Emission Energies and Stokes Shifts for Single Polycyclic

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Spectroscopy and Photochemistry; General Theory

Emission Energies and Stokes Shifts for Single Polycyclic Aromatic Hydrocarbon Sheets in Comparison to the Effect of Excimer Formation Baimei Shi, Dana Nachtigallova, Adelia J. A. Aquino, Francisco Bolivar Correto Machado, and Hans Lischka J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.9b02214 • Publication Date (Web): 03 Sep 2019 Downloaded from pubs.acs.org on September 3, 2019

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The Journal of Physical Chemistry Letters

Emission Energies and Stokes Shifts for Single Polycyclic Aromatic Hydrocarbon Sheets in Comparison to the Effect of Excimer Formation Baimei Shi,a Dana Nachtigallová,*,b,c Adélia J. A. Aquino,a,d Francisco B. C. Machado,e and Hans Lischkaa,d* a

School of Pharmaceutical Sciences and Technology, Tianjin University, Tianjin 300072, P.R. China b

Institute of Organic Chemistry and Biochemistry v.v.i., The Czech Academy of Sciences, Flemingovo nám. 2, 16610 Prague 6, Czech Republic c

Regional Centre of Advanced Technologies and Materials, Palacký University, 78371 Olomouc, Czech Republic

d

Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, United States

e

Departamento de Química, Instituto Tecnológico de Aeronáutica, São José dos Campos 12228900, São Paulo, Brazil

ACS Paragon Plus Environment

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ABSTRACT Emission spectra of paradigmatic single-sheet polycyclic aromatic hydrocarbons (PAHs), pyrene, circum-1-pyrene, coronene, circum-1-coronene and circum-2-coronene and Stokes shifts were computed and compared with previously calculated comparable data for relaxed excimer structures using the SOS-ADC(2), TD-B3LYP and TD-CAM-B3LYP methods with multireference DFT/MRCI data as benchmark. Vertical emission transitions and Stokes shifts were extrapolated to infinite PAH size. Comparison of Stokes shifts computed from theoretical monomer and dimer data confirm assumptions that relaxed excimers are responsible for the unusually large Stokes shifts in carbon dots observed in experimental investigations.

TOC GRAPHICS


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Polycyclic aromatic hydrocarbons (PAHs), conjugated aromatic molecules composed of fused benzenoid rings, have drawn particular attention as building units of carbon dots structures (CDs) which include graphene quantum dots (GQDs), composed of one or few graphene layers of size of few tens of a nm and carbon quantum dots (CQDs), possessing crystalline structure.1 CDs are 3dimensional systems containing graphitic regions, which, in contrast to graphene, exhibit discrete absorption and emission spectra arising from their quantum confinement.1-2 Because of their attractive photoluminescence properties and photostability, these materials find promising applications as photodetectors, solar cells and light-emitting diodes.3-4 The biocompatibility of CDs make them ideal candidates for bio-sensors,5-8 for bioimaging, drug delivery, and anticancer therapy.9-10 However, despite their practical importance, major questions concerning the actual mechanisms of CD photoluminescence are still open,1 especially whether the fluorescence properties can be explained by single fluorophores or by aggregates.11 PAHs of various sizes have been used as model systems for abovementioned studies on the luminescent behavior of CDs.1, 12-13 Recently, Fu et al.14 have performed spectroscopic studies of model systems based on the three PAHs anthracene, pyrene, and perylene embedded in a poly(methyl methacrylate) matrix to reproduce the features observed in actual CDs. An exciton self-trapping originating from relaxed excimer structures has been considered responsible for the large Stokes shifts observed. Even though these investigations point clearly to the important role of trapped excitons, a direct structural verification would be advantageous. The purpose of this work is to show, in combination with recent theoretical investigations on PAH dimers performed by our group15 that these trapping effects induced by excimer formation indeed lead to significant Stokes shifts.


