Excited states of OsO₄: A comprehensive time‐dependent relativistic density functional theory study

Abstract

A large number of scalar as well as spinor excited states of OsO(4), in the experimentally accessible energy range of 3-11 eV, have been captured by time-dependent relativistic density functional linear response theory based on an exact two-component Hamiltonian resulting from the symmetrized elimination of the small component. The results are grossly in good agreement with those by the singles and doubles coupled-cluster linear response theory in conjunction with relativistic effective core potentials. The simulated-excitation spectrum is also in line with the available experiment. Furthermore, combined with detailed analysis of the excited states, the nature of the observed optical transitions is clearly elucidated. It is found that a few scalar states of (3)T(1) and (3)T(2) symmetries are split significantly by the spin-orbit coupling. The possible source for the substantial spin-orbit splittings of ligand molecular orbitals is carefully examined, leading to a new interpretation on the primary valence photoelectron ionization spectrum of OsO(4).

Two-Component Relativistic Equation-of-Motion Coupled-Cluster Methods for Excitation Energies and Ionization Potentials of Atoms and Molecules

“…We apply the present IP-EOM-SOCCSD method to molecular ionization potentials of OsO 4 . Ionization spectra of the OsO 4 molecule have been known to exhibit a clear splitting due to spin–orbit interaction, and a number of computational studies on ionization potentials as well as excitation energies of OsO 4 have been published. − Nakajima et al successfully reproduced the OsO 4 ionization spectra using CASPT2 combined with the RESC (relativistic elimination of small component) scheme, ,, where the spin–orbit interaction was taken into account at the RESC-CASPT2 stage. In the present two-component IP-EOM-SOCC calculation, the spin–orbit interaction is considered from the beginning.…”

Time-dependent relativistic density functional study of Yb and YbO

“…The so generated Kramers paired symmetry functions and product basis render the respective Kohn-Sham and coupling matrices to be real-valued even though the integrands themselves are complex. This not only simplifies the calculation but also facilitates the analysis of the excited states; (3) The excited states can further be analyzed in terms of a compact and intuitive orbital representation via the natural transition orbitals [24] . The spinor states can also be projected onto scalar states via the state-interaction approach.…”

“…The remaining task is to combine the exact two-component Hamiltonians with know-how electron correlation methods so as to generate a new generation of relativistic many-body theories for the whole Periodic Table of elements. In the present work, the SESC (symmetrized elimination of the small component) Hamiltonian [37,38] is combined with TD-DFT, which has been used for a large number of excited states of ReO 4 − and OsO 4 [23,24] . It is well recognized that, for compact molecular systems, the adiabatic local density approximation (LDA) is sufficient for the exchange-correlation kernel.…”

“…Both issues can be avoided by means of time-dependent density functional theory (TD-DFT) [17][18][19] . Therefore, it is worthwhile to reinvestigate the excited states of YbO with the relativistic counterpart of TD-DFT (TD-RDFT) [20][21][22][23][24] . To the best of our knowledge, this is the first assessment of the performance of TD-RDFT for excitations involving compact f-orbitals.…”

Yb、YbO电子激发态的相对论含时密度泛函理论研究

“…其中向量 σ 的 3 个分量是 2×2 的Pauli自旋矩阵, "自旋 密度"s定义为磁化向量 M 的长度 [25] | |, . [24] . 另外, 通过态相互作用 (stateinteraction) 方法还可以把旋量波函数投影到标量态.…”