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Ghalami F, Dohmen PM, Krämer M, Elstner M, Xie W. Nonadiabatic Simulation of Exciton Dynamics in Organic Semiconductors Using Neural Network-Based Frenkel Hamiltonian and Gradients. J Chem Theory Comput 2024; 20:6160-6174. [PMID: 38976696 DOI: 10.1021/acs.jctc.4c00220] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/10/2024]
Abstract
In this study, we present a multiscale method to simulate the propagation of Frenkel singlet excitons in organic semiconductors (OSCs). The approach uses neural network models to train a Frenkel-type Hamiltonian and its gradient, obtained by the long-range correction version of density functional tight-binding with self-consistent charges. Our models accurately predict site energies, excitonic couplings, and corresponding gradients, essential for the nonadiabatic molecular dynamics simulations. Combined with the fewest switches surface hopping algorithm, the method was applied to four representative OSCs: anthracene, pentacene, perylenediimide, and diindenoperylene. The simulated exciton diffusion constants align well with experimental and reported theoretical values and offer valuable insights into exciton dynamics in OSCs.
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Affiliation(s)
- Farhad Ghalami
- Institute of Physical Chemistry (IPC), Karlsruhe Institute of Technology, Kaiserstr. 12, 76131 Karlsruhe, Germany
- Institute of Nano Technology (INT), Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
| | - Philipp M Dohmen
- Institute of Physical Chemistry (IPC), Karlsruhe Institute of Technology, Kaiserstr. 12, 76131 Karlsruhe, Germany
| | - Mila Krämer
- Institute of Physical Chemistry (IPC), Karlsruhe Institute of Technology, Kaiserstr. 12, 76131 Karlsruhe, Germany
| | - Marcus Elstner
- Institute of Physical Chemistry (IPC), Karlsruhe Institute of Technology, Kaiserstr. 12, 76131 Karlsruhe, Germany
- Institute of Nano Technology (INT), Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
- Institute of Biological Interfaces (IBG-2), Karlsruhe Institute of Technology, Kaiserstr. 12, 76131 Karlsruhe, Germany
| | - Weiwei Xie
- Frontiers Science Center for New Organic Matter, Key Laboratory of Advanced Energy Materials Chemistry (Ministry of Education), State Key Laboratory of Advanced Chemical Power Sources, College of Chemistry, Nankai University, Tianjin 300071, China
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Alvertis AM, Williams-Young DB, Bruneval F, Neaton JB. Influence of Electronic Correlations on Electron-Phonon Interactions of Molecular Systems with the GW and Coupled Cluster Methods. J Chem Theory Comput 2024; 20:6175-6183. [PMID: 38954597 DOI: 10.1021/acs.jctc.4c00327] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/04/2024]
Abstract
Electron-phonon interactions are of great importance to a variety of physical phenomena, and their accurate description is an important goal for first-principles calculations. Isolated examples of materials and molecular systems have emerged where electron-phonon coupling is enhanced over density functional theory (DFT) when using the Green's-function-based ab initio GW method, which provides a more accurate description of electronic correlations. It is, however, unclear how general this enhancement is and how employing high-end quantum chemistry methods, which further improve the description of electronic correlations, might further alter electron-phonon interactions over GW or DFT. Here, we address these questions by computing the renormalization of the highest occupied molecular orbital energies of Thiel's set of organic molecules by harmonic vibrations using DFT, GW, and equation-of-motion coupled-cluster calculations. We find that, depending on the amount of exact exchange included in the DFT starting point, GW can increase the magnitude of the electron-phonon coupling across Thiel's set of molecules by an average factor of 1.1-1.8 compared to the underlying DFT, while equation-of-motion coupled-cluster leads to an increase of 1.4-2. The electron-phonon coupling predicted with the ab initio GW method is generally in much closer agreement to coupled cluster values compared to DFT, establishing GW as a promising route for accurately computing electron-phonon phenomena in molecules and beyond at a much lower computational cost than higher-end quantum chemistry techniques.
