Strong Electronic Coupling Dominates the Absorption and

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Strong Electronic Coupling Dominates the Absorption and Fluorescence Spectra of Covalently Bound BisBODIPYs Stefan Knippenberg, Mercedes Vanessa Bohnwagner, Philipp H. P. Harbach, and Andreas Dreuw J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b00637 • Publication Date (Web): 30 Jan 2015 Downloaded from http://pubs.acs.org on February 2, 2015

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The Journal of Physical Chemistry

Strong Electronic Coupling Dominates the Absorption and Fluorescence Spectra of Covalently Bound BisBODIPYs S. Knippenberg,∗,† M. V. Bohnwagner,¶ P. H. P. Harbach,¶ and A. Dreuw∗,¶ Laboratoire de chimie physique théorique, Département de Chimie B6c, Université de Liège, B-4000 Liège, Belgium, Division of Theoretical Chemistry and Biology, KTH Royal Institute of Technology, Roslagstullsbacken 15, S-106 91 Stockholm, Sweden, and Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany E-mail: [email protected]; [email protected]

∗

To whom correspondence should be addressed Laboratoire de chimie physique théorique, Département de Chimie B6c, Université de Liège, B-4000 Liège, Belgium ‡ Division of Theoretical Chemistry and Biology, KTH Royal Institute of Technology, Roslagstullsbacken 15, S-106 91 Stockholm, Sweden ¶ Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany †

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Abstract The absorption spectrum of a representative BisBODIPY molecule is investigated using high-level quantum chemical methodology; the results are compared with experimental data. The S1 and S2 excited states are examined in detail to illuminate and to understand the electronic coupling between them. With the help of model systems in which the distance between the BODIPY monomers is increased or in which the dihedral angle between the subunits is changed, the electronic coupling is quantified and its influence on energetics and oscillator strengths is highlighted. For the explanation of the experimental spectrum, orbital interaction effects are found to be important. Because of the large experimental Stokes’ shift of BisBODIPY, the nature of the emissive state is investigated and found to remain C2 symmetric as the ground state, and no localization of the excitation on one BODIPY subunit occurs. The excitonic coupling is in BisBODIPY still larger than the geometry relaxation energy, which explains the absence of a pseudo Jahn-Teller effect.

1

Introduction

Fluorophores are continuously attracting interest of researchers from all areas of science. Developments in the fields of personal diagnostics and organic electroluminescent devices have recently further boosted the development of next-generation emissive dyes. 1 Countless classes of highly fluorescent organic compounds are now known, out of which difluoro-boraindacenes (4,4-difluoro-4-borata-3a-azonia-4a-aza-s-indacene, Figure 1a) have gained recognition as being one of the most versatile fluorophores. This dye has first been reported by Treibs and Kreuzer in 1968 2 and has since then steadily increased in popularity over the past two decades, because its potential in biological labeling was soon recognized. 3 Nowadays, these difluoroboraindacenes, or in short BODIPYs, are used in several research fields, ranging from material science to biological applications. 4,5 High molecular stability combined with visible light absorbance, their high luminescence quantum yield and the possibility to tune 2 ACS Paragon Plus Environment

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the absorption and emission wavelengths by convenient substitution are the most important reasons for their success. For example, functionalisation of the BODIPY fluorophore at the 3- and 5-positions with aryl rings yields fluorophores with emission maxima ranging from green to infrared. 6 Recently, covalently bound BisBODIPYs have been synthesized via the reaction of boron trifluoride diethyletherate with a certain class of artificial open-chain tetrapyrroles, the 2,2’bidipyrrins. 7 In general, BisBODIPYs can hence also be seen as dinuclear difluoridoboron complexes of 2,2’-bidipyrrin ligands, which represent potent novel fluorophors. 8,9 The photophysical properties of BisBODIPYs are governed by narrow excitonically coupled absorption bands and a large Stokes’ shift of about 70 nm. These features are present in addition to a high fluorescence quantum yield of about 70 %, which is typical for most BODIPY dyes. 1,8 Such high quantum yields are however usually only present in rigid compounds, which are devoid of significant intramolecular motion, as vibrations and rotations facilitate non-radiative processes hence quenching fluorescence. 10 Hence, the flexible structure of BisBODIPYs is at first glance contradicting the high fluorescence quantum yield. A quantitative understanding of the electronic coupling of the excited states of the individual BODIPYs composing the dimer absorption and fluorescence spectra paves the way to investigate energy transfer in molecular assemblies built around BODIPY dyes. For example, considering BODIPY-based triads, which are bound to each other using ethynyldibutoxyphenyl linkers, it was shown that energy transfer between the terminal BODIPYs occurs primarily by way of through-bond, i.e. electron exchange interactions. 11 Along the same line of thought, BisBODIPY derivatives were investigated using (time-dependent) density functional theory (TDDFT) and they were found to have both a high charge-transfer rate and high photoluminiscence efficiency in the solid state, 12 which makes them excellent candidates for ambipolar materials for use in OLEDs for instance. In the current study, we aim at understanding the structure of the observed absorption spectrum and the fluorescence properties of BisBODIPY. For this objective, the focus will be 3 ACS Paragon Plus Environment


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put on the electronic coupling interactions between two covalently bound BODIPY molecules and on the most important motions, the intermolecular distance and the central dihedral angle, modulating the relative orientation of the two BODIPY subunits. The direct motif for this investigation are the observed differences in the absorption spectra of a monomeric BODIPY and the corresponding BisBODIPY species. 7 The experimental absorption spectrum of BisBODIPY is dominated by two bands at 490 and 559 nm with equal intensity, which are centered around the main absorption band of the monomeric BODIPY at 529 nm (see Figure 5 (a) from Ref. 7 ). This finding is very suggestive of dominating excitonic coupling. Focussing at the electrostatic interactions between dipoles, it can be estimated at large intermolecular separations via 13–15

V12 = κ

|~µ1 ||~µ2 | R3

with

(1)

κ = ~n1 · ~n2 − 3(~n1 · ~eR )(~n2 · ~eR ),

with ~n1 and ~n2 the unit vectors pointing in the directions of the transition dipole moments µ ~1 ~ = R~eR between the centers of charges of the two moieties. and µ ~ 2 , and the distance vector R κ is the so-called orientation factor and depends on the relative orientation of the transition dipole moments. From equation 1, it is clear that the excitonic coupling is mathematically dependent upon the intermolecular separation as well as the orientation of the dipole vectors, and so, of the constituting subunits. In BisBODIPY, the BODIPY subunits are however spatially not well separated and hence electronic effects beyond the dipole-dipole approximation will contribute significantly to the electronic coupling of the monomeric excited states. Hence, the total electronic coupling between the excited states of the two individual BODIPYs will consist of classical Förster-type and Dexter-type interactions, as well as contributions originating from molecular orbital interactions. These contributions will be qualitatively estimated using state-of-the-art quantum chemical methodology beyond density functional theory. In this study, the simplest, parent (BF2)-2-2’-bidipyrrin (Figure 1b) 7–9,16


