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Miranda-Salinas H, Rodriguez-Serrano A, Kaminski JM, Dinkelbach F, Hiromichi N, Kusakabe Y, Kaji H, Marian CM, Monkman AP. Conformational, Host, and Vibrational Effects Giving Rise to Dynamic TADF Behavior in the Through-Space Charge Transfer, Triptycene Bridged Acridine-Triazine Donor Acceptor TADF Molecule TpAT-tFFO. J Phys Chem C Nanomater Interfaces 2023; 127:8607-8617. [PMID: 37197385 PMCID: PMC10184167 DOI: 10.1021/acs.jpcc.2c07529] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/26/2022] [Revised: 04/12/2023] [Indexed: 05/19/2023]
Abstract
We present a joint experimental and theoretical study of the through-space charge transfer (CT) TADF molecule TpAT-tFFO. The measured fluorescence has a singular Gaussian line shape but two decay components, coming from two distinct molecular CT conformers, energetically only 20 meV apart. We determined the intersystem crossing rate (1 × 107 s-1) to be 1 order of magnitude faster than radiative decay, and prompt emission (PF) is therefore quenched within 30 ns, leaving delayed fluorescence (DF) observable from 30 ns onward as the measured reverse intersystem crossing (rISC) rate is >1 × 106 s-1, yielding a DF/PF ratio >98%. Time-resolved emission spectra measured between 30 ns and 900 ms in films show no change in the spectral band shape, but between 50 and 400 ms, we observe a ca. 65 meV red shift of the emission, ascribed to the DF to phosphorescence transition, with the phosphorescence (lifetime >1 s) emanating from the lowest 3CT state. A host-independent thermal activation energy of 16 meV is found, indicating that small-amplitude vibrational motions (∼140 cm-1) of the donor with respect to the acceptor dominate rISC. TpAT-tFFO photophysics is dynamic, and these vibrational motions drive the molecule between maximal rISC rate and high radiative decay configurations so that the molecule can be thought to be "self-optimizing" for the best TADF performance.
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Affiliation(s)
| | - Angela Rodriguez-Serrano
- Institut
für Theoretische Chemie und Computerchemie, Heinrich-Heine-Universität
Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Jeremy M. Kaminski
- Institut
für Theoretische Chemie und Computerchemie, Heinrich-Heine-Universität
Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Fabian Dinkelbach
- Institut
für Theoretische Chemie und Computerchemie, Heinrich-Heine-Universität
Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Nakagawa Hiromichi
- Institute
for Chemical Research Kyoto University, Uji, Kyoto 611-0011, Japan
| | - Yu Kusakabe
- Institute
for Chemical Research Kyoto University, Uji, Kyoto 611-0011, Japan
| | - Hironori Kaji
- Institute
for Chemical Research Kyoto University, Uji, Kyoto 611-0011, Japan
| | - Christel M. Marian
- Institut
für Theoretische Chemie und Computerchemie, Heinrich-Heine-Universität
Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Andrew P. Monkman
- OEM
Research Group, Department of Physics, Durham
University, Durham DH1 3LE, UK
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Wu Z, Dinkelbach F, Kerner F, Friedrich A, Ji L, Stepanenko V, Würthner F, Marian CM, Marder TB. Aggregation‐Induced Dual Phosphorescence from (
o
‐Bromophenyl)‐Bis(2,6‐Dimethylphenyl)Borane at Room Temperature. Chemistry 2022; 28:e202200525. [PMID: 35324026 PMCID: PMC9325438 DOI: 10.1002/chem.202200525] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2022] [Indexed: 11/09/2022]
Abstract
Designing highly efficient purely organic phosphors at room temperature remains a challenge because of fast non‐radiative processes and slow intersystem crossing (ISC) rates. The majority of them emit only single component phosphorescence. Herein, we have prepared 3 isomers (o, m, p‐bromophenyl)‐bis(2,6‐dimethylphenyl)boranes. Among the 3 isomers (o‐, m‐ and p‐BrTAB) synthesized, the ortho‐one is the only one which shows dual phosphorescence, with a short lifetime of 0.8 ms and a long lifetime of 234 ms in the crystalline state at room temperature. Based on theoretical calculations and crystal structure analysis of o‐BrTAB, the short lifetime component is ascribed to the T1M state of the monomer which emits the higher energy phosphorescence. The long‐lived, lower energy phosphorescence emission is attributed to the T1A state of an aggregate, with multiple intermolecular interactions existing in crystalline o‐BrTAB inhibiting nonradiative decay and stabilizing the triplet states efficiently.
