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Zhang X, Chen X, Sun Y, Zhao J. Radical enhanced intersystem crossing mechanism, electron spin dynamics of high spin states and their applications in the design of heavy atom-free triplet photosensitizers. Org Biomol Chem 2024; 22:5257-5283. [PMID: 38884590 DOI: 10.1039/d4ob00520a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/18/2024]
Abstract
Heavy atom-free triplet photosensitizers (PSs) can overcome the high cost and biological toxicity of traditional molecular systems containing heavy atoms (such as Pt(II), Ir(III), Ru(II), Pd(II), Lu(III), I, or Br atoms) and, therefore, are developing rapidly. Connecting a stable free radical to the chromophore can promote the intersystem crossing (ISC) process through electron spin exchange interaction to produce the triplet state of the chromophore or the doublet (D) and quartet (Q) states when taking the whole spin system into account. These molecular systems based on the radical enhanced ISC (REISC) mechanism are important in the field of heavy atom-free triplet PSs. The REISC system has a simple molecular structure and good biocompatibility, and it is especially helpful for building high-spin quantum states (D and Q states) that have the potential to be developed as qubits in quantum information science. This review introduces the molecular structure design for the purpose of high-spin states. Time-resolved electron paramagnetic resonance (TREPR) is the most important characterization method to reveal the properties of these molecular systems, generation mechanism and electron spin polarization (ESP) of the high spin states. The spin polarization manipulation of high spin states and potential application in the field of quantum information engineering are also summarized. Moreover, molecular design principles of the REISC system to obtain long absorption wavelength, high triplet state quantum yield and long triplet state lifetime are introduced, as well as applications of the compounds in triplet-triplet annihilation upconversion, photodynamic therapy and bioimaging. This review is useful for the design of heavy atom-free triplet PSs based on the radical-chromophore molecular structure motif and the study of the photophysics of the compounds, as well as the electron spin dynamics of the multi electron system upon photoexcitation.
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Affiliation(s)
- Xue Zhang
- State Key Laboratory of Fine Chemicals, Frontiers Science Centre for Smart Materials, School of Chemical Engineering, Dalian University of Technology, Dalian 116024, P. R. China.
| | - Xi Chen
- State Key Laboratory of Fine Chemicals, Frontiers Science Centre for Smart Materials, School of Chemical Engineering, Dalian University of Technology, Dalian 116024, P. R. China.
| | - Yue Sun
- State Key Laboratory of Fine Chemicals, Frontiers Science Centre for Smart Materials, School of Chemical Engineering, Dalian University of Technology, Dalian 116024, P. R. China.
| | - Jianzhang Zhao
- State Key Laboratory of Fine Chemicals, Frontiers Science Centre for Smart Materials, School of Chemical Engineering, Dalian University of Technology, Dalian 116024, P. R. China.
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2
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Hudson JM, Evans EW. Radical Spin Polarization and Magnetosensitivity from Reversible Energy Transfer. J Phys Chem Lett 2024; 15:4130-4135. [PMID: 38593182 PMCID: PMC11033935 DOI: 10.1021/acs.jpclett.4c00656] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/29/2024] [Revised: 03/27/2024] [Accepted: 03/29/2024] [Indexed: 04/11/2024]
Abstract
Molecular spins provide potential building units for future quantum information science and spintronic technologies. In particular, doublet (S = 1/2) and triplet (S = 1) molecular spin states have the potential for excellent optical and spin properties for these applications if useful photon-spin mechanisms at room temperature can be devised. Here we explore the potential of exploiting reversible energy transfer between triplet and doublet states to establish magnetosensitive luminescence and spin polarization. We investigate the dependence of the photon-spin mechanism on the magnitude and sign of the exchange interaction between the doublet and triplet spin components in amorphous and crystalline model systems. The design of a magnetic field inclination sensor is proposed from understanding the required "structure" (spin interactions) to "function" (magnetosensitivity).
