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":null,"pages":null},"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.
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