Excited states calculations on fluorene-based polymer ...

Excited states calculations on fluorene-based polymer blends: Effect of stacking orientation and solvation John Glenn S. Ramon 1 and Eric R. Bittner 1

1

Department of Chemistry and Center for Materials Chemistry, University of Houston,

Houston, Texas USA 77204

The utilization of polyfluorene-derivative polymer blends in the development of optoelectronic devices has continued to gain ground over the past few years. Marked strides have been taken towards better understanding the charge-transfer dynamics in these systems1–5 . The constituent polymers have been chemically designed to facilitate more efficient electron/hole mobility6 thereby enhancing control over exciton formation and dissociation. When appropriate pairs of these polymers are blended together, intermolecular charged-particle localizations are induced to such an extent that the lowest excited state takes on a significant intermolecular charge-transfer character4, 5 and the luminescence from these blends exhibits some sensitivity to their interfacial orientation7 . In this letter we report on a quantum chemical investigation of the relevant excited states of the polymer blend of poly(9,9dioctylfluorene-co-N-(4-butylphenyl)diphenylamine) (TFB) with poly(9,9-dioctylfluorene-cobenzothiadiazole) (F8BT) by time-dependent density functional theory (TD-DFT)8–10 . We show that the TD-DFT results general agree with experimental observations although there is a consistent underestimation of the charge-transfer states. We further show the calculated excited states to be sensitive to the stacking orientation and that solvation with a low

1

dielectric solvent greatly stabilizes the charge-transfer states.

Since the advent of conducting polymers, considerable attention has focused on the design and synthesis of materials that efficiently form and transport charge-carriers. Control over such processes are paramount to their utilization in device applications. In recent years, a number of polyfluorene-derived polymers have been designed to stimulate efficient electron-hole localizations upon excitation. By copolymerizing a dioctylfluorene(F8) monomer given in Fig. 1 with another monomer having a slightly different ionization potential(IP) and electron affinity(EA), the charges localize on either one or the other depending on how the respective IPs and EAs match up. In the case of F8 copolymerized with benzothiadiazole (BT) (see Fig. 1) to form F8BT, a net partial negative charge develops on the BT subunit while the F8 subunit gains a net partial positive charge (See (1)) upon photoexcitation.6 F8BT∗ : (−F8δ+ − BTδ− −)n

(1)

Similarly, when bis-N,N-(4-butylphenyl)-bis-N,N-phenyl-1,4-phenylenediamine (PB) (see Fig. 1) is used as the comonomer to F8 to form poly(9,9-dioctylfluorene-co-bis-N,N-(4-butylphenyl)-bisN,N-phenyl-1,4-phenylenediamine (PFB), F8 gains a partial negative charge while PB gains a partial positive charge upon photoexcitation (See (2)).7 PFB∗ : (−PBδ+ − F8δ− −)n

(2)

Furthermore, when F8BT is blended with PFB, excitation leads to intermolecular charge localizations4, 5 in addition to the intramolecular localizations.1–3 Sreearunothai et al.7 suggested that the presence of intramolecular localizations within the constituent polymers upon excitation leads to π-stacking 2

characterized by either attractive or repulsive orientations (See (3) and (4), respectively). (−F8δ+ −BTδ− −)n (−F8δ− −PBδ+ −)n

i

(3)

(−F8δ+ −BTδ− −)n (−PBδ+ −F8δ− −)n

i

(4)

Attractive :

h

Repulsive :

h

This creates a difference in the rate of formation of intermolecular charge localizations resulting to the observation of a blue shift in the exciton emission peaks in the blend compared to the pure constituent copolymers.

Another compound that is chemically similar to PB is N-(4-butylphenyl)diphenylamine (TB) given in Fig. 1. When TB is copolymerized with F8, poly(9,9-dioctylfluorene-co-N-(4-butylphenyl) diphenylamine) (TFB) is formed. Blending TFB with F8BT yields a material chemically similar to PFB/F8BT.1–5 Despite the similarity, however, TFB/F8BT exhibits decreased photovoltaic but substantially greater photoluminesence behavior than PFB/F8BT. This is a consequence of the band-edge offset (e.i. the difference between either the IEs or the EAs of the constituent polymers), ∆ε, between PFB and F8BT being very much greater than the typical exciton stabilization threshold, εB , of ∼0.5 eV such that interchain charge separation becomes favorable leading to better photovoltaic behavior. In contrast, with TFB and F8BT, ∆ε is only slightly larger than εB to the extent that interchain charge separation and exciton formation become competitive with one another. Interestingly, upon photoexcitation of TFB, TB gains a partial positive charge while F8 gains a partial negative charge(See (5)). TFB∗ : (−TBδ+ − F8δ− −)n 3

