Spin–Orbit Natural Transition Orbitals and Spin-Forbidden Transitions

Abstract

Natural transition orbitals (NTOs) are in widespread use for visualizing and analyzing electronic transitions. The present work introduces the analysis of formally spin-forbidden transitions with the help of complex-valued spin−orbit (SO) NTOs. The analysis specifically focuses on the components in such transitions that cause their intensity to be nonzero because of SO coupling. Transition properties such as transition dipole moments are partitioned into SO-NTO hole−particle pairs, such that contributions to the intensity from specific occupied and unoccupied orbitals are obtained. The method has been implemented within the restricted active space (RAS) self-consistent field wave function theory framework, with SO coupling treated by RAS state interaction. SO-NTOs have a broad range of potential applications, which is illustrated by the T 2 −S 1 state mixing in pyrazine, spin-forbidden versus spin-allowed 4f−5d transitions in the Tb 3+ ion, and the phosphorescence of tris(2-phenylpyridine) iridium [Ir(ppy) 3 ].

The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry

“…Recent developments in the code, have made it possible to extract important properties and information from SO-coupled RASSI wave functions via (1) natural orbitals (NOs) and associated natural spin orbitals (NSOs) and their populations, ,, (2) natural bond orbital (NBO) and natural localized molecular orbital (NLMO) analyses of the associated density matrices in the atomic orbital (AO) basis and accompanying utility software , interfacing with the popular NBO toolkit, , and (3) spin–orbit natural transition orbitals (SO-NTOs) . This functionality generalizes and extends previously available functionality at the spin-free level.…”

“…Left: A dominant NTO pair (±0.03 isosurfaces), the associated singular value Λ, and the weighted transition dipole moment NTO contribution | μΛ | ( e a 0 ), for the spin-forbidden T 1 –S 0 transition of [Ir­(ppy) 3 ]. SO-NTO analysis reported in ref . Right: Calculated Ce L 3 edge for a cluster-embedded model of solid CeO 2 vs experimental data .…”

Enhanced thermal assisted photocatalysis reduction of carbon dioxide over a Fe2−xGaxO3 solid solution

“…Specifically, the electron spin state is not changed during the excitation process for α-Fe 2 O 3 , which is reversed for Fe 2−x Ga x O 3 . The reversion of spin state suppresses the recombination of photogenerated charge carriers, 38,39 which is beneficial to improve the activity.…”

Optical Activity of Spin‐Forbidden Electronic Transitions in Metal Complexes from Time‐Dependent Density Functional Theory with Spin‐Orbit Coupling

“…Among phosphorescent emitters, Ir(III) compounds with a pseudo‐octahedral coordination environment and Pt(II) systems with square‐planar structures have emerged as particularly appealing and thus have been developed and examined extensively [1–4] . For example, Ir(ppy) 3 (ppy=2‐phenylpyridine) has been studied intensely by theory and experiment in the context of developing complexes with strong emission in different parts of the visible spectrum [5–15] …”

“…[1][2][3][4] For example, Ir(ppy) 3 (ppy = 2-phenylpyridine) has been studied intensely by theory and experiment in the context of developing complexes with strong emission in different parts of the visible spectrum. [5][6][7][8][9][10][11][12][13][14][15] Chiral enantiopure systems give access not only to desired emission wavelengths, but also the ability to modulate circularly polarized (CP) luminescence (CPL). [16][17][18][19] Strong optical activity of metal complexes can be obtained, in particular, when not only the relative arrangement of the ligands is chiral, but when the ligands themselves are inherently chiral and display strong optical activity themselves.…”