{"title":"Single vibronic level fluorescence spectra from Hagedorn wavepacket dynamics.","authors":"Zhan Tong Zhang, Jiří J L Vaníček","doi":"10.1063/5.0219005","DOIUrl":null,"url":null,"abstract":"<p><p>In single vibronic level (SVL) fluorescence experiments, the electronically excited initial state is also excited in one or several vibrational modes. Because computing such spectra by evaluating all contributing Franck-Condon factors becomes impractical (and unnecessary) in large systems, here we propose a time-dependent approach based on Hagedorn wavepacket dynamics. We use Hagedorn functions-products of a Gaussian and carefully generated polynomials-to represent SVL initial states because in systems whose potential is at most quadratic, Hagedorn functions are exact solutions to the time-dependent Schrödinger equation and can be propagated with the same equations of motion as a simple Gaussian wavepacket. Having developed an efficient recursive algorithm to compute the overlaps between two Hagedorn wavepackets, we can now evaluate emission spectra from arbitrary vibronic levels using a single trajectory. We validate the method in two-dimensional global harmonic models by comparing it with quantum split-operator calculations. In addition, we study the effects of displacement, distortion (squeezing), and Duschinsky rotation on SVL fluorescence spectra. Finally, we demonstrate the applicability of the Hagedorn approach to high-dimensional systems on a displaced, distorted, and Duschinsky-rotated harmonic model with 100 degrees of freedom.</p>","PeriodicalId":15313,"journal":{"name":"Journal of Chemical Physics","volume":null,"pages":null},"PeriodicalIF":3.1000,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Chemical Physics","FirstCategoryId":"92","ListUrlMain":"https://doi.org/10.1063/5.0219005","RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 0
Abstract
In single vibronic level (SVL) fluorescence experiments, the electronically excited initial state is also excited in one or several vibrational modes. Because computing such spectra by evaluating all contributing Franck-Condon factors becomes impractical (and unnecessary) in large systems, here we propose a time-dependent approach based on Hagedorn wavepacket dynamics. We use Hagedorn functions-products of a Gaussian and carefully generated polynomials-to represent SVL initial states because in systems whose potential is at most quadratic, Hagedorn functions are exact solutions to the time-dependent Schrödinger equation and can be propagated with the same equations of motion as a simple Gaussian wavepacket. Having developed an efficient recursive algorithm to compute the overlaps between two Hagedorn wavepackets, we can now evaluate emission spectra from arbitrary vibronic levels using a single trajectory. We validate the method in two-dimensional global harmonic models by comparing it with quantum split-operator calculations. In addition, we study the effects of displacement, distortion (squeezing), and Duschinsky rotation on SVL fluorescence spectra. Finally, we demonstrate the applicability of the Hagedorn approach to high-dimensional systems on a displaced, distorted, and Duschinsky-rotated harmonic model with 100 degrees of freedom.
期刊介绍:
The Journal of Chemical Physics publishes quantitative and rigorous science of long-lasting value in methods and applications of chemical physics. The Journal also publishes brief Communications of significant new findings, Perspectives on the latest advances in the field, and Special Topic issues. The Journal focuses on innovative research in experimental and theoretical areas of chemical physics, including spectroscopy, dynamics, kinetics, statistical mechanics, and quantum mechanics. In addition, topical areas such as polymers, soft matter, materials, surfaces/interfaces, and systems of biological relevance are of increasing importance.
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