(5)

Consequently, blending with F8BT leads to attractive and repulsive π-stacked orientations (See (6) and (7), respectively). (−F8δ+ −BTδ− −)n (−F8δ− −TBδ+ −)n

i

(6)

(−F8δ+ −BTδ− −)n (−TBδ+ −F8δ− −)n

i

(7)

Attractive :

h

Repulsive :

h

While semiempirical models1–3 have been used to examine the energetics of these systems, rigorous quantum chemical treatment of such polymer heterojunction systems has yet to be done partly due to the extent of the computational effort involved and availability of required computational resources. Nevertheless, such studies are required in order to quantitatively examine structural and solvation effects in the excited states. The results presented here represent, to date, the most extensive quantum chemical investigations of the excited states of a molecular heterojunction system.

The constituent polymers of the TFB/F8BT polymer blend were constructed as shown in Fig. 2. The F8BT consists of 6 comonomer units (3 benzothiadiazole[BT] units alternating with 3 fluorene[F] units) while the TFB consists of 5 comonomer units (3 F units alternating with 2 triarylamine[TB] units). All alkyl chains were substituted with methyl groups. Doing so saves tremendous computational effort while having minimal effect on the results.6 The two polymers were stacked in an eclipsed and staggered configuration as shown in Fig. 2(a) and 2(b), respectively. The two structures were optimized using MM311–14 force field as implemented in TINKER15 . Subsequently, the excited states were calculated by time-dependent density functional theory (TDDFT) method using the ORCA16 quantum chemical package. Restricted Kohn-Sham (RKS) reference states were constructed using B3LYP hybrid functional19 with the 6-31G(d) basis set17, 18 . 4

These calculations were done in gas-phase and with the incorporation of solvent (toluene) using a conductor-like screening model (COSMO)20, 21 .

The total single point ground state energies of the two heterojunctions indicate the staggered orientation to be more stable than the eclipsed orientation by 45 meV. Upon excitation, charges tend to localize at various parts of the system (vide supra) leading to electron-hole configurations that are either on the same polymer chain (FBT∗ or TFB∗ ) or on different chains (TFB+ /FBT− or TFB− /FBT+ ). We characterize the calculated excited states as either an excitonic (XT) state or a charge-transfer (CT) state depending on the predominant configuration for that state. The excited state energies for the systems studied are shown in Fig. 3 with the corresponding states correlated and the lowest CT and XT states highlighted. The excited states of the staggered orientation generally have lower energies than their eclipsed orientation counterpart. For the eclipsed TFB/FBT orientation, the calculated energies for the CT and XT states are 1.96 eV and 2.40 eV, respectively, with the former being 92% TFB+ /FBT− and 8% FBT∗ in character while the latter having 26% TFB+ /FBT− and 74% FBT∗ character as shown in Fig. 4(a). For the staggered TFB/FBT orientation, the CT and XT state energies are 1.95 eV and 2.36 eV with the former being purely TFB+ /FBT− in character while the latter having 51% TFB+ /FBT− and 49% FBT∗ character as shown in Fig. 4(b). The XT states exhibit greater oscillator strengths relative to the CT states and have energies that are in general agreement with the experimental F8BT emission at 2.3 eV.