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compound is used as representative example for BisBODIPYs. The paper is organized as follows. After outlining the applied theoretical methods (Section 2), their accuracy and applicability for the description of the ground state (Section 3) and the absorption spectra of the BisBODIPY molecules is evaluated (Section 4). In a second step the electronic coupling in BisBODIPY is studied by estimating the magnitude and importance of different influences originating from Förster and Dexter coupling as well as shifts in the orbital energies (Section 5). Then, the fluorescence properties of BisBODIPY are investigated (Section 6). Here, comparison to BODIPY is made and focus is put on the question whether fluorescence occurs from a delocalized, strongly coupled S1 state or whether the coupld excited state prefers to localize on one BODIPY unit. The paper concludes with a brief summary of the main conclusions (Section 7).

a) C1 C2

C3

C C5 14

C10

B11

N4 F13

C2

F12’ b)

C8’ C7’

F13’ N9’ C10’

C6’

N9 F12

C1

B11’CC3 3’

C6 C7 C8

C14

C6 C10

N4 F12

N B119 F13

C5

C2’

N4’

C7 C8

C1’

C5’ C14’

Figure 1: Molecular structure of (a) BODIPY and (b) BisBODIPY. For BODIPY, the transition state dipole moment for the excitation to the S1 state (S0 → S1 ) is indicated as red arrow. For BisBODIPY, the C2 symmetry is stressed by applying quoted labels for symmetrically identical atoms.



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2

Computational details

The equilibrium geometries of BODIPY and BisBODIPY have been obtained using density functional theory (DFT) along with the standard B3LYP 17,18 exchange-correlation (xc) functional and Pople’s double-ζ plus polarization (6-31G*) basis set 19,20 with and without including Grimme’s correction scheme for dispersion 21 (B3LYP-D), as well as with the BHLYP xc-functional exhibiting 50% non-local orbital exchange. 22 For comparison, the geometries have also been optimized at the ab initio level of approximate second order coupled cluster exploiting the resolution-of-the-identity (RI-CC2). 23–25 The vertical electronic spectra have been computed at various theoretical levels of approximation. The conceptually simplest excited state method configuration interaction singles (CIS), time-dependent density functional theory (TDDFT), 26–29 as well as the more advanced ab initio algebraic diagrammatic construction method for the polarization propagator of second order (ADC(2)) 30,31 and linear-response approximate coupled-cluster (RI-CC2) in second order have been used. 24,25 It is worth to note that xc-functionals with at least 50% non-local orbital exchange are required at TDDFT level to treat systems like BisBODIPY due to the dimeric nature of the system, since otherwise charge-transfer excited states may occur at drastically too low excitation energies. 27 Hence, the BHLYP xc-functional as well as the long-range corrected ωB97X 32 and ωPBE 33 functionals have been used. The single-point ADC(2), RI-CC2 results, and BHLYP data have been obtained using Ahlrichs’ SVP basis set. 34 For the computation of the fluorescence wavelengths, the S1 excited state geometries of BODIPY and BisBODIPY have been optimized at the level of TDDFT/BHLYP/SVP, since this functional/basis set combination showed the best agreement with the ab initio ADC(2) and CC2 data. All calculations have been performed using Turbomole 5.10 35 and Q-Chem. 36


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3

Ground state equilibrium geometry of BisBODIPY

The geometrical parameters of the experimental X-ray structure 7 of BisBODIPY are compared in Table 1 with the corresponding calculated values obtained at different levels of theory. In contrast to the computed unsubstituted parent BisBODIPY, the experimental X-ray structure has been obtained for a derivative exhibiting methyl groups at positions C1 , C01 ,C8 ,C08 , ethyl groups at the positions C2 , C02 , C6 , C06 , C7 , C07 as well as phenyl groups at C14 , C014 . Although the experimental data for the substituted BisBODIPY derivative do not cope with symmetry, C2 symmetry has been taken into account in the calculations for the parent BisBODIPY model presented here. In Table 1, it can be seen that the overall agreement between bond lengths and angles is reasonable with the typical accuracy of the applied theoretical methods. Larger discrepancies are given for the N-B-F and F-B-F angles: the optimized DFT and RI-CC2 values differ from the experimental data by an amount up to 2.5◦ . More serious is the difference in the dihedral angles N-C-C-N (4’-3’-3-4) and C-C-C-C (2’-3’-3-2), which characterize the relative orientation of the two BODIPY units in BisBODIPY. They amount to 96.5◦ and 84◦ for the experimentally determined X-ray structure of the substituted derivative of BisBODIPY as described above, while the gas-phase optimization of the model compound yields values of of 149-151◦ and 137-144◦ , respectively, depending on the level of theory. This deviation, however originates from the neglect of the bulky substituent in our model complex, since geometry optimization at DFT/B3LYP-D level of theory of the full BisBODIPY derivative gives values of 101.3◦ and 105.7◦ for the central N-C-C-N (4’-3’-3-4) and C-C-C-C (2’-3’-3-2) dihedral angles. 7 The remaining deviation from the experimental values can most likely be attributed to missing packing effects in the gas-phase calculations, which do have a larger impact on soft large-scale motions like the central dihedral angles than on hard modes like bond lengths and angles. Since all applied levels of theory yield very similar geometrical parameters in particular for the constitutent BODIPY core structure, the standard DFT/B3LYP method was chosen simply due to ease and efficiency of the computations. 7 ACS Paragon Plus Environment