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Inspired by the experimental observations of excitation-dependent photoluminescence, theoretical calculations, almost exclusively at the time dependent density functional theory (TDDFT)16 level, have been performed to rationalize luminescent spectra of CDs based on calculations of pyrene, coronene or even larger PAHs.17-22 They have shown that with the CD size in the range from 0.89 (coronene) to 1.80 nm the entire VIS spectrum (400–770 nm) is covered.20 However, previous calculations have shown problems in the interpretation of UV spectra, in particular to describe correctly the energy ordering of excited states of linear and non-linear PAHs.23-29 Such problems make the use of these methods somewhat risky for the interpretation of luminescent spectra since in many calculations a bright La state has been wrongly predicted to be the lowest state in pyrene instead of the dark Lb state. The strategy of this work is to use the wave function-based algebraic diagrammatic construction to second-order (ADC(2))30-31 method in combination with the resolution of the identity (RI) approach32 and the scaled opposite-spin33 (SOS) modification (SOS-ADC(2)) which allow the calculation of emission spectra of medium and large-sized PAHs34 due to the fact that analytic energy gradients for geometry optimizations are available for this method. Even higher accuracy is provided by the DFT/multireference configuration interaction (DFT/MRCI) method35-38 which does not have, however, the possibility of analytic energy gradients. Our strategy is to use a combination of both methods by means of SOS-ADC(2) geometry optimizations for the excited state with single-point verification of excitation energies by DFT/MRCI. Using the abovementioned methods, it has been shown in our previous calculations that the correct ordering of above-mentioned excited states La and Lb of pyrene and its extension to circum-1-pyrene has been obtained34 and that the SOS-ADC(2) results provide reliable information. In addition, calculations


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with the popular TD- Becke-3-Lee-Yang-Parr (TD-B3LYP) and TD-Coulomb-attenuating method (CAM)-B3LYP (TD-CAM-B3LYP) approaches have been performed as well. The exciton-phonon coupling plays an important role for the exciton trapping. Therefore, we start the discussion with geometry relaxation effects and discuss their relation to the changes on electronic excitation based on natural transition orbitals (NTOs).39 Based on the geometries in S1, vertical emission energies are calculated and compared with available experimental data. Finally, comparison of Stokes shifts for PAH monomers and dimers are made to analyze excimer trapping effects and the experimentally observed large Stokes shifts. The structures of pyrene and coronene and its larger circular extensions to circum-1-pyrene, circum-1-coronene, and circum-2-coronene are displayed in Figure 1 and Figure 2 together with color-coded differences in the CC bond distances between ground- and S1 state minima. The SOSADC(2) calculations for pyrene and circum-1-pyrene (Figure 1a and 1a’) show an alternating shortening-lengthening of the double bonds concentrated on the central naphthalene subunit. The same feature occurs also at the TD-CAM-B3LYP level (Figure 1a and 1a’). For coronene (Figure 2), the CC distances in the central ring are reduced in S1 and the radially outward pointing distances are increased. SOS-ADC(2), B3LYP and CAM-B3LYP show a similar pattern. With increasing system size, the structural changes become smaller, which is consistent with smaller energy changes between the vertical and adiabatic excitation energies as the systems extends (see later). Remarkable is also the alternant behavior of the changes of the bond distances in the central bond of the pyrene-based systems with contraction for pyrene and stretching for circum-1-pyrene. Similar behavior is observed for bond distances in the innermost benzene ring, i.e. contraction for coronene, stretching for circum-1-coronene and contraction again for circum-2-coronene. The TDB3LYP changes in bond distances have been calculated for pyrene also, but, as will be discussed


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below, the S1 state has the wrong character (La instead of Lb) and, therefore, the bond-change pattern is not correct in this case.

a

b

a'

b'

Figure 1. Geometry differences (Å) between S1 state and S0 states of pyrene (a,b) and of circum1-pyrene (a',b') calculated with the SOS-ADC(2)) (a and a') and TD-CAM-B3LYP (b and b') methods, respectively.

a

b

c

a’

b’

c’

a”

b”

c”

Figure 2. Geometry differences (Å) between S1 state and S0 states of coronene (a-c), circum-1coronene (a'-c') and circum-2-coronene (a''-c'') calculated with the SOS-ADC(2)) (a-a''), TDB3LYP(b-b'') and TD-CAM-B3LYP(c-c'') methods, respectively.


