Fluorene-imidazole dyes excited states from first-principles calculations—Topological insights

  • Thibaud EtienneEmail author
  • Hugo Gattuso
  • Catherine Michaux
  • Antonio Monari
  • Xavier Assfeld
  • Eric A. Perpète
Regular Article
Part of the following topical collections:
  1. Health & Energy from the Sun: a Computational Perspective


We report the theoretical investigation of four organic dyes containing imidazole and fluorene moieties as donor and bridge in donor–bridge–acceptor molecular structures. Those target dyes were recently reported as potential agents for building metal-free light-to-electricity conversion devices [J. Org. Chem. (2014) 79, 3159]. Our contribution consists in the establishment of an appropriate computational protocol for obtaining the excited states of these dyes from a reliable level of theory. This benchmark was performed based on the possibilities offered by density functional theory and its time-dependent variant. The outcome of this screening allowed us to compute absorption properties of the target dyes, as well as the emission properties for one of them. Afterward, the electronic transitions computed from this reference method were characterized by a series of topological analysis tools, aimed for a qualitative and quantitative probing of the excited states nature. These tools rely on the formal depiction of the photogenerated hole and particle from density matrices or through the exploitation of the exciton wavefunction. Further linear algebraic operations based on these two types of objects lead to the elaboration of detachment/attachment density matrices and natural transition orbitals respectively, so that the outcome of these operations provides a qualitative depiction of the photoinduced electronic cloud polarization. Finally, quantitative insights were provided by the evaluation of quantum-mechanical metrics related to the charge transfer phenomenon caused by light absorption.


Canonical Transition Ground State Density Electronic Transition Topology Excited State Calculation Topological Quantity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



C.M. and E.A.P. thank the Belgian National Fund for Scientific Research for their research associate and senior research associate positions, respectively.

Supplementary material

214_2016_1866_MOESM1_ESM.pdf (1.3 mb)
Supplementary material 1 (pdf 1343 KB)


