对闭壳系统单态和三重态激发态的典型精度，也符合自旋自适应TD-DFT对开壳体系自旋守恒激发态的总体精度。
Compared with closed-shell systems, open-shell systems place three additional challenges to time-dependent density functional theory (TD-DFT) for electronically excited states: (a) the spin-contamination problem is a serious issue; (b) the exchange-correlation (XC) kernel may be numerically instable; and (c) the single-determinant description of open-shell ground states readily becomes energetically instable. Confined to flip-up single excitations, the spin-contamination problem can largely be avoided by using the spin-flip TD-DFT (SF-TD-DFT) formalism, provided that a noncollinear XC kernel is employed. As for the numerical instabilities associated with such a kernel, only an ad hoc scheme has been proposed so far, viz., the ALDA0 kernel, which amounts to setting the divergent components (arising from density gradients and kinetic energy density) simply to zero. The ground-state instability problem can effectively be avoided by introducing the Tamm-Dancoff approximation (TDA) to TD-DFT. Therefore, on a general basis, the SF-TDA/ALDA0 Ansatz is so far the only promising means within the TD-DFT framework for flip-up single excitations of open-shell systems. To assess systematically the performance of SF-TDA/ALDA0, in total 61 low-lying quartet excited states of the benchmark set of 11 small radicals [J. Chem. Theory Comput. 2016, 12, 238] are investigated with various XC functionals. Taking the MRCISD+Q (multireference configuration interaction with singles and doubles plus the Davidson correction) results as benchmark, it is found that the mean absolute errors of SF-TDA/ALDA0 with the SAOP (statistical averaging of model orbital potentials), global hybrid, and range-separated hybrid functionals are in the range of 0.20.4 eV. This is in line not only with the typical accuracy of TD-DFT for singlet and triplet excited states of closed-shell systems but also with the gross accuracy of spin-adapted TD-DFT for spin-conserving excited states of open-shell systems.