1
|
Reddy SR, Coto PB, Thoss M. Intramolecular singlet fission: Quantum dynamical simulations including the effect of the laser field. J Chem Phys 2024; 160:194306. [PMID: 38767260 DOI: 10.1063/5.0209546] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2024] [Accepted: 04/30/2024] [Indexed: 05/22/2024] Open
Abstract
In the previous work [Reddy et al., J. Chem. Phys. 151, 044307 (2019)], we have analyzed the dynamics of the intramolecular singlet fission process in a series of prototypical pentacene-based dimers, where the pentacene monomers are covalently bonded to a phenylene linker in ortho, meta, and para positions. The results obtained were qualitatively consistent with the experimental data available, showing an ultrafast population of the multiexcitonic state that mainly takes place via a mediated (superexchange-like) mechanism involving charge transfer and doubly excited states. Our results also highlighted the instrumental role of molecular vibrations in the process as a sizable population of the multiexcitonic state could only be obtained through vibronic coupling. Here, we extend these studies and investigate the effect of the laser field on the dynamics of intramolecular singlet fission by explicitly including the coupling to the laser field in our model. In this manner, and by selectively tuning the laser field to the different low-lying absorption bands of the systems investigated, we analyze the wavelength dependence of the intramolecular singlet fission process. In addition, we have also analyzed how the nature of the initially photoexcited electronic state (either localized or delocalized) affects its dynamics. Altogether, our results provide new insights into the design of intramolecular singlet fission-active molecules.
Collapse
Affiliation(s)
- S Rajagopala Reddy
- Department of Chemistry, School of Chemical Sciences and Pharmacy, Central University of Rajasthan, NH-8, Bandarsindri, Ajmer, Rajasthan 305817, India
| | - Pedro B Coto
- Materials Physics Center (CFM), Spanish National Research Council (CSIC) and Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal 5, 20018 Donostia-San Sebastián, Spain
| | - Michael Thoss
- Institute of Physics, Albert-Ludwigs University Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
| |
Collapse
|
2
|
Mencaroni L, Elisei F, Marrocchi A, Spalletti A, Carlotti B. Intramolecular Singlet Fission Coupled with Intermolecular Triplet Separation as a Strategy to Achieve High Triplet Yields in Fluorene-Based Small Molecules. J Phys Chem B 2024; 128:3442-3453. [PMID: 38544417 DOI: 10.1021/acs.jpcb.4c00194] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/12/2024]
Abstract
In this work, detailed experimental proof and in-depth analysis of the singlet fission (SF) mechanism, operative in fluorene-based small molecules, are carried out by employing advanced time-resolved spectroscopies with nanosecond and femtosecond resolution. The investigation of the effect of solution concentration and solvent viscosity together with temperature and excitation wavelength demonstrates INTRAmolecular formation of the correlated triplet pair followed by INTERmolecular independent triplet separation via a "super-diffusional" triplet-triplet transfer process. This unconventional INTRA- to INTERmolecular SF may be considered an "ideal" mechanism. Indeed, intramolecular formation of the correlated triplet pair is here interestingly proved for small molecules rather than large multichromophoric systems, allowing easy synthesis and processability while maintaining good control over the SF process. On the other hand, the intermolecular triplet separation may be exploited to achieve high triplet quantum yields in these new SF small molecules.
Collapse
Affiliation(s)
- Letizia Mencaroni
- Department of Chemistry, Biology and Biotechnology and CEMIN, University of Perugia, via dell'Elce di sotto n.8, Perugia 06123, Italy
| | - Fausto Elisei
- Department of Chemistry, Biology and Biotechnology and CEMIN, University of Perugia, via dell'Elce di sotto n.8, Perugia 06123, Italy
| | - Assunta Marrocchi
- Department of Chemistry, Biology and Biotechnology and CEMIN, University of Perugia, via dell'Elce di sotto n.8, Perugia 06123, Italy
| | - Anna Spalletti
- Department of Chemistry, Biology and Biotechnology and CEMIN, University of Perugia, via dell'Elce di sotto n.8, Perugia 06123, Italy
| | - Benedetta Carlotti
- Department of Chemistry, Biology and Biotechnology and CEMIN, University of Perugia, via dell'Elce di sotto n.8, Perugia 06123, Italy
| |
Collapse
|
3
|
Wang K, Chen X, Xu J, Peng S, Wu D, Xia J. Recent Advance in the Development of Singlet-Fission-Capable Polymeric Materials. Macromol Rapid Commun 2024; 45:e2300241. [PMID: 37548255 DOI: 10.1002/marc.202300241] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2023] [Revised: 07/24/2023] [Indexed: 08/08/2023]
Abstract
Singlet fission (SF) is a spin-allowed process in which a higher-energy singlet exciton is converted into two lower-energy triplet excitons via a triplet pair intermediate state. Implementing SF in photovoltaic devices holds the potential to exceed the Shockley-Queisser limit of conventional single-junction solar cells. Although great progress has been made in exploiting the underlying mechanism of SF over the past decades, the scope of materials capable of SF, particularly polymeric materials, remains poor. SF-capable polymer is one of the most potential candidates in the implementation of SF into devices due to their distinct superiorities in flexibility, solution processability and self-assembly behavior. Notably, recent advancements have demonstrated high-performance SF in isolated donor-acceptor (D-A) copolymer chains. This review provides an overview of recent progress in the development of SF-capable polymeric materials, with a significant focus on elucidating the mechanisms of SF in polymers and optimizing the design strategies for SF-capable polymers. Additionally, the paper discusses the challenges encountered in this field and presents future perspectives. It is expected that this comprehensive review will offer valuable insights into the design of novel SF-capable polymeric materials, further advancing the potential for SF implementation in photovoltaic devices.