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The just-discussed geometry changes correlate well with the orbital excitation scheme based on natural transition orbitals (NTOs) (Figure 3 for pyrene and circum-1-pyrene and Figure 4 for coronene to circum-2-coronene) for the transition to S1. For example, the shortening of the central CC bond has its counterpart in the population of a bonding orbital contribution (electron NTO for the first configuration). A similar analysis applies to the changes of the remaining bond distances. For example, the weakening of the central bond in circum-1-pyrene has its origin in the missing bonding orbital in the central bond of the electron NTO in the first configuration (Figure 3) and in the occurrence of an antibonding orbital in the second configuration. For the coronene systems, the pattern of geometry changes (Figure 2) between S0 and S1 states correlates also well with the nodal pattern of the respective NTOs (Figure 4).

Figure 3. NTO of pyrene and circum-1-pyrene for the S1 state based on SOS-ADC(2) calculations.


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Figure 4. NTO of coronene, circum-1-coronene and circum-2-coronene for the S1 state The emission energies, given as the vertical S1–S0 energy difference at the S1 minimum, are collected in Table 1. An excellent agreement between the calculated and experimental values of pyrene is obtained for DFT/MRCI energies obtained at the SOS-ADC(2) optimized geometry. The SOS-ADC(2) emission energy is in good agreement with both, experimental and DFT/MRCI results, with differences not larger than 0.2 eV. TD-CAM-B3LYP overestimates the emission energy significantly by 0.53 eV. At the DFT/MRCI level the emission energy decreases significantly by 0.38 eV, bringing the emission energy to a very good agreement with experiment. This higher value of DFT/MRCI energy calculated at the TD-CAM-B3LYP geometry compared to the SOS-ADC(2) geometry is consistent with smaller geometry changes upon the relaxation to


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the S1 minimum. As already observed in the case of absorption spectra of pyrene,34 the wrong state character is obtained at TD-B3LYP level for the emission spectrum as well, as can be seen from the large oscillator strengths in this case as opposed to zero value for the other two methods. The same wrong state ordering at TD-B3LYP level occurs for circum-1-pyrene also. Comparison of the DFT/MRCI and SOS-ADC(2) energies computed at the SOS-ADC(2) geometry shows an overestimation of the emission energy by 0.27 eV, which is still acceptable for further analyses. For the coronene series, all methods used perform well. They all give the correct state ordering of a dark S1 state, and smaller differences to the experimental value in most cases. In particular, the SOS-ADC(2) and TD-B3LYP emission energies are only slightly (by ~ 0.1 eV) overestimated with respect to the experiment. The DFT/MRCI method lowers these values by ~0.27 eV, giving slightly underestimated (by 0.20 and 0.13 eV) emission energies, still in very good agreement with the experiment. TD-CAM-B3LYP method performs slightly worse, the energies are overestimated by 0.38 eV.

Table 1. Emission energies (eV) and wavelengths of pyrene, circum-1-pyrene, coronene, circum1-coronene and circum-2-coronene with optimized geometries calculated at the ADC(2), TDB3LYP and TD-CAM-B3LYP levels. DFT/MRCI emission energies (in italics) were calculated at the respective SOS-ADC(2), B3LYP and CAM-B3LYP S1 geometries.

