Strongly Bound Frenkel Excitons on TiO2 Nanoparticles: An Evolutionary and DFT Approach

IF 2.1 4区 工程技术 Q3 CHEMISTRY, PHYSICAL
Oscar Olvera-Neria, Raúl García-Cruz, Julio Gonzalez-Torres, Luz María García-Cruz, Jean Luis Castillo-Sánchez, Enrique Poulain
{"title":"Strongly Bound Frenkel Excitons on TiO2 Nanoparticles: An Evolutionary and DFT Approach","authors":"Oscar Olvera-Neria, Raúl García-Cruz, Julio Gonzalez-Torres, Luz María García-Cruz, Jean Luis Castillo-Sánchez, Enrique Poulain","doi":"10.1155/2024/4014216","DOIUrl":null,"url":null,"abstract":"An evolutionary algorithm was employed to locate the global minimum of <svg height=\"12.5794pt\" style=\"vertical-align:-3.29107pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 40.3374 12.5794\" width=\"40.3374pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,4.498,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,12.31,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,15.837,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,25.585,3.132)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,30.531,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,35.029,3.132)\"></path></g></svg> nanoparticles with <span><svg height=\"8.55521pt\" style=\"vertical-align:-0.2063904pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.34882 17.789 8.55521\" width=\"17.789pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,10.158,0)\"></path></g></svg><span></span><span><svg height=\"8.55521pt\" style=\"vertical-align:-0.2063904pt\" version=\"1.1\" viewbox=\"21.3711838 -8.34882 25.728 8.55521\" width=\"25.728pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,21.421,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,27.661,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,34.446,0)\"><use xlink:href=\"#g113-51\"></use></g><g transform=\"matrix(.013,0,0,-0.013,40.686,0)\"></path></g></svg>.</span></span> More than 61,000 structures were calculated with a semiempirical method and reoptimized using density functional theory. The exciton binding energy of TiO<sub>2</sub> nanoparticles was determined through the fundamental and optical band gap. Frenkel exciton energy scales as <span><svg height=\"14.7729pt\" style=\"vertical-align:-3.181499pt\" version=\"1.1\" viewbox=\"-0.0498162 -11.5914 50.365 14.7729\" width=\"50.365pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,7.943,3.132)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,15.987,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,20.485,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,25.41,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,34.604,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,42.734,0)\"><use xlink:href=\"#g117-34\"></use></g></svg><span></span><svg height=\"14.7729pt\" style=\"vertical-align:-3.181499pt\" version=\"1.1\" viewbox=\"53.9471838 -11.5914 27.042 14.7729\" width=\"27.042pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,53.997,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,60.237,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,63.201,0)\"><use xlink:href=\"#g113-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,69.441,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,75.683,0)\"></path></g></svg><span></span><span><svg height=\"14.7729pt\" style=\"vertical-align:-3.181499pt\" version=\"1.1\" viewbox=\"80.9941838 -11.5914 22.844 14.7729\" width=\"22.844pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,81.044,0)\"><use xlink:href=\"#g113-111\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,87.57,-5.741)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,92.002,-5.741)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,94.159,-5.741)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,98.59,-5.741)\"></path></g></svg>,</span></span> resulting in strongly bound excitons of 0.132–1.2 eV for about 1.4 nm nanoparticles. Although the exciton energy decreases with the system size, these tightly bound Frenkel excitons inhibit the separation of photogenerated charge carriers, making their application in photocatalysis and photovoltaic devices difficult, and imposing a minimum particle size. In contrast, the exciton binding energy of rutile is 4 meV, where the Wannier exciton energy scales as <span><svg height=\"15.0208pt\" style=\"vertical-align:-3.429399pt\" version=\"1.1\" viewbox=\"-0.0498162 -11.5914 50.365 15.0208\" width=\"50.365pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-70\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,7.943,3.132)\"><use xlink:href=\"#g190-67\"></use></g><g transform=\"matrix(.013,0,0,-0.013,15.987,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,20.485,0)\"><use xlink:href=\"#g190-102\"></use></g><g transform=\"matrix(.013,0,0,-0.013,25.41,0)\"><use xlink:href=\"#g190-87\"></use></g><g transform=\"matrix(.013,0,0,-0.013,34.604,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,42.734,0)\"><use xlink:href=\"#g117-34\"></use></g></svg><span></span><svg height=\"15.0208pt\" style=\"vertical-align:-3.429399pt\" version=\"1.1\" viewbox=\"53.9471838 -11.5914 42.672 15.0208\" width=\"42.672pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,53.997,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,60.237,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,66.477,0)\"><use xlink:href=\"#g113-47\"></use></g><g transform=\"matrix(.013,0,0,-0.013,69.441,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,75.681,0)\"><use xlink:href=\"#g113-50\"></use></g><g transform=\"matrix(.013,0,0,-0.013,84.096,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,91.313,0)\"><use xlink:href=\"#g113-48\"></use></g></svg><span></span><span><svg height=\"15.0208pt\" style=\"vertical-align:-3.429399pt\" version=\"1.1\" viewbox=\"96.62418380000001 -11.5914 10.633 15.0208\" width=\"10.633pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,96.674,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,102.005,-5.741)\"><use xlink:href=\"#g50-51\"></use></g></svg>.</span></span> Moreover, the Wannier excitons in bulk TiO<sub>2</sub> are delocalized according to the Bohr radii: 3.9 nm for anatase and 7.7 nm for rutile.","PeriodicalId":14195,"journal":{"name":"International Journal of Photoenergy","volume":"116 1","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Photoenergy","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1155/2024/4014216","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 0

