Sugisaki Kenji, Toyota Kazuo, Sato Kazunobu, Shiomi Daisuke, Takui Takeji
Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University , 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan.
J Phys Chem A. 2016 Dec 15;120(49):9857-9866. doi: 10.1021/acs.jpca.6b10253. Epub 2016 Dec 2.
A quasi-restricted orbital (QRO) approach for the calculation of the spin-orbit term of zero-field splitting tensors (D tensors) by means of density functional theory (DFT) importantly features in the fact that it is free from spin contamination problems because it uses spin eigenfunctions for the zeroth order wave functions. In 2011, however, Schmitt and co-workers pointed out that in the originally proposed QRO working equation some possible excitations were not included in their sum-over-states procedure, which causes spurious D contributions from closed-shell subsystems located far from the magnetic molecule under study. We have revisited the derivation of the QRO working equation and modified it, making it include all possible types of excitations in the sum-over-states procedure. We have found that the spurious D contribution can be eliminated by taking into account contributions from all possible types of singly excited configuration state functions. We have also found that only the SOMO(α) → SOMO(β) excited configurations have nonzero contributions to the D tensors as long as α and β spin orbitals have the same spatial distributions and orbital energies. For the D tensor calculations, by using a ground state wave function free from spin contamination, we propose a natural orbital-based Pederson-Khanna (NOB-PK) method, which utilizes the single determinant wave function consisting of natural orbitals in conjunction with the Pederson-Khanna (PK) type perturbation treatment. Some relevant calculations revealed that the NOB-PK method can afford more accurate D tensors than the conventional PK method as well as the QRO approach in Mn complexes and Re-based single molecule magnets.
一种通过密度泛函理论（DFT）计算零场分裂张量（D张量）自旋 - 轨道项的准受限轨道（QRO）方法，其重要特点是不存在自旋污染问题，因为它对零阶波函数使用了自旋本征函数。然而，2011年施密特及其同事指出，在最初提出的QRO工作方程中，其态叠加过程未包含一些可能的激发，这导致远离所研究磁性分子的闭壳层子系统产生虚假的D贡献。我们重新审视了QRO工作方程的推导并对其进行了修改，使其在态叠加过程中包含所有可能类型的激发。我们发现，通过考虑所有可能类型的单激发组态态函数的贡献，可以消除虚假的D贡献。我们还发现，只要α和β自旋轨道具有相同的空间分布和轨道能量，只有SOMO(α) → SOMO(β)激发组态对D张量有非零贡献。对于D张量计算，通过使用无自旋污染的基态波函数，我们提出了一种基于自然轨道的佩德森 - 卡纳（NOB - PK）方法，该方法利用由自然轨道组成的单行列式波函数并结合佩德森 - 卡纳（PK）型微扰处理。一些相关计算表明，在锰配合物和基于铼的单分子磁体中，NOB - PK方法比传统的PK方法以及QRO方法能提供更精确的D张量。