Structure

Pyreneb

State

11B3u

ADC(2)

TD-B3LYP

3.40

3.39 (11B2u, 0.32)

3.26b

3.38(11B3u)b

TD-CAMB3LYP f

3.76

Emission Exp. 3.22d

3.38


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Circum-1-pyreneb

11B3u

Coroneneb

11B

Circum-1coroneneb

11B2u

Circum-2coronenec

11B2u

2u

2.24 (11B2u, 0.39)

f 2.51 (11B2u, f 0.54)

2.17c

2.26 (11B2u, 0.70)c

f 2.27 (11B2u, f 0.71)c

3.03

3.09

3.33

2.75

2.82

2.87

2.21

2.16

2.46

1.90c

1.95c

1.99c

1.74

1.61

1.95

2.44

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2.95e

a

oscillator strengths f are zero unless values are given in parentheses; b def2-TZVP basis set unless marked differently; c SV(P) basis set; dexperimental value from 40; eexperimental value from 41. Similar to coronene, circum-1-coronene emission energies obtained with SOS-ADC(2) and TDB3LYP are almost the same. They are overestimated by 0.30 and 0.21 eV, respectively, with respect to DFT/MRCI results. The TD-CAM-B3LYP method gives a larger emission energy compared to DFT/MRCI by 0.47 eV. A similar situation can be observed also for circum-2-pyrene.


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4.0

SOS-ADC(2) DFT/MRCI based on SOS-ADC(2) optimized S1 geometry TD-CAM-B3LYP

333

3.5

py

3.0

407 444

cor

2.5

c-1-c

481

c-2-c 2.0

c-1-p

1.5 0

5

10

15

20

25

30

35

518 555 592 629 666 703 740 777 814 40

Wavelength (nm)

370

Emi. en. (eV))

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Number of aromatic rings

Figure 5. Emission energies (eV) in dependence of the number of aromatic rings calculated with the SOS-ADC(2), DFT/MRCI and TD-CAM-B3LYP methods, respectively. Interpolation curves are shown using Equ. (2).

The trend of a monotoneous decline of emission energies with increasing molecular size is shown in Figure 5. Similar trends were observed for S0 → S1 absorption energies also.34 As in Ref. 34,

the emission energies of Figure 5 were fitted by means of the exponential expression 𝑦 = 𝑦0 + 𝑎𝑒 ―𝑏𝑛.

(2)

The extrapolation to infinite ring number gives emission energies of 1.63 eV for SOS-ADC(2) and 1.77 eV for TD-CAM-B3LYP. Stokes shifts (differences between vertical absorption and emission) are collected in Table 2. These differences decrease with increasing system size showing that the geometry relaxation in S1 is becoming less important. Both SOS-ADC(2) and TD-CAM-B3LYP reach a finite limit. An exponential fitting performed for the ADC(2) data (Figure S1) leads to an extrapolated value for infinite system size of 0.14 eV (1129 cm-1). On the contrary, TD-B3LYP results seem to approach


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a zero value for the Stokes shift. Thus, the experimental observation of unusually large Stokes shifts (up to 5000-6000 cm-1) observed in several CD structures11, 14, 42-43 can certainly not be explained by the small shift found in pristine single-sheet PAHs. They originate very likely from other phenomena, like aggregation11, 42 or self-trapping14 rather than from isolated CD sheets. That excimer interaction in stacked arrangements plays a significant role for emission energies can already be seen from a comparison of the just-discussed Stokes shift for the monomers in comparison to the shift between the same vertical monomer excitation and the vertical dimer emission.15 For the circum-1-coronene as example (SOS-ADC(2), Table 2), the monomer shift amounts to 0.17 eV (1400 cm-1) whereas for the shift of the same monomer excitation to the dimer emission,15 indeed a much larger shift of 0.53 eV (4300 cm-1) is obtained. Larger aggregates can lead to even larger shifts as discussed e.g. in Ref. 11 Table 2. Stokes shift (eV) of the monomers pyrene, circum-1-pyrene, coronene, circum-1coronene and circum-2-coronene calculated at the SOS-ADC(2), TD-B3LYP and TD-CAMB3LYP levels.a Comparison to shifts based on dimer emission ids given in parentheses at SOSADC(2) level.