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Affiliation(s)
- John M. Hudson
- Department
of Chemistry, Swansea University, Swansea SA2 8PP, United Kingdom
- Centre
for Integrative Semiconductor Materials, Swansea SA1 8EN, United Kingdom
| | - Emrys W. Evans
- Department
of Chemistry, Swansea University, Swansea SA2 8PP, United Kingdom
- Centre
for Integrative Semiconductor Materials, Swansea SA1 8EN, United Kingdom
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3
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Kirk ML, Shultz DA, Marri AR, van der Est A. Photoinduced Magnetic Exchange-Jump Promotes Ground State Biradical Electron Spin Polarization. J Am Chem Soc 2024; 146:9285-9292. [PMID: 38518125 DOI: 10.1021/jacs.4c00930] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/24/2024]
Abstract
Photoinduced electron spin polarization (ESP) is reported in the electronic ground states of three Pt(II) complexes comprised of two S = 1/2 nitronyl nitroxide (NN) radicals attached through different length para-phenylethynyl bridges to the 3,6 positions of a catecholate (CAT, donor) and 4,4'-di-tert-butyl-2,2'-bipyridine (bpy, acceptor). Complexes 1-3 have from 17 to 41 bonds separating NN radicals and display cw-EPR spectra consistent with |JNN-NN| ≫ |aN|, |JNN-NN| ≥ |aN|, and |JNN-NN| < |aN|, respectively, where JNN-NN is the magnetic exchange coupling between NN radicals in the electronic ground state, and aN is the isotropic 14N hyperfine coupling constant. Light-induced transient EPR spectra characterized as enhanced ground-state absorption were observed for all three complexes using 532 nm pulsed laser excitation into the ligand-to-ligand charge transfer (LL'CT) band of the (CAT)Pt(bpy) chromophore. The magnitude of the observed ESP increases in the order 1 < 2 < 3 and is inversely correlated with the magnitude of ground-state JNN-NN. In addition to the experimental observation of net absorptive polarization in 1-3, light excitation also produces multiplet polarization in 2. Since the weak dipolar coupling leads to a strong spectral overlap of the absorptive and emissive components, the multiplet polarization is not observed in 1 and 3 and is very weak in 2. The ability to spin-polarize multiple radical spins with a single photon is anticipated to advance new photoinduced multi qubit/qudit ESP protocols for quantum information science applications.
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Affiliation(s)
- Martin L Kirk
- Department of Chemistry and Chemical Biology, The University of New Mexico, MSC03 2060, 1 University of New Mexico, Albuquerque, New Mexico 87131-0001, United States
- The Center for High Technology Materials, The University of New Mexico, Albuquerque, New Mexico 87106, United States
- Center for Quantum Information and Control (CQuIC), The University of New Mexico, Albuquerque, New Mexico 87131-0001, United States
- Center for Computational Chemistry, The University of New Mexico, Albuquerque, New Mexico 87131-0001, United States
| | - David A Shultz
- Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695-8204, United States
| | - Anil Reddy Marri
- Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695-8204, United States
| | - Art van der Est
- Department of Chemistry, Brock University, St. Catharines, Ontario L2S 3A1, Canada
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4
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Kato K, Teki Y. Theoretical investigation of multi-spin excited states of anthracene radical-linked π-conjugated spin systems by computational chemistry. Phys Chem Chem Phys 2024; 26:8106-8114. [PMID: 38407399 DOI: 10.1039/d3cp06335f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/27/2024]
Abstract
Multi-spin excited states of chromophore radical-linked π-conjugated spin systems are investigated by molecular orbital calculations based on density functional theory (DFT). The investigated systems consist of an anthracene photosensitive unit leading to a triplet-excited-state (S = 1), π-conjugated linker to propagate spin exchange-coupling, and stable organic radical with a doublet-ground-state (S = 1/2). The intramolecular exchange coupling (JDQ), g value, and fine-structure interaction of their excited states depended on the π-conjugation network (π-topology), type of radical, and molecular structure of the π-linker (length and dihedral angle). The exchange interaction was dependent on the π-topology and the type of radical species. A decrease in the dihedral angle between the anthracene moiety and phenyl linker in the photo-excited state led to larger exchange coupling. With an increase in the π-linker length (r), the magnitude of the exchange coupling gradually decreased in the photoexcited states according to JDQ = JEx0 exp(-βr), similar to the ground-state exchange. The g values of the quartet (Q) state depended only on the radical type (independent of the linker). Conversely, the fine-structure interaction of the Q state was independent of the radical type and depended on both the linker length and the dihedral angle.