Collapse
Affiliation(s)
- Kangwei Wang
- State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Center of Smart Materials and Devices, Wuhan University of Technology, Wuhan, 430070, China
| | - Xingyu Chen
- International School of Materials Science and Engineering, Wuhan University of Technology, Wuhan, 430070, China
| | - Jingwen Xu
- International School of Materials Science and Engineering, Wuhan University of Technology, Wuhan, 430070, China
| | - Shaoqian Peng
- State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Center of Smart Materials and Devices, Wuhan University of Technology, Wuhan, 430070, China
| | - Di Wu
- State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Center of Smart Materials and Devices, Wuhan University of Technology, Wuhan, 430070, China
- School of Chemistry, Chemical Engineering and Life Science, Wuhan University of Technology, Wuhan, 430070, China
| | - Jianlong Xia
- State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Center of Smart Materials and Devices, Wuhan University of Technology, Wuhan, 430070, China
- International School of Materials Science and Engineering, Wuhan University of Technology, Wuhan, 430070, China
- School of Chemistry, Chemical Engineering and Life Science, Wuhan University of Technology, Wuhan, 430070, China
| |
Collapse
|
4
|
Blaskovits JT, Laplaza R, Vela S, Corminboeuf C. Data-Driven Discovery of Organic Electronic Materials Enabled by Hybrid Top-Down/Bottom-Up Design. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2024; 36:e2305602. [PMID: 37815223 DOI: 10.1002/adma.202305602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2023] [Revised: 09/05/2023] [Indexed: 10/11/2023]
Abstract
The high-throughput exploration and screening of molecules for organic electronics involves either a 'top-down' curation and mining of existing repositories, or a 'bottom-up' assembly of user-defined fragments based on known synthetic templates. Both are time-consuming approaches requiring significant resources to compute electronic properties accurately. Here, 'top-down' is combined with 'bottom-up' through automatic assembly and statistical models, thus providing a platform for the fragment-based discovery of organic electronic materials. This study generates a top-down set of 117K synthesized molecules containing structures, electronic and topological properties and chemical composition, and uses them as building blocks for bottom-up design. A tool is developed to automate the coupling of these building blocks at their C(sp2/sp)-H bonds, providing a fundamental link between the two dataset construction philosophies. Statistical models are trained on this dataset and a subset of resulting top-down/bottom-up compounds, enabling on-the-fly prediction of ground and excited state properties with high accuracy across organic compound space. With access to ab initio-quality optical properties, this bottom-up pipeline may be applied to any materials design campaign using existing compounds as building blocks. To illustrate this, over a million molecules are screened for singlet fission. tThe leading candidates provide insight into the features promoting this multiexciton-generating process.
Collapse
Affiliation(s)
- J Terence Blaskovits
- Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École Polytechnique Fedéralé de Lausanne (EPFL), Lausanne, 1015, Switzerland
| | - Ruben Laplaza
- Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École Polytechnique Fedéralé de Lausanne (EPFL), Lausanne, 1015, Switzerland
- National Centre for Competence in Research "Sustainable chemical processes through catalysis (NCCR Catalysis)" École Polytechnique Fédérale de Lausanne, Lausanne, 1015, Switzerland
| | - Sergi Vela
- Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École Polytechnique Fedéralé de Lausanne (EPFL), Lausanne, 1015, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials (NCCR MARVEL),Ecole Polytechnique Fédérale de Lausanne, Lausanne, 1015, Switzerland
| | - Clémence Corminboeuf
- Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École Polytechnique Fedéralé de Lausanne (EPFL), Lausanne, 1015, Switzerland
- National Centre for Competence in Research "Sustainable chemical processes through catalysis (NCCR Catalysis)" École Polytechnique Fédérale de Lausanne, Lausanne, 1015, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials (NCCR MARVEL),Ecole Polytechnique Fédérale de Lausanne, Lausanne, 1015, Switzerland
| |
Collapse
|
5
|
Mencaroni L, Alebardi M, Elisei F, Škorić I, Spalletti A, Carlotti B. Unveiling the double triplet nature of the 2Ag state in conjugated stilbenoid compounds to achieve efficient singlet fission. Phys Chem Chem Phys 2023; 25:21089-21099. [PMID: 37527269 DOI: 10.1039/d3cp02805d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/03/2023]
Abstract
In this investigation, the excited-state evolution in a series of all-trans stilbenoid compounds, displaying a low-lying dark singlet state of 2Ag-like symmetry nearly degenerate with the bright 1Bu state, was unveiled by employing advanced ultrafast spectroscopies while probing the effect of solvent polarizability. Together with the dual emission, femtosecond transient absorption and broadband fluorescence up-conversion disclosed the double nature of the 2Ag-like state showing both singlet features, a lifetime typical of a singlet and the ability to emit, and a triplet character, exhibiting a triplet-like absorption spectrum. The ultrafast formation (in hundreds of femtoseconds) from the non-relaxed upper singlet state led to the identification of 2Ag as the correlated triplet pair of singlet fission. The spectral difference obtained by comparison of transient absorption peaks of the 2Ag (1TT) and the triplet states was found to be in remarkable agreement with the observed triplet yield and the 1(TT) separation rate constant. Indeed, this spectral shift provided an experimental method to gain qualitative insight into the ease of separation of the 1(TT) and the relative SF efficiency. The highly conjugated polyene-like structures enable the ultrafast formation of the double triplet, but then the large binding energy prevents the triplet separation and thus the effective completion of singlet fission. Even though thermodynamically feasible for all the investigated stilbenoids according to TD-DFT calculations, singlet fission resulted to occur efficiently in the case of 1-(pyridyl-4-ylethenyl)-4-(p-nitrostyryl)benzene and nitro-styrylfuran with the triplet yield reaching 120% and 140%, respectively, triggered by their greatly enhanced intramolecular charge transfer character relative to the other compounds in the series.