We digress a bit to note that the FBT chain geometry is non-planar in the ground state not only for the heterojunction but even for the isolated FBT chain. Using TD-DFT, we calculated

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the lowest excited states of four different geometries of isolated FBT chains: the two isolated FBT chains taken from the eclipsed and staggered orientated heterojunctions (while preserving their geometries) and two other geometries optimized at the PM322 and DFT/B3LYP16 levels, respectively. The PM3 optimized FBT showed a highly planar structure with the lowest excited state energy being 1.936 eV. This is about 400 meV lower than the 2.3 eV experimental emission of F8BT indicating that the PM3 optimized geometry is not a good representation of the ground state equilibrium geometry. In contrast, the DFT/B3LYP optimized geometry has a non-planar backbone chain with the lowest excited state at 2.325 eV which is in very good agreement with experimental emission spectra. The FBT configurations taken from the heterojunction models above, on the other-hand, are also non-planar with the lowest excited state at around 2.4 eV, about 100 meV higher but certainly in better agreement with spectroscopic measurements. This lends credibility to our choice of molecular geometry. While planarity in π-systems encourages stability by extending conjugation lengths, it is common to see non-planar ground states in linear conjugated polymers especially those involving adjacent phenyl groups such as F8BT and poly(p-phenylene) (PPP). Studies on biphenyls by Rao et al.23 showed that this is due to the steric interaction between the ortho groups of the rings. Such interactions may be captured by including correlation and polarizations through the use of higher levels of theory and better basis sets.

The slightly higher energies of the XT states in the heterojunctions relative to the experimental F8BT emission by about 100 meV are, in part, due to the fact that we are computing vertical states i.e. we do not account for geometry relaxation upon excitation. Following excitation, lattice relaxation ensues as a response to the instantaneous change in the electronic wavefunction. 6

This would occur prior to other decay mechanisms most notably radiative decay to the ground state. Thus, emission typically occurs from relaxed excited state configurations and are observed at longer wavelengths relative to the absorption. Efforts to calculate relaxed excited state geometries, however, are currently prohibitive due to the size of these systems and the required potential energy surface (PES) scan over multiple normal modes.∗ Although the CT states were expected to be overestimated as well since they are also vertical states, they are instead underestimated by as much as 200 meV. This underestimation of the CT state energies have been noted as a shortcoming of TD-DFT calculations for long-range charge-transfer excitations due to the local nature of the approximate exchange-correlation functionals.24–26 While suggestions have been made to correct this underestimation, these suggestions are only practical for small systems.24, 25, 27 Nevertheless, the underestimation here is much less than in other systems where the errors have been reported to be greater than 1 eV.24, 25

The absorption peak at around 2.9 eV in Fig. 5(a) is due to TFB exciton formation which is at least 100 meV higher than the experimentally observed TFB emission at 2.8 eV4, 5 . These correspond to state S9 with energy 2.93 eV in the eclipsed orientation which is 62% TFB∗ , 26% ∗

We note here that a complete TD-DFT excited states calculation for a single system took at least 3 weeks to

complete on a single processor of an AMD Opteron Cluster. A PES scan for a single normal mode requires at least 3 geometry configuration points each representing 1 iteration of the complete excited states calculation. Considering the size of the constituent chains (at least 250 atoms), the number of normal modes easily tops 500. If we then consider only those that have significant impact on the conjugation of the system, specifically, C-C double bond stretching and ring torsional modes, then 10 might seemed to be a very conservative estimate of normal modes to consider. Even then, such a calculation would require at least 30 iterations.

7

TFB+ /FBT− , 7% FBT∗ and 5% TFB− /FBT+ in character as shown in Fig. 4(a) and S10 with energy 2.94 eV in the staggered orientation characterized by 25% TFB∗ , 52% TFB+ /FBT− and 23% FBT∗ as shown in Fig.4(b). The difference in energies from experiment are again partly due to these states being vertical states with some lattice relaxation expected. However, the lattice relaxation is likely to be mostly on the F8BT chain. Excited state calculations on the TFB chains isolated from the heterojunctions indicates that the lowest excited state have energies of 3.01 eV and 3.02 eV for the eclipsed and staggered orientations, respectively. These are not much different compared to the 2.99 eV energy of the lowest excited state calculated for the PM322 optimized geometry of isolated TFB in Fig. 6(a). All three structures indicate that the phenyl ring of TB and that of F are coplanar. Interestingly, the DFT/B3LYP geometry optimized isolated TFB chain in Fig. 6(b) predicted a nonplanar structure with the lowest excited state being even higher at 3.13 eV. We point out that the presence of the triaryl amine group (TB) in TFB effectively limits the conjugation length to less than 2 copolymer subunits i.e. F and the 2 TB phenyl groups bonded on either side of it. In the DFT optimized geometry, these TB phenyl groups are rotated ∼45◦ from the F ring plane. Further, the terminal F subunits assume an orientation as far away from one another as possible such that their dihedral angle about the line connecting the N-N’ atoms is ∼108◦ . This configuration, however, minimizes the ability of TFB to effectively π-stack due to steric hindrance. Hence, to achieve optimal π-stacking at the heterojunction, the TFB needs to assume a geometry more like that of Fig. 6(a). This also suggests that one cannot safely describe the geometry and energetics at the heterojunction using results from isolated calculations.

