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首页> 外文期刊>The Journal of Chemical Physics >Spin-adapted open-shell random phase approximation and time-dependent density functional theory. I. Theory
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Spin-adapted open-shell random phase approximation and time-dependent density functional theory. I. Theory

机译：自旋自适应开壳随机相位逼近和时间相关的密度泛函理论。一，理论

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The spin-adaptation of single-reference quantum chemical methods for excited states of open-shell systems has been nontrivial. The primary reason is that the configuration space, generated by a truncated rank of excitations from only one component of a reference multiplet, is spin-incomplete. Those "missing" configurations are of higher ranks and can, in principle, be recaptured by a particular class of excitation operators. However, the resulting formalisms are then quite involved and there are situations [e.g., time-dependent density functional theory (TD-DFT) under the adiabatic approximation] that prevent one from doing so. To solve this issue, we propose here a tensor-coupling scheme that invokes all the components of a reference multiplet (i.e., a tensor reference) rather than increases the excitation ranks. A minimal spin-adapted n -tuply excited configuration space can readily be constructed by tensor products between the n -tuple tensor excitation operators and the chosen tensor reference. Further combined with the tensor equation-of-motion formalism, very compact expressions for excitation energies can be obtained. As a first application of this general idea, a spin-adapted open-shell random phase approximation is first developed. The so-called "translation rule" is then adopted to formulate a spin-adapted, restricted open-shell Kohn-Sham (ROKS)-based TD-DFT (ROKS-TD-DFT). Here, a particular symmetry structure has to be imposed on the exchange-correlation kernel. While the standard ROKS-TD-DFT can access only excited states due to singlet-coupled single excitations, i.e., only some of the singly excited states of the same spin (S_i) as the reference, the new scheme can capture all the excited states of spin S_i -1, S_i, or S_i +1 due to both singlet- and triplet-coupled single excitations. The actual implementation and computation are very much like the (spin-contaminated) unrestricted Kohn-Sham-based TD-DFT. It is also shown that spin-contaminated spin-flip configuration interaction approaches can easily be spin-adapted via the tensor-coupling scheme.
机译：单参考量子化学方法对开壳系统激发态的自旋适应是不平凡的。主要原因是，仅从参考多重峰的一个分量的激发的截断秩生成的配置空间是自旋不完整的。那些“缺失”的构型具有较高的等级，并且原则上可以由特定类别的激励算子重新捕获。但是，由此产生的形式主义相当复杂，并且存在某些情况（例如，在绝热近似下的时变密度泛函理论（TD-DFT））阻止了这样做。为了解决这个问题，我们在这里提出一种张量耦合方案，该方案调用参考多重峰的所有分量（即张量参考）而不增加激励等级。可以通过n元组张量激励算子和所选张量参考之间的张量积轻松构造自旋适应性最强的n重激发配置空间。进一步与张量运动方程形式相结合，可以获得非常紧凑的激发能表达式。作为该一般思想的第一个应用，首先开发了一种自旋适应的开壳随机相位逼近法。然后采用所谓的“翻译规则”来制定自旋适应的，受限制的开壳式Kohn-Sham（ROKS）基TD-DFT（ROKS-TD-DFT）。在此，必须将特定的对称结构强加在交换相关内核上。尽管标准ROKS-TD-DFT由于单线态耦合的单个激发而只能访问激发态，即，只有相同自旋（S_i）的一些单个激发态作为参考，但是新方案可以捕获所有激发态由于单重态和三重态耦合的单激发，自旋S_i -1，S_i或S_i +1的变化。实际的实现和计算非常类似于（受旋转污染的）不受限制的基于Kohn-Sham的TD-DFT。还显示出，通过张量耦合方案可以容易地自旋适应自旋污染的自旋-翻转构型相互作用方法。

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