Collapse
Affiliation(s)
- Letizia Mencaroni
- Department of Chemistry, Biology and Biotechnology, University of Perugia, via elce di sotto 8, 06123 Perugia, Italy.
| | - Martina Alebardi
- Department of Chemistry, Biology and Biotechnology, University of Perugia, via elce di sotto 8, 06123 Perugia, Italy.
| | - Fausto Elisei
- Department of Chemistry, Biology and Biotechnology, University of Perugia, via elce di sotto 8, 06123 Perugia, Italy.
| | - Irena Škorić
- Department of Organic Chemistry, Faculty of Chemical Engineering and Technology, University of Zagreb, 10000 Zagreb, Croatia
| | - Anna Spalletti
- Department of Chemistry, Biology and Biotechnology, University of Perugia, via elce di sotto 8, 06123 Perugia, Italy.
| | - Benedetta Carlotti
- Department of Chemistry, Biology and Biotechnology, University of Perugia, via elce di sotto 8, 06123 Perugia, Italy.
| |
Collapse
|
6
|
Walia R, Yang J. Exploring optimal multimode vibronic pathways in singlet fission of azaborine analogues of perylene. Photochem Photobiol Sci 2022; 21:1689-1700. [PMID: 35716333 DOI: 10.1007/s43630-022-00251-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2022] [Accepted: 05/23/2022] [Indexed: 10/18/2022]
Abstract
The development of new singlet fission chromophores is a vibrant area of research to explore the possibility of efficient photovoltaic devices. Using high-level ab-initio density matrix renormalization group calculations, we present a systematic analysis of BN-doped perylenes for their potential application as singlet fission candidates. Four singlet fission chromophores are identified considering the monomer-based properties and their excitonic characters are further analyzed in a dimer configuration optimized in a six-dimensional space for local maxima of fission rates. Furthermore, a multistate multimode vibronic Hamiltonian is employed to identify intra- and interstate vibrational pathways for excitation energy modulation. Several photophysical properties such as Davydov splitting, activation energy and vibronic admixture of multiexcitonic and charge-transfer states are calculated for physically accessible dimers. The optimal dimer packing results in appropriate vibrational relaxation of singlet fission states and promotes significant population transfer which would be more attenuated without such couplings. This work not only identifies potential singlet fission systems with favorable electronic properties but also highlights the sensitivity of dimer packings with respect to the substitution patterns in singlet fission chromophores.
Collapse
Affiliation(s)
- Rajat Walia
- Department of Chemistry, The University of Hong Kong, Pokfulam Road, Hong Kong, People's Republic of China
| | - Jun Yang
- Department of Chemistry, The University of Hong Kong, Pokfulam Road, Hong Kong, People's Republic of China.
| |
Collapse
|
7
|
Fumanal M, Corminboeuf C. Optimizing the Thermodynamics and Kinetics of the Triplet-Pair Dissociation in Donor-Acceptor Copolymers for Intramolecular Singlet Fission. CHEMISTRY OF MATERIALS : A PUBLICATION OF THE AMERICAN CHEMICAL SOCIETY 2022; 34:4115-4121. [PMID: 35573105 PMCID: PMC9097278 DOI: 10.1021/acs.chemmater.2c00367] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/04/2022] [Revised: 03/09/2022] [Indexed: 06/15/2023]
Abstract
Singlet fission (SF) is a two-step process in which a singlet splits into two triplets throughout the so-called correlated triplet-pair (1TT) state. Intramolecular SF (iSF) materials, in particular, have attracted growing interest as they can be easily implemented in single-junction solar cells and boost their power conversion efficiency. Still, the potential of iSF materials such as polymers and oligomers for photovoltaic applications has been partially hindered by their ability to go beyond the 1TT intermediate and generate free triplets, whose mechanism remains poorly understood. In this work, the main aspects governing the 1TT dissociation in donor-acceptor copolymers and the key features that optimize this process are exposed. First, we show that both thermodynamics and kinetics play a crucial role in the intramolecular triplet-pair separation and second, we uncover the inherent flexibility of the donor unit as the fundamental ingredient to optimize them simultaneously. Overall, these results provide a better understanding of the intramolecular 1TT dissociation process and establish a new paradigm for the development of novel iSF active materials.
