Abstract
Context
The study of molecular aggregation effects on the electronic spectrum is essential for the development of optoelectronic devices. However, investigating the entire valence absorption spectrum of aggregates using quantum mechanical methods is a challenging task. In this work, we perform systematic simulations of the absorption spectrum of benzene molecular clusters up to 35 eV applying two approaches based on time-dependent density functional theory. The results show that depending on the dimer packing, different energy shifts occur for the symmetry allowed \(\varvec{\pi } \varvec{\rightarrow } \varvec{\pi }^{\varvec{*}}\) transition, in comparison to the monomer. The transition intensity increases for the band around 6 eV for larger aggregates from the monomer to dimers and tetramer, indicating the occurrence of the symmetry forbidden (in \(\varvec{D}_{\varvec{6h}}\) point group) \(^{\varvec{1}}{\varvec{A}}_{\varvec{1g}} \varvec{\rightarrow }\) \(^{\varvec{1}}{\varvec{B}}_{\varvec{1u}}\) transition. The benzene crystal exhibits a large redshift following the experimental spectrum. Also, the continuum regions of all spectra show a good agreement with the experiments both in gas and solid phases.
Methods
Geometry optimization of the monomer was carried out with Gaussian 09 software using the PBE0/def2-TZVP level of theory. We used dimers and tetramer molecular geometries extracted from the experimental crystal structure. The absorption spectra were directly obtained by the Liouville-Lanczos TDDFT approach with plane waves basis set or indirectly by TDDFT pseudo-spectra calculated in a \(\varvec{L}^{\varvec{2}}\) basis followed by analytic continuation procedure to obtain complex polarizability. The former is available at Quantum ESPRESSO, and the latter was calculated using Gaussian 09 with the post-processing performed with a code previously developed in our group.
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Code availability
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References
Runge E, Gross EK (1984) Density-functional theory for time-dependent systems. Phys Rev Lett 52(12):997
Walker B, Saitta AM, Gebauer R, Baroni S (2006) Efficient approach to time-dependent density-functional perturbation theory for optical spectroscopy. Phys Rev Lett 96(11):113001
Rocca D, Gebauer R, Saad Y, Baroni S (2008) Turbo charging time-dependent density-functional theory with Lanczos chains. J Chem Phys 128(15)
Malcioǧlu OB, Gebauer R, Rocca D, Baroni S (2011) turboTDDFT-a code for the simulation of molecular spectra using the Liouville-Lanczos approach to time-dependent density-functional perturbation theory. Comput Phys Commun 182(8):1744–1754
Langhoff P (1973) Stieltjes imaging of atomic and molecular photoabsorption profiles. Chem Phys Lett 22(1):60–64
Tenorio BNC, Nascimento MAC, Coriani S, Rocha AB (2016) Coupled cluster study of photoionization and photodetachment cross sections. J Chem Theory Comput 12(9):4440–4459
Tenorio BNC, Nascimento MAC, Rocha AB (2018) Time-dependent density functional theory description of total photoabsorption cross sections. J Chem Phys 148(7)
Tenorio BNC, Nascimento MAC, Rocha AB (2019) Theoretical study of the absolute inner-shell photoionization cross sections of the formic acid and some of its hydrogen-bonded clusters. J Chem Phys 150(15)
Tenorio BNC, Oliveira RR, Nascimento MAC, Rocha AB (2018) Coupled cluster and time-dependent density functional theory description of inner shell photoabsorption cross sections of molecules. Jo Chem Theory Comput 14(10):5324–5338. https://doi.org/10.1021/acs.jctc.8b00375
Yabana K, Bertsch G (1996) Time-dependent local-density approximation in real time. Phys Rev B 54(7):4484
Marques MA, Castro A, Bertsch GF, Rubio A (2003) octopus: a first-principles tool for excited electron-ion dynamics. Comput Phys Commun 151(1):60–78
Stener M, Decleva P (2000) Time-dependent density functional calculations of molecular photoionization cross sections: N 2 and PH 3. J Chem Phys 112(24):10871–10879