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Affiliation(s)
- Zhu Wu
- Institut für Anorganische Chemie and Institute for Sustainable Chemistry & Catalysis with Boron Julius-Maximilians-Universität Würzburg Am Hubland 97074 Würzburg Germany
| | - Fabian Dinkelbach
- Institut für Theoretische Chemie und Computerchemie Heinrich-Heine-Universität Düsseldorf Universitätsstr. 1 40225 Düsseldorf Germany
| | - Florian Kerner
- Institut für Anorganische Chemie and Institute for Sustainable Chemistry & Catalysis with Boron Julius-Maximilians-Universität Würzburg Am Hubland 97074 Würzburg Germany
| | - Alexandra Friedrich
- Institut für Anorganische Chemie and Institute for Sustainable Chemistry & Catalysis with Boron Julius-Maximilians-Universität Würzburg Am Hubland 97074 Würzburg Germany
| | - Lei Ji
- Institut für Anorganische Chemie and Institute for Sustainable Chemistry & Catalysis with Boron Julius-Maximilians-Universität Würzburg Am Hubland 97074 Würzburg Germany
- Frontiers Science Center for Flexible Electronics (FSCFE) & Shaanxi Institute of Flexible Electronics (SIFE) Northwestern Polytechnical University Xi An Shi 127 West Youyi Road 710072 Xi'an P. R. China
| | - Vladimir Stepanenko
- Institut für Organische Chemie and Center for Nanosystems Chemistry Julius-Maximilians-Universität Würzburg Am Hubland 97074 Würzburg Germany
| | - Frank Würthner
- Institut für Organische Chemie and Center for Nanosystems Chemistry Julius-Maximilians-Universität Würzburg Am Hubland 97074 Würzburg Germany
| | - Christel M. Marian
- Institut für Theoretische Chemie und Computerchemie Heinrich-Heine-Universität Düsseldorf Universitätsstr. 1 40225 Düsseldorf Germany
| | - Todd B. Marder
- Institut für Anorganische Chemie and Institute for Sustainable Chemistry & Catalysis with Boron Julius-Maximilians-Universität Würzburg Am Hubland 97074 Würzburg Germany
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Kaminski JM, Rodríguez-Serrano A, Dinkelbach F, Miranda-Salinas H, Monkman AP, Marian CM. Vibronic effects accelerate the intersystem crossing processes of the through-space charge transfer states in the triptycene bridged acridine–triazine donor–acceptor molecule TpAT-tFFO. Chem Sci 2022; 13:7057-7066. [PMID: 35774172 PMCID: PMC9200131 DOI: 10.1039/d1sc07101g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2021] [Accepted: 02/16/2022] [Indexed: 11/21/2022] Open
Abstract
Quantum chemical studies employing combined density functional and multireference configuration interaction methods suggest five excited electronic states to be involved in the prompt and delayed fluorescence emission of TpAT-tFFO. Three of them, a pair of singlet and triplet charge transfer (CT) states (S1 and T1) and a locally excited (LE) triplet state (T3), can be associated with the (Me → N) conformer, the other two CT-type states (S2 and T2) form the lowest excited singlet and triplet states of the (Me → Ph) conformer. The two conformers, which differ in essence by the shearing angle of the face-to-face aligned donor and acceptor moieties, are easily interconverted in the electronic ground state whereas the reorganization energy is substantial in the excited singlet state, thus explaining the two experimentally observed time constants of prompt fluorescence emission. Forward and reverse intersystem crossing between the singlet and triplet CT states is mediated by vibronic spin–orbit interactions involving the LE T3 state. Low-frequency vibrational modes altering the distance and alignment of the donor and acceptor π-systems tune the S1 and T3 states (likewise S2 and T3) into and out of resonance. The enhancement of intersystem crossing due to the interplay of vibronic and spin–orbit coupling is considered a general feature of organic through-space charge-transfer thermally activated delayed fluorescence emitters. DFT/MRCI quantum chemical studies suggest five excited electronic states to be involved in the prompt and delayed fluorescence emission of TpAT-tFFO.![]()