Collapse
|
8
|
Chen WK, Cui G, Liu XY. Solvent effects on excited-state relaxation dynamics of paddle-wheel BODIPY-Hexaoxatriphenylene conjugates: Insights from non-adiabatic dynamics simulations. CHINESE J CHEM PHYS 2022. [DOI: 10.1063/1674-0068/cjcp2110214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Abstract
Understanding the excited state dynamics of donor-acceptor (D-A) complexes is of fundamental importance both experimentally and theoretically. Herein, we have first explored the photoinduced dynamics of a recently synthesized paddle-wheel BODIPY-hexaoxatriphenylene (BODIPY is the abbreviation for BF2-chelated dipyrromethenes) conjugates D-A complexes with the combination of both electronic structure calculations and non-adiabatic dynamics simulations. On the basis of computational results, we concluded that the BODIPY-hexaoxatriphenylene (BH) conjugates will be promoted to the local excited (LE) states of the BODIPY fragments upon excitation, which is followed by the ultrafast exciton transfer from LE state to charge transfer (CT). Instead of the photoinduced electron transfer process proposed in previous experimental work, such a exciton transfer process is accompanied with the photoinduced hole transfer from BODIPY to hexaoxatriphenylene. Additionally, solvent effects are found to play an important role in the photoinduced dynamics. Specifically, the hole transfer dynamics is accelerated by the acetonitrile solvent, which can be ascribed to significant influences of the solvents on the charge transfer states, i.e. the energy gaps between LE and CT excitons are reduced greatly and the non-adiabatic couplings are increased in the meantime. Our present work not only provides valuable insights into the underlying photoinduced mechanism of BH, but also can be helpful for the future design of novel donor-acceptor conjugates with better optoelectronic performance.
Collapse
Affiliation(s)
- Wen-Kai Chen
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Ganglong Cui
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Xiang-Yang Liu
- College of Chemistry and Material Science, Sichuan Normal University, Chengdu 610068, China
| |
Collapse
|
9
|
Fumanal M, Corminboeuf C. Pushing the Limits of the Donor-Acceptor Copolymer Strategy for Intramolecular Singlet Fission. J Phys Chem Lett 2021; 12:7270-7277. [PMID: 34318679 DOI: 10.1021/acs.jpclett.1c01986] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Donor-acceptor (D-A) copolymers have shown great potential for intramolecular singlet fission (iSF). Nonetheless, very few design principles exist for optimizing these systems for iSF, with very little knowledge about how to engineer them for this purpose. In recent work, a fundamental trade-off between the main electronic ingredients required for iSF capable D-A coplanar copolymers was revealed. Still, further investigations are needed to understand these limitations and learn how to bypass them. In this work, we propose to induce torsion as an effective way to circumvent the limits of the coplanar approach. We disclose the potential of noncoplanar copolymers with inherently low triplet energies that encompass all the characteristics required for iSF beyond the limiting values associated with fully coplanar systems. Our findings shed some light on the electronic structure aspects of D-A copolymers for iSF and offer a new avenue for the rational design of novel promising candidates.
Collapse
Affiliation(s)
- Maria Fumanal
- Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Clémence Corminboeuf
- Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| |
Collapse
|
10
|
Pandya R, Alvertis AM, Gu Q, Sung J, Legrand L, Kréher D, Barisien T, Chin AW, Schnedermann C, Rao A. Exciton Diffusion in Highly-Ordered One Dimensional Conjugated Polymers: Effects of Back-Bone Torsion, Electronic Symmetry, Phonons and Annihilation. J Phys Chem Lett 2021; 12:3669-3678. [PMID: 33829788 PMCID: PMC8154834 DOI: 10.1021/acs.jpclett.1c00193] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2021] [Accepted: 03/23/2021] [Indexed: 06/12/2023]
Abstract
Many optoelectronic devices based on organic materials require rapid and long-range singlet exciton transport. Key factors controlling exciton transport include material structure, exciton-phonon coupling and electronic state symmetry. Here, we employ femtosecond transient absorption microscopy to study the influence of these parameters on exciton transport in one-dimensional conjugated polymers. We find that excitons with 21Ag- symmetry and a planar backbone exhibit a significantly higher diffusion coefficient (34 ± 10 cm2 s-1) compared to excitons with 11Bu+ symmetry (7 ± 6 cm2 s-1) with a twisted backbone. We also find that exciton transport in the 21Ag- state occurs without exciton-exciton annihilation. Both 21Ag- and 11Bu+ states are found to exhibit subdiffusive behavior. Ab initio GW-BSE calculations reveal that this is due to the comparable strengths of the exciton-phonon interaction and exciton coupling. Our results demonstrate the link between electronic state symmetry, backbone torsion and phonons in exciton transport in π-conjugated polymers.