Kolesov G, Grånäs O, Hoyt R, Vinichenko D, Kaxiras E (2016) Real-time TD-DFT with classical ion dynamics: methodology and applications. J Chem Theory Comput 12(2):466–476
Jornet-Somoza J, Lebedeva I (2019) Real-time propagation TDDFT and density analysis for exciton coupling calculations in large systems. J Chem Theory Comput 15(6):3743–3754
Brabec J, Lin L, Shao M, Govind N, Yang C, Saad Y, Ng EG (2015) Efficient algorithms for estimating the absorption spectrum within linear response TDDFT. J Chem Theory Comput 11(11):5197–5208
Ma S, Du S, Pan G, Dai S, Xu B, Tian W (2021) Organic molecular aggregates: from aggregation structure to emission property. Aggregate 2(4):96
Mao L, Wu Y, Jiang J, Guo X, Heng P, Wang L, Zhang J (2020) Rational design of phenothiazine-based organic dyes for dye-sensitized solar cells: the influence of \(\pi \)-spacers and intermolecular aggregation on their photovoltaic performances. J Phys Chem C 124(17):9233–9242
Nabil E, Hasanein AA, Alnoman RB, Zakaria M (2021) Optimizing the cosensitization effect of SQ02 dye on BP-2 dye-sensitized solar cells: a computational quantum chemical study. J Chem Inf Model 61(10):5098–5116
Mall C, Tiwari S, Solanki PP (2022) A plausible mechanism in premicellar aggregates for photocurrent generation in photogalvanic cell for simultaneously solar power conversion and storage. Energy Convers Manag 268:116039
Sonalin S, Mishra A, Sahu AK, Mishra AK, Imran PM, Bhuvanesh NS, Nagarajan S (2020) Aggregation behavior and high charge-carrier OFET-mobility of functionalized phenanthro [9, 10-d] imidazoles. J Phys Chem C 124(24):13053–13062
Hoffmann J, Geffroy B, Jaques E, Hissler M, Staubitz A (2021) Tuning the aggregation behaviour of BN-coronene diimides with imide substituents and their performance in devices (OLEDs and OFETs). J Mater Chem C 9(41):14720–14729
Lorenzoni A, Gallino F, Muccini M, Mercuri F (2016) Theoretical insights on morphology and charge transport properties of two-dimensional n, n’- ditridecylperylene-3, 4, 9, 10-tetra carboxylic diimide aggregates. RSC Adv 6(47):40724–40730
Furue R, Nishimoto T, Park IS, Lee J, Yasuda T (2016) Aggregation-induced delayed fluorescence based on donor/acceptor-tethered Janus carborane triads: unique photophysical properties of nondoped OLEDs. Angew Chem Int Ed 55(25):7171–7175
Huo Y, Qi H, He S, Li J, Song S, Lv J, Liu Y, Peng L, Ying S, Yan S (2023) Aggregation-induced narrowband isomeric fluorophores for ultraviolet nondoped OLEDs by engineering multiple nonbonding interactions. Aggregate 391
Kasha M, Rawls HR, Ashraf El-Bayoumi M (1965) The exciton model in molecular spectroscopy. Pure and Applied Chemistry VIIIth 11(3–4):371–392
Kasha M (1963) Energy transfer mechanisms and the molecular exciton model for molecular aggregates. Radiat Res 20(1):55–70
McRae EG, Kasha M (1958) Enhancement of phosphorescence ability upon aggregation of dye molecules. J Chem Phys 28(4):721–722
Hestand NJ, Spano FC (2018) Expanded theory of h-and j-molecular aggregates: the effects of vibronic coupling and intermolecular charge transfer. Chem Rev 118(15):7069–7163
Testoff TT, Aikawa T, Tsung E, Lesko E, Wang L (2022) DFT studies of aggregation induced energy splitting and excitonic diversification in benzene and anthracene multimers. Chem Phys 562
Li Y, Wan J, Xu X (2007) Theoretical study of the vertical excited states of benzene, pyrimidine, and pyrazine by the symmetry adapted cluster-configuration interaction method. J Comput Chem 28(10):1658–1667
Li J, Lin C-K, Li XY, Zhu CY, Lin SH (2010) Symmetry forbidden vibronic spectra and internal conversion in benzene. Phys Chem Chem Phys 12(45):14967–14976
Borges I, Varandas AJC, Rocha AB, Bielschowsky CE (2003) Forbidden transitions in benzene. Journal of Molecular Structure: THEOCHEM 621(1):99–105. https://doi.org/10.1016/S0166-1280(02)00537-7. 2001 Quitel S.I
Stener M, Fronzoni G, Decleva P (2005) Time-dependent density-functional theory for molecular photoionization with noniterative algorithm and multicenter b-spline basis set: Cs2 and c6h6 case studies. J Chem Phys 122(23)
