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Lieberherr AZ, Gori-Giorgi P, Giesbertz KJH. Optimal Transport Distances to Characterize Electronic Excitations. J Chem Theory Comput 2024; 20:5635-5642. [PMID: 38874479 PMCID: PMC11238536 DOI: 10.1021/acs.jctc.4c00289] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2024] [Revised: 05/31/2024] [Accepted: 06/03/2024] [Indexed: 06/15/2024]
Abstract
Understanding the character of electronic excitations is important in computational and reaction mechanistic studies, but their classification from simulations remains an open problem. Distances based on optimal transport have proven very useful in a plethora of classification problems and, therefore, seem a natural tool to try to tackle this challenge. We propose and investigate a new diagnostic Θ based on the Sinkhorn divergence from optimal transport. We evaluate a k-NN classification algorithm on Θ, the popular Λ diagnostic, and their combination, and assess their performance in labeling excitations, finding that (i) the combination only slightly improves the classification, (ii) Rydberg excitations are not separated well in any setting, and (iii) Θ breaks down for charge transfer in small molecules. We then define a length-scale-normalized version of Θ and show that the result correlates closely with Λ for results obtained with Gaussian basis functions. Finally, we discuss the orbital dependence of our approach and explore an orbital-independent version. Using an optimized combination of the optimal transport and overlap diagnostics together with a different metric is in our opinion the most promising for future classification studies.
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Affiliation(s)
- Annina Z. Lieberherr
- Department
of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, U.K.
| | - Paola Gori-Giorgi
- Department
of Chemistry and Pharmaceutical Sciences, Amsterdam Institute of Molecular
and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
- Microsoft
Research AI for Science, Evert van de Beekstraat 354, 1118CZ Schiphol, The Netherlands
| | - Klaas J. H. Giesbertz
- Department
of Chemistry and Pharmaceutical Sciences, Amsterdam Institute of Molecular
and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
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2
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Noguchi Y. Exciton maps for thermally activated delayed fluorescence active/inactive carbazole benzonitrile derivatives. J Chem Phys 2021; 155:204302. [PMID: 34852472 DOI: 10.1063/5.0068402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Abstract
The all-electron first-principles GW+Bethe-Salpeter method was applied to six carbazole benzonitrile (CzBN) derivatives, which were recently reported to be both thermally activated delayed fluorescence (TADF) active and inactive despite their singlet-triplet splittings being commonly around 0.2 eV. The present method successfully reproduced very similar photoabsorption spectra as experiments from the viewpoint of the peak positions and relative peak heights. We also performed exciton analysis with the exciton wave functions for several lowest singlet and triplet exciton states to reveal the details of the optical properties. We applied this to not only the present six CzBN derivatives but also 18 other TADF molecules and proposed a new exciton map to classify the molecules as the TADF active/inactive by using the exciton binding energy in the vertical axis and the ratio of electron and hole delocalization in the horizontal axis. Our results suggest two possible TADF mechanisms: spatially less localized hole states than the electron states where the exciton binding energy is proportional to the ratio of hole and electron delocalization and spatially more localized hole states than the electron states where the exciton binding energy should be large.
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Affiliation(s)
- Yoshifumi Noguchi
- Department of Applied Chemistry and Biochemical Engineering, Graduate School of Engineering, Shizuoka University, Johoku 3-5-1, Hamamatsu, Shizuoka 432-8561, Japan
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3
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Abstract
The ab initio determination of electronic excited state (ES) properties is the cornerstone of theoretical photochemistry. Yet, traditional ES methods become impractical when applied to fairly large molecules, or when used on thousands of systems. Machine learning (ML) techniques have demonstrated their accuracy at retrieving ES properties of large molecular databases at a reduced computational cost. For these applications, nonlinear algorithms tend to be specialized in targeting individual properties. Learning fundamental quantum objects potentially represents a more efficient, yet complex, alternative as a variety of molecular properties could be extracted through postprocessing. Herein, we report a general framework able to learn three fundamental objects: the hole and particle densities, as well as the transition density. We demonstrate the advantages of targeting those outputs and apply our predictions to obtain properties, including the state character and the exciton topological descriptors, for the two bands (nπ* and ππ*) of 3427 azoheteroarene photoswitches.