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Affiliation(s)
- Antonios M Alvertis
- KBR, Inc., NASA Ames Research Center, Moffett Field, California 94035, United States
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - David B Williams-Young
- Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Fabien Bruneval
- Université Paris-Saclay, CEA, Service de Corrosion et de Comportement des Matériaux, SRMP, 91191 Gif-sur-Yvette, France
| | - Jeffrey B Neaton
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Department of Physics, University of California Berkeley, Berkeley, California 94720, United States
- Kavli Energy NanoScience Institute at Berkeley, Berkeley, California 94720, United States
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Stojanovic L, Giannini S, Blumberger J. Exciton Transport in the Nonfullerene Acceptor O-IDTBR from Nonadiabatic Molecular Dynamics. J Chem Theory Comput 2024; 20:6241-6252. [PMID: 38967252 PMCID: PMC11270823 DOI: 10.1021/acs.jctc.4c00605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2024] [Revised: 06/11/2024] [Accepted: 06/12/2024] [Indexed: 07/06/2024]
Abstract
Theory, computation, and experiment have given strong evidence that charge carriers in organic molecular crystals form partially delocalized quantum objects that diffuse very efficiently via a mechanism termed transient delocalization. It is currently unclear how prevalent this mechanism is for exciton transport. Here we carry out simulation of singlet Frenkel excitons (FE) in a molecular organic semiconductor that belongs to the class of nonfullerene acceptors, O-IDTBR, using the recently introduced FE surface hopping nonadiabatic molecular dynamics method. We find that FE are, on average, localized on a single molecule in the crystal due to sizable reorganization energy and moderate excitonic couplings. Yet, our simulations suggest that the diffusion mechanism is more complex than simple local hopping; in addition to hopping, we observe frequent transient delocalization events where the exciton wave function expands over 10 or more molecules for a short period of time in response to thermal excitations within the excitonic band, followed by de-excitation and contraction onto a single molecule. The transient delocalization events lead to an increase in the diffusion constant by a factor of 3-4, depending on the crystallographic direction as compared to the situation where only local hopping events are considered. Intriguingly, O-IDTBR appears to be a moderately anisotropic 3D "conductor" for excitons but a highly anisotropic 2D conductor for electrons. Taken together with previous simulation results, two trends seem to emerge for molecular organic crystals: excitons tend to be more localized and slower than charge carriers due to higher internal reorganization energy, while exciton transport tends to be more isotropic than charge transport due to the weaker distance dependence of excitonic versus electronic coupling.
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Affiliation(s)
- Ljiljana Stojanovic
- Department
of Physics and Astronomy and Thomas Young Centre, University College London, London WC1E 6BT, U.K.
| | - Samuele Giannini
- Institute
of Chemistry of OrganoMetallic Compounds, National Research Council (ICCOM-CNR), Pisa I-56124, Italy
| | - Jochen Blumberger
- Department
of Physics and Astronomy and Thomas Young Centre, University College London, London WC1E 6BT, U.K.
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Alvertis AM, Haber JB, Li Z, Coveney CJN, Louie SG, Filip MR, Neaton JB. Phonon screening and dissociation of excitons at finite temperatures from first principles. Proc Natl Acad Sci U S A 2024; 121:e2403434121. [PMID: 39024110 PMCID: PMC11287246 DOI: 10.1073/pnas.2403434121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2024] [Accepted: 06/11/2024] [Indexed: 07/20/2024] Open
Abstract
The properties of excitons, or correlated electron-hole pairs, are of paramount importance to optoelectronic applications of materials. A central component of exciton physics is the electron-hole interaction, which is commonly treated as screened solely by electrons within a material. However, nuclear motion can screen this Coulomb interaction as well, with several recent studies developing model approaches for approximating the phonon screening of excitonic properties. While these model approaches tend to improve agreement with experiment, they rely on several approximations that restrict their applicability to a wide range of materials, and thus far they have neglected the effect of finite temperatures. Here, we develop a fully first-principles, parameter-free approach to compute the temperature-dependent effects of phonon screening within the ab initio [Formula: see text]-Bethe-Salpeter equation framework. We recover previously proposed models of phonon screening as well-defined limits of our general framework, and discuss their validity by comparing them against our first-principles results. We develop an efficient computational workflow and apply it to a diverse set of semiconductors, specifically AlN, CdS, GaN, MgO, and [Formula: see text]. We demonstrate under different physical scenarios how excitons may be screened by multiple polar optical or acoustic phonons, how their binding energies can exhibit strong temperature dependence, and the ultrafast timescales on which they dissociate into free electron-hole pairs.