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Affiliation(s)
- Jeremy M. Kaminski
- Institute of Theoretical and Computational Chemistry, Heinrich-Heine-University Düsseldorf, D-40204 Düsseldorf, Germany
| | - Angela Rodríguez-Serrano
- Institute of Theoretical and Computational Chemistry, Heinrich-Heine-University Düsseldorf, D-40204 Düsseldorf, Germany
| | - Fabian Dinkelbach
- Institute of Theoretical and Computational Chemistry, Heinrich-Heine-University Düsseldorf, D-40204 Düsseldorf, Germany
| | | | - Andrew P. Monkman
- Dept of Physics, OEM Research Group, Durham University, Durham, DH1 3LE, UK
| | - Christel M. Marian
- Institute of Theoretical and Computational Chemistry, Heinrich-Heine-University Düsseldorf, D-40204 Düsseldorf, Germany
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Dinkelbach F, Bracker M, Kleinschmidt M, Marian CM. Large Inverted Singlet-Triplet Energy Gaps Are Not Always Favorable for Triplet Harvesting: Vibronic Coupling Drives the (Reverse) Intersystem Crossing in Heptazine Derivatives. J Phys Chem A 2021; 125:10044-10051. [PMID: 34756038 DOI: 10.1021/acs.jpca.1c09150] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Heptazine derivatives are promising dopants for electroluminescent devices. Recent studies raised the question whether heptazines exhibit a small regular or an inverted singlet-triplet (IST) gap. It was argued that the S1 ← T1 reverse intersystem crossing (RISC) is a downhill process in IST emitters and therefore does not require thermal activation, thus enabling efficient harvesting of triplet excitons. Rate constants were not determined in these studies. Modeling the excited-state properties of heptazine proves challenging because fluorescence and intersystem crossing (ISC) are symmetry-forbidden in first order. In this work, we present a comprehensive theoretical study of the photophysics of heptazine and its derivative HAP-3MF. The calculations of electronic excitation energies and vibronic coupling matrix elements have been conducted at the density functional theory/multireference configuration interaction (DFT/MRCI) level of theory. We have employed a finite difference approach to determine nonadiabatic couplings and derivatives of spin-orbit coupling and electric dipole transition matrix elements with respect to normal coordinate displacements. Kinetic constants for fluorescence, phosphorescence, internal conversion (IC), ISC, and RISC have been computed in the framework of a static approach. Radiative S1 ↔ S0 transitions borrow intensity mainly from optically bright E' π → π* states, while S1 ↔ T1 (R)ISC is mediated by E″ states of n → π* character. Test calculations show that IST gaps as large as those reported in the literature are counterproductive and slow down the S1 ← T1 RISC process. Using the adiabatic DFT/MRCI singlet-triplet splitting of -0.02 eV, we find vibronically enhanced ISC and RISC to be fast in the heptazine core compound. Nevertheless, its photo- and electroluminescence quantum yields are predicted to be very low because S1 → S0 IC efficiently quenches the luminescence. In contrast, fluorescence, IC, ISC, and RISC proceed at similar time scales in HAP-3MF.
