AI 中文总结
该研究基于atomx程序计算的118种中性原子全电子Dirac--Fock密度，提出带Dirac--Padé项的元素自适应散射参数化方法，显著提升拟合精度，对高角散射等应用有重要价值。
AI 中文摘要
本文提出了适用于全部118种中性原子的更新参考数据，以及弹性电子与X射线散射的解析参数化方法。针对原子序数Z=2--118的多电子元素，参考电子密度通过相对论B样条Dirac--Fock程序atomx计算得到；氢原子的电子密度则由精确的相对论单电子Dirac 1s解构建；电子散射因子f_e(g)、X射线散射因子f_x(g)以及径向矩均由这些密度推导得出。本文提出的参数化方法扩展了固定规模的Lobato--Van Dyck类氢展开式，同时保留了f_x(g)、ρ(r)、静电势V(r)和投影势V(R)的闭式表达式。这些扩展包括：元素自适应的基组规模n_t(Z)、实空间与倒易空间的同时拟合、以精确的⟨r^4⟩约束替代非相对论Kato尖点条件，以及带电荷的Dirac--Padé基项——该基项新增了多项式乘指数形式的形状通道，无需用列表形式的Dirac径向函数替换类氢基组，也无需将该项指派给某个物理壳层。在总参数数量相同的情况下，经Dirac--Padé丰富的基组在118种元素中的111种上，表现优于参数匹配的非相对论基组，将平均总代价降低了39%。与在相同参考网格和目标函数下进行的受控固定五项重拟合相比，元素自适应基组将倒易空间偏差的中位数降低了约3到4个数量级，并且能够解析4πr²ρ(r)中的壳层结构，这是固定五项基组无法做到的。最大的变化出现在原子核附近，以及超出传统12埃⁻¹范围的倒易空间尾部区域，这与定量高角散射和电子衍射测量直接相关。
英文摘要
Updated reference data and an analytic parameterisation of elastic electron and X-ray scattering are presented for all 118 neutral atoms. The reference electron densities for the multi-electron elements $Z=2$--$118$ are computed with the relativistic B-spline Dirac--Fock code atomx, while hydrogen is constructed from the exact relativistic one-electron Dirac $1s$ solution; the electron scattering factor $f_e(g)$, X-ray scattering factor $f_x(g)$ and radial moments are derived from these densities. The reported parameterisation extends the fixed-size Lobato--Van Dyck hydrogenic expansion while retaining closed-form expressions for $f_x(g)$, $ρ(r)$, the electrostatic potential $V(r)$ and the projected potential $V(R)$. These extensions are an element-adaptive basis size $n_t(Z)$, a simultaneous real- and reciprocal-space fit, an exact $\langle r^4\rangle$ constraint in place of the non-relativistic Kato cusp, and a charge-carrying Dirac--Padé basis term that adds a polynomial-times-exponential shape channel without replacing the hydrogenic basis by a tabulated Dirac radial function or assigning the term to a physical shell. For the same total parameter count, the Dirac--Padé-enriched basis improves on the parameter-matched non-relativistic basis for 111 of the 118 elements, lowering the mean total cost by 39\%. Relative to a controlled fixed five-term refit on the same reference grid and objective, the element-adaptive bases improve the median reciprocal-space deviations by about three to four orders of magnitude and resolve shell structure in $4πr^2ρ(r)$ that the fixed five-term basis cannot. The largest changes occur near the nucleus and in the reciprocal-space tail beyond the legacy 12 inverse angstroms range, which is directly relevant to quantitative high-angle scattering and electron-diffraction measurements.
Comments45 pages, 5 figures. Submitted to Acta Crystallographica Section A