Structure

SOS-ADC(2)b

TD-B3LYP

TD-CAM-B3LYP

Pyrene

0.31 (0.96)

-c

0.27

Circum-1-pyrene

0.21 (0.72)

-c

-c

Coronenea

0.29 (0.46)

0.13

0.22

Circum-1-coronenea

0.17 (0.53)

0.07

0.16

Circum-2-coroneneb

0.15

0.03

0.12c


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adef2-TZVP

basis set except for circum-2-coronene where the SV(P) basis set was used; bStokes shift of vertical monomer to vertical dimer emission in parentheses;15 cnot evaluated due to the wrong S1/S2 ordering. In summary, geometry changes upon the excitation to S1 minima, an alternate shortening and lengthening of CC bond distances, correlate well with the character of NTO orbitals. The emission spectra calculations confirm well the argumentations that large Stokes shifts should originate from excimer aggregates formed in stacked arrangements rather than from the monomer emission of pristine PAHs. It should be noted though that doping PAHs with heteroatoms17 or edge substitution20 provide alternative pathways to significant red shifts in the fluorescence spectra.

COMPUTATIONAL METHODS The computational methods SOS-ADC(2), B3LYP, CAM-B3LYP and DFT/MRCI have already been referenced in the text above. The triple-zeta valence polarization with (2d,f) on carbon (def2TZVP)44 basis set was used for S1 optimization under D2h symmetry restriction. The same basis has also been used for emission energy calculations of pyrene, circum-1-pyrene, coronene and circum-1-coronene. The split valence basis set (SV(P))45 basis set was used for the larger circum2-coronene. Cartesian geometries for all structures are collected in the Supporting Information. The ground state structures were taken from Ref.

34

consistent with above methods. In case of

SOS-ADC(2), the ground-state calculations had been performed at SOS-MP2 level. Both TDDFT-B3LYP and SOS-ADC(2) calculations were performed with the Turbomole 7.2 program.46 For the TDDFT-CAM-B3LYP computations the Gaussian 09 program was used.47 The DFT/MRCI calculation were carried out with the program developed by Grimme and Waletzke35 and further developed by the group of Marian.36-38 The initial DFT calculation with Becke’s hybrid


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exchange-correlation functional (BHLYP)48 were performed with the Turbomole 7.2 program. NTOs39 have been computed using the TheoDORE program.49-51

ASSOCIATED CONTENT Supporting Information: Plot of Stokes shift with number of aromatic rings, Cartesian coordinates of optimized structures. AUTHOR INFORMATION Corresponding Authors *Email: [email protected] (D.N.) *Email: [email protected] (H.L.)

ACKNOWLEDGMENTS We are grateful for generous support by the School of Pharmaceutical Science and Technology, Tianjin University, Tianjin, China, including computer time on the SPST computer cluster Arran. DN acknowledges the support from research project RVO (61388963) of the IOCB of the CAS and of the Czech Science Foundation (GA16-16959S). FBCM. gratefully acknowledges the financial assistance of the Brazilian agencies Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) under Projects Nos. 307052/2016-8, 404337/2016-3 and Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) under Project No. 2017/07707-3. FBCM, AJAA and HL are thankful to the FAPESP/Tianjin University SPRINT program (project no. 2017/50157-4) for travel support. This work was supported by the Center for Integrated Nanotechnologies (Project No. C2013A0070), an Office of Science User Facility operated for the U.S. Department of Energy Office of Science by Los Alamos National Laboratory (Contract DEAC52-06NA25396) and Sandia National Laboratories (Contract DE-AC04-94AL85000).


