Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing 100871, People's Republic of China.
J Chem Phys. 2012 Jan 14;136(2):024107. doi: 10.1063/1.3676736.
Spin-flip time-dependent density functional theory (SF-TD-DFT) with the full noncollinear hybrid exchange-correlation kernel and its approximate variants are critically assessed, both formally and numerically. As demonstrated by the ethylene torsion and the C(2v) ring-opening of oxirane, SF-TD-DFT is very useful for describing nearly degenerate situations. However, it may occasionally yield unphysical results. This stems from the noncollinear form of the generalized gradient approximation, which becomes numerically instable in the presence of spin-flip excitations from the closed- to vacant-shell orbitals of an open-shell reference. To cure this defect, a simple modification, dubbed as ALDA0, is proposed in the spirit of adiabatic local density approximation (ALDA). It is applicable to all kinds of density functionals and yields stable results without too much loss of accuracy. In particular, the combination of ALDA0 with the Tamm-Dancoff approximation is a promising tool for studying global potential energy surfaces. In addition to the kernel problem, SF-TD-DFT is also rather sensitive to the choice of reference states, as demonstrated by the spin multiplet states of closed-shell molecules of H(2)O, CH(2)O, and C(2)H(4). Surprisingly, SF-TD-DFT with pure density functionals may also fail for valance excitations with large orbital overlaps, at variance with the spin-conserving counterpart (SC-TD-DFT). In this case, the inclusion of a large amount of Hartree-Fock exchange is mandatory for quantitative results. Nonetheless, for spatially degenerate cases such as CF, CH, and NH(+), SF-TD-DFT is more advantageous than SC-TD-DFT, unless the latter is also space adapted. These findings are very instructive for future development and applications of TD-DFT.
自旋翻转含时密度泛函理论（SF-TD-DFT）与全非共线混合交换相关核及其近似变体在形式上和数值上都得到了严格评估。正如乙烯扭转和环氧乙烷的 C(2v)开环所证明的那样，SF-TD-DFT 非常适合描述近简并情况。然而，它有时可能会产生不符合物理事实的结果。这源于广义梯度近似的非共线形式，在开壳参考的满壳轨道到空壳轨道的自旋翻转激发存在的情况下，数值上变得不稳定。为了纠正这个缺陷，根据绝热局域密度近似（ALDA）的精神，提出了一种简单的修正方法，称为 ALDA0。它适用于所有种类的密度泛函，并且在没有太多精度损失的情况下产生稳定的结果。特别是，ALDA0 与 Tamm-Dancoff 近似的组合是研究全局势能面的有前途的工具。除了核问题之外，SF-TD-DFT 对参考状态的选择也非常敏感，这可以从 H(2)O、CH(2)O 和 C(2)H(4)等闭壳分子的自旋多重态得到证明。令人惊讶的是，对于具有大轨道重叠的价激发，纯密度泛函的 SF-TD-DFT 也可能失败，与自旋守恒对应物（SC-TD-DFT）不同。在这种情况下，为了获得定量结果，必须包含大量的 Hartree-Fock 交换。尽管如此，对于空间简并的情况，如 CF、CH 和 NH(+)，SF-TD-DFT 比 SC-TD-DFT 更有利，除非后者也进行了空间适配。这些发现对于 TD-DFT 的未来发展和应用非常有启发性。