Collapse
Affiliation(s)
- Raj Pandya
- Cavendish
Laboratory, University of Cambridge, J.J. Thomson Avenue, CB3 0HE, Cambridge, United Kingdom
| | - Antonios M. Alvertis
- Cavendish
Laboratory, University of Cambridge, J.J. Thomson Avenue, CB3 0HE, Cambridge, United Kingdom
| | - Qifei Gu
- Cavendish
Laboratory, University of Cambridge, J.J. Thomson Avenue, CB3 0HE, Cambridge, United Kingdom
| | - Jooyoung Sung
- Cavendish
Laboratory, University of Cambridge, J.J. Thomson Avenue, CB3 0HE, Cambridge, United Kingdom
| | - Laurent Legrand
- Sorbonne
Université, CNRS, Institut
des NanoSciences de Paris, INSP, 4 place Jussieu, F-75005 Paris, France
| | - David Kréher
- Sorbonne
Université, CNRS, Institut
Parisien de Chimie Moléculaire (IPCM) UMR 8232, Chimie des
Polymères, 4 Place
Jussieu, 75005 Paris, France
| | - Thierry Barisien
- Sorbonne
Université, CNRS, Institut
des NanoSciences de Paris, INSP, 4 place Jussieu, F-75005 Paris, France
| | - Alex W. Chin
- Sorbonne
Université, CNRS, Institut
des NanoSciences de Paris, INSP, 4 place Jussieu, F-75005 Paris, France
| | - Christoph Schnedermann
- Cavendish
Laboratory, University of Cambridge, J.J. Thomson Avenue, CB3 0HE, Cambridge, United Kingdom
| | - Akshay Rao
- Cavendish
Laboratory, University of Cambridge, J.J. Thomson Avenue, CB3 0HE, Cambridge, United Kingdom
| |
Collapse
|
11
|
He G, Busby E, Appavoo K, Wu Q, Xia J, Campos LM, Sfeir MY. Charge transfer states impact the triplet pair dynamics of singlet fission polymers. J Chem Phys 2020; 153:244902. [PMID: 33380093 DOI: 10.1063/5.0029858] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
Polymers are desirable optoelectronic materials, stemming from their solution processability, tunable electronic properties, and large absorption coefficients. An exciting development is the recent discovery that singlet fission (SF), the conversion of a singlet exciton to a pair of triplet states, can occur along the backbone of an individual conjugated polymer chain. Compared to other intramolecular SF compounds, the nature of the triplet pair state in SF polymers remains poorly understood, hampering the development of new materials with optimized excited state dynamics. Here, we investigate the effect of solvent polarity on the triplet pair dynamics in the SF polymer polybenzodithiophene-thiophene-1,1-dioxide. We use transient emission measurements to study isolated polymer chains in solution and use the change in the solvent polarity to investigate the role of charge transfer character in both the singlet exciton and the triplet pair multiexciton. We identify both singlet fluorescence and direct triplet pair emission, indicating significant symmetry breaking. Surprisingly, the singlet emission peak is relatively insensitive to solvent polarity despite its nominal "charge-transfer" nature. In contrast, the redshift of the triplet pair energy with increasing solvent polarity indicates significant charge transfer character. While the energy separation between singlet and triplet pair states increases with solvent polarity, the overall SF rate constant depends on both the energetic driving force and additional environmental factors. The triplet pair lifetime is directly determined by the solvent effect on its overall energy. The dominant recombination channel is a concerted, radiationless decay process that scales as predicted by a simple energy gap law.
Collapse
Affiliation(s)
- Guiying He
- Department of Physics, Graduate Center, City University of New York, New York, New York 10016, USA
| | - Erik Busby
- Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - Kannatassen Appavoo
- Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - Qin Wu
- Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - Jianlong Xia
- School of Chemistry, Chemical Engineering and Life Science; State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, China
| | - Luis M Campos
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Matthew Y Sfeir
- Department of Physics, Graduate Center, City University of New York, New York, New York 10016, USA
| |
Collapse
|
12
|
Fumanal M, Corminboeuf C. Direct, Mediated, and Delayed Intramolecular Singlet Fission Mechanism in Donor-Acceptor Copolymers. J Phys Chem Lett 2020; 11:9788-9794. [PMID: 33147966 DOI: 10.1021/acs.jpclett.0c03076] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Donor-acceptor (D-A) extended copolymers have shown great potential to be exploited for intramolecular singlet fission (iSF) because of their modular tunability and intrinsic ability to incorporate low-lying charge-transfer (CT) and a triplet-pair (1TT) states. While the SF mechanism has been widely debated in homo- and heterodimers, little is known about the singlet splitting process in A-D-A copolymer trimers. Unlike traditional two-site SF, the process of iSF in D-A copolymers involves three molecular units consisting of two A's and one D following an A-D-A polymeric chain. This scenario is, therefore, different from that of the homodimer analogues in terms of which states (if any) may drive the SF process. In this work, we identify how singlet splitting occurs in prototypical iSF D-A copolymer poly(benzodithiophene-alt-thiophene-1,1-dioxide) by means of wave packet propagations on the basis of the linear vibronic coupling model Hamiltonian. Our results reveal that three different mechanisms drive the S1 → 1TT population transfer via antisymmetric and symmetric vibrational motion, including two favorable mechanisms of direct and mediated interactions, as well as a parasitic decay pathway that potentially delays the process. Remarkably, we uncover the interplay between an upper state of marked multiexcitonic character and a low-lying CT state in balancing the splitting efficiency, which anticipates their major role in defining future guidelines for the molecular design of D-A copolymers for iSF.