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Affiliation(s)
- Ken Kato
- Institute for Protein Research, Osaka University, 3-2 Yamadaoka, Suita-shi, Osaka 565-0871, Japan.
| | - Yoshio Teki
- Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
- Graduate School of Engineering, Osaka Metropolitan University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan.
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Miller PD, Shultz DA, Mengell J, Kirk ML, Wojtas L. Variation from closed-shell to open shell electronic structures in oligothiophene bis(dioxolene) complexes. Chem Sci 2023; 14:12264-12276. [PMID: 37969598 PMCID: PMC10631215 DOI: 10.1039/d3sc02341a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2023] [Accepted: 10/07/2023] [Indexed: 11/17/2023] Open
Abstract
A series of oligothiophene bis(dioxolene) complexes, SQ-Thn-SQ (SQ = S = ½TpCum,MeZnII(3-tert-butyl-orthosemiquinonate); TpCum,Me = tris(5-cumenyl-3-methylpyrazolyl)borate anion) have been synthesized, structurally characterized, and studied as a function of the number of thiophene bridging units, n (n = 0-3) using a combination of variable-temperature (VT) electronic absorption and EPR spectroscopies, and VT magnetic susceptibility measurements. The thiophene bridge bond lengths determined by X-ray crystallography display dramatic differences across the SQ-Thn-SQ series. Bridge bond deviation values (Σ|Δi|) display a progressive change in the nature of the bridge fragment bonding as the number of thiophene groups increases, with quinoidal bridge character for n = 1 (SQ-Th-SQ) and biradical character with "aromatic" bridge bond lengths for n = 3 (SQ-Th3-SQ). Remarkably, for n = 2 (SQ-Th2-SQ) the nature of the bridge fragment is intermediate between quinoid and biradical aromatic, which we describe as having open-shell character as opposed to biradicaloid since the open-shell biradical configuration does not have the correct symmetry to mix with the quinoidal ground-state configuration. This bridge bonding character is reflected in the energies of the lowest lying open-shell states for these three molecules. The SQ-Th-SQ molecule is diamagnetic at all temperatures studied, and we provide evidence for SQ-SQ antiferromagnetic exchange coupling and population of triplet states in SQ-Th2-SQ and SQ-Th3-SQ, with JSQ-SQ(ave) = -279 cm-1 (VT EPR/electronic absorption/magnetic susceptibility) and JSQ-SQ = -117 cm-1 (VT EPR/electronic absorption/magnetic susceptibility), respectively. The results have been interpreted in the context of state configurational mixing within a simplified 4-electron, 3-orbital model that explicitly contains contributions of a bridge fragment. Variable-temperature spectroscopic- and magnetic susceptibility data are consistent with two low-lying open-shell states for SQ-Th3-SQ, but three low-lying states (one closed-shell and two open-shell) for SQ-Th2-SQ. This model provides a simple symmetry-based framework to understand the continuum of electronic and geometric structures of this class of molecules as a function of the number of thiophene units in the bridge.
