发表机构
Vrije Universiteit Brussel (VUB); McMaster University（布鲁塞尔自由大学; 麦克马斯特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
PyCDFT是首个开源可脚本化库，从单一收敛波函数解析计算二阶概念密度泛函理论描述符，支持基态和激发态，仅需少量代码。
AI 中文摘要
概念密度泛函理论（CDFT）将化学反应性描述符定义为电子能量相对于电子数和外部势或其组合的导数；然而，在实践中，研究人员几乎总是用有限差分和前沿轨道近似来替代这些导数，并且不存在用于其解析评估的通用软件。我们提出了PyCDFT，据我们所知，这是第一个标准化、开源且可脚本化的代码，能够从几乎任何电子结构软件包导入的单个收敛平均场波函数中，解析计算基态和激发态的概念密度（矩阵）泛函理论描述符，最高至二阶，包括轨道硬度、Fukui函数和Fukui矩阵，以及线性响应函数。这些描述符通过无矩阵、预条件Krylov子空间求解耦合微扰自洽场方程获得，适用于自旋非极化和自旋极化参考态，计算工作分布在MPI ranks上，所有数据流经单个HDF5检查点文件，支持重启、后处理以及将实空间描述符导出为cube文件以进行可视化。该设计将积分、网格和交换相关核委托给PySCF和Libxc，使库保持紧凑、用户友好且可互操作。关于H$_2$O基态和NH$_3$的破对称性$\Delta$SCF激发态的示例表明，完整的二阶CDFT分析仅需几行用户代码。
英文摘要
Conceptual density functional theory (CDFT) defines chemical reactivity descriptors as derivatives of the electronic energy with respect to the number of electrons and the external potential, or combinations thereof; in practice, however, researchers almost always replace these derivatives with finite-difference and frontier-orbital approximations, and no common software exists for their analytical evaluation. We present PyCDFT, to our knowledge, the first standardized, open-source, and scriptable code that analytically computes the descriptors of conceptual density (matrix) functional theory for ground and excited states up to second order, including the orbital hardness, the Fukui function and Fukui matrix, and the linear response function, from a single converged mean-field wavefunction imported from virtually any electronic-structure package. The descriptors are obtained from matrix-free, preconditioned Krylov-subspace solutions of the coupled-perturbed self-consistent-field equations for both spin-unpolarized and spin-polarized references, with the work distributed over MPI ranks and all data flowing through a single HDF5 checkpoint file that supports restart, post-processing, and the export of real-space descriptors as cube files for visualization. The design delegates integrals, grids, and exchange-correlation kernels to PySCF and Libxc, keeping the library compact, user-friendly, and interoperable. Worked examples on the ground state of H$_2$O and a broken-symmetry $Δ$SCF excited state of NH$_3$ show that a complete second-order CDFT analysis requires only a few lines of user code.