Miura M, Aoki Y, Champagne B (2007) Assessment of time-dependent density functional schemes for computing the oscillator strengths of benzene, phenol, aniline, and fluorobenzene. J Chem Phys 127(8)
Dawes A, Pascual N, Hoffmann SV, Jones NC, Mason NJ (2017) Vacuum ultraviolet photoabsorption spectroscopy of crystalline and amorphous benzene. Phys Chem Chem Phys 19(40):27544–27555
Capalbo FJ, Bénilan Y, Fray N, Schwell M, Champion N, Es-Sebbar E-T, Koskinen TT, Lehocki I, Yelle RV (2016) New benzene absorption cross sections in the VUV, relevance for Titan’s upper atmosphere. Icarus 265:95–109
Killat U (1974) Optical properties of c6h12, c6h10, c6h8, c6h6, c7h8, c6h5cl and c5h5n in the solid and gaseous state derived from electron energy losses. Journal of Physics C: Solid State Physics 7(13):2396
Koch E-E, Otto A (1976) Vacuum ultra-violet and electron energy loss spectroscopy of gaseous and solid organic compounds. Int J Radiat Phys Chem 8(1–2):113–150
Sanche L, Michaud M (1981) Electron energy-loss vibronic spectroscopy of matrixisolated benzene and multilayer benzene films. Chem Phys Lett 80(1):184–187
Killat U (1973) Optical properties of solid benzene derived from electron energy losses. Zeitschrift für Physik 263(1):83–88
Feng R, Cooper G, Brion C (2002) Dipole (e, e) spectroscopic studies of benzene: quantitative photoabsorption in the uv, vuv and soft x-ray regions. J Electron Spectrosc Relat Phenom 123(2–3):199–209
Murrell, J.N., Pople, J.A. (1956) The intensities of the symmetry-forbidden electronic bands of benzene. Proceedings of the Physical Society. Section A 69(3):245. https://doi.org/10.1088/0370-1298/69/3/307
Bernhardsson A, Forsberg N, Malmqvist P, Roos BO, Serrano-Andrés L (2000) A theoretical study of the 1B2u and 1B1u vibronic bands in benzene. J Chem Phys 112(6):2798–2809. https://doi.org/10.1063/1.480854
Thulstrup, E.W. (1969) Assignment of the lowest electronic transitions in benzene. International Journal of Quantum Chemistry 4(S3B), 641–649. https://doi.org/10.1002/qua.560040727
Petrushenko I, Petrushenko K (2022) Electronic transitions in noncovalent BODIPY dimers: TD-DFT study. Spectrochimica acta part A: molecular and Biomolecular Spectroscopy 275
Preciado-Rivas MR, Mowbray DJ, Lyon K, Larsen AH, Milne BF (2019) Optical excitations of chlorophyll a and b monomers and dimers. J Chem Phys 151(17)
Walter C, Kraemer V, Engels B (2017) On the applicability of time-dependent density functional theory (TDDFT) and semiempirical methods to the computation of excited-state potential energy surfaces of perylene-based dye-aggregates. Int J Quantum Chem 117(6):25337
Muhammed MM, Mokkath JH (2019) Linear acene molecules in plasmonic cavities: map** evolution of optical absorption spectra and electric field intensity enhancements. N J Chem 43(27):10774–10783
Cardozo TM, Galliez AP, Borges I, Plasser F, Aquino AJ, Barbatti M, Lischka H (2019) Dynamics of benzene excimer formation from the parallel-displaced dimer. Phys Chem Chem Phys 21(26):13916–13924
Budzianowski A, Katrusiak A (2006) Pressure-frozen benzene i revisited. Acta Crystallographica Section B: Structural Science 62(1):94–101
Adamo C, Barone V (1999) Toward reliable density functional methods without adjustable parameters: the pbe0 model. J Chem Phys 110(13):6158–6170
Weigend F, Ahlrichs R (2005) Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to RN: design and assessment of accuracy. Phys Chem Chem Phys 7(18):3297–3305
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 JA Jr, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, 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. Gaussian09 Revision A.01. https://gaussian.com/
Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavazzoni C, Ceresoli D, Chiarotti GL, Cococcioni M, Dabo I et al (2009) Quantum espresso: a modular and open-source software project for quantum simulations of materials. Journal of physics: Condensed matter 21(39):395502
Giannozzi P, Andreussi O, Brumme T, Bunau O, Nardelli MB, Calandra M, Car R, Cavazzoni C, Ceresoli D, Cococcioni M et al (2017) Advanced capabilities for materials modelling with Quantum ESPRESSO. Journal of physics: Condensed matter 29(46)