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Affiliation(s)
- Antonios M. Alvertis
- KBR, Inc., NASA Ames Research Center, Moffett Field, CA94035
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA94720
| | - Jonah B. Haber
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA94720
- Department of Materials Science and Engineering, Stanford University, Stanford, CA94305
| | - Zhenglu Li
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA94720
- Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, CA90089
- Department of Physics, University of California Berkeley, Berkeley, CA94720
| | | | - Steven G. Louie
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA94720
- Department of Physics, University of California Berkeley, Berkeley, CA94720
| | - Marina R. Filip
- Department of Physics, University of Oxford, OxfordOX1 3PJ, United Kingdom
| | - Jeffrey B. Neaton
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA94720
- Department of Physics, University of California Berkeley, Berkeley, CA94720
- Kavli Energy NanoScience Institute at Berkeley, Berkeley, CA94720
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Zhang Q, Wang RS, Wang L. Neural canonical transformations for vibrational spectra of molecules. J Chem Phys 2024; 161:024103. [PMID: 38979703 DOI: 10.1063/5.0209255] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2024] [Accepted: 06/19/2024] [Indexed: 07/10/2024] Open
Abstract
The behavior of polyatomic molecules around their equilibrium positions can be regarded as that of quantum-coupled anharmonic oscillators. Solving the corresponding Schrödinger equations enables the interpretation or prediction of the experimental spectra of molecules. In this study, we developed a novel approach for solving the excited states of anharmonic vibrational systems. The normal coordinates of the molecules are transformed into new coordinates through a normalizing flow parameterized by a neural network. This facilitates the construction of a set of orthogonal many-body variational wavefunctions. This methodology has been validated on an exactly solvable 64-dimensional coupled harmonic oscillator, yielding numerical results with a relative error of 10-6. The neural canonical transformations are also applied to calculate the energy levels of two specific molecules, acetonitrile (CH3CN) and ethylene oxide (C2H4O). These molecules involve 12 and 15 vibrational modes, respectively. A key advantage of this approach is its flexibility concerning the potential energy surface, as it requires no specific form. Furthermore, this method can be readily implemented on large-scale distributed computing platforms, making it easy to extend to investigating complex vibrational structures.
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Affiliation(s)
- Qi Zhang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Rui-Si Wang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Lei Wang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
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Hubenko K, Kusber A, Naumann M, Büchner B, Knupfer M. Evolution of the pentacene exciton band width in pentacene-tetracene blends. J Chem Phys 2024; 160:144708. [PMID: 38597316 DOI: 10.1063/5.0188846] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2023] [Accepted: 03/25/2024] [Indexed: 04/11/2024] Open
Abstract
Pentacene is one of the most investigated organic semiconductors. It is well known that the motion of excitons in pentacene and other organic semiconductors is determined by inter-molecular exciton coupling based on charge-transfer processes. In the present study, we demonstrate the impact of the admixture of tetracene, which has a larger band gap and interrupts the pentacene-pentacene interaction, on the exciton behavior in pentacene. Using a combination of optical absorption and electron energy-loss spectroscopy, we show that both the Davydov splitting and the exciton band width in pentacene strongly decrease with increasing tetracene concentration, while the decrease of the exciton band width is substantially larger.
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Affiliation(s)
- Kateryna Hubenko
- Leibniz Institute for Solid State and Materials Research, Helmholtz Str. 20, D-01069 Dresden, Germany
- Institute for Scintillation Materials National Academy of Sciences of Ukraine, 60 Nauky ave., 61072 Kharkiv, Ukraine
| | - Anncharlott Kusber
- Leibniz Institute for Solid State and Materials Research, Helmholtz Str. 20, D-01069 Dresden, Germany
| | - Marco Naumann
- Leibniz Institute for Solid State and Materials Research, Helmholtz Str. 20, D-01069 Dresden, Germany
| | - Bernd Büchner
- Leibniz Institute for Solid State and Materials Research, Helmholtz Str. 20, D-01069 Dresden, Germany
| | - Martin Knupfer
- Leibniz Institute for Solid State and Materials Research, Helmholtz Str. 20, D-01069 Dresden, Germany
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7
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Cohen G, Haber JB, Neaton JB, Qiu DY, Refaely-Abramson S. Phonon-Driven Femtosecond Dynamics of Excitons in Crystalline Pentacene from First Principles. PHYSICAL REVIEW LETTERS 2024; 132:126902. [PMID: 38579218 DOI: 10.1103/physrevlett.132.126902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2023] [Revised: 08/24/2023] [Accepted: 02/11/2024] [Indexed: 04/07/2024]
Abstract
Nonradiative exciton relaxation processes are critical for energy transduction and transport in optoelectronic materials, but how these processes are connected to the underlying crystal structure and the associated electron, exciton, and phonon band structures, as well as the interactions of all these particles, is challenging to understand. Here, we present a first-principles study of exciton-phonon relaxation pathways in pentacene, a paradigmatic molecular crystal and optoelectronic semiconductor. We compute the momentum- and band-resolved exciton-phonon interactions, and use them to analyze key scattering channels. We find that both exciton intraband scattering and interband scattering to parity-forbidden dark states occur on the same ∼100 fs timescale as a direct consequence of the longitudinal-transverse splitting of the bright exciton band. Consequently, exciton-phonon scattering exists as a dominant nonradiative relaxation channel in pentacene. We further show how the propagation of an exciton wave packet is connected with crystal anisotropy, which gives rise to the longitudinal-transverse exciton splitting and concomitant anisotropic exciton and phonon dispersions. Our results provide a framework for understanding the role of exciton-phonon interactions in exciton nonradiative lifetimes in molecular crystals and beyond.