  1. 1.
    Mishra A, Fischer MKR, Bäuerle P (2009) Metal-free organic dyes for dye-sensitized solar cells: from structure: property relationships to design rules. Angew Chem Int Ed 48:2474–2499CrossRefGoogle Scholar
  2. 2.
    Clifford JN, Martínez-Ferrero E, Viterisi A, Palomares E (2011) Sensitizer molecular structure-device efficiency relationship in dye sensitized solar cells. Chem Soc Rev 40:1635–1646CrossRefGoogle Scholar
  3. 3.
    Kumar D, Justin Thomas KR, Lee C-P, Ho K-C (2014) Organic dyes containing fluorene decorated with imidazole units for dye-sensitized solar cells. J Org Chem 79:3159–3172CrossRefGoogle Scholar
  4. 4.
    Hwang S, Lee JH, Park C, Lee H, Kim C, Park C, Lee M-H, Lee W, Park J, Kim K, Park N-G, Kim C (2007) A highly efficient organic sensitizer for dye-sensitized solar cells. Chem Commun (46):4887–4889 Google Scholar
  5. 5.
    Koumura N, Wang Z-S, Mori S, Miyashita M, Suzuki E, Hara K (2006) Alkyl-functionalized organic dyes for efficient molecular photovoltaics. J Am Chem Soc 128:14256–14257CrossRefGoogle Scholar
  6. 6.
    Tang J, Qu S, Hu J, Wu W, Hua J (2012) A new organic dye bearing aldehyde electron-withdrawing group for dye-sensitized solar cell. Sol Energy 86:2306–2311CrossRefGoogle Scholar
  7. 7.
    Erten-Ela S, Yilmaz MD, Icli B, Dede Y, Icli S, Akkaya EU (2008) A panchromatic boradiazaindacene (BODIPY) sensitizer for dye-sensitized solar cells. Org Lett 10:3299–3302CrossRefGoogle Scholar
  8. 8.
    Hagfeldt A, Boschloo G, Sun L, Kloo L, Pettersson H (2010) Dye-sensitized solar cells. Chem Rev 110:6595–6663CrossRefGoogle Scholar
  9. 9.
    Pastore M, Mosconi E, De Angelis F, Grätzel M (2010) A computational investigation of organic dyes for dye-sensitized solar cells: benchmark, strategies, and open issues. J Phys Chem C 114:7205–7212CrossRefGoogle Scholar
  10. 10.
    Preat J, Michaux C, André J-M, Perpète EA (2012) Pyrrolidine-based dye-sensitized solar cells: a time-dependent density functional theory investigation of the excited state electronic properties. Int J Quantum Chem 112:2072–2084CrossRefGoogle Scholar
  11. 11.
    Etienne T, Chbibi L, Michaux C, Perpète EA, Assfeld X, Monari A (2014) All-organic chromophores for dye-sensitized solar cells: a theoretical study on aggregation. Dyes Pigments 101:203–211CrossRefGoogle Scholar
  12. 12.
    Le Bahers T, Pauporté T, Lainé PP, Labat F, Adamo C, Ciofini I (2013) Modeling dye-sensitized solar cells: from theory to experiment. J Phys Chem Lett 4:1044–1050CrossRefGoogle Scholar
  13. 13.
    Labat F, Le Bahers T, Ciofini I, Adamo C (2012) First-principles modeling of dye-sensitized solar cells: challenges and perspectives. Acc Chem Res 45:1268–1277CrossRefGoogle Scholar
  14. 14.
    Zegkinoglou I, Ragoussi M-E, Pemmaraju CD, Johnson PS, Pickup DF, Ortega JE, Prendergast D, de la Torre G, Himpsel FJ (2013) Spectroscopy of donor-\(\pi\)-acceptor porphyrins for dye-sensitized solar cells. J Phys Chem C 117:13357–13364CrossRefGoogle Scholar
  15. 15.
    Plasser F, Wormit M, Dreuw A (2014) New tools for the systematic analysis and visualization of electronic excitations. I. Formalism. J Chem Phys 141:024106CrossRefGoogle Scholar
  16. 16.
    Plasser F, Bäppler SA, Wormit M, Dreuw A (2014) New tools for the systematic analysis and visualization of electronic excitations. II. Applications. J Chem Phys 141:024107CrossRefGoogle Scholar
  17. 17.
    Bäppler SA, Plasser F, Wormit M, Dreuw A (2014) Exciton analysis of many-body wave functions: bridging the gap between the quasiparticle and molecular orbital pictures. Phys Rev A. doi: 10.1103/PhysRevA.90.052521
  18. 18.
    Plasser F, Lischka H (2012) Analysis of excitonic and charge transfer interactions from quantum chemical calculations. J Chem Theory Comput 8:2777–2789CrossRefGoogle Scholar
  19. 19.