Giannozzi P, Baseggio O, Bonfá, P, Brunato D, Car R, Carnimeo I, Cavazzoni C, De Gironcoli S, Delugas P, Ferrari Ruffino F et al (2020) Quantum espresso toward the exascale. J Chem Phys 152(15)
Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77(18):3865
Vanderbilt D (1990) Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys Rev B 41(11):7892
Kresse G, Joubert D (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59(3):1758
Tao J, Perdew JP, Staroverov VN, Scuseria GE (2003) Climbing the density functional ladder: nonempirical meta-generalized gradient approximation designed for molecules and solids. Phys Rev Lett 91(14)
Chai J-D, Head-Gordon M (2008) Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections. Phys Chem Chem Phys 10(44):6615–6620
Hariharan PC, Pople JA (1973) The influence of polarization functions on molecular orbital hydrogenation energies. Theor Chim Acta 28:213–222
McLean A, Chandler G (1980) Contracted gaussian basis sets for molecular calculations. i. second row atoms, z= 11-18. J Chem Phys 72(10): 5639–5648
Dunning Jr TH (1989) Gaussian basis sets for use in correlated molecular calculations. i. the atoms boron through neon and hydrogen. J Chem Phys 90(2):1007–1023
Kaufmann K, Baumeister W, Jungen M (1989) Universal Gaussian basis sets for an optimum representation of Rydberg and continuum wavefunctions. Journal of Physics B: Atomic, Molecular and Optical Physics 22(14):2223
Neese F (2006) A critical evaluation of DFT, including time-dependent DFT, applied to bioinorganic chemistry. J Biol Inorg Chem 11(6):702–711. https://doi.org/10.1007/s00775-006-0138-1
Chai JD, Head-Gordon M (2008) Systematic optimization of long-range corrected hybrid density functionals. J Chem Phys 128(8). https://doi.org/10.1063/1.2834918
Goerigk L, Grimme S (2009) Calculation of electronic circular dichroism spectra with time-dependent double-hybrid density functional theory. J Phys Chem A 113(4):767–776. https://doi.org/10.1021/jp807366r
Goerigk L, Casanova-Paéz M (2021) The trip to the density functional theory zoo continues: making a case for time-dependent double hybrids for excited-state problems. Aust J Chem 74(1):3–15. https://doi.org/10.1071/CH20093
Rocha-Rinza T, De Vico L, Veryazov V, Roos BO (2006) A theoretical study of singlet low-energy excited states of the benzene dimer. Chem Phys Lett 426(4):268–272. https://doi.org/10.1016/j.cplett.2006.05.123
Nemeth G, Selzle H, Schlag E (1993) Magnetic ZEKE experiments with mass analysis. Chem Phys Lett 215(1–3):151–155
Diri K, Krylov AI (2012) Electronic states of the benzene dimer: a simple case of complexity. J Phys Chem A 116(1):653–662
Acknowledgements
The authors acknowledge Conselho Nacional de Desenvolvimento Cientıfico e Tecnologico (CNPq), Coordenacao de Aperfeicoamento Pessoal de Nıvel Superior (CAPES), and Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ) for financial support. Furthermore, the National Laboratory for Scientific Computing (LNCC/MCTI, Brazil) for providing HPC resources of the SDumont supercomputer, which have contributed to the research results reported within this paper (http://sdumont.lncc.br) and DIRAC computer cluster from ”Rede de Teoria, Modelagem e Simulação de Materiais para Nanotecnologia.”
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Coordenação de Aperfeiçoamento Pessoal de Nível Superior (CAPES) and Fundação de Amparo á Pesquisa do Estado do Rio de Janeiro (FAPERJ)
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R.M.: calculations, main manuscript text, and prepared figures. R.O.: advisory, revision, and writing. A. B.: conception, advisory, revision, and writing.
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Montserrat, R., Oliveira, R.R. & Rocha, A.B. Total absorption spectrum of benzene aggregates obtained from two different approaches. J Mol Model 30, 66 (2024). https://doi.org/10.1007/s00894-024-05859-7
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DOI: https://doi.org/10.1007/s00894-024-05859-7