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Affiliation(s)
- Galit Cohen
- Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Jonah B Haber
- Department of Physics, University of California Berkeley, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Jeffrey B Neaton
- Department of Physics, University of California Berkeley, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Kavli Energy Nanosciences Institute at Berkeley, Berkeley, California 94720, USA
| | - Diana Y Qiu
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
| | - Sivan Refaely-Abramson
- Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovot 7610001, Israel
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8
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Akimov AV. Energy-Conserving and Thermally Corrected Neglect of Back-Reaction Approximation Method for Nonadiabatic Molecular Dynamics. J Phys Chem Lett 2023; 14:11673-11683. [PMID: 38109379 DOI: 10.1021/acs.jpclett.3c03029] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2023]
Abstract
In this work, the energy-conserving and thermally corrected neglect of the back-reaction approximation approach for nonadiabatic molecular dynamics in extended atomistic systems is developed. The new approach introduces three key corrections to the original method: (1) it enforces the total energy conservation, (2) it introduces an explicit coupling of the system to its environment, and (3) it introduces a renormalization of nonadiabatic couplings to account for a difference between the instantaneous nuclear kinetic energy and the kinetic energy of guiding trajectories. In the new approach, an auxiliary kinetic energy variable is introduced as an independent dynamical variable. The new approach produces nonzero equilibrium populations, whereas the original neglect of the back-reaction approximation method does not. It yields population relaxation time scales that are favorably comparable to the reference values, and it introduces an explicit and controllable way of dissipating energy into a bath without an assumption of the bath being at equilibrium.
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Affiliation(s)
- Alexey V Akimov
- Department of Chemistry, University at Buffalo, The State University of New York, Buffalo, New York 14260 United States
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9
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Chen Y, Filip MR. Tunable Interlayer Delocalization of Excitons in Layered Organic-Inorganic Halide Perovskites. J Phys Chem Lett 2023; 14:10634-10641. [PMID: 37983171 PMCID: PMC10694835 DOI: 10.1021/acs.jpclett.3c02339] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2023] [Revised: 10/20/2023] [Accepted: 11/09/2023] [Indexed: 11/22/2023]
Abstract
Layered organic-inorganic halide perovskites exhibit remarkable structural and chemical diversity and hold great promise for optoelectronic devices. In these materials, excitons are thought to be strongly confined within the inorganic metal halide layers with interlayer coupling generally suppressed by the organic cations. Here, we present an in-depth study of the energy and spatial distribution of the lowest-energy excitons in layered organic-inorganic halide perovskites from first-principles many-body perturbation theory, within the GW approximation and the Bethe-Salpeter equation. We find that the quasiparticle band structures, linear absorption spectra, and exciton binding energies depend strongly on the distance and the alignment of adjacent metal halide perovskite layers. Furthermore, we show that exciton delocalization can be modulated by tuning the interlayer distance and alignment, both parameters determined by the chemical composition and size of the organic cations. Our calculations establish the general intuition needed to engineer excitonic properties in novel halide perovskite nanostructures.
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Affiliation(s)
- Yinan Chen
- Department of Physics, University
of Oxford, Clarendon Laboratory, Oxford OX1 3PU, U.K.
| | - Marina R. Filip
- Department of Physics, University
of Oxford, Clarendon Laboratory, Oxford OX1 3PU, U.K.