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Affiliation(s)
- Fabian Dinkelbach
- Institute of Theoretical and Computational Chemistry, Heinrich-Heine-University Düsseldorf, 40225 Düsseldorf, Germany
| | - Mario Bracker
- Institute of Theoretical and Computational Chemistry, Heinrich-Heine-University Düsseldorf, 40225 Düsseldorf, Germany
| | - Martin Kleinschmidt
- Institute of Theoretical and Computational Chemistry, Heinrich-Heine-University Düsseldorf, 40225 Düsseldorf, Germany
| | - Christel M Marian
- Institute of Theoretical and Computational Chemistry, Heinrich-Heine-University Düsseldorf, 40225 Düsseldorf, Germany
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5
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Rodriguez-Serrano A, Dinkelbach F, Marian CM. Intersystem crossing processes in the 2CzPN emitter: a DFT/MRCI study including vibrational spin-orbit interactions. Phys Chem Chem Phys 2021; 23:3668-3678. [PMID: 33527934 DOI: 10.1039/d0cp06011a] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Multireference quantum chemical calculations were performed in order to investigate the (reverse) intersystem crossing ((R)ISC) mechanisms of 4,5-di(9H-carbazol-9-yl)-phthalonitrile (2CzPN). A combination of density funcional theory (DFT) and multireference configuration interaction methods (MRCI) was used. The excellent agreement of the computed absorption spectrum with available experimental absorption spectra lends confidence to the chosen computational protocol. Vertically, two triplet excited states (T1 and T2) are found below the S1 state. At the excited state minima, the calculated adiabatic energies locate only the T1 state below the S1 state. The enhanced charge transfer (CT) character of the geometrically relaxed excited states causes their mutual (direct) spin-orbit coupling (SOC) interaction to be low. Contributions of vibronic SOC to the (R)ISC probability, evaluated by a Herzberg-Teller-like procedure for a temperature of 300 K, are small but not negligible. For ISC, the S1→ T1 channel is the fastest (8 × 106 s-1), while the S1→ T2 channel is found to be thermally activated (9 × 104 s-1) and less efficient when proceeding from the adiabatic S1 state. Our calculations also reveal, however, a barrierless S1→ T2 ISC pathway near the Franck-Condon region. RISC is found to essentially proceed via the T1→ S1 channel, with a rate constant of (3 × 104 s-1) if our adiabatic singlet-triplet energy gap in vacuum (ΔEST = 0.12 eV) is employed. Shifting the potentials to match two experimentally reported singlet-triplet energy gaps in toluene (ΔEST = 0.21 and 0.31 eV, respectively) leads to a drastic reduction of the computed rate constant by up to 4 orders of magnitude. The T2 state is not expected to play a major role in mediating triplet-singlet transitions in 2CzPN unless it is directly populated by hot excitons. No indication for a strong vibronic coupling of the T2 and T1 potentials is found, which could help overcome the negative exponential dependence of the RISC rate constant on the magnitude of the energy gap.
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Affiliation(s)
- Angela Rodriguez-Serrano
- Institut für Theoretische Chemie und Computerchemie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany.
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Wu Z, Nitsch J, Schuster J, Friedrich A, Edkins K, Loebnitz M, Dinkelbach F, Stepanenko V, Würthner F, Marian CM, Ji L, Marder TB. Persistent Room Temperature Phosphorescence from Triarylboranes: A Combined Experimental and Theoretical Study. Angew Chem Int Ed Engl 2020; 59:17137-17144. [PMID: 32573931 PMCID: PMC7540320 DOI: 10.1002/anie.202007610] [Citation(s) in RCA: 50] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2020] [Indexed: 12/11/2022]
Abstract
Achieving highly efficient phosphorescence in purely organic luminophors at room temperature remains a major challenge due to slow intersystem crossing (ISC) rates in combination with effective non-radiative processes in those systems. Most room temperature phosphorescent (RTP) organic materials have O- or N-lone pairs leading to low lying (n, π*) and (π, π*) excited states which accelerate kisc through El-Sayed's rule. Herein, we report the first persistent RTP with lifetimes up to 0.5 s from simple triarylboranes which have no lone pairs. RTP is only observed in the crystalline state and in highly doped PMMA films which are indicative of aggregation induced emission (AIE). Detailed crystal structure analysis suggested that intermolecular interactions are important for efficient RTP. Furthermore, photophysical studies of the isolated molecules in a frozen glass, in combination with DFT/MRCI calculations, show that (σ, B p)→(π, B p) transitions accelerate the ISC process. This work provides a new approach for the design of RTP materials without (n, π*) transitions.
