On the calculation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model.
On the calculation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model.
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从非球面赝原子模型计算静电势、电场和电场梯度。
DOI：
10.1107/s0108767306026298
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
L. Farrugia
中科院分区：
文献类型：
--
作者：
A. Volkov;H. F. King;P. Coppens;L. Farrugia
提出了准确、简单且高效的公式，用于根据电子密度的非球面 Hansen-Coppens 伪原子模型计算静电势 (ESP)、电场 (EF) 和电场梯度 (EFG) [Hansen & Coppens (1978)。阿克塔水晶。 A34，909-921]。它们基于球谐函数中 |r' - r|(-1) 的展开式以及 R(l)(r) = r(n) exp(-alpha ) 形式的 Slater 型函数的不完全 gamma 函数。这些公式对于 0 < 或 = r < 或 = 无穷大有效，并且很容易扩展到更高的 l 值。仅当 r = 0 时，n = l 和 n = l + 1 的函数才需要对积分进行特殊处理。该方法使用通过 PBE/6-31G** 密度的倒易空间拟合获得的甲酰胺分子的理论伪原子参数和 Fe(CO)(5) 的实验 X 射线数据进行测试。甲酰胺中核位置处的 ESP、EF 和 EFG 值与通过使用 6-31G**、aug-cc-pVDZ 和 aug-cc-pVTZ 基组的密度泛函 PBE 计算直接评估的值非常一致。观察到的小差异归因于核附近高斯型和斯莱特型函数的不同行为以及倒易空间拟合的缺陷。显示 EF 图，可有效可视化甲酰胺晶体结构中的晶格 EF 效应。通过对 Fe(CO)(5) 实验 100 K X 射线数据的分析，在考虑堆芯的 Sternheimer 屏蔽/反屏蔽效应后，得出核四极矩 Q((57)Fe(m)) = 0.12 x 10(-28) m(2) 的值。该值与 Su & Coppens [Acta Cryst. (1996), A52, 748-756]，但略小于从综合理论/光谱研究中获得的普遍接受的值 0.16 +/- 5% x 10(-28) m(2) [Dufek, Blaha & Schwarz (1995)。物理。莱特牧师。 25、3545-3548]。
Accurate, yet simple and efficient, formulae are presented for calculation of the electrostatic potential (ESP), electric field (EF) and electric field gradient (EFG) from the aspherical Hansen-Coppens pseudoatom model of electron density [Hansen & Coppens (1978). Acta Cryst. A34, 909-921]. They are based on the expansion of |r' - r|(-1) in spherical harmonics and the incomplete gamma function for a Slater-type function of the form R(l)(r) = r(n) exp(-alpha ). The formulae are valid for 0 < or = r < or = infinity and are easily extended to higher values of l. Special treatment of integrals is needed only for functions with n = l and n = l + 1 at r = 0. The method is tested using theoretical pseudoatom parameters of the formamide molecule obtained via reciprocal-space fitting of PBE/6-31G** densities and experimental X-ray data of Fe(CO)(5). The ESP, EF and EFG values at the nuclear positions in formamide are in very good agreement with those directly evaluated from density-functional PBE calculations with 6-31G**, aug-cc-pVDZ and aug-cc-pVTZ basis sets. The small observed discrepancies are attributed to the different behavior of Gaussian- and Slater-type functions near the nuclei and to imperfections of the reciprocal-space fit. An EF map is displayed which allows useful visualization of the lattice EF effects in the crystal structure of formamide. Analysis of experimental 100 K X-ray data of Fe(CO)(5) yields the value of the nuclear quadrupole moment Q((57)Fe(m)) = 0.12 x 10(-28) m(2) after taking into account Sternheimer shielding/antishielding effects of the core. This value is in excellent agreement with that reported by Su & Coppens [Acta Cryst. (1996), A52, 748-756] but slightly smaller than the generally accepted value of 0.16 +/- 5% x 10(-28) m(2) obtained from combined theoretical/spectroscopic studies [Dufek, Blaha & Schwarz (1995). Phys. Rev. Lett. 25, 3545-3548].