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Affiliation(s)
- Paul D Miller
- Department of Chemistry, North Carolina State University Raleigh North Carolina 27695-8204 USA
| | - David A Shultz
- Department of Chemistry, North Carolina State University Raleigh North Carolina 27695-8204 USA
| | - Joshua Mengell
- Department of Chemistry and Chemical Biology, The University of New Mexico MSC03 2060, 1 University of New Mexico Albuquerque NM 87131-0001 USA
| | - Martin L Kirk
- Department of Chemistry and Chemical Biology, The University of New Mexico MSC03 2060, 1 University of New Mexico Albuquerque NM 87131-0001 USA
- The Center for High Technology Materials, The University of New Mexico Albuquerque New Mexico 87106 USA
- Center for Quantum Information and Control (CQuIC), The University of New Mexico Albuquerque New Mexico 87131-0001 USA
| | - Lukasz Wojtas
- Department of Chemistry, University of South Florida 4202 E. Fowler Avenue, CHE 205 Tampa FL 33620-5250 USA
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Kirk ML, Shultz DA, Hewitt P, Marri AR, van der Est A. Competitive reversed quartet mechanisms for photogenerated ground state electron spin polarization. Chem Sci 2023; 14:9689-9695. [PMID: 37736649 PMCID: PMC10510625 DOI: 10.1039/d3sc03049k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2023] [Accepted: 08/06/2023] [Indexed: 09/23/2023] Open
Abstract
Photoinduced electron spin polarization (ESP) of a spin-½ organic radical (nitronyl nitroxide, NN) in a series of Pt(ii) complexes comprised of 4,4'-di-tert-butyl-2,2'-bipyridine (bpy) and 3-tert-butylcatecholate (CAT) ligands, where the CAT ligand is substituted with (CH3)n-meta-phenyl-NN (bridge-NN) groups, is presented and discussed. We show the importance of attenuating the energy gap between localized NN radical and chromophoric excited states to control both the magnitude and sign of the optically-generated ESP, and to provide deeper insight into the details of the ESP mechanism. Understanding electronic structure contributions to optically generated ESP will enhance our ability to control the nature of prepared states for a variety of quantum information science applications, where strong ESP facilitates enhanced sensitivity and readout capabilities at low applied magnetic fields and higher temperatures.
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Affiliation(s)
- Martin L Kirk
- Department of Chemistry and Chemical Biology, The University of New Mexico MSC03 2060, 1 University of New Mexico Albuquerque NM 87131-0001 USA
- The Center for High Technology Materials, The University of New Mexico Albuquerque New Mexico 87106 USA
- Center for Quantum Information and Control (CQuIC), The University of New Mexico Albuquerque New Mexico 87131-0001 USA
| | - David A Shultz
- Department of Chemistry, North Carolina State University Raleigh North Carolina 27695-8204 USA
| | - Patrick Hewitt
- Department of Chemistry, North Carolina State University Raleigh North Carolina 27695-8204 USA
| | - Anil Reddy Marri
- Department of Chemistry, North Carolina State University Raleigh North Carolina 27695-8204 USA
| | - Art van der Est
- Department of Chemistry, Brock University St. Catharines Ontario Canada L2S 3A1
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7
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Shultz DA, Stephenson R, Kirk ML. Dinuclear ligand-to-ligand charge transfer complexes. Dalton Trans 2023; 52:1970-1976. [PMID: 36691821 DOI: 10.1039/d2dt03385b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Abstract
The synthesis and characterization of dinuclear ligand-to-ligand charge transfer complexes are described. Each complex is comprised of square-planar platinum(II) coordinated to a 3-tert-butyl-orthocatecholate donor and a 4,4'-di-tert-butyl-2,2'-bipyridine acceptor. Both complexes exhibit donor → acceptor ligand-to-ligand charge transfer (LL'CT) bands in the visible spectrum. The platinum complexes are covalently attached at the catecholate 5-position to either a meta- or para-phenylene bridge fragment. Both cyclic voltammetry and electronic absorption spectroscopy exhibit features characteristic of intramolecular interaction between the platinum centres. The LL'CT excited state lifetimes are ∼twofold longer than the mononuclear parent complex. The properties of these complexes are discussed and compared to similar complexes in the literature.