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Affiliation(s)
- Zhu Wu
- Institut für Anorganische Chemie and Institute for Sustainable Chemistry & Catalysis with BoronJulius-Maximilians-Universität WürzburgAm Hubland97074WürzburgGermany
| | - Jörn Nitsch
- Institut für Anorganische Chemie and Institute for Sustainable Chemistry & Catalysis with BoronJulius-Maximilians-Universität WürzburgAm Hubland97074WürzburgGermany
| | - Julia Schuster
- Institut für Anorganische Chemie and Institute for Sustainable Chemistry & Catalysis with BoronJulius-Maximilians-Universität WürzburgAm Hubland97074WürzburgGermany
| | - Alexandra Friedrich
- Institut für Anorganische Chemie and Institute for Sustainable Chemistry & Catalysis with BoronJulius-Maximilians-Universität WürzburgAm Hubland97074WürzburgGermany
| | - Katharina Edkins
- Institut für Anorganische Chemie and Institute for Sustainable Chemistry & Catalysis with BoronJulius-Maximilians-Universität WürzburgAm Hubland97074WürzburgGermany
- School of Health SciencesThe University of ManchesterOxford RoadManchesterM13 9PLUK
| | - Marcel Loebnitz
- Institut für Theoretische Chemie und ComputerchemieHeinrich-Heine-Universität DüsseldorfUniversitätsstr. 140225DüsseldorfGermany
| | - Fabian Dinkelbach
- Institut für Theoretische Chemie und ComputerchemieHeinrich-Heine-Universität DüsseldorfUniversitätsstr. 140225DüsseldorfGermany
| | - Vladimir Stepanenko
- Institut für Organische ChemieJulius-Maximilians-Universität WürzburgAm Hubland97074WürzburgGermany
| | - Frank Würthner
- Institut für Organische ChemieJulius-Maximilians-Universität WürzburgAm Hubland97074WürzburgGermany
| | - Christel M. Marian
- Institut für Theoretische Chemie und ComputerchemieHeinrich-Heine-Universität DüsseldorfUniversitätsstr. 140225DüsseldorfGermany
| | - Lei Ji
- Institut für Anorganische Chemie and Institute for Sustainable Chemistry & Catalysis with BoronJulius-Maximilians-Universität WürzburgAm Hubland97074WürzburgGermany
- Frontiers Science Center for Flexible Electronics (FSCFE) &Shaanxi Institute of Flexible Electronics (SIFE)Northwestern Polytechnical University127 West Youyi Road710072Xi'anChina
| | - Todd B. Marder
- Institut für Anorganische Chemie and Institute for Sustainable Chemistry & Catalysis with BoronJulius-Maximilians-Universität WürzburgAm Hubland97074WürzburgGermany
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7
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Wu Z, Nitsch J, Schuster J, Friedrich A, Edkins K, Loebnitz M, Dinkelbach F, Stepanenko V, Würthner F, Marian CM, Ji L, Marder TB. Persistent Room Temperature Phosphorescence from Triarylboranes: A Combined Experimental and Theoretical Study. Angew Chem Int Ed Engl 2020. [DOI: 10.1002/ange.202007610] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Zhu Wu
- Institut für Anorganische Chemie and Institute for Sustainable Chemistry & Catalysis with Boron Julius-Maximilians-Universität Würzburg Am Hubland 97074 Würzburg Germany
| | - Jörn Nitsch
- Institut für Anorganische Chemie and Institute for Sustainable Chemistry & Catalysis with Boron Julius-Maximilians-Universität Würzburg Am Hubland 97074 Würzburg Germany
| | - Julia Schuster
- Institut für Anorganische Chemie and Institute for Sustainable Chemistry & Catalysis with Boron Julius-Maximilians-Universität Würzburg Am Hubland 97074 Würzburg Germany
| | - Alexandra Friedrich
- Institut für Anorganische Chemie and Institute for Sustainable Chemistry & Catalysis with Boron Julius-Maximilians-Universität Würzburg Am Hubland 97074 Würzburg Germany