    Guido CA, Cortona P, Adamo C (2014) Effective electron displacements: a tool for time-dependent density functional theory computational spectroscopy. J Chem Phys 140:104101CrossRefGoogle Scholar
  20. 20.
    Etienne T (2015) Transition matrices and orbitals from reduced density matrix theory. J Chem Phys 2015(142):244103CrossRefGoogle Scholar
  21. 21.
    Etienne T, Assfeld X, Monari A (2014) Toward a quantitative assessment of electronic transitions’ charge-transfer character. J Chem Theory Comput 10:3896–3905CrossRefGoogle Scholar
  22. 22.
    Etienne T, Assfeld X, Monari A (2014) A new insight into the topology of excited states through detachment/attachment density matrices-based centroids of charge. J Chem Theory Comput 10:3906–3914CrossRefGoogle Scholar
  23. 23.
    Etienne T (2015) Probing the locality of excited states with linear algebra. J Chem Theory Comput 11:1692–1699CrossRefGoogle Scholar
  24. 24.
    Guido CA, Cortona P, Mennucci B, Adamo C (2013) On the metric of charge transfer molecular excitations: a simple chemical descriptor. J Chem Theory Comput 9:3118–3126CrossRefGoogle Scholar
  25. 25.
    Ciofini I, Le Bahers T, Adamo C, Odobel F, Jacquemin D (2012) Through-space charge transfer in rod-like molecules: lessons from theory. J Phys Chem C 116:11946–11955CrossRefGoogle Scholar
  26. 26.
    Ciofini I, Le Bahers T, Adamo C, Odobel F, Jacquemin D (2012) Correction to “through-space charge transfer in rod-like molecules: lessons from theory”. J Phys Chem C 116:14736–14736CrossRefGoogle Scholar
  27. 27.
    Le Bahers T, Adamo C, Ciofini I (2011) A qualitative index of spatial extent in charge-transfer excitations. J Chem Theory Comput 7:2498–2506CrossRefGoogle Scholar
  28. 28.
    Garcia G, Adamo C, Ciofini I (2013) Evaluating push-pull dye efficiency using TD-DFT and charge transfer indices. Phys Chem Chem Phys 15:20210–20219CrossRefGoogle Scholar
  29. 29.
    Jacquemin D, Le Bahers T, Adamo C, Ciofini I (2012) What is the “best” atomic charge model to describe through-space charge-transfer excitations? Phys Chem Chem Phys 14:5383–5388CrossRefGoogle Scholar
  30. 30.
    Céron-Carrasco JP, Siard A, Jacquemin D (2013) Spectral signatures of thieno[3,4-b]pyrazines: theoretical interpretations and design of improved structures. Dyes Pigments 99:972–978CrossRefGoogle Scholar
  31. 31.
    Ronca E, Pastore M, Belpassi L, Angelis FD, Angeli C, Cimiraglia R, Tarantelli F (2014) Charge-displacement analysis for excited states. J Chem Phys 140:054110CrossRefGoogle Scholar
  32. 32.
    Ronca E, Angeli C, Belpassi L, De Angelis F, Tarantelli F, Pastore M (2014) Density relaxation in time-dependent density functional theory: combining relaxed density natural orbitals and multireference perturbation theories for an improved description of excited states. J Chem Theory Comput 10:4014–4024CrossRefGoogle Scholar
  33. 33.
    Luzanov AV, Zhikol OA (2010) Electron invariants and excited state structural analysis for electronic transitions within CIS, RPA, and TDDFT models. Int J Quantum Chem 110:902–924Google Scholar
  34. 34.
    NANCY-EX. Accessed 14 Sep 2015
  35. 35.
    Dreuw A, Head-Gordon M (2005) Single-reference ab Initio methods for the calculation of excited states of large molecules. Chem Rev 105:4009–4037CrossRefGoogle Scholar
  36. 36.
    Luzanov AV, Sukhorukov AA, Umanskii VÉ (1976) Application of transition density matrix for analysis of excited states. Theor Exp Chem 10:354–361CrossRefGoogle Scholar
  37. 37.
    Martin RL (2003) Natural transition orbitals. J Chem Phys 118:4775–4777CrossRefGoogle Scholar
  38. 38.
    Mayer I (2007) Using singular value decomposition for a compact presentation and improved interpretation of the CIS wave functions. Chem Phys Lett 437:284–286CrossRefGoogle Scholar
  39. 39.
    Handy NC, Iii HFS (1984) On the evaluation of analytic energy derivatives for correlated wave functions. J Chem Phys 81:5031–5033CrossRefGoogle Scholar