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Table 1: Comparison of geometrical parameters of the experimental X-ray structure with those of the model structure calculated at the theoretical levels of DFT/B3LYP, DFT/B3LYP-D, DFT/BHLYP and RI-CC2.a ExperimentI B3LYP Bodipy 1 Bodipy 2 B-N (4-11) 1.544 1.538 1.580 B-F (11-12) 1.384 1.368 1.377 C-N (8-9) 1.341 1.344 1.341 N-C (9-10) 1.402 1.403 1.391 C-C (10-14) 1.387 1.383 1.391 B · · · C (11 · · · 14) 2.992 2.987 2.997 N · · · N (4 · · · 9) 2.480 2.475 2.519 N-B-N (4-11-9) 107.1 107.3 106.3 N1-B-F1 (4-11-12;) 109.2 110.7 111.1 F-B-F (12-11-13) 109.9 109.0 111.8 N1-B-F2 (4-11-13) 108.8 108.5 109.6 N2-B-F1 (9-11-12) 110.8 110.8 109.7 N2-B-F2 (9-11-13) 111.0 110.5 108.2 C-C-N1-B (14-5-4-11) -5.6 C-C-N2-B (14-10-9-11) 8.5 C-C-C (3-3’-2’) 126.8 C-C-N (3-3’-4’) 123.6 N-C-C-N (4’-3’-3-4) 96.5 150.3 C-C-C-C (2’-3’-3-2) ∼ 84 142.1

B3LYP BHLYP (DFT-D) 1.578 1.568 1.378 1.366 1.340 1.326 1.390 1.379 1.391 1.382 2.998 2.974 2.512 2.500 106.0 106.3 111.0 111.2 111.9 111.5 109.6 109.6 109.9 109.8 108.1 108.3 -6.1 -6.5 9.1 8.8 127.1 126.6 123.3 123.6 151.1 149.1 144.5 141.1

RI-CC2 1.581 1.380 1.349 1.387 1.394 2.999 2.503 105.2 111.1 112.4 109.4 109.9 108.6 -8.5 12.1 127.4 123.1 149.3 137.5

Distances are given in ˚ A, angles in degrees. The 6-31G* basis set is used for B3LYP, B3LYP-D and BHLYP, while DZP and SVP are employed as main and auxiliary basis sets for RI-CC2, respectively. I Crystal structure of compound 12 from Bröring, M.; Kr¨ uger, R.; Link, S.; Kleeberg, C.; Köhler, S.; Xie, X.; Ventura, B.; Flamigni, L. Chem. Eur. J. 2008, 14, 2976. a


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4

Vertical excited states of BisBODIPY

The four energetically lowest excited states relating to the experimental absorption spectrum of BisBODIPY have been calculated at various theoretical levels of theory at the equilibrium structure of the ground state optimized at the level of DFT/B3LYP/6-31G* (Table 2). We have chosen to use time-dependent density functional theory (TDDFT) with hybrid xcfunctionals containing a constant fraction of non-local orbital exchange (B3LYP (20%) and BHLYP (50 %)) as well as long-range corrected ones ωB97X and ωPBE. Wavefunction-based ab initio methods ranging from simple configuration interaction singles (CIS), to algebraic diagrammatic construction of second order (ADC(2)) and approximate coupled cluster theory of second order (CC2) have also been employed. The last approaches are the most accurate ones and serve thus as benchmark methods here. The selection of methods provides a basis for a theoretical assessment of the reliability of the methods in the description of the excited states of BisBODIPY. As can be seen in Table 2, all different methods agree that the first excited S1 state of BisBODIPY is a 11 B state, which is in the molecular orbital picture described as the promotion of an electron from the highest occupied molecular orbital (HOMO, H) to the lowest unoccupied molecular orbital (LUMO, L) (Figure 2). It is important to recognize that the frontier molecular orbitals correspond to linear combinations of the molecular orbitals of the monomeric BODIPY. For example, the HOMO and LUMO of BisBODIPY (BB) are a linear combination of the HOMOs and LUMOs of the monomeric BODIPYS (MB), i.e. |HiBB = |HiM B1 − |HiM B2 and |LiBB = |LiM B1 + |LiM B2 reflecting the strong coupling between the two monomeric BODIPYs. The S1 state has substantial oscillator strength at all levels of theory ranging between 0.7 at ADC(2)-x level and 1.59 at CIS level of theory. The vertical excitation energy of the S1 state has values of 2.24 and 2.31 eV at the most accurate levels of ADC(2)-s and CC2. TDDFT gives values in good agreement in combination with all tested functionals for the 11 B state, which is due to its ππ ∗ character, for which TDDFT



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is known to deliver accurate values. 27,37 The strong underestimation of the excitation energy of this state by ADC(2)-x is a wellknown issue 38–40 which is due to the imbalanced inclusion of doubly excited configurations in the ADC(2) matrix, as the 2p-2h block is expanded through first order in correlation like in ADC(3) - instead of the standard zeroth order in plain ADC(2)-s. Most importantly therefore here, ADC(2)-x reveals that the 11 B state is a true single excitation with no double excitation character. The S2 and S3 states are the 11 A and 21 A states, which in the MO representation correspond to the negative and positive linear combinations of the excited determinants reflecting HOM O −1 to LU M O and HOM O to LU M O +1 excitations (Table 2). The vertical excitation energy of the 11 A has values of 2.95 and 3.05 eV at the theoretical levels of ADC(2)-s and CC2. A typical behavior of the other methods is found in comparison to these benchmark values. TDDFT in combination with the BHLYP, ωB97X and ωPBE slightly overestimates the excitation energy by about 0.25 eV, while B3LYP slightly underestimates by the same amount. CIS grossly overestimates it by 0.7 eV due to lacking electron pair correlation, while ADC(2)-x largely underestimates it as is to be expected. All methods yield negligible oscillator strength for this state and again, the ADC(2)-x method reveals no double excitation character of this state. Also the so-called ’Λ’ parameter of Peach et al. amounts to comfortable values of 0.69 and 0.72 for S2 and S3 states, respectively, which are much larger than the critical value of 0.30. 41 While all other methods exhibit a similar trend for the S3 state as well, with excitation energies of 3.48 and 3.34 eV at ADC(2)-s and CC2 level, ADC(2)-x finds a non-negligible contribution of 35 % of double excitation character for this state. Hence, one can conclude that the excitation energy of the 21 A state is possibly lower, and the state lies closer in energy to the 11 A than predicted by ADC(2)-s and CC2, but will still be the S3 state of BisBODIPY. At all levels of theory the 21 A state is found to exhibit no oscillator strength. The fourth excited state exhibits B symmetry, and corresponds in the molecular orbital 10 ACS Paragon Plus Environment