| | - Katharina Edkins
- Institut für Anorganische Chemie and Institute for Sustainable Chemistry & Catalysis with Boron Julius-Maximilians-Universität Würzburg Am Hubland 97074 Würzburg Germany
- School of Health Sciences The University of Manchester Oxford Road Manchester M13 9PL UK
| | - Marcel Loebnitz
- Institut für Theoretische Chemie und Computerchemie Heinrich-Heine-Universität Düsseldorf Universitätsstr. 1 40225 Düsseldorf Germany
| | - Fabian Dinkelbach
- Institut für Theoretische Chemie und Computerchemie Heinrich-Heine-Universität Düsseldorf Universitätsstr. 1 40225 Düsseldorf Germany
| | - Vladimir Stepanenko
- Institut für Organische Chemie Julius-Maximilians-Universität Würzburg Am Hubland 97074 Würzburg Germany
| | - Frank Würthner
- Institut für Organische Chemie Julius-Maximilians-Universität Würzburg Am Hubland 97074 Würzburg Germany
| | - Christel M. Marian
- Institut für Theoretische Chemie und Computerchemie Heinrich-Heine-Universität Düsseldorf Universitätsstr. 1 40225 Düsseldorf Germany
| | - Lei Ji
- Institut für Anorganische Chemie and Institute for Sustainable Chemistry & Catalysis with Boron Julius-Maximilians-Universität Würzburg Am Hubland 97074 Würzburg Germany
- Frontiers Science Center for Flexible Electronics (FSCFE) & Shaanxi Institute of Flexible Electronics (SIFE) Northwestern Polytechnical University 127 West Youyi Road 710072 Xi'an China
| | - Todd B. Marder
- Institut für Anorganische Chemie and Institute for Sustainable Chemistry & Catalysis with Boron Julius-Maximilians-Universität Würzburg Am Hubland 97074 Würzburg Germany
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Bracker M, Dinkelbach F, Weingart O, Kleinschmidt M. Impact of fluorination on the photophysics of the flavin chromophore: a quantum chemical perspective. Phys Chem Chem Phys 2019; 21:9912-9923. [DOI: 10.1039/c9cp00805e] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
10-Methylisoalloxazine (MIA) and its fluorinated derivatives (6-9F-MIA) were investigated by means of quantum chemistry, looking into the influence of fluorination on fluorescence, absorption and inter-system crossing (ISC) in vacuum and in aqueous solution.
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Affiliation(s)
- Mario Bracker
- Institut für Theoretische Chemie und Computerchemie
- Heinrich-Heine-Universität Düsseldorf
- 40225 Düsseldorf
- Germany
| | - Fabian Dinkelbach
- Institut für Theoretische Chemie und Computerchemie
- Heinrich-Heine-Universität Düsseldorf
- 40225 Düsseldorf
- Germany
| | - Oliver Weingart
- Institut für Theoretische Chemie und Computerchemie
- Heinrich-Heine-Universität Düsseldorf
- 40225 Düsseldorf
- Germany
| | - Martin Kleinschmidt
- Institut für Theoretische Chemie und Computerchemie
- Heinrich-Heine-Universität Düsseldorf
- 40225 Düsseldorf
- Germany
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9
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Affiliation(s)
- Fabian Dinkelbach
- Institute of Theoretical
and Computational Chemistry, Heinrich Heine University Düsseldorf, Universitätsstr. 1, D-40225 Düsseldorf, Germany
| | - Martin Kleinschmidt
- Institute of Theoretical
and Computational Chemistry, Heinrich Heine University Düsseldorf, Universitätsstr. 1, D-40225 Düsseldorf, Germany
| | - Christel M. Marian
- Institute of Theoretical
and Computational Chemistry, Heinrich Heine University Düsseldorf, Universitätsstr. 1, D-40225 Düsseldorf, Germany
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