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10
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Scholes GD. Large Coherent States Formed from Disordered k-Regular Random Graphs. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1519. [PMID: 37998211 PMCID: PMC10670866 DOI: 10.3390/e25111519] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2023] [Revised: 11/01/2023] [Accepted: 11/03/2023] [Indexed: 11/25/2023]
Abstract
The present work is motivated by the need for robust, large-scale coherent states that can play possible roles as quantum resources. A challenge is that large, complex systems tend to be fragile. However, emergent phenomena in classical systems tend to become more robust with scale. Do these classical systems inspire ways to think about robust quantum networks? This question is studied by characterizing the complex quantum states produced by mapping interactions between a set of qubits from structure in graphs. We focus on maps based on k-regular random graphs where many edges were randomly deleted. We ask how many edge deletions can be tolerated. Surprisingly, it was found that the emergent coherent state characteristic of these graphs was robust to a substantial number of edge deletions. The analysis considers the possible role of the expander property of k-regular random graphs.
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Affiliation(s)
- Gregory D Scholes
- Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
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11
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Müller K, Schellhammer KS, Gräßler N, Debnath B, Liu F, Krupskaya Y, Leo K, Knupfer M, Ortmann F. Directed exciton transport highways in organic semiconductors. Nat Commun 2023; 14:5599. [PMID: 37699907 PMCID: PMC10497625 DOI: 10.1038/s41467-023-41044-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2022] [Accepted: 08/21/2023] [Indexed: 09/14/2023] Open
Abstract
Exciton bandwidths and exciton transport are difficult to control by material design. We showcase the intriguing excitonic properties in an organic semiconductor material with specifically tailored functional groups, in which extremely broad exciton bands in the near-infrared-visible part of the electromagnetic spectrum are observed by electron energy loss spectroscopy and theoretically explained by a close contact between tightly packing molecules and by their strong interactions. This is induced by the donor-acceptor type molecular structure and its resulting crystal packing, which induces a remarkable anisotropy that should lead to a strongly directed transport of excitons. The observations and detailed understanding of the results yield blueprints for the design of molecular structures in which similar molecular features might be used to further explore the tunability of excitonic bands and pave a way for organic materials with strongly enhanced transport and built-in control of the propagation direction.
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Affiliation(s)
- Kai Müller
- Center for Advancing Electronics Dresden, Technische Universität Dresden, 01062, Dresden, Germany
- Institut für Theoretische Physik, Technische Universität Dresden, 01062, Dresden, Germany
| | - Karl S Schellhammer
- Center for Advancing Electronics Dresden, Technische Universität Dresden, 01062, Dresden, Germany
- Dresden Integrated Center for Applied Physics and Photonic Materials (IAPP) and Institute for Applied Physics, Technische Universität Dresden, 01062, Dresden, Germany
| | - Nico Gräßler
- Dresden Integrated Center for Applied Physics and Photonic Materials (IAPP) and Institute for Applied Physics, Technische Universität Dresden, 01062, Dresden, Germany
- Leibniz Institute for Solid State and Materials Research Dresden, Helmholtzstr. 20, 01069, Dresden, Germany
| | - Bipasha Debnath
- Leibniz Institute for Solid State and Materials Research Dresden, Helmholtzstr. 20, 01069, Dresden, Germany
| | - Fupin Liu
- Leibniz Institute for Solid State and Materials Research Dresden, Helmholtzstr. 20, 01069, Dresden, Germany
| | - Yulia Krupskaya
- Leibniz Institute for Solid State and Materials Research Dresden, Helmholtzstr. 20, 01069, Dresden, Germany
| | - Karl Leo
- Dresden Integrated Center for Applied Physics and Photonic Materials (IAPP) and Institute for Applied Physics, Technische Universität Dresden, 01062, Dresden, Germany
| | - Martin Knupfer
- Leibniz Institute for Solid State and Materials Research Dresden, Helmholtzstr. 20, 01069, Dresden, Germany
| | - Frank Ortmann
- Center for Advancing Electronics Dresden, Technische Universität Dresden, 01062, Dresden, Germany.
- Department of Chemistry, TUM School of Natural Sciences, Technische Universität München, Lichtenbergstr. 4, 85748, Garching b. München, Germany.
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