AI 中文总结
针对RDMFT中键断裂模拟难题，通过校正PNOF5泛函累积量贡献构建自然轨道泛函，强制累积量对局部自旋碎片和离域指数的贡献，纯化密度矩阵，改进强关联体系表现，基准测试显示能准确重现CASSCF能量，为改进泛函提供途径。
AI 中文摘要
准确模拟键断裂仍是约化密度矩阵泛函理论（RDMFT）的核心挑战。虽一些现代泛函能给出合理准确的解离能，但常无法重现解离碎片的关键性质。本文通过校正PNOF5泛函产生的累积量贡献，重新构建自然轨道泛函。方法在解离极限下强制累积量对局部自旋碎片和离域指数的已知贡献，得到符合物理约束的累积量并纯化一、二电子约化密度矩阵。结果泛函在强关联体系中有更好表现。对\ce{N2}、\ce{NO+}、\ce{O2}、\ce{S2}和\ce{CO}单重态解离的基准测试表明，更新累积量计算的能量能准确重现完全活性空间自洽场（CASSCF）能量。还分析了方法局限性。此工作为系统改进自然轨道泛函以在RDMFT中实现可靠键断裂计算提供了途径。
英文摘要
Accurate modeling of bond breaking remains a central challenge for reduced density matrix functional theory (RDMFT). Although some modern functionals can yield reasonably accurate dissociation energies, they often fail to reproduce key properties of the dissociated fragments, such as a vanishing fragment population covariance (also known as the delocalization index) and the correct total spin angular momentum of each fragment (local spin). In this work, we revisit the construction of natural orbital functionals by correcting the cumulant contribution produced by the PNOF5 functional. Our method enforces known contributions of the cumulant to local spin fragments and the delocalization index at the dissociation limit. We obtain the closest cumulant consistent with these physically motivated constraints and subsequently purify the corresponding one- and two-electron reduced density matrices by imposing the standard $P, Q, \text{and } G$ $N$-representability conditions. The resulting functional yields improved behavior in strongly correlated regimes. Benchmarking on the dissociation of the singlet states of \ce{N2}, \ce{NO+}, \ce{O2}, \ce{S2}, and \ce{CO} shows that in the dissociation regime the energies computed from the updated cumulant exactly reproduce the complete active space self-consistent field (CASSCF) energies. We further analyze the limitations of the approach and identify scenarios in which the current approach performs poorly. This work provides a pathway for systematically improving natural orbital functionals to achieve reliable bond-breaking calculations within RDMFT.