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picture to an electron transition from the HOM O − 2 to the LU M O of BisBODIPY. The HOMO-2 of BisBODIPY is easily characterized as linear combination of the orginal HOMO-1 orbitals of the monomeric BODIPY units (Figure 2). The most accurate methods, ADC(2)-s and CC2 give values for the vertical excitation energy of 3.67 and 3.63 eV, respectively, and all other methods show the same trend as observed for the previous states. The S4 state exhibits some oscillator strength ranging between 0.04 and 0.17 depending on the level of theory, and is found as the second strongest absorbing state in the low energy regime of the excitation spectrum. A word can be said upon the use of the limited basis sets, whose use cannot be avoided in view of the quite large BisBODIPY molecule and the various model cases investigated in the current study. However, test-calculations with CC2 and the TZVP basis set are found to confirm the general picture discussed here, with S1 , S2 , S3 and S4 excitation energies of 2.25, 2.98, 3.25 and 3.56 eV and oscillator strengths of 1.18, 0.09, 0.00 and 3.56, respectively. Due to the symmetric, delocalized nature of the molecular orbitals of BisBODIPY it is in general extremely tedious to distinguish between locally excited states and charge-transfer excited states. 42,43 However, due to the uniform performance of the different xc-functionals within TDDFT in the calculation of the vertical excited states of BisBODIPY, one can practically exclude intramolecular charge-transfer excited states, in which an electron is transferred from one BODIPY to the other, to occur in the low-energy region of the absorption spectrum. This is further corroborated in the following subsection below, in which the excitonic coupling between two BODIPYs is quantified depending on their intermolecular separation.



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(H-1)MB+(H-1)MB

(H-1)MB- (H-1)MB

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HMB - HMB

HMB + HMB

LMB - LMB

LMB + LMB

Figure 2: Frontier molecular orbitals of BisBODIPY computed at the theoretical level of HF/cc-pVDZ; each BisBODIPY orbital can be characterized as linear combination of the constituting orbitals of monomeric BODIPY (M B), which is also given. Table 2: Vertical excitation energies of the four lowest excited singlet states of BisBODIPY at its ground state (X 1 A) equilibrium geometry.a State S1 (11 B) S2 (11 A) S3 (21 A) S4 (21 B)

Character H→L H-1→L; H→L+1 H→L+1; H-1→L H-1→L+1

B3LYPb 2.28 (0.97) 2.63 (0.00) 3.10 (0.03) 3.23 (0.04)

BHLYPc 2.42 (1.16) 3.33 (0.11) 3.41 (0.00) 3.91 (0.06)

ωB97Xb 2.43 (1.17) 3.22 (0.12) 4.06 (0.02) 4.03 (0.09)

ωPBEb 2.43 (1.11) 3.23 (0.10) 3.72 (0.01) 3.77 (0.08)

CISb 2.69 (1.59) 3.73 (0.20) 4.82 (0.00) 4.93 (0.13)

ADC(2)-sd 2.24 (1.15) 2.95 (0.10) 3.48 (0.00) 3.67 (0.15)

ADC(2)-xd 1.46 (0.70) 2.05 (0.06) 2.14e (0.01) 2.84 (0.17)

CC2c 2.31 (1.21) 3.05 (0.09) 3.34 (0.00) 3.63 (0.11)

a

Energies are given in eV (oscillator strengths in parenthesis). At the BHLYP/SVP level, the so-called ’Λ’ parameter of Peach et al. 41 amounts to 0.67, 0.69, 0.72, 0.65 for S1 , S2 , S3 , S4 , respectively. The geometry has been optimized at the B3LYP/6-31G* level of theory.b cc-pVDZ basis set; c SVP basis set, the values for a CC2/TZVP test calculation amount to 2.25 (1.18) (S1 ), 2.98 (0.09) (S2 ), 3.25 (0.00) (S3 ), and 3.56 (0.11) (S4 ); d 6-31G basis set; e pronounced double excitation character of 35 %.

5

Electronic coupling of the excited states of BisBODIPYs

The structure of the absorption spectrum of BisBODIPY suggests that the corresponding excited states correspond to excitonically coupled excited states of the individual BODIPY units (see above). 7 In particular the S1 states seem to strongly couple leading to an enhanced red-shifted absorption band in BisBODIPY. In general, the magnitude of excitonic coupling depends on the intermolecular distance between the coupling subunits and their relative orientation (see equation 1). Hence, one can expect the influence of the coupling of the S1 state in the absorption spectrum of BisBODIPY to be modulated by the distance between the monomers and by the angle between them, i.e. by the C2 ’-C3 ’-C3 -C2 dihedral angle. Since 12 ACS Paragon Plus Environment

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Förster and Dexter coupling, as well as quantum mechanical electron correlation effects are acting together at the equilibrium distance of the BODIPYs in BisBODIPY of 1.45 ˚ A, the influence of excitonic Förster coupling has been quantified for large distances first and then extrapolated onto the equilibrium distance. For that objective, BisBODIPY is modelled via two unbound BODIPY molecules put in the same relative orientation as in BisBODIPY. The covalent bond between the BODIPY subunits has been saturated with hydrogen atoms. The intermolecular distance is then varied from 20 ˚ A to 3 ˚ A along the C3-C3’ bond direction and the vertical excitation energies are calculated at the theoretical level of RI-CC2/SVP (Figure 3). For the S1 and S2 states of the BisBODIPY model, a typical Coulomb-type splitting of the excitation energies is seen by gradually decreasing the distance (Figure 3), which demonstrates that the S1 and S2 excited states are indeed excitonically coupled. Calculations at the lower theoretical levels of CIS/cc-pVDZ and TDDFT/BHLYP/SVP reveal qualitatively the same picture, however with slightly larger splittings of the curves. Based on these curves, the magnitude of Förster coupling in BisBODIPY can be estimated at RI-CC2 level, since the energy difference between the S1 and S2 state is at large distances directly related to the excitonic coupling via 13

V12 =

1 [E(S2 ) − E(S1 )] . 2

(2)

From equation 1, it is possible to fit an according function f (R) = a(R + R0 )−3 to the energy splitting at large intermolecular distances in the model system of two unbound BODIPYs. The fitting procedure gives values of 2.5×104 cm−1 ˚ A−3 for the parameter a and -0.44 ˚ A for R0 . Following this procedure, the Förster-type Coulomb coupling can be estimated to amount to about 3500 cm−1 (0.43 eV) at the equilibrium distance of 1.45 ˚ A C3-C3’ bond length of BisBODIPY (Figure 3). In addition to the intermolecular distance, also the dihedral angle C2 ’-C3 ’-C3 -C2 is expected to influence the size of the dipolar coupling, since it modulates the relative orientation



3.02

3

S2

Excitation energy [eV]

2.98

Excitonic coupling strength [cm-1]

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2.96

2.94

S1

2.92

2.9

2.88

2.86

2.84 2

4

6

8

10

12

14

Intermolecular separation R [Å]

16

18

20

0.5 (E(S2)-E(S1))

Intermolecular separation R [Å]

