发表机构
The Ohio State University（俄亥俄州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从信息论视角研究相对论性 Hirshfeld 原子，提出 Drude 振子色散模型的闭式解，并扩展至相对论情形，为重元素色散模型提供参考数据。
AI 中文摘要
若干用于密度泛函理论的临时色散模型基于对分子电荷密度进行 Hirshfeld（或“股东”）划分，该划分提供了原子尺寸的原位定义。我们表明，最近引入的用于色散的“优化”量子 Drude 振子模型允许通过 Lambert $W$ 函数获得闭式解，其分支识别紧凑和弥散振子解。紧凑解从自由原子极化率、$C_6$ 系数和范德华半径解析地确定 $C_8$（偶极-四极）色散系数，无需任何参考 $C_8$ 数据。接下来，我们为分子中原子 Hirshfeld 划分的相对论版本提供形式基础。使用孤立原子的四分量 Dirac-Hartree-Fock 密度定义了一个严格正的形变场，该场将原子密度的相对论变化带入 Hirshfeld 划分。非相对论情形的唯一性定理被扩展到相对论 Hirshfeld 原子，并允许通过精细结构常数的二次阶进行渐近展开。归一化要求相对论密度修正重塑参考原子，同时保持其布居数。最后，报告了闭壳层原子和离子的四分量极化率和 C6 系数，这些数据提供了将分子中原子色散模型扩展到重元素区域所需的参考数据。在衡量相对论效应的标量收缩因子中可观察到周期性趋势。
英文摘要
Several ad hoc dispersion models for density-functional theory are based on the use of Hirshfeld (or "stockholder") partition of a molecular charge density, which provides an in situ definition of atomic size. We show that a recently introduced "optimized" quantum Drude oscillator model for dispersion admits a closed-form solution in terms of the Lambert $W$ function, whose branches identify the compact and diffuse oscillator solutions. The compact solution determines the $C_8$ (dipole-quadrupole) dispersion coefficient analytically from the free-atom polarizability, $C_6$ coefficient, and van der Waals radius, without any reference $C_8$ data. Next, we provide a formal basis for a relativistic version of the atoms-in-molecule Hirshfeld partition. Using four-component Dirac-Hartree-Fock densities for isolated atoms defines a strictly positive deformation field that carries the relativistic changes in atomic density into the Hirshfeld partition. A uniqueness theorem for the non-relativistic case is extended to relativistic Hirshfeld atoms and admits an asymptotic expansion through quadratic order in the fine-structure constant. Normalization requires the relativistic density correction to reshape the reference atom while preserving its population. Finally, four-component polarizabilities and C6 coefficients are reported for closed-shell atoms and ions, which supply the reference data required to extend atoms-in-molecules dispersion models into the heavy-element regime. Periodic trends are observable in a scalar contraction factor that measures relativistic effects.
Comments22 pages, 1 figure, 2 tables
