A Tutorial Review on the Nonradiative Energy Transfer Rates between Lanthanide Ions

Albano N Carneiro Neto; Renaldo T Moura; Jorge A A Coelho; Mauro E Silva⁃Junior; Janderson L Costa; Oscar L Malta; Ricardo L Longo

doi:10.37188/CJL.EN20220007

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A Tutorial Review on the Nonradiative Energy Transfer Rates between Lanthanide Ions

Views on Basic Knowledge of Luminescence | 更新时间：2023-02-13

- A Tutorial Review on the Nonradiative Energy Transfer Rates between Lanthanide Ions
  增强出版
- Chinese Journal of Luminescence Vol. 43, Issue 12, Pages: 1871-1891(2022)
- 作者机构：
  
  1.阿威罗大学物理系和 CICECO⁃阿威罗材料研究所，阿威罗，葡萄牙， 3810-193
  2.南卫理公会大学化学系，达拉斯，美国， 75275⁃0314
  3.帕拉伊巴联邦大学化学与物理系，阿雷亚，巴西， 58397⁃000
  4.伯南布哥联邦大学基础化学系，累西腓，巴西， 50740⁃560
  5.伯南布哥联邦大学材料科学研究生院，累西腓，巴西， 50670⁃901
- 作者简介：
  
  [ "Albano N. Carneiro Neto （1985-）, received his Ph.D. in Chemistry from Federal University of Pernambuco （Brazil） in 2018, started as a pos⁃doc from 2019 to 2021 at University of Aveiro （Portugal） and nowadays he is a Researcher at the Physics Department and CICECO⁃Aveiro Institute of Materials, University of Aveiro. He acted as guest editor of Journal of Luminescence in 2018 and he is a member of the topical advisory panel of Applied Sciences. His scientific interests are lanthanides chemistry; quantum chemistry calculations; covalency and chemical bonding; thermometry; f⁃f intensities; Judd⁃Ofelt theory; ligand⁃ and lanthanide⁃to⁃lanthanide energy transfer. He authored 47 papers in international journals and 04 book chapters. According to Google Scholar （November 2022）, he has more than 920 citations with an h⁃index of 18. E-mail： albanoneto@ua.pt " ]
  [ "Oscar L. Malta （1954-）, Ph.D. at Université Pierre et Marie Curie-Paris 6 （France, 1981）. He is a Full Professor in the Department of Fundamental Chemistry of the UFPE （Brazil）, researcher 1A of the National Council of Scientific and Technological Development, and member of the Brazilian Academy of Science. He was awarded the Prof. Ricardo Ferreira Award for Scientific Merit （granted by Pernambuco State Foundation for Science and Technology） and the Prof. Paulo Duarte medal （granted by The Brazilian Association of Chemistry）. Received the medal of the National Order of the Scientific Merit （Brazilian Government, 2018）. He had a Special Issue in the Journal of Luminescence dedicated to his 60s. He was the Chairman of the 18th International Conference on Luminescence, ICL-2017. He is Doctor Honoris Causa by the University of Wrocław. His research interests are in Chemistry and Physics, with emphasis on atomic and molecular spectroscopy, compounds with lanthanide ions, and nanostructured materials.oscar. malta@ufpe. br" ]
  [ "Ricardo L. Longo （1964-）, Ph. D. from University of Florida（USA, 1993）and pos-doc at the QuantumTheory Project（U. of Florida）. Since 1994 he is a professor at the Department of Fundamental Chemistry, Federal University at Pernambuco, Recife, Brazil. He was a visiting at McGill University, Montrèal,Canada（2016）and visiting consultant at University of Aveiro, Portugal（2019）. Served as associate editor of Journal of the Brazilian Chemical Society（2006-2012）and guest editor of Journal of Luminescence （2016 and 2018）. He is an advisor/reviewer in Brazilian funding agencies（CAPES, FACEPE）. His scientific interests cover the development of theoretical and computational methods to physical chemistry, particularly to molecular spectroscopy, thermometry, chemical reactions, hydrogen bonded systems and complex networks. Supervised 10 post-docs, 22 Ph. D. , 21 MSc, and 26 undergraduate students in the Chemistry and Materials Science Programs. Currently, he is supervising 08 Ph. D. and 04 MSc students. He au‑thored 04 book chapters and about 110 papers.ricardo. longo@ufpe. br" ]
- 基金信息：
- DOI：10.37188/CJL.EN20220007
  CLC： O482.31
- Published：05 December 2022，
  