Collapse
Affiliation(s)
- Maria Fumanal
- Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Clémence Corminboeuf
- Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| |
Collapse
|
13
|
Shizu K, Adachi C, Kaji H. Visual Understanding of Vibronic Coupling and Quantitative Rate Expression for Singlet Fission in Molecular Aggregates. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 2020. [DOI: 10.1246/bcsj.20200159] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Affiliation(s)
- Katsuyuki Shizu
- Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan
| | - Chihaya Adachi
- Center for Organic Photonics and Electronics Research (OPERA), Kyushu University, 744 Motooka, Nishi, Fukuoka 819-0395, Japan
- International Institute for Carbon Neutral Energy Research (WPI-I2CNER), Kyushu University, 744 Motooka, Nishi, Fukuoka 819-0395, Japan
- Japan Science and Technology Agency (JST), ERATO, Adachi Molecular Exciton Engineering Project, 744 Motooka, Nishi, Fukuoka 819-0395, Japan
| | - Hironori Kaji
- Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan
| |
Collapse
|
14
|
Optical Projection and Spatial Separation of Spin-Entangled Triplet Pairs from the S1 (21 Ag–) State of Pi-Conjugated Systems. Chem 2020. [DOI: 10.1016/j.chempr.2020.09.011] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
|
15
|
Mai S, González L. Molecular Photochemistry: Recent Developments in Theory. Angew Chem Int Ed Engl 2020; 59:16832-16846. [PMID: 32052547 PMCID: PMC7540682 DOI: 10.1002/anie.201916381] [Citation(s) in RCA: 77] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2019] [Revised: 02/12/2020] [Indexed: 12/16/2022]
Abstract
Photochemistry is a fascinating branch of chemistry that is concerned with molecules and light. However, the importance of simulating light-induced processes is reflected also in fields as diverse as biology, material science, and medicine. This Minireview highlights recent progress achieved in theoretical chemistry to calculate electronically excited states of molecules and simulate their photoinduced dynamics, with the aim of reaching experimental accuracy. We focus on emergent methods and give selected examples that illustrate the progress in recent years towards predicting complex electronic structures with strong correlation, calculations on large molecules, describing multichromophoric systems, and simulating non-adiabatic molecular dynamics over long time scales, for molecules in the gas phase or in complex biological environments.
Collapse
Affiliation(s)
- Sebastian Mai
- Photonics InstituteVienna University of TechnologyGusshausstrasse 27–291040ViennaAustria
| | - Leticia González
- Institute of Theoretical ChemistryFaculty of ChemistryUniversity of ViennaWähringer Strasse 171090ViennaAustria
| |
Collapse
|
16
|
Mai S, González L. Molekulare Photochemie: Moderne Entwicklungen in der theoretischen Chemie. Angew Chem Int Ed Engl 2020. [DOI: 10.1002/ange.201916381] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Affiliation(s)
- Sebastian Mai
- Institut für Photonik Technische Universität Wien Gußhausstraße 27–29 1040 Wien Österreich
| | - Leticia González
- Institut für theoretische Chemie Fakultät für Chemie Universität Wien Währinger Straße 17 1090 Wien Österreich
| |
Collapse
|
17
|
Wang L, Bai S, Wu Y, Liu Y, Yao J, Fu H. Revealing the Nature of Singlet Fission under the Veil of Internal Conversion. Angew Chem Int Ed Engl 2020. [DOI: 10.1002/ange.201912202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Long Wang
- Beijing Key Laboratory for Optical Materials and Photonic DevicesDepartment of ChemistryCapital Normal University Beijing 100048 P. R. China
- Key Laboratory of Interface Science and Engineering in Advanced MaterialsMinistry of EducationTaiyuan University of Technology Taiyuan 030024 P. R. China
| | - Shuming Bai
- Department of ChemistryDuke University Durham NC 27708 USA
| | - Yishi Wu
- Beijing Key Laboratory for Optical Materials and Photonic DevicesDepartment of ChemistryCapital Normal University Beijing 100048 P. R. China
| | - Yanping Liu
- Beijing Key Laboratory for Optical Materials and Photonic DevicesDepartment of ChemistryCapital Normal University Beijing 100048 P. R. China
| | - Jiannian Yao
- Beijing Key Laboratory for Optical Materials and Photonic DevicesDepartment of ChemistryCapital Normal University Beijing 100048 P. R. China
- Institute of Molecular PlusSchool of Chemical Engineering and TechnologyTianjin UniversityCollaborative Innovation Center of Chemical Science and Engineering (Tianjin) Tianjin 300072 P. R. China
| | - Hongbing Fu
- Beijing Key Laboratory for Optical Materials and Photonic DevicesDepartment of ChemistryCapital Normal University Beijing 100048 P. R. China
- Institute of Molecular PlusSchool of Chemical Engineering and TechnologyTianjin UniversityCollaborative Innovation Center of Chemical Science and Engineering (Tianjin) Tianjin 300072 P. R. China
| |
Collapse
|
18
|
Wang L, Bai S, Wu Y, Liu Y, Yao J, Fu H. Revealing the Nature of Singlet Fission under the Veil of Internal Conversion. Angew Chem Int Ed Engl 2019; 59:2003-2007. [PMID: 31729139 DOI: 10.1002/anie.201912202] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2019] [Revised: 11/02/2019] [Indexed: 11/07/2022]
Abstract
Singlet fission (SF) holds the potential to boost the maximum power conversion efficiency of photovoltaic devices. Internal conversion (IC) has been considered as one of the major competitive deactivation pathways to transform excitation energy into heat. Now, using time-resolved spectroscopy and theoretical calculation, it is demonstrated that, instead of a conventional IC pathway, an unexpected intramolecular singlet fission (iSF) process is responsible for excited state deactivation in isoindigo derivatives. The 1 TT state could form at ultrafast rate and nearly quantitatively in solution. In solid films, the slipped stacked intermolecular packing of a thiophene-functionalized derivative leads to efficient triplet pair separation, giving rise to an overall triplet yield of 181 %. This work not only enriches the pool of iSF-capable materials, but also contributes to a better understanding of the iSF mechanism, which could be relevant for designing new SF sensitizers.