  40. 40.
    Amos AT, Hall GG (1961) Single determinant wave functions. Proc R Soc Lond Ser A 263:483–493CrossRefGoogle Scholar
  41. 41.
    Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery Jr JA, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Keith T, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam JM, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas O, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2014) Gaussian 09, revision D.01. Gaussian, Inc., WallingfordGoogle Scholar
  42. 42.
    Tomasi J, Mennucci B, Cammi R (2005) Quantum mechanical continuum solvation models. Chem Rev 105:2999–3094CrossRefGoogle Scholar
  43. 43.
    Cancès E, Mennucci B, Tomasi J (1997) A new integral equation formalism for the polarizable continuum model: theoretical background and applications to isotropic and anisotropic dielectrics. J Chem Phys 107:3032–3041CrossRefGoogle Scholar
  44. 44.
    Mennucci B, Cancès E, Tomasi J (1997) Evaluation of solvent effects in isotropic and anisotropic dielectrics and in ionic solutions with a unified integral equation method: theoretical bases, computational implementation, and numerical applications. J Phys Chem B 101:10506–10517CrossRefGoogle Scholar
  45. 45.
    Frisch MJ, Pople JA, Binkley JS (1984) Self-consistent molecular orbital methods 25. Supplementary functions for Gaussian basis sets. J Chem Phys 80:3265–3269CrossRefGoogle Scholar
  46. 46.
    Adamo C, Barone V (1999) Toward reliable density functional methods without adjustable parameters: the PBE0 model. J Chem Phys 110:6158–6170CrossRefGoogle Scholar
  47. 47.
    Adamo C, Scuseria GE, Barone V (1999) Accurate excitation energies from time-dependent density functional theory: assessing the PBE0 model. J Chem Phys 111:2889–2899CrossRefGoogle Scholar
  48. 48.
    Becke AD (1993) Density-functional thermochemistry. III. The role of exact exchange. J Chem Phys 98:5648–5652CrossRefGoogle Scholar
  49. 49.
    Lee C, Yang W, Parr RG (1988) Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys Rev B 37:785–789CrossRefGoogle Scholar
  50. 50.
    Zhao Y, Truhlar DG (2008) The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor Chem Acc 120:215–241CrossRefGoogle Scholar
  51. 51.
    Yanai T, Tew DP, Handy NC (2004) A new hybrid exchange-correlation functional using the Coulomb-attenuating method (CAM-B3LYP). Chem Phys Lett 393:51–57CrossRefGoogle Scholar
  52. 52.
    Vydrov OA, Scuseria GE (2006) Assessment of a long-range corrected hybrid functional. J Chem Phys 125:234109–234109-9CrossRefGoogle Scholar
  53. 53.
    Chai J-D, Head-Gordon M (2008) Long-range corrected hybrid density functionals with damped atom–atom dispersion corrections. Phys Chem Chem Phys 10:6615–6620CrossRefGoogle Scholar
  54. 54.
    Li R, Zheng J, Truhlar DG (2010) Density functional approximations for charge transfer excitations with intermediate spatial overlap. Phys Chem Chem Phys 12:12697–12701CrossRefGoogle Scholar
  55. 55.
    Mewes SA, Plasser F, Dreuw A (2015) Communication: exciton analysis in time-dependent density functional theory: how functionals shape excited-state characters. J Chem Phys 143:171101CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Thibaud Etienne
    • 1
    Email author
  • Hugo Gattuso
    • 2
    • 3
  • Catherine Michaux
    • 4
  • Antonio Monari
    • 2
    • 3
  • Xavier Assfeld
    • 2
    • 3
  • Eric A. Perpète
    • 4
  1. 1.Computational Laboratory for Hybrid/Organic Photovoltaics (CLHYO), CNR-ISTMPerugiaItaly
  2. 2.Université de Lorraine – Nancy, Théorie-Modélisation-Simulation, SRSMCVandoeuvre-lès-NancyFrance
  3. 3.CNRS, Théorie-Modélisation-Simulation, SRSMCVandoeuvre-lès-NancyFrance
  4. 4.Unité de Chimie Physique Théorique et StructuraleUniversité de NamurNamurBelgium

Personalised recommendations