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REFERENCES (1) Zhu, S. J.; Song, Y. B.; Zhao, X. H.; Shao, J. R.; Zhang, J. H.; Yang, B. The photoluminescence mechanism in carbon dots (graphene quantum dots, carbon nanodots, and polymer dots): current state and future perspective. Nano Research 2015, 8, 355-381. (2) Chen, B. B.; Liu, M. L.; Li, C. M.; Huang, C. Z. Fluorescent carbon dots functionalization. Adv. Colloid Interface Sci. 2019, 270, 165-190. (3) Choi, S. H. Unique properties of graphene quantum dots and their applications in photonic/electronic devices. J. Phys. D: Appl. Phys. 2017, 50, 103002. (4) Richter, M.; Heumüller, T.; Matt, G. J.; Heiss, W.; Brabec, C. J. Carbon photodetectors: the versatility of carbon allotropes. Adv. Ener. Mat. 2017, 7, 1601574. (5) Zheng, P.; Wu, N. Q. Fluorescence and sensing applications of graphene oxide and graphene quantum dots: a review. Chemistry-an Asian Journal 2017, 12, 2343-2353. (6) Suvarnaphaet, P.; Pechprasarn, S. Graphene-based materials for biosensors: a review. Sensors 2017, 17, 2161. (7) Chauhan, N.; Maekawa, T.; Kumar, D. N. S. Graphene based biosensors-accelerating medical diagnostics to new-dimensions. J. Mater. Res. 2017, 32, 2860-2882. (8) Shivananju, B. N.; Yu, W. Z.; Liu, Y.; Zhang, Y. P.; Lin, B.; Li, S. J.; Bao, Q. L. The roadmap of graphene-based optical biochemical sensors. Adv. Funct. Mater. 2017, 27, 1603918. (9) Li, K. H.; Liu, W.; Ni, Y.; Li, D. P.; Lin, D. M.; Su, Z. Q.; Wei, G. Technical synthesis and biomedical applications of graphene quantum dots. J. Mater. Chem. B 2017, 5, 4811-4826. (10) Iannazzo, D.; Ziccarelli, I.; Pistone, A. Graphene quantum dots: multifunctional nanoplatforms for anticancer therapy. J. Mater. Chem. B 2017, 5, 6471-6489. (11) Malyukin, Y.; Viagin, O.; Maksimchuk, P.; Dekaliuk, M.; Demchenko, A. Insight into the mechanism of the photoluminescence of carbon nanoparticles derived from cryogenic studies. Nanoscale 2018, 10, 9320-9328. (12) Xiao, L.; Sun, H. D. Novel properties and applications of carbon nanodots. Nanoscale Horizons 2018, 3, 565-597. (13) Grimsdale, A. C.; Müllen, K. The chemistry of organic nanomaterials. Angew. Chem. Int. Ed. 2005, 44, 5592-5629. (14) Fu, M.; Ehrat, F.; Wang, Y.; Milowska, K. Z.; Reckmeier, C.; Rogach, A. L.; Stolarczyk, J. K.; Urban, A. S.; Feldmann, J. Carbon dots: a unique fluorescent cocktail of polycyclic aromatic hydrocarbons. Nano Lett. 2015, 15, 6030-6035. (15) Shi, B. M.; Nachtigallova, D.; Aquino, A. J. A.; Machado, F. B. C.; Lischka, H. Excited states and excitonic interactions in prototypic polycyclic aromatic hydrocarbon dimers as models for graphitic interactions in carbon dots. PCCP 2019, 21 9077-9088. (16) Furche, F.; Ahlrichs, R. Adiabatic time-dependent density functional methods for excited state properties. J. Chem. Phys. 2002, 117, 7433-7447.