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Affiliation(s)
- David A Shultz
- Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695-8204, USA.
| | - Riley Stephenson
- Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695-8204, USA.
| | - Martin L Kirk
- Department of Chemistry and Chemical Biology, The University of New Mexico, MSC03 2060, 1 University of New Mexico, Albuquerque, NM 87131-0001, USA.,The Center for High Technology Materials, The University of New Mexico, Albuquerque, New Mexico 87106, USA.,Center for Quantum Information and Control (CQuIC), The University of New Mexico, Albuquerque, New Mexico 87131-0001, USA
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8
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Chen J, Yang J, Yadav M, Shultz DA, Kirk ML. Origin of Ferromagnetic Exchange Coupling in Donor-Acceptor Biradical Analogues of Charge-Separated Excited States. Inorg Chem 2023; 62:739-747. [PMID: 36598509 DOI: 10.1021/acs.inorgchem.2c02903] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
A new donor-acceptor biradical complex, TpCum,MeZn(SQ-VD) (TpCum,MeZn+ = zinc(II) hydro-tris(3-cumenyl-5-methylpyrazolyl)borate complex cation; SQ = orthosemiquinone; VD = oxoverdazyl), which is a ground-state analogue of a charge-separated excited state, has been synthesized and structurally characterized. The magnetic exchange interaction between the S = 1/2 SQ and the S = 1/2 VD within the SQ-VD biradical ligand is observed to be ferromagnetic, with JSQ-VD = +77 cm-1 (H = -2JSQ-VDŜSQ·ŜVD) determined from an analysis of the variable-temperature magnetic susceptibility data. The pairwise biradical exchange interaction in TpCum,MeZn(SQ-VD) can be compared with that of the related donor-acceptor biradical complex TpCum,MeZn(SQ-NN) (NN = nitronyl nitroxide, S = 1/2), where JSQ-NN ≅ +550 cm-1. This represents a dramatic reduction in the biradical exchange by a factor of ∼7, despite the isolobal nature of the VD and NN acceptor radical SOMOs. Computations assessing the magnitude of the exchange were performed using a broken-symmetry density functional theory (DFT) approach. These computations are in good agreement with those computed at the CASSCF NEVPT2 level, which also reveals an S = 1 triplet ground state as observed in the magnetic susceptibility measurements. A combination of electronic absorption spectroscopy and CASSCF computations has been used to elucidate the electronic origin of the large difference in the magnitude of the biradical exchange coupling between TpCum,MeZn(SQ-VD) and TpCum,MeZn(SQ-NN). A Valence Bond Configuration Interaction (VBCI) model was previously employed to highlight the importance of mixing an SQSOMO → NNLUMO charge transfer configuration into the electronic ground state to facilitate the stabilization of the high-spin triplet (S = 1) ground state in TpCum,MeZn(SQ-NN). Here, CASSCF computations confirm the importance of mixing the pendant radical (e.g., VD, NN) LUMO (VDLUMO and NNLUMO) with the SOMO of the SQ radical (SQSOMO) for stabilizing the triplet, in addition to spin polarization and charge transfer contributions to the exchange. An important electronic structure difference between TpCum,MeZn(SQ-VD) and TpCum,MeZn(SQ-NN), which leads to their different exchange couplings, is the reduced admixture of excited states that promote ferromagnetic exchange into the TpCum,MeZn(SQ-VD) ground state, and the intrinsically weaker mixing between the VDLUMO and the SQSOMO compared to that observed for TpCum,MeZn(SQ-NN), where this orbital mixing is significant. The results of this comparative study contribute to a greater understanding of biradical exchange interactions, which are important to our understanding of excited-state singlet-triplet energy gaps, electron delocalization, and the generation of electron spin polarization in both the ground and excited states of (bpy)Pt(CAT-radical) complexes.