Figure 3: Half of the excitation energy difference of the coupled S1 and S2 states (crosses) are given in cm−1 and extrapolated using a f (R) = a(R + R0 )−3 function. In the inset, excitation energies of first two excited states S1 and S2 of the model BisBODIPY system are plotted along the intermolecular separation coordinate at the RI-CC2/svp level of theory. The splitting can also be seen; it corresponds in a two-state model to twice the excitonic coupling 2V12 (eq. 2).

of the transition dipole moments of the locally excited states on the BODIPY monomers. This hypothesis can be challenged by keeping the distance between the two BODIPYs in the model system constant at 3 ˚ A and simultaneous gradual variation of the C2 ’-C3 ’-C3 C2 dihedral angle between 142 and 82◦ thereby covering the optimized value of the model BisBODIPY and the experimentally determined value of 96◦ of the substituted derivative (see above). Along this intermolecular torsion coordinate, however, the coupling strength is not modulated, as is readily apparent from the plotted computed spectra at the different dihedral angles (Figure 4). The peak positions remain the same along the torsion of the BODIPY subunits. In contrast to the excitation energies, a change in oscillator strength is observed (Figure 4). The S2 state corresponding to the peak at ∼ 415 nm (3.0 eV) at RI-CC2 level loses its oscillator strength, i.e. spectral intensity, when the C2 ’-C3 ’-C3 -C2 torsion angle between the bodipy molecules increases from 82 to 142◦ . On the other hand, the S1 state representing the band at ∼ 436 nm (2.8 eV) gains oscillator strength, i.e. spectral intensity, 14 ACS Paragon Plus Environment

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along the dihedral angle. BODIPY-BODIPY 3 Ang, RICC2/svp, increasing angle, geom=B3LYP/6-31G*, FWHM=30 nm 82 92 102 112 122 132 142

1

0.75 Oscillator strength

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0.5

0.25

0 150

200

250

300

350

400

450

500

550

600

Wavelength (nm)

Figure 4: Of a model system, which consists out of two monobodipys put at a distance of 3˚ A from each other, the RI-CC2/svp absorption spectra are obtained at different dihedral angles between the two bodipy entities. The CIS/cc-pVDZ and BHLYP/svp are found to be very analogous.

Going from the BisBODIPY model system with two unbound BODIPYs at 3 ˚ A to the covalently bound BisBODIPY, a change of the C2 ’-C3 ’-C3 -C2 dihedral angle between the two BODIPY subunits has a more severe influence on the spectrum (Figure 5). In BisBODIPY, changing the C2 ’-C3 ’-C3 -C2 torsion angle from 82 to 142◦ within the covalently bound bisbodipy molecule results in absorption spectra, which show a substantial shift of the S1 absorption band from a large absorption wavelength of ∼ 540 nm (2.29 eV) to a smaller one of only ∼ 455 nm (2.73 eV) at the RI-CC2 level of theory. In contrast to the model BisBODIPY system, the S1 state of BisBODIPY is shifted remarkably by 0.44 eV upon torsion, while the oscillator strength decreases similarly. The S2 state of BisBODIPY is practically not shifted in energy, but the oscillator strength decreases from 82 to 142◦ torsion angles at the RI-CC2 level of theory, in agreement with the S2 state of the unbound BisBODIPY model system. The energy shifts of the S1 to S4 states of the covalently bound BisBODIPY are displayed in Figure 6 A. Summarizing, it is clearly seen that the S4 state increases in energy, the S3 and S2 stay together and do not dramatically change throughout the change of the 15 ACS Paragon Plus Environment


C2 ’-C3 ’-C3 -C2 dihedral angle from 82 to 142◦ , and that the S1 state decreases in energy. The excited states computed at CIS and TDDFT/BHLYP level of theory reveal a strictly analogous behaviour. Comparison of the excited states of the unbound BisBODIPY model, which includes excitonic coupling, and the excited states of BisBODIPY clearly demonstrates that effects beyond excitonic coupling must be invoked to explain the strong red-shift of the S1 band in the absorption spectrum of BisBODIPY. Bisbodipy_I - fixed grad alle -cc2/SVP - FWHM=30 - geom=B3LYP/6-31G* 82 92 102 122 142

1.4

1.2

1 Oscillator strength

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0.8

0.6

0.4

0.2

0 150

200

250

300

350 400 Wavelength (nm)

450

500

550

Figure 5: Computed absorption spectra of the BisBODIPY model obtained for different intermolecular torsion (C2 ’-C3 ’-C3 -C2 ) angles between the BODIPY subunits at RI-CC2/svp data.

An answer is however found in the structure of the molecular orbitals (see Figure 2). Indeed, HOMO and HOMO-1 of BisBODIPY are found to be anti-bonding and bonding combinations of the HOMOs of the constituting BODIPY subunits, respectively, while the LUMO and LUMO+1 are the bonding and anti-bonding combinations of the corresponding BODIPY LUMOs. In the same way, the HOMO-3 and HOMO-2 are the bonding and anti-bonding combinations of the HOMO-1 of BODIPY, respectively. As a result of these molecular orbital structures of BisBODIPY, their energies change when the C2 ’-C3 ’-C3 -C2 dihedral angle is altered due to the attracting and repulsive interactions of the orbitals along the torsional motion. The energies of the relevant valence molecular orbitals have been analyzed


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along the torsional motion and are displayed in Figure 6 B. It can be seen that the orbital energies of the HOMO and LUMO+1, i.e. the anti-bonding combinations of the original BODIPY orbitals, increase with increasing torsion angle, while the energy of the HOMO-1 and LUMO of BisBODIPY, the bonding combination of the original orbitals, decrease with increasing torsion angle. Following the trend of the orbital energies, it is now clear that the S1 excitation energy of the HOMO→LUMO transition shifts to lower energies or to larger wavelength when the angle between the monomers is increased, since the HOMO-LUMO gap gets significantly smaller. From Figure 6 B, it can also be seen that states involving HOMO-1→LUMO and HOMO→LUMO+1 transitions should not change largely in energy upon torsion, which is indeed the case for the S2 and S3 states of BisBODIPY. The energy of the S4 state on the other hand, which is mostly a HOMO-1→LUMO+1 transition, increases and the band is shifted to lower absorption wavelengths. This energy shift of S4 is however not visible in the computed absorption spectrum of BisBODIPY (Figure 5) as it has only a very small oscillator strength. Not surprisingly, the absorption spectrum of covalently bound BisBODIPYs can not be interpreted in terms of excitonic coupling alone, since at such short intermolecular distances other quantum mechanical effects start to influence the interaction of the excited states. These effects manifest themselves here in large orbital energy shifts, which of course also modulate the excitation energies of the correponding states. Hence the distribution of the oscillator strengths of the coupled S1 and S2 states can be understood in terms of excitonic coupling theory, as the computations on the unbound model system have revealed. For an understanding of the large red-shift of the S1 state, however, a thorough analysis of the underlying molecular orbital structure has been necessary. The analysis performed in the current section has been focussing on the core BisBODIPY molecule as its structure is given in Figure 1. The experimental data cited in this study are mainly related to structure 12 in Ref. 7 (see also Table 3). As is shown in Figure 7, which gives the computed absorption spectra of the experimental BisBODIPY molecule for various 17 ACS Paragon Plus Environment