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Page 17 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(17) Hola, K.; Sudolska, M.; Kalytchuk, S.; Nachtigallova, D.; Rogach, A. L.; Otyepka, M.; Zboril, R. Graphitic nitrogen triggers red fluorescence in carbon dots. ACS Nano 2017, 11, 1240212410. (18) Hola, K.; Bourlinos, A. B.; Kozak, O.; Berka, K.; Siskova, K. M.; Havrdova, M.; Tucek, J.; Safarova, K.; Otyepka, M.; Giannelis, E. P.; Zboril, R. Photoluminescence effects of graphitic core size and surface functional groups in carbon dots: COO- induced red-shift emission. Carbon 2014, 70, 279-286. (19) Chen, S. W.; Ullah, N.; Wang, T. Q.; Zhang, R. Q. Tuning the optical properties of graphene quantum dots by selective oxidation: a theoretical perspective. J. Mater. Chem. C 2018, 6, 6875-6883. (20) Sk, M. A.; Ananthanarayanan, A.; Huang, L.; Lim, K. H.; Chen, P. Revealing the tunable photoluminescence properties of graphene quantum dots. J. Mater. Chem. C 2014, 2, 6954-6960. (21) Sarkar, S.; Sudolska, M.; Dubecky, M.; Reckmeier, C. J.; Rogach, A. L.; Zboril, R.; Otyepka, M. Graphitic nitrogen doping in carbon dots causes red-shifted absorption. J. Phys. Chem. C 2016, 120, 1303-1308. (22) Kozak, O.; Sudolska, M.; Pramanik, G.; Cigler, P.; Otyepka, M.; Zboril, R. Photoluminescent carbon nanostructures. Chem. Mater. 2016, 28, 4085-4128. (23) Parac, M.; Grimme, S. A TDDFT study of the lowest excitation energies of polycyclic aromatic hydrocarbons. Chem. Phys. 2003, 292, 11-21. (24) Grimme, S.; Parac, M. Substantial errors from time-dependent density functional theory for the calculation of excited states of large pi systems. Chemphyschem 2003, 4, 292. (25) Wang, Y. L.; Wu, G. S. Improving the TDDFT calculation of low-lying excited states for polycyclic aromatic hydrocarbons using the Tamm-Dancoff approximation. Int. J. Quantum Chem 2008, 108, 430-439. (26) Wong, B. M.; Hsieh, T. H. Optoelectronic and excitonic properties of oligoacenes: substantial improvements from range-separated time-dependent density functional theory. J. Chem. Theory Comput. 2010, 6, 3704-3712. (27) Richard, R. M.; Herbert, J. M. Time-dependent density-functional description of the La state in polycyclic aromatic hydrocarbons: charge-transfer character in disguise? J. Chem. Theory Comput. 2011, 7, 1296-1306. (28) Görigk, L.; Grimme, S. Double-hybrid density functionals provide a balanced description of excited La and Lb states in polycyclic aromatic hydrocarbons. J. Chem. Theory Comput. 2011, 7, 3272-3277. (29) Görigk, L.; Möllmann, J.; Grimme, S. Computation of accurate excitation energies for large organic molecules with double-hybrid density functionals. PCCP 2009, 11, 4611-4620. (30) Schirmer, J. Beyond the random-phase approximation - a new approximation scheme for the polarization propagator. Physical Review A 1982, 26, 2395-2416. (31) Trofimov, A. B.; Schirmer, J. An efficient polarization propagator approach to valence electron-excitation spectra. J. Phys. B: At., Mol. Opt. Phys. 1995, 28, 2299-2324.


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(32) Hättig, C.; Weigend, F. CC2 excitation energy calculations on large molecules using the resolution of the identity approximation. J. Chem. Phys. 2000, 113, 5154-5161. (33) Jung, Y. S.; Lochan, R. C.; Dutoi, A. D.; Head-Gordon, M. Scaled opposite-spin second order Møller-Plesset correlation energy: An economical electronic structure method. J. Chem. Phys. 2004, 121, 9793-9802. (34) Shi, B. M.; Nachtigallova, D.; Aquino, A. J. A.; Machado, F. B. C.; Lischka, H. High-level theoretical benchmark investigations of the UV-vis absorption spectra of paradigmatic polycyclic aromatic hydrocarbons as models for graphene quantum dots. J. Chem. Phys. 2019, 150, 124302. (35) Grimme, S.; Waletzke, M. A combination of Kohn-Sham density functional theory and multi-reference configuration interaction methods. J. Chem. Phys. 1999, 111, 5645-5655. (36) Lyskov, I.; Kleinschmidt, M.; Marian, C. M. Redesign of the DFT/MRCI Hamiltonian. J. Chem. Phys. 2016, 144, 034104. (37) Marian, C. M.; Heil, A.; Kleinschmidt, M. The DFT/MRCI method. Wiley Interdisc. Rev.Comp. Mol. Sci. 2019, 9. (38) Heil, A.; Kleinschmidt, M.; Marian, C. M. On the performance of DFT/MRCI Hamiltonians for electronic excitations in transition metal complexes: The role of the damping function. J. Chem. Phys. 2018, 149, 164106. (39)

Martin, R. L. Natural transition orbitals. J. Chem. Phys. 2003, 118, 4775-4777.