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Affiliation(s)
- Ju Chen
- Department of Chemistry and Chemical Biology, The University of New Mexico, MSC03 2060, 1 University of New Mexico, Albuquerque, New Mexico87131-0001, United States
| | - Jing Yang
- Department of Chemistry and Chemical Biology, The University of New Mexico, MSC03 2060, 1 University of New Mexico, Albuquerque, New Mexico87131-0001, United States
| | - Munendra Yadav
- Department of Chemistry and Chemical Biology, The University of New Mexico, MSC03 2060, 1 University of New Mexico, Albuquerque, New Mexico87131-0001, United States
| | - David A Shultz
- Department of Chemistry, North Carolina State University, Raleigh, North Carolina27695-8204, United States
| | - Martin L Kirk
- Department of Chemistry and Chemical Biology, The University of New Mexico, MSC03 2060, 1 University of New Mexico, Albuquerque, New Mexico87131-0001, United States.,The Center for High Technology Materials, The University of New Mexico, Albuquerque, New Mexico87106, United States.,Center for Quantum Information and Control (CQuIC), The University of New Mexico, Albuquerque, New Mexico87131-0001, United States
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9
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Kirk ML, Shultz DA, Marri AR, Hewitt P, van der Est A. Single-Photon-Induced Electron Spin Polarization of Two Exchange-Coupled Stable Radicals. J Am Chem Soc 2022; 144:21005-21009. [DOI: 10.1021/jacs.2c09680] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Affiliation(s)
- Martin L. Kirk
- Department of Chemistry and Chemical Biology, The University of New Mexico, MSC03 2060, 1 University of New Mexico, Albuquerque, New Mexico87131-0001, United States
- Center for High Technology Materials, The University of New Mexico, Albuquerque, New Mexico87106, United States
- Center for Quantum Information and Control (CQuIC), The University of New Mexico, Albuquerque, New Mexico87131-0001, United States
| | - David A. Shultz
- Department of Chemistry, North Carolina State University, Raleigh, North Carolina27695-8204, United States
| | - Anil Reddy Marri
- Department of Chemistry, North Carolina State University, Raleigh, North Carolina27695-8204, United States
| | - Patrick Hewitt
- Department of Chemistry, North Carolina State University, Raleigh, North Carolina27695-8204, United States
| | - Art van der Est
- Department of Chemistry, Brock University, St. Catharines, Ontario, CanadaL2S 3A1
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Franz M, Neese F, Richert S. Calculation of exchange couplings in the electronically excited state of molecular three-spin systems. Chem Sci 2022; 13:12358-12366. [PMID: 36382276 PMCID: PMC9629084 DOI: 10.1039/d2sc04701b] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2022] [Accepted: 09/17/2022] [Indexed: 09/19/2023] Open
Abstract
Photogenerated molecular three-spin systems, composed of a chromophore and a covalently bound stable radical, are promising candidates for applications in the field of molecular spintronics. Through excitation with light, an excited doublet state and a quartet state are generated, whereby their energy difference depends on the exchange interaction J TR between the chromophore triplet state (T) and the stable radical (R). In order to establish design rules for new materials to be used in molecular spintronics devices, it is of great importance to gain knowledge on the magnitude of J TR as well as the factors influencing J TR on a molecular level. Here, we present a robust and reliable computational method to determine excited state exchange couplings in three-electron-three-centre systems based on a CASSCF/QD-NEVPT2 approach. The methodology is benchmarked and then applied to a series of molecules composed of a perylene chromophore covalently linked to various stable radicals. We calculate the phenomenological exchange interaction J TR between chromophore and radical, which can be compared directly to the experiment, but also illustrate how the individual exchange interactions J ij can be extracted using an effective Hamiltonian that corresponds to the Heisenberg-Dirac-Van-Vleck Hamiltonian. The latter procedure enables a more detailed analysis of the contributions to the exchange interaction J TR and yields additional insight that will be invaluable for future design optimisation.
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Affiliation(s)
- Michael Franz
- Institute of Physical Chemistry, University of Freiburg Albertstraße 21 79104 Freiburg Germany
| | - Frank Neese
- Max-Planck-Institut für Kohlenforschung Kaiser-Wilhelm-Platz 1 45470 Mülheim an der Ruhr Germany
| | - Sabine Richert
- Institute of Physical Chemistry, University of Freiburg Albertstraße 21 79104 Freiburg Germany
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