AI 中文总结
研究为PASPT2奠定基础，指出其虽非严格尺寸扩展但严格尺寸一致，引入PASPT2X，无侵入性的PASPT2H忽略对特定态重要的二阶修正，对于\(\mathcal{M}_0\)支持的目标态尺寸扩展性违反微弱，强化了PASPT2H理论基础。
AI 中文摘要
最近提出的部分活性空间（PAS）多态二阶微扰理论（PASPT2）具有连接振幅和连接的封闭中间哈密顿量。尽管有这些特点，但PASPT2并不严格具有尺寸扩展性，不过严格具有尺寸一致性。引入严格尺寸扩展的变体PASPT2X后，无侵入性的PASPT2H仅忽略了对封闭空间中\(\mathcal{M}_0\)正交补\(\mathcal{R}_X\)上有主要投影的态才重要的二阶修正。对于\(\mathcal{M}_0\)支持的目标态，尺寸扩展性的微弱违反在数值上不显著，强化了PASPT2H的理论基础。
英文摘要
The recently proposed partial-active-space (PAS) multi-state second-order perturbation theory (PASPT2) [Precis. Chem. 4, 997 (2026)] features connected amplitudes and a connected, closed intermediate Hamiltonian. Despite these hallmarks, PASPT2 (denoted as PASPT2H from now on) is not strictly size-extensive, as originally thought (and numerically confirmed), albeit strictly size-consistent. Nevertheless, PASPT2 is near-extensive for the states with major projections on the chosen PAS $\mathcal{M}_0$. This becomes more transparent upon introducing PASPT2X, a strictly size-extensive variant. Compared with the intruder-prone PASPT2X, the intruder-free PASPT2H merely neglects the second-order corrections that are important only for those states with major projections on the orthogonal complement $\mathcal{R}_X$ of $\mathcal{M}_0$ within the closed space $\mathcal{M}_X$ ($=\mathcal{M}_0\oplus\mathcal{R}_X$); however, such states are not supported by the chosen finite one-particle basis set. The weak violation of size-extensivity is therefore numerically insignificant for the target states supported by $\mathcal{M}_0$, reinforcing the theoretical basis of PASPT2H.
Comments3 figures,1 table