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Affiliation(s)
- Sergi Vela
- Institute of Chemical Sciences and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), Laboratory for Computational Molecular Design, Lausanne, CH-1015, Switzerland
| | - Alberto Fabrizio
- Institute of Chemical Sciences and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), Laboratory for Computational Molecular Design, Lausanne, CH-1015, Switzerland
| | - Ksenia R Briling
- Institute of Chemical Sciences and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), Laboratory for Computational Molecular Design, Lausanne, CH-1015, Switzerland
| | - Clémence Corminboeuf
- Institute of Chemical Sciences and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), Laboratory for Computational Molecular Design, Lausanne, CH-1015, Switzerland
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Liu C, Kloppenburg J, Yao Y, Ren X, Appel H, Kanai Y, Blum V. All-electron ab initio Bethe-Salpeter equation approach to neutral excitations in molecules with numeric atom-centered orbitals. J Chem Phys 2020; 152:044105. [DOI: 10.1063/1.5123290] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Chi Liu
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Jan Kloppenburg
- Institute of Condensed Matter and Nanoscience, Université Catholique de Louvain, Louvain-la-Neuve 1348, Belgium
| | - Yi Yao
- Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599, USA
- Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708, USA
| | - Xinguo Ren
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Heiko Appel
- Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, 22761 Hamburg, Germany
| | - Yosuke Kanai
- Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599, USA
| | - Volker Blum
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
- Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708, USA
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Mewes SA, Dreuw A. Density-based descriptors and exciton analyses for visualizing and understanding the electronic structure of excited states. Phys Chem Chem Phys 2019; 21:2843-2856. [PMID: 30687866 DOI: 10.1039/c8cp07191h] [Citation(s) in RCA: 32] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
Analysis and interpretation of the electronic structure of excited electronic states are prerequisites for developing a fundamental understanding of photochemistry and optical properties of molecular systems and an everyday task for a computational photochemist. Hence, wavefunction-based and density-based analysis tools have been devised over the last decades, and most recently also a family of quantitative exciton-wavefunction based descriptors has been developed. While the latter represent the main focus of this perspective, they are also discussed in the context of other existing analysis methods. Exciton analysis bridges the gap between the physically intuitive exciton picture and complex quantum-chemical wavefunctions by yielding insightful quantitative descriptors like exciton size, hole and electron size, electron-hole distance and exciton correlation. Thereby, not only a comprehensive characterization of the electronic structure is provided, but moreover, the formalism is automatizable and thus also optimally suited for benchmarking excited-state electronic structure methods.
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Affiliation(s)
- Stefanie A Mewes
- Interdisciplinary Center for Scientific Computing, Im Neuenheimer Feld 205 A, 69120 Heidelberg, Germany.
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6
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Fujita T, Mochizuki Y. Development of the Fragment Molecular Orbital Method for Calculating Nonlocal Excitations in Large Molecular Systems. J Phys Chem A 2018; 122:3886-3898. [DOI: 10.1021/acs.jpca.8b00446] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Affiliation(s)
| | - Yuji Mochizuki
- Department of Chemistry and Research Center for Smart Molecules, Faculty of Science, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima-ku, Tokyo 171-8501, Japan
- Institute for Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
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7
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Blase X, Duchemin I, Jacquemin D. The Bethe–Salpeter equation in chemistry: relations with TD-DFT, applications and challenges. Chem Soc Rev 2018; 47:1022-1043. [DOI: 10.1039/c7cs00049a] [Citation(s) in RCA: 120] [Impact Index Per Article: 20.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
We review the Bethe–Salpeter formalism and analyze its performances for the calculation of the excited state properties of molecular systems.
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Affiliation(s)
- Xavier Blase
- Univ. Grenoble Alpes
- CNRS
- Inst NEEL
- F-38042 Grenoble
- France
| | - Ivan Duchemin
- Univ. Grenoble Alpes
- CEA
- INAC-MEM
- L-Sim
- F-38000 Grenoble
| | - Denis Jacquemin
- CEISAM UMR CNRS 6230
- Université de Nantes
- 44322 Nantes Cedex 3
- France
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Azarias C, Habert C, Budzák Š, Blase X, Duchemin I, Jacquemin D. Calculations of n→π* Transition Energies: Comparisons Between TD-DFT, ADC, CC, CASPT2, and BSE/GW Descriptions. J Phys Chem A 2017; 121:6122-6134. [DOI: 10.1021/acs.jpca.7b05222] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Affiliation(s)
- Cloé Azarias
- CEISAM,
BP 92208, UMR CNRS 6230, Université de Nantes, 2, Rue de
la Houssiniere, 44322 Nantes, Cedex 3, France
| | - Chloé Habert
- CEISAM,
BP 92208, UMR CNRS 6230, Université de Nantes, 2, Rue de
la Houssiniere, 44322 Nantes, Cedex 3, France
| | - Šimon Budzák
- Department
of Chemistry, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-97400 Banská Bystrica, Slovak Republic
| | - Xavier Blase
- CNRS, Inst NEEL, F-38042 Grenoble, France
- Univ.
Grenoble Alpes, Inst NEEL, F-38042 Grenoble, France
| | - Ivan Duchemin
- Univ.
Grenoble Alpes, Inst NEEL, F-38042 Grenoble, France
- Univ.
Grenobles Alpes, CEA, INAC-MEM, L_Sim, F-38000 Grenoble, France
| | - Denis Jacquemin
- CEISAM,
BP 92208, UMR CNRS 6230, Université de Nantes, 2, Rue de
la Houssiniere, 44322 Nantes, Cedex 3, France
- Institut Universitaire de France, 1, rue Descartes, F-75231 Paris Cedex 05, France
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9
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Noguchi Y, Sugino O. Molecular size insensitivity of optical gap of [n]cycloparaphenylenes (n = 3-16). J Chem Phys 2017; 146:144304. [DOI: 10.1063/1.4979911] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
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