(40) Guldi, D. M.; Spanig, F.; Kreher, D.; Perepichka, I. F.; van der Pol, C.; Bryce, M. R.; Ohkubo, K.; Fukuzumi, S. Contrasting photodynamics between C-60-dithiapyrene and C-60pyrene dyads. Chem. Eur. J. 2008, 14, 250-258. (41) Bermudez, G.; Chan, I. Y. Excitation and fluorescence-spectra of coronene in a jet. J. Phys. Chem. 1986, 90, 5029-5034. (42) Gude, V.; Das, A.; Chatterjee, T.; Mandal, P. K. Molecular origin of photoluminescence of carbon dots: aggregation-induced orange-red emission. PCCP 2016, 18, 28274-28280. (43) Li, L. L.; Wu, G. H.; Yang, G. H.; Peng, J.; Zhao, J. W.; Zhu, J. J. Focusing on luminescent graphene quantum dots: current status and future perspectives. Nanoscale 2013, 5, 4015-4039. (44) Weigend, F.; Ahlrichs, R. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. PCCP 2005, 7, 3297-3305. (45) Schäfer, A.; Horn, H.; Ahlrichs, R. Fully optimized contracted Gaussian-basis sets for atoms Li to Kr. J. Chem. Phys. 1992, 97, 2571-2577. (46) Ahlrichs, R.; Bär, M.; Häser, M.; Horn, H.; Kölmel, C. Electronic-structure calculations on workstation computers - the program system Turbomole. Chem. Phys. Lett. 1989, 162, 165-169. (47) Frisch, M. J. T., G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, G. A.; Nakatsuji, H.; Li, X.; Caricato, M.; Marenich, A.; Bloino, J.; Janesko, B. G.; Gomperts, R.; Mennucci, B.; Hratchian, H. P.; Orti, J. V.; Izmaylov, A. F.; Sonnenber, J. L.; Williams-Young, D.; Din, F.; Lipparin, F.; Egidi, F.; Goings, J.; Peng, B.; Petrone, A.; Henderson, T.; Ranasinghe, D.; Zakrzewski, V. G.; Gao, J.; Rega, N.; Zheng, G.; Liang, W.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.;


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Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Throssell, K.; Montgomery, J. A.; Jr.; Peralta, J. E.; Ogliaro, F.; Bearpar, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Keith, T.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendel, A.; Buran, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Millam, J. M.; Klene, M.; Adamo, C.; Cammi, R.; Ochtersk, J. W.; Martin, R. L.; Morokuma, K.; Farkas, O.; Foresman, J. B.; Fox, D. J. Gaussian 09, revision A.02, Inc., Wallingford, CT, 2009. (48) Becke, A. D. A new mixing of Hartree-Fock and local density-functional theories. J. Chem. Phys. 1993, 98, 1372-1377. (49) Plasser, F.; Lischka, H. Analysis of Excitonic and Charge Transfer Interactions from Quantum Chemical Calculations. J. Chem. Theory Comput. 2012, 8, 2777-2789. (50) Plasser, F.; Bäppler, S. A.; Wormit, M.; Dreuw, A. New tools for the systematic analysis and visualization of electronic excitations. II. Applications. J. Chem. Phys. 2014, 141. (51) Plasser, F. TheoDORE: A package for theoretical density, orbital relaxation, and exciton analysis; available at http://Theodore-Qc.Sourceforge.Net.


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Emission Energies and Stokes Shifts for Single Polycyclic

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