Collapse
Affiliation(s)
- Long Wang
- Beijing Key Laboratory for Optical Materials and Photonic Devices, Department of Chemistry, Capital Normal University, Beijing, 100048, P. R. China
- Key Laboratory of Interface Science and Engineering in Advanced Materials, Ministry of Education, Taiyuan University of Technology, Taiyuan, 030024, P. R. China
| | - Shuming Bai
- Department of Chemistry, Duke University, Durham, NC, 27708, USA
| | - Yishi Wu
- Beijing Key Laboratory for Optical Materials and Photonic Devices, Department of Chemistry, Capital Normal University, Beijing, 100048, P. R. China
| | - Yanping Liu
- Beijing Key Laboratory for Optical Materials and Photonic Devices, Department of Chemistry, Capital Normal University, Beijing, 100048, P. R. China
| | - Jiannian Yao
- Beijing Key Laboratory for Optical Materials and Photonic Devices, Department of Chemistry, Capital Normal University, Beijing, 100048, P. R. China
- Institute of Molecular Plus, School of Chemical Engineering and Technology, Tianjin University, Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300072, P. R. China
| | - Hongbing Fu
- Beijing Key Laboratory for Optical Materials and Photonic Devices, Department of Chemistry, Capital Normal University, Beijing, 100048, P. R. China
- Institute of Molecular Plus, School of Chemical Engineering and Technology, Tianjin University, Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300072, P. R. China
| |
Collapse
|
19
|
Cho D, Rouxel JR, Mukamel S, Kin-Lic Chan G, Li Z. Stimulated X-ray Raman and Absorption Spectroscopy of Iron-Sulfur Dimers. J Phys Chem Lett 2019; 10:6664-6671. [PMID: 31532691 DOI: 10.1021/acs.jpclett.9b02414] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Iron-sulfur complexes play an important role in biological processes such as metabolic electron transport. A detailed understanding of the mechanism of long-range electron transfer requires knowledge of the electronic structure of the complexes, which has traditionally been challenging to obtain, either by theory or by experiment, but the situation has begun to change with advances in quantum chemical methods and intense free electron laser light sources. We compute the spectra for stimulated X-ray Raman spectroscopy (SXRS) and absorption spectroscopy of homovalent and mixed-valence [2Fe-2S] complexes, using the ab initio density matrix renormalization group algorithm. The simulated spectra show clear signatures of the theoretically predicted dense low-lying excited states within the d-d manifold. Furthermore, the difference in spectral intensity between the absorption-active and Raman-active states provides a potential mechanism to selectively excite states by a proper tuning of the excitation pump, to access the electronic dynamics within this manifold.
Collapse
Affiliation(s)
- Daeheum Cho
- Department of Chemistry and Physics and Astronomy , University of California , Irvine , California 92697-2025 , United States
| | - Jeremy R Rouxel
- Department of Chemistry and Physics and Astronomy , University of California , Irvine , California 92697-2025 , United States
| | - Shaul Mukamel
- Department of Chemistry and Physics and Astronomy , University of California , Irvine , California 92697-2025 , United States
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering , California Institute of Technology , Pasadena , California 91125 , United States
| | - Zhendong Li
- Division of Chemistry and Chemical Engineering , California Institute of Technology , Pasadena , California 91125 , United States
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry , Beijing Normal University , Beijing 100875 , China
| |
Collapse
|
20
|
Musser AJ, Al-Hashimi M, Heeney M, Clark J. Heavy-atom effects on intramolecular singlet fission in a conjugated polymer. J Chem Phys 2019; 151:044902. [DOI: 10.1063/1.5110269] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Affiliation(s)
- Andrew J. Musser
- Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Mohammed Al-Hashimi
- Department of Chemistry, Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar
| | - Martin Heeney
- Department of Chemistry and Centre for Plastic Electronics, Imperial College London, Exhibition Rd., London SW7 2AZ, United Kingdom
| | - Jenny Clark
- Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom
| |
Collapse
|
21
|
Reddy SR, Coto PB, Thoss M. Quantum dynamical simulation of intramolecular singlet fission in covalently coupled pentacene dimers. J Chem Phys 2019; 151:044307. [DOI: 10.1063/1.5109897] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- S. Rajagopala Reddy
- Institute of Physics, Albert-Ludwigs University Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
| | - Pedro B. Coto
- Department of Physical and Analytical Chemistry, University of Oviedo, Avda. Julián Clavería 8, 33006, Oviedo, Spain
| | - Michael Thoss
- Institute of Physics, Albert-Ludwigs University Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
| |
Collapse
|
22
|
Xie X, Santana-Bonilla A, Fang W, Liu C, Troisi A, Ma H. Exciton–Phonon Interaction Model for Singlet Fission in Prototypical Molecular Crystals. J Chem Theory Comput 2019; 15:3721-3729. [DOI: 10.1021/acs.jctc.9b00122] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Xiaoyu Xie
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
| | | | - Weihai Fang
