{"title":"Relativistic Effects in Ligand Field Theory (I): Optical Properties of d<sup>1</sup> Atoms in <i>O</i><sub><i>h</i></sub><sup>'</sup> Symmetry.","authors":"Jhon Fredy Pérez-Torres","doi":"10.1021/acs.inorgchem.4c01771","DOIUrl":null,"url":null,"abstract":"<p><p>Ligand field theory, which explains the splitting of degenerate <i>n</i>d atomic orbitals due to static electric fields from point-charge ligands, is rederived using Dirac orbitals instead of Schrödinger orbitals, specifically using the <i>n</i>d<sub>3/2</sub> and <i>n</i>d<sub>5/2</sub> spinors. This formalism is, to some extent, equivalent to incorporating the spin-orbit interaction either in the <i>n</i>d atomic orbitals or in the ligand field orbitals (e.g., the t<sub>2g</sub> and e<sub>g</sub> orbitals arising from <i>O</i><sub><i>h</i></sub> symmetry). The spin-orbit interaction is of fundamental importance in the description of the magnetic and optical properties of the 4d and 5d transition metal complexes. Algebraic equations for the relativistic energy levels of d<sup>1</sup> octahedral complexes as functions of the spin-orbit coupling constant ξ<sub><i>n</i>d</sub> and the ligand field parameters <i>Dq</i> and <i>Dp</i> are derived. It is demonstrated that these parameters allow a direct link between the ligand field theory and ab initio relativistic calculations, consistent with the emerging ab initio ligand field theory. The spin-orbit coupling constant and ligand field parameters of ReF<sub>6</sub> obtained from optical absorption spectra are carefuly in the light of the new theory.</p>","PeriodicalId":40,"journal":{"name":"Inorganic Chemistry","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Inorganic Chemistry","FirstCategoryId":"92","ListUrlMain":"https://doi.org/10.1021/acs.inorgchem.4c01771","RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/7/31 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"CHEMISTRY, INORGANIC & NUCLEAR","Score":null,"Total":0}
引用次数: 0
Abstract
Ligand field theory, which explains the splitting of degenerate nd atomic orbitals due to static electric fields from point-charge ligands, is rederived using Dirac orbitals instead of Schrödinger orbitals, specifically using the nd3/2 and nd5/2 spinors. This formalism is, to some extent, equivalent to incorporating the spin-orbit interaction either in the nd atomic orbitals or in the ligand field orbitals (e.g., the t2g and eg orbitals arising from Oh symmetry). The spin-orbit interaction is of fundamental importance in the description of the magnetic and optical properties of the 4d and 5d transition metal complexes. Algebraic equations for the relativistic energy levels of d1 octahedral complexes as functions of the spin-orbit coupling constant ξnd and the ligand field parameters Dq and Dp are derived. It is demonstrated that these parameters allow a direct link between the ligand field theory and ab initio relativistic calculations, consistent with the emerging ab initio ligand field theory. The spin-orbit coupling constant and ligand field parameters of ReF6 obtained from optical absorption spectra are carefuly in the light of the new theory.
期刊介绍:
Inorganic Chemistry publishes fundamental studies in all phases of inorganic chemistry. Coverage includes experimental and theoretical reports on quantitative studies of structure and thermodynamics, kinetics, mechanisms of inorganic reactions, bioinorganic chemistry, and relevant aspects of organometallic chemistry, solid-state phenomena, and chemical bonding theory. Emphasis is placed on the synthesis, structure, thermodynamics, reactivity, spectroscopy, and bonding properties of significant new and known compounds.