Abstract

An evolutionary algorithm was employed to locate the global minimum of nanoparticles with . More than 61,000 structures were calculated with a semiempirical method and reoptimized using density functional theory. The exciton binding energy of TiO2 nanoparticles was determined through the fundamental and optical band gap. Frenkel exciton energy scales as , resulting in strongly bound excitons of 0.132–1.2 eV for about 1.4 nm nanoparticles. Although the exciton energy decreases with the system size, these tightly bound Frenkel excitons inhibit the separation of photogenerated charge carriers, making their application in photocatalysis and photovoltaic devices difficult, and imposing a minimum particle size. In contrast, the exciton binding energy of rutile is 4 meV, where the Wannier exciton energy scales as . Moreover, the Wannier excitons in bulk TiO2 are delocalized according to the Bohr radii: 3.9 nm for anatase and 7.7 nm for rutile.
二氧化钛纳米粒子上的强结合 Frenkel 激子:演化和 DFT 方法
采用进化算法找出了具有......和......的纳米粒子的全局最小值。使用半经验方法计算了 61,000 多种结构,并使用密度泛函理论进行了重新优化。通过基带隙和光带隙确定了二氧化钛纳米粒子的激子结合能。Frenkel 激子能量的刻度为 ,因此,对于约 1.4 nm 的纳米粒子,强结合激子的能量为 0.132-1.2 eV。虽然激子能量随系统尺寸的增大而降低,但这些紧密结合的 Frenkel 激子会抑制光生电荷载流子的分离,使其难以应用于光催化和光伏设备,并对最小粒径提出了要求。相比之下,金红石的激子结合能为 4 meV,其中 Wannier 激子能的尺度为 。此外,根据玻尔半径,块状二氧化钛中的万尼尔激子是分散的:锐钛型为 3.9 纳米,金红石型为 7.7 纳米。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
CiteScore
6.00
自引率
3.10%
发文量
128
审稿时长
3.6 months
期刊介绍: International Journal of Photoenergy is a peer-reviewed, open access journal that publishes original research articles as well as review articles in all areas of photoenergy. The journal consolidates research activities in photochemistry and solar energy utilization into a single and unique forum for discussing and sharing knowledge. The journal covers the following topics and applications: - Photocatalysis - Photostability and Toxicity of Drugs and UV-Photoprotection - Solar Energy - Artificial Light Harvesting Systems - Photomedicine - Photo Nanosystems - Nano Tools for Solar Energy and Photochemistry - Solar Chemistry - Photochromism - Organic Light-Emitting Diodes - PV Systems - Nano Structured Solar Cells
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信