Neese Frank, Solomon Edward I.
Department of Chemistry, Stanford University, Stanford, California 94305.
Inorg Chem. 1998 Dec 28;37(26):6568-6582. doi: 10.1021/ic980948i.
Equations are derived and discussed that allow the computation of zero-field splitting (ZFS) tensors in transition metal complexes for any value of the ground-state total spin S. An effective Hamiltonian technique is used and the calculation is carried to second order for orbitally nondegenerate ground states. The theory includes contributions from excited states of spin S and S +/- 1. This makes the theory more general than earlier treatments. Explicit equations are derived for the case where all states are well described by single-determinantal wave functions, for example restricted open shell Hartree-Fock (HF) and spin-polarized HF or density functional (DFT) calculation schemes. Matrix elements are evaluated for many electron wave functions that result from a molecular orbital (MO) treatment including configuration interaction (CI). A computational implementation in terms of bonded functions is outlined. The problem of ZFS in high-spin ferric complexes is treated at some length, and contributions due to low-symmetry distortions, anisotropic covalency, charge-transfer states, and ligand spin-orbit coupling are discussed. ROHF-INDO/S-CI results are presented for FeCl(4)(-) and used to evaluate the importance of the various terms. Finally, contributions to the experimentally observed reduction of the metal spin-orbit coupling constants (the relativistic nephelauxetic effect) are discussed. B3LYP and Hartree-Fock calculations for FeCl(4)(-) are used to characterize the change of the iron 3d radial function upon complex formation. It is found that the iron 3d radial distribution function is significantly expanded and that the expansion is anisotropic. This is interpreted as a combination of reduction in effective charge on the metal 3d electrons (central field covalence) together with expansive promotion effects that are a necessary consequence of chemical bond formation. The <r(-)(3)>(3d) values that are important in the interpretation of magnetic data are up to 15% reduced from their free-ion value before any metal-ligand orbital mixing (symmetry-restricted covalency) is taken into account. Thus the use of free-ion values for spin-orbit coupling and related constants in the analysis of experimental data leads to values for MO coefficients that overestimate the metal-ligand covalency.
本文推导并讨论了一些方程，这些方程可用于计算过渡金属配合物中零场分裂（ZFS）张量，适用于基态总自旋S的任意值。采用了有效哈密顿量技术，并对轨道非简并基态进行了二阶计算。该理论包括自旋为S和S±1的激发态的贡献。这使得该理论比早期的处理方法更具普遍性。对于所有状态都能用单行列式波函数很好描述的情况，例如受限开壳层哈特里 - 福克（HF）、自旋极化HF或密度泛函（DFT）计算方案，推导了显式方程。对由包括组态相互作用（CI）的分子轨道（MO）处理产生的多电子波函数的矩阵元进行了评估。概述了基于键合函数的计算实现。详细讨论了高自旋铁配合物中的ZFS问题，并讨论了低对称畸变、各向异性共价性、电荷转移态和配体自旋 - 轨道耦合的贡献。给出了FeCl₄⁻的ROHF - INDO/S - CI结果，并用于评估各项的重要性。最后，讨论了对实验观察到的金属自旋 - 轨道耦合常数降低（相对论性电子云扩展效应）的贡献。使用FeCl₄⁻的B3LYP和哈特里 - 福克计算来表征配合物形成时铁3d径向函数的变化。发现铁3d径向分布函数显著扩展且扩展是各向异性的。这被解释为金属3d电子有效电荷的减少（中心场共价性）与作为化学键形成必然结果的膨胀促进效应的结合。在考虑任何金属 - 配体轨道混合（对称受限共价性）之前，对解释磁数据很重要的<r⁻³>(3d)值比其自由离子值降低了高达15%。因此，在实验数据分析中使用自由离子值来计算自旋 - 轨道耦合及相关常数会导致MO系数值高估金属 - 配体共价性。