A

S4

energy (eV) TotalRel.Energy (eV)

2

1.5

S3 1

S2 0.5

S1 0 80

90

100

110

120

130

140

Dihedral angle (degrees) BISBODIPY 82 - 142 degrees, HF/cc-pVDZ 6

H-3 H-2

B

H-1 LUMO+2 H

4

OrbitalEnergy energy (eV) (eV) Orbital

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L L+1 L+2

2

LUMO+1 LUMO

0 -2

S1

-4 -6 -8

S4 S3 S2

-10

HOMO HOMO-1 HOMO-2

-12 80

90

100

110

120

130

140

150

(degrees) DihedralAngle Angle N-C-C-N

Figure 6: A) Relative energies of S1 (H→L), S2 (H-1→L,H→L+1), S3 (H→L+1,H-1→L) and S4 (H-1→L+1) of BisBODIPY along the C2 ’-C3 ’-C3 -C2 torsion angle at RI-CC2/SVP level. The energy of the S1 state at 142◦ is set to zero. B) Orbital energies of the relevant frontier orbitals of BisBODIPY along the C2 ’-C3 ’-C3 -C2 torsion angle at HF/SVP level in eV.

intermolecular torsion angles, the photochemical picture for the latter species is very much analogous to the one obtained by the calculations upon the core BisBODIPY structure.

6

Nature of the emissive state of BisBODIPY

As we have seen in the previous sections, the molecular orbitals of the two covalently bound BODIPY subunits are mixed and the excited states are strongly coupled in BisBODIPY leading to a strongly red-shifted first excited state in the experimental absorption spectrum. 7


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BISBODIPY_EXP, BHLYP/SVP, increasing angle, FWHM=30 nm; geom=B3LYP/6-31G* (DFT-D Grimme) 94 104 114 144

1

0.8 Oscillator strength

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0.6

0.4

0.2

0 150

200

250

300

350

400

450

500

550

Wavelength (nm)

Figure 7: Computed absorption spectra of the experimental BisBODIPY molecule obtained for different intermolecular torsion (C2 ’-C3 ’-C3 -C2 ) angles between the BODIPY subunits at BHLYP/svp data (the geometry is obtained at the B3LYP-D/6-31G* level incorporating Grimme’s dispersion correction).

Also, the fluorescence spectrum of BisBODIPY is strongly red shifted compared to BODIPY, and in addition, BisBODIPY exhibits a pronounced Stokes’ shift of 80 nm from 559 nm absorption to 638 nm fluorescence wavelength, which corresponds to an energy of 0.27 eV. In comparison, the Stokes’ shift of BODIPY is very small with only 9 nm from 529 nm absorption to 538 nm fluorescence, which are only 0.04 eV. The much larger Stokes’ shift hints towards a more pronounced geometry relaxation in BisBODIPY than in BODIPY. Computations of the equilibrium structures of the S1 states of BisBODIPY and BODIPY at the theoretical level of TDDFT/BHLYP/SVP reveal the same trend of the corresponding computed fluorescence wavelengths. For BisBODIPY, the calculated Stokes’ shift amounts to 46 nm, while for monobodipy a value of only 12 nm is obtained. Obviously, geometry relaxation is more pronounced in BisBODIPY than in BODIPY and it is thus natural to ask for the difference between these two. In general, the initially delocalized excitation of the S1 state of BisBODIPY can remain delocalized upon geometry relaxation or can become localized on one BODIPY. It has been demonstrated previously that excitonically coupled chromophores can be seen 19 ACS Paragon Plus Environment


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as pseudo Jahn-Teller systems, when the excitonic coupling strength does not exceed the geometry relaxation energy. 44,45 In that case, the initially symmetric structure of the chromophores is destorted in such a way that one of the two chromophores adopts the equilibrium structure of the S0 ground state, while the other takes on the equilibrium structure of its S1 state. In dimers of identical chromophores, the potential energy surface must then have the shape of a double well potential along the distortion coordinate, since the symmetric set up requires that it is energetically identical whether the one or the other chromophore adopts the S1 or S0 equilibrium structure. In other words, when it is energetically more favorable for two coupled chromophores to decouple, the geometrical symmetry is reduced. Previously studied examples in this respect are a carbon monoxide dimer (CO), which is kept in an aligned parallel position, and the benzene dimer in a cofacial arrangement. 44,45 Dependent on the distance R between the monomers, which tunes the excitonic coupling strength, the S1 potential energy surface exhibits two minima or only one: the latter case is found when R is relatively small and the excitonic coupling strength V12 surpasses the geometry relaxation energy. 44 From our calculations, it has been estimated that the Förster coupling V12 for BisBODIPY amounts to ∼ 0.43 eV (see Chapter 5), which is larger than the calculated geometrical relaxation energies and the Stokes’ shifts. It is therefore not surprising that the BisBODIPY molecule, in which both BODIPY units are only separated from each other by a covalent bond, the emissive S1 state remains C2 symmetric. From Table 3, it can be seen that the resulting geometry is indeed a combination of the S1 and S0 optimized monoBODIPY ones. It is thus clear that the emissive S1 state remains delocalized over both BODIPY units. Also, the symmetry conservation in the S1 state, together with its relatively high excitation energy and the flatness of the rotation potential energy surface, induce a profound stability of the emissive state and therefore a high fluorescence quantum yield.


