Covalency Effects in KNi F 3 . III. Theoretical Studies
Covalency Effects in KNi F 3 . III. Theoretical Studies
复制标题
KNi F 3 中的共价效应。
DOI：
10.1103/physrev.130.517
复制
发表时间：
1963
期刊：
影响因子：
--
通讯作者：
R. Shulman
中科院分区：
文献类型：
--
作者：
S. Sugano;R. Shulman
对于KNi F3中的（N i F6）4−络合物，我们构造了分子轨道（MO），它是Ni 2+和F− Hartree-Fock原子轨道的线性组合。这些LCAO-MO由货车Vleck引入，其形式为：λ = N− 1 2（λ − λ χ），其中λ是Ni 2+ 3 d函数，χ是合适的F−函数的线性组合。轨道被假定为薛定谔方程h = E的解，其中哈密顿量为h=− Δ 2+ V M+ V L。术语VM和VL分别描述了与金属离子和配体的库仑相互作用和交换相互作用。矩阵元素的形式|H| Ψ>在IBM 7090上进行了数值评估。假设λ以及λ和χ之间的重叠很小，能量被最小化并且参数λ被确定。对于2 p σ键和2 s键，计算值分别为Ne − 1 2 λ σ= 0.383和Ne − 1 2 λ s= 0.109，与核磁共振实验中测定的Ne − 1 2 λ p σ= 0.337和Ne − 1 2 λ s= 0.116非常一致。用分子轨道计算了立方晶场分裂1 0 Dq =（？e| H| e）−（|H|它是电子从t 2 g轨道到e g轨道的促进能。考虑到计算的准确性，计算值1 0 D q= 6 3 5 0 cm-1与观测值1 0 D q= 7 2 5 0 cm-1相当吻合。此外，自旋轨道参数和Racah参数B从它们的自由离子值的减少满意地解释了分子轨道方法。这些结果的物理解释强调。特别是，对1 0 D q的贡献只有来自与共价性相关的非对角矩阵元，π电子混合量很大，一种新的物理机制部分地解释了大π键的形成，即Ni 2+离子对F− p σ和p π能级的晶场分裂;扩展Ni 2+径向函数对于某些目的是不必要的，而对于其余目的是不正确的。详细的计算和LCAO-MO模型的影响进行了讨论。
For the (N i F 6) 4− complex in KNi F 3 we have constructed molecular orbitals (MO) which are linear combinations of the Ni 2+ and F− Hartree-Fock atomic orbitals. These LCAO-MO, introduced by Van Vleck, are of the form Ψ= N− 1 2 (ϕ− λ χ) in which ϕ is the Ni 2+ 3 d function and χ a linear combination of the suitable F− functions. The orbitals were assumed to be solutions of Schrödinger's equation h Ψ= E Ψ, where the Hamiltonian was h=− Δ 2+ V M+ V L. The terms V M and V L describe the Coulombic and exchange interactions with the metal ion and ligands, respectively. Matrix elements of the form< Ψ| h| Ψ> were evaluated numerically on an IBM 7090. Assuming λ and the overlap between ϕ and χ to be small, the energy was minimized and the parameters λ were determined. For the 2 p σ bonding and the 2 s bonding the calculated values were N e− 1 2 λ σ= 0.383 and N e− 1 2 λ s= 0.109 which agreed very well with the values N e− 1 2 λ p σ= 0.337 and N e− 1 2 λ s= 0.116 determined in the nuclear magnetic resonance experiment. The molecular orbitals were used to calculate the cubic crystal field splitting 1 0 D q=(Ψ e| h| Ψ e)−(Ψ t| h| Ψ t) which is the promotion energy of an electron from a t 2 g orbital to an e g orbital. The calculated value of 1 0 D q= 6 3 5 0 cm− 1 agreed quite well with the observed value of 1 0 D q= 7 2 5 0 cm− 1 considering the accuracy of the calculation. Furthermore, the reduction of the spin-orbit parameter and the Racah parameter B from their free-ion values are satisfactorily explained by the molecular orbital approach. The physical interpretation of these results is emphasized. In particular, the only contributions to 1 0 D q with the correct sign come from the off-diagonal matrix elements associated with the covalency; the amount of π electron admixture is shown to be large; one novel physical mechanism partly responsible for the large π bonding is the crystal field splitting of the F− p σ and p π levels by the Ni 2+ ions; expanding the Ni 2+ radial function is shown to be unnecessary for some purposes and incorrect for the remainder. Details of the calculation are presented and implications of the LCAO-MO model discussed.