  Received：20 May 2022，
  
  Revised：19 June 2022，
- 稿件说明：
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Albano N Carneiro Neto,Renaldo T Moura Jr,Jorge A A Coelho等.镧系离子间无辐射能量传递速率的教程综述[J].发光学报,2022,43(12):1871-1891.

Neto Albano N Carneiro,Moura Renaldo T,Coelho Jorge A A,et al.A Tutorial Review on the Nonradiative Energy Transfer Rates between Lanthanide Ions[J].Chinese Journal of Luminescence,2022,43(12):1871-1891.
Albano N Carneiro Neto,Renaldo T Moura Jr,Jorge A A Coelho等.镧系离子间无辐射能量传递速率的教程综述[J].发光学报,2022,43(12):1871-1891. DOI： 10.37188/CJL.EN20220007.

Neto Albano N Carneiro,Moura Renaldo T,Coelho Jorge A A,et al.A Tutorial Review on the Nonradiative Energy Transfer Rates between Lanthanide Ions[J].Chinese Journal of Luminescence,2022,43(12):1871-1891. DOI： 10.37188/CJL.EN20220007.

摘要

在本教程综述中，我们重新阐述和表达了镧系离子间无辐射能量传递（ET）速率的理论形式，并且强调了考虑镧系离子本身特异性所引发的与 Förster 和 Dexter 理论不同之处。所给出的表达式遵循了Judd‑Ofelt的4f‑4f跃迁理论框架之下的 Kushida 方法，并计入了如下电多极机制：偶极‑偶极（

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）、偶极‑四极（

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）和四极-四极（

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）。更为重要的是，当前的机制也扩展包括了交换（

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）和磁偶极子⁃磁偶极子（

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）作用，并经过改进进一步包含了屏蔽效应以及给出了

因子（费米黄金规则中的态密度）的解析表达式。与 Kushida 的原始方法类似，我们只考虑了强制电偶极子（FED）对 Judd⁃Ofelt 强度参数的贡献，并细节性地讨论了磁偶极⁃磁偶极相互作用的选择定则以及相关矩阵元的计算。此外，我们还以Tb（Ⅲ）‑Eu（Ⅲ）和 Yb（Ⅲ）⁃Er（Ⅲ）的能量传递速率计算为例，逐步展示了计算过程、主要的计算支撑信息以及所使用的计算脚本。

Abstract

In this tutorial review， we present nonradiative energy transfer（ET） rates between lanthanides in a rearranged form. We emphasize the nature of the contributions which are different from those developed by Förster and Dexter theories because of the unique properties of the lanthanide ions. The expressions discussed here were based on Kushida's approach （electric multipolar mechanisms： dipole‑dipole（

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）， dipole‑quadrupole（

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）， and quadrupole‑quadrupole（

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）） within the Judd-Ofelt framework for 4f-4f transitions. Notice that these mechanisms were extended to include the exchange（

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） and magnetic dipole‑magnetic dipole mechanisms（

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）， and were improved to include shielding effects as well as an analytical expression for the

-factor （density of states in Fermi’s golden rule）. Similar to the original approach of Kushida， only the Forced Electric Dipole（FED） contributions to the Judd-Ofelt intensity parameters should be considered. A detailed discussion of selection rules and matrix elements calculations for the magnetic dipole‑magnetic dipole interaction is presented. In addition， step-by-step examples of Tb（Ⅲ）-Eu（Ⅲ） and Yb（Ⅲ）-Er（Ⅲ） energy transfer rates calculations are provided， with extensive Supporting Information， including scripts for calculations.

关键词

无辐射能量传递镧系理论计算Ln-Ln 能量传递速率选择定则

Keywords

nonradiative energy transferlanthanidestheoretical calculationsLn-Ln energy transfer ratesselection rules

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