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Table 3: Equilibrium geometries of the excited S1 (H → L) states of BisBODIPY and BODIPY optimized at the TDDFT/BHLYP/SVP level of theory and of the electronic ground state S0 optimized at DFT/BHLYP/SVP level. a BisBODIPY (S1 ) B-N (4-11) 1.562 B-F (11-12) 1.370 C-N (8-9) 1.327 N-C (9-10) 1.381 C-C (10-14) 1.386 B · · · C (11 · · · 14) 2.983 N · · · N (4 · · · 9) 2.500 N-B-N (4-11-9) 106.8 N1-B-F1 (4-11-12) 111.2 F-B-F (12-11-13) 110.6 N1-B-F2 (4-11-13) 110.4 N2-B-F1 (9-11-12) 109.6 N2-B-F2 (9-11-13) 108.2 C-C-N1-B (14-5-4-11 -3.1 C-C-N2-B (14-10-9-11) 8.0 C-C-C (3-3’-2’) 126.4 C-C-N (3-3’-4’) 125.0 N-C-C-N (4’-3’-3-4) 160.6 C-C-C-C (2’-3’-3-2) 152.7 a

BODIPY (S1 ) 1.552 1.373 1.327 1.400 1.401 3.055 2.457 104.7 110.4 110.4 110.4 110.4 110.4 0 0

Distances are given in ˚ A, angles in degrees.


BODIPY (S0 ) 1.563 1.369 1.325 1.381 1.385 3.002 2.490 105.6 110.0 111.2 110.0 110.0 110.0 0 0


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7

Brief Summary and Conclusions

The experimental absorption spectrum of the BisBODIPY molecule is dominated by two symmetrical bands with an almost equal intensity. 7 Since these bands are located symmetrically at both sides of the absorption band of BODIPY, it was immediately concluded that excitonic coupling of the two BODIPYs is the origin. 7 Here, we have demonstrated that a delicate interplay of excitonic coupling and orbital interactions exists, which determine the energetic positions and intensities of the S1 and S2 absorption peaks. In a first step, second order coupled cluster and density functional theory have been used to optimize the geometries of BisBODIPY and the obtained structures have been evaluated against the experimental X-ray data. For an understanding of the absorption and fluorescence spectra, the influence of the intermolecular distance and the dihedral angle have been analyzed as well as the orbital interactions have been studied. For that objective, first the distance between the substituent BODIPY units has been increased and the energies of the excited states have been monitored. In a second step, the influence of the dihedral angle between the BODIPY subunits on the oscillator strengths of the absorption bands has been clearly seen. However, the rotation of the BODIPY units within the real BisBODIPY molecule does not only change the intensities of the bands, but also their energies due to significant orbital interactions. Finally, at short distances between the monomers, it is theoretically not well justified to distinguish between orbital interactions and Dexter exchange coupling. The fluorescence wavelength and the large Stokes’ shift of BisBODIPY have also been computed, and it could be shown that the excitonic coupling energy is larger than the energy released by geometry relaxation after excitation into the S1 state. This explains that the equilibrium structure of the emissive state of BisBODIPY keeps the C2 symmetry of the ground state, and that a pseudo Jahn-Teller distortion does not occur in the BisBODIPY molecule. The excited state remains delocalized over both BODIPY subunits in BisBODIPY.


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Acknowledgement S.K. is grateful to the Alexander von Humboldt foundation for his return grant in spring 2013. He acknowledges also the Fonds National de la Recherche Scientifique (FNRS), the French speaking branch of the Belgian National Science foundation, for his post-doctoral funding (Chargé de Recherches) in Liège.

References (1) Ulrich, G.; Ziessel, R.; Harriman, A. The Chemistry of Fluorescent Bodipy Dyes: Versatility Unsurpassed. Angew. Chem. Int. Ed. 2008, 47, 1184–1201. (2) Treibs, A.; Kreuzer, F.-H. Difluorboryl-Komplexe von Di- und Tripyrrylmethenen. Justus Liebigs Ann. Chem. 1968, 718, 208–223. (3) Monsma, F. J.; Barton, A. C.; Kang, H. C.; Brassard, D. L.; Haughland, R. P.; Sibley, D. R. Characterization of Novel Fluorescent Ligands with High-Affinity for D1 and D2 Dopaminergic Receptors. J. Neurochem. 1989, 52, 1641–1644. (4) Boens, N.; Leen, V.; Dehaen, W. Fluorescent Indicators Based on BODIPY. Chem. Soc. Rev. 2012, 41, 1130–1172. (5) Kamkaew, A.; Lim, S. H.; Lee, H. B.; Kiew, L. V.; Chung, L. Y.; Burgess, K. BODIPY Dyes in Photodynamic Therapy. Chem. Soc. Rev. 2013, 42, 77–88. (6) Rohand, T.; Qin, W.; Boens, N.; Dehaen, W. Palladium-Catalyzed Coupling Reactions for the Functionalization of BODIPY Dyes with Fluorescence Spanning the Visible Spectrum. Eur. J. Org. Chem. 2006, 4658–4663. (7) Bröring, M.; Kr¨ uger, R.; Link, S.; Kleeberg, C.; Köhler, S.; Xie, X.; Ventura, B.; Flamigni, L. Bis(BF(2))-2,2 ‘-Bidipyrrins (BisBODIPYs): Highly Fluorescent BODIPY Dimers with Large Stokes Shifts. Chem. Eur. J. 2008, 14, 2976–2983. 23 ACS Paragon Plus Environment


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

(8) Ventura, B.; Marconi, G.; Bröring, M.; Kr¨ uger, R.; Flamigni, L. Bis(BF2)-2,2 ‘Bidipyrrins, a Class of BODIPY Dyes with New Spectroscopic and Photophysical Properties. New J. Chem. 2009, 33, 428–438. (9) Bröring, M.; Yuan, Y.; Kr¨ uger, R.; Kleeberg, C.; Xie, X. Solution and Solid State Structure of a BisBODIPY Fluorophor. Z. Anorg. Allg. Chem. 2010, 636, 518–523. (10) Valeur, B. Molecular Fluorescence Principles and Applications; Wiley-VCH: Weinheim, 2001. (11) Harriman, A.; Mallon, L. J.; Elliot, K. J.; Haefele, A.; Ulrich, G.; Ziessel, R. Length Dependence for Intramolecular Energy Transfer in Three- and Four-Color Donor-SpacerAcceptor Arrays. J. Am. Chem. Soc. 2009, 131, 13375–13386. (12) Jin, J. L.; Wu, S. X.; Geng, Y.; Yang, S. Y.; Yang, G. C.; Yang, G. C.; Wu, J.; Muhammad, S.; Liao, Y.; Su, Z. M. et al. Theoretical Study on Photophysical Properties of Novel Bis(BF2)-2,2 ‘-Bidipyrrins Dyes: Effect of Variation in Monomer Structure. Int. J. Quant. Chem. 2012, 112, 440–452. (13) May, V.; K¨ uhn, O. Charge and Energy Transfer Dynamics in Molecular Systems, Second Edition; Wiley, Weinheim, 2004. (14) Scholes, G. D. Long-Range Resonance Energy Transfer in Molecular Systems. Annu. Rev. Phys. Chem. 2003, 54, 57–87. (15) Stone, A. J. The theory of intermolecular forces; Clarendon press, 1996. (16) Bröring, M.; Brégier, F.; Kr¨ uger, R.; Kleeberg, C. Functional Porphyrinoids from a Biomimetically Decorated Bipyrrole. Eur. J. Inorg. Chem. 2008, 5505–5512. (17) Becke, A. D. A New Mixing of Hartree-Fock and Local Density-Functional Theories. J. Chem. Phys. 1993, 98, 1372–1377.


