Spin−Orbit Splittings in the Third-Row Transition Elements:  Comparison of Effective Nuclear Charge and Full Breit−Pauli Calculations

Abstract

The spin−orbit splittings of low-lying states in third-row transition elements were calculated using both an effective core potential (ECP) method within the one-electron (Zeff) approximation and all-electron (AE) methods using three different approaches. The wave functions were obtained using the multiconfiguration self consistent field (MCSCF) method followed by second-order configuration interaction (SOCI) calculations. All calculated results, except for the ones on atomic Ir, are in reasonable agreement with the corresponding experimental observations. The unsatisfactory results for atomic Ir are attributed to the poor theoretical prediction of the adiabatic energy gap between the lowest two 4F states. This gap has an incorrect sign in AE calculations without scalar relativistic corrections, but the gap can be reproduced qualitatively if these corrections are added using the newly developed RESC (relativistic elimination of small components) scheme. As a result, the AE calculations with the RESC approximation give spin−orbit splittings similar to those obtained by the ECP calculations with the Zeff approximation. Disciplines Chemistry CommentsReprinted (adapted) The spin-orbit splittings of low-lying states in third-row transition elements were calculated using both an effective core potential (ECP) method within the one-electron (Z eff ) approximation and all-electron (AE) methods using three different approaches. The wave functions were obtained using the multiconfiguration self consistent field (MCSCF) method followed by second-order configuration interaction (SOCI) calculations. All calculated results, except for the ones on atomic Ir, are in reasonable agreement with the corresponding experimental observations. The unsatisfactory results for atomic Ir are attributed to the poor theoretical prediction of the adiabatic energy gap between the lowest two 4 F states. This gap has an incorrect sign in AE calculations without scalar relativistic corrections, but the gap can be reproduced qualitatively if these corrections are added using the newly developed RESC (relativistic elimination of small components) scheme. As a result, the AE calculations with the RESC approximation give spin-orbit splittings similar to those obtained by the ECP calculations with the Z eff approximation.

Vibration Correlation Function Investigation on the Phosphorescence Quantum Efficiency and Spectrum for Blue Phosphorescent Ir(III) Complex

“…基于优化的基态平衡构型, 我们在 Dalton 程序包 [21] 里采用密度泛函理论的线性响应和二次响应理论分别 计算了两电子态之间的自旋轨道耦合常数和跃迁偶极 矩 [22,23] . 其中, 我们在自旋轨道耦合常数计算中使用了 有 效 单 电 子 近 似 [24,25] ,…”

Effective Valence Shell Hamiltonian Calculations on Spin-Orbit Coupling of SiH, SiH+, and SiH2+

“…The effective nuclear charges used are 1.0 au for H and 12.25 au for Si as obtained from the studies of Gordon and coworkers. [18][19][20][21] Sun and Freed's test H v calculations on SiH at a fixed internuclear distance shows that the introduction of the above effective nuclear charges recovers the most of contributions from the two-electron term. 5 The effective valence shell wave functions and therefore the energies of valence states are evaluated using the H v perturbation expansion through second order in correlation (V).…”

Dissociation Potential Curves of Low-Lying States in Transition Metal Hydrides. 3. Hydrides of Groups 6 and 7

“…The previous study (Part I of this series) reported on Group 4 hydrides, TiH, ZrH, and HfH, 28 in which multiconfiguration self-consistent field (MCSCF) methods were employed and followed by second-order configuration interaction (SOCI) calculations, using limited external spaces. We concluded that the one-electron approximation 22,26,27 performed very well for TiH and ZrH, but the agreement between the effective core potential (ECP) and all-electron (AE) results is somewhat worse for HfH.…”

“…To enable an entry level of theory, we have proposed effective nuclear charges for the first-through sixth-row main-group elements, as well as those for the first-through third-row transition elements, to estimate spin-orbit splittings within the one-electron (Z eff ) approximation. [22][23][24][25][26][27][28] Although higher levels of relativistic theories are nowadays available for the estimation of spin-orbit coupling effects, it is time-consuming to apply such high levels of theory to large molecular systems. Therefore, the Z eff approximation is still useful for estimating spin-orbit coupling effects in large molecular systems.…”