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
- Department of Chemistry, Beijing Normal University, Beijing, 100875, China
| | - Chungen Liu
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
| | - Alessandro Troisi
- Department of Chemistry, University of Liverpool, Liverpool L69 3BX, United Kingdom
| | - Haibo Ma
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
| |
Collapse
|
23
|
Abstract
The highly unusual state, 1(TT), is a coupled, double triplet state that has recently garnered significant attention. This multiexcitonic state can be formed by a quantum transition from a single-photon bright state in a variety of organic semiconducting materials. 1(TT)'s transient nature and similarity to independent triplets, however, has led to significant difficulties in characterization and prediction of its properties. Recent progress describing 1(TT) from theory and experiment are breaking through these difficulties, and have greatly advanced our comprehension of this state. Starting from the early description of 1(TT) in polyenes, this perspective discusses formation mechanisms, spectroscopic signatures, and the scope of intertriplet interactions. When employing singlet fission to generate charge carriers in a solar cell, 1(TT) has a central role. Due to the variety of coupling strengths between triplet states in 1(TT) amongst different chromophores, two different strategies are discussed to enable efficient charge carrier extraction. Continued growth in our understanding of 1(TT) may lead to control over complex quantum states for intriguing applications beyond high-efficiency, organic solar cells.
Collapse
Affiliation(s)
- Hyungjun Kim
- Department of Chemistry, Incheon National University, Incheon 22012, Republic of Korea.
| | | |
Collapse
|
24
|
Abstract
Singlet fission is a photophysical reaction in which a singlet excited electronic state splits into two spin-triplet states. Singlet fission was discovered more than 50 years ago, but the interest in this process has gained a lot of momentum in the past decade due to its potential as a way to boost solar cell efficiencies. This review presents and discusses the most recent advances with respect to the theoretical and computational studies on the singlet fission phenomenon. The work revisits important aspects regarding electronic states involved in the process, the evaluation of fission rates and interstate couplings, the study of the excited state dynamics in singlet fission, and the advances in the design and characterization of singlet fission compounds and materials such as molecular dimers, polymers, or extended structures. Finally, the review tries to pinpoint some aspects that need further improvement and proposes future lines of research for theoretical and computational chemists and physicists in order to further push the understanding and applicability of singlet fission.
Collapse
Affiliation(s)
- David Casanova
- Kimika Fakultatea , Euskal Herriko Unibertsitatea (UPV/EHU) and Donostia International Physics Center (DIPC) , P.K. 1072, 20080 Donostia , Euskadi, Spain.,IKERBASQUE, Basque, Foundation for Science , 48013 Bilbao , Euskadi, Spain
| |
Collapse
|
25
|
Japahuge A, Zeng T. Theoretical Studies of Singlet Fission: Searching for Materials and Exploring Mechanisms. Chempluschem 2018; 83:146-182. [PMID: 31957288 DOI: 10.1002/cplu.201700489] [Citation(s) in RCA: 64] [Impact Index Per Article: 10.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2017] [Revised: 12/31/2017] [Indexed: 02/02/2023]
Abstract
In this Review article, a survey is given for theoretical studies in the subject of singlet fission. Singlet fission converts one singlet exciton to two triplet excitons. With the doubled number of excitons and the longer lifetime of the triplets, singlet fission provides an avenue to improve the photoelectric conversion efficiency in organic photovoltaic devices. It has been a subject of intense research in the past decade. Theoretical studies play an essential role in understanding singlet fission. This article presents a Review of theoretical studies in singlet fission since 2006, the year when the research interest in this subject was reignited. Both electronic structure and dynamics studies are covered. Electronic structure studies provide guidelines for designing singlet fission chromophores and insights into the couplings between single- and multi-excitonic states. The latter provides fundamental knowledge for engineering interchromophore conformations to enhance the fission efficiency. Dynamics studies reveal the importance of vibronic couplings in singlet fission.
Collapse
Affiliation(s)
- Achini Japahuge
- Department of Chemistry, Carleton University, 1125 Colonel By Drive, Ottawa, ON, K1S5B6, Canada
| | - Tao Zeng
- Department of Chemistry, Carleton University, 1125 Colonel By Drive, Ottawa, ON, K1S5B6, Canada
| |
Collapse
|
26
|
Sun KW, Yao Y. Beating maps of singlet fission: Simulation of coherent two-dimensional electronic spectroscopy by Davydov ansatz in organic molecules. J Chem Phys 2017; 147:224905. [DOI: 10.1063/1.5005564] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Ke-Wei Sun
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Yao Yao
- Department of Physics, South China University of Technology, Guangzhou 510640, China
| |
Collapse
|