Page 24 of 28

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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


(18) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron-Density. Phys. Rev. B 1988, 37, 785–789. (19) Hariharan, P. C.; Pople, J. A. The Influence of Polarization Functions on Molecular Orbital Hydrogenation Energies. Theoret. Chimica Acta 1973, 28, 213–222. (20) Huzinaga, S. Basis-sets for Mulecular Calculations. Comp. Phys. Rep. 1985, 2, 281–339. (21) Grimme, S. Semiempirical GGA-Type Density Functional Constructed with a LongRange Dispersion Correction. J. Comput. Chem. 2006, 27, 1787–1799. (22) Becke, A. D. Density-Functional Thermochemistry .3. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648–5652. (23) Christiansen, O.; Koch, H.; Jørgensen, P. Response Functions in the CC3 Iterative Triple Excitation Model. J. Chem. Phys. 1995, 103, 7429–7441. (24) Haettig, C.; Weigend, F. CC2 Excitation Energy Calculations on Large Molecules Using the Resolution of the Identity Approximation. J. Chem. Phys. 2000, 113, 5154–5161. (25) Haettig, C.; Hald, K. Implementation of RI-CC2 Triplet Excitation Energies with an Application to Trans-Azobenzene. Phys. Chem. Chem. Phys. 2002, 4, 2111–2118. (26) Casida, M. E. In Recent Advances in Density Functional Methods, Part I ; Chong, D. P., Ed.; World Scientific: Singapore, 1995; pp 155–192. (27) Dreuw, A.; Head-Gordon, M. Single-Reference Ab Initio Methods for the Calculation of Excited States of Large Molecules. Chem. Rev. 2005, 105, 4009–4037. (28) Hirata, S.; Head-Gordon, M. Time-Dependent Density Functional Theory within the Tamm–Dancoff Approximation. Chem. Phys. Lett. 1999, 314, 291–299. (29) Furche, F. On the Density Matrix Based Approach to Time-Dependent Density Functional Response Theory. J. Chem. Phys. 2001, 114, 5982–5992. 25 ACS Paragon Plus Environment


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(30) Trofimov, A. B.; Schirmer, J. An Efficient Polarization Propagator Approach to Valence Electron-Excitation Spectra. J. Phys. B 1995, 28, 2299–2324. (31) Wormit, M.; Rehn, D. R.; Harbach, P. H. P.; Wenzel, J.; Krauter, C. M.; Epifanovskyc, E.; Dreuw, A. Investigating Excited Electronic States Using the Algebraic Diagrammatic Construction ( ADC) Approach of the Polarisation Propagator. Mol. Phys. 2014, 112, 774–784. (32) Chai, J.-D.; Head-Gordon, M. Systematic Optimization of Long-Range Corrected Hybrid Density Functionals. J. Chem. Phys. 2008, 128, 084106. (33) Vydrov, O. A.; Scuseria, G. E. Assessment of a Long-Range Corrected Hybrid Functional. J. Chem. Phys. 2006, 125, 234109. (34) 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. Phys. Chem. Chem. Phys. 2005, 7, 3297–3305. (35) TURBOMOLE Version 5.10, R. Ahlrichs, University of Karlsruhe, 2008. (36) Shao, Y.; Molnar, L. F.; Jung, Y.; Kussmann, J.; Ochsenfeld, C.; Brown, S. T.; Gilbert, A. T. B.; Slipchenko, L. V.; Levchenko, S. V.; O’Neill, D. P. et al. Advances in Methods and Algorithms in a Modern Quantum Chemistry Program Package. Phys. Chem. Chem. Phys. 2006, 8, 3172–3191. (37) Harbach, P. H. P.; Dreuw, A. In Modeling of Molecular Properties; Comba, P., Ed.; Wiley-VCH: Weinheim, 2011; p 29. (38) Starcke, J. H.; Wormit, M.; Schirmer, J.; Dreuw, A. How Much Double Excitation Character Do the Lowest Excited States of Linear Polyenes Have? Chem. Phys. 2006, 329, 39–49.


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(39) Starcke, J. H.; Wormit, M.; Dreuw, A. Unrestricted Algebraic Diagrammatic Construction Scheme of Second Order for the Calculation of Excited States of Medium-Sized and Large Molecules. J. Chem. Phys. 2009, 130, 024104. (40) Knippenberg, S.; Starcke, J. H.; Wormit, M.; Dreuw, A. The Low-Lying Excited States of Neutral Polyacenes and Their Radical Cations: a Quantum Chemical Study Employing the Algebraic Diagrammatic Construction Scheme of Second Order. Mol. Phys. 2010, 108, 2801–2813. (41) Peach, M. J.; Benfield, P.; Helgaker, T.; Tozer, D. J. Excitation Energies in Density Functional Theory: An Evaluation and a Diagnostic Test. J. Chem. Phys. 2008, 128, 044118. (42) Hieringer, W.; Görling, A. Failure of Time-Dependent Density Functional Methods for Excitations in Spatially Separated Systems. Chem. Phys. Lett. 2006, 419, 557–562. (43) Dreuw, A.; Head-Gordon, M. Comment on: ‘Failure of Time-Dependent Density Functional Methods for Excitations in Spatially Separated Systems’ by Wolfgang Hieringer and Andreas Gorling. Chem. Phys. Lett. 2006, 426, 231–233. (44) Harbach, P. H. P.; Dreuw, A. A Fresh Look at Excitonically Coupled Chromophores from a Jahn-Teller Perspective. Chemical Physics 2010, 377, 78–85. (45) Garcia-Fernandez, P.; Andjelkovi, L.; Zlatar, M.; Gruden-Pavlovi, M.; Dreuw, A. A Simple Monomer-Based Model-Hamiltonian Approach to Combine Excitonic Coupling and Jahn-Teller Theory. J. Chem. Phys. 2013, 139, 174101.



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Strong Electronic Coupling Dominates the Absorption and

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