Since PFB and TFB are chemically similar, we draw some parallelism to the exposition of 8

Sreearunothai et al.7 with regard to attractive and repulsive interactions of the component chains. Here, the eclipsed orientation would have attractive interaction while the staggered orientation would have repulsive interaction between the interfacial constituent polymer moieties owing to the intra-chain charge localizations on the corresponding co-monomers (vide supra). Comparing the relevant excitonic states, i.e. those that correspond to the experimental F8BT∗ and TFB∗ emissions, for both orientations, we find the XT and S10 states in the staggered orientation(see Fig. 4(b)) to exhibit greater mixing of configurations compared to the corresponding states, XT and S9 , in the eclipsed orientation(see Fig. 4(a)). Comparing the charge-transfer states, S4 , in both orientations reveals similar mixing of configurations in the staggered orientation. The repercussions of such are profound in that this mixing leads to a broadening of the absorption spectra (see Fig. 5(a)) of the staggered orientation as more states gain higher oscillator strengths. All of this underscores the sensitivity of the excited states to small translational shifts in orientation from eclipsed to staggered. More importantly, this slight orientational shift from eclipsed to staggered not only produces an observable shift in the energetics, in addition, it changes the nature of the excited states altogether.

While the relaxation (radiative and non-radiative) dynamics is beyond the scope of this study, we can surmise energetically, that emission from the vertical excitonic states in both orientations are at higher energies than for the isolated chains. This is consistent with the observations of Sreearunothai et al.7 . It is unclear at this point, however, how the changes in the nature of the excited states effected by the shift in orientation affect the interconversion rates between the various excited states. This emphasizes the need for theoretical models that would probe the relaxation dynamics in this systems and ascertain how competitive the emissive decay is relative to the other 9

non-radiative relaxation pathways.2

Composite materials such as the ones used in organic light-emitting devices are typically formed by spin-coating or demixing. This process necessarily involves dissolving the component materials in a common solvent such as xylene or chloroform. It has also been shown that the nature of the solvent used to cast these materials ultimately influences their electronic properties.28 This effect is mostly due to the solvent’s influence on the resulting morphology but it may also be due to its solvation. Thus, we explore the effect of solvation by incorporating an effective solvent field, particularly toluene, into the calculation of excited states for the systems studied as implemented in ORCA16 . Here, the solvent field is modeled as a dielectric continuum using the conductorlike screening model(COSMO) introduced by Klamt and Schüu¨ rmann20 . Initially, the continuum is treated as a perfect conductor (i.e. with an infinite dielectric constant) that completely screens the molecular charge-density before scaling it down to a finite dielectric constant and incorporating into the system Hamiltonian. The solvent accessible surface (SAS), for which the charge-screening is determined, is modeled as a realistic cavity that conforms to the molecular shape of the solute rather than simply assuming spherical or ellipsoidal shapes.21 We examined the slow and fast contributions† to the solvent shifts from the gas-phase energies for each excited state. The slow part represents the interaction between the charge-screening of the ground state solvent cavity and the change in the electron density of the heterojunction system as a result of the excitation. The fast part represents the instantaneous electronic response of the solvent to the same change in the electron density of the system. We may thus think of the slow part as the non-equilibrium solvent †

Tabulated values for the 10 lowest excited states are given in the supplemental materials.

10

response to the charge distribution of the excited state while the fast part represents the instantaneous solvent polarization.29 While the slow term tended to increase the energy of each state, the fast term tended to decrease the energy of each. The destabilization effect of the slow term is brought about by the fact that the screening charges of the solvent cavity are optimized for the ground state since the calculated excited states are vertical states. While it is possible to do relaxed excited state calculations involving solvent effects, again the size of the system involved in this case prohibits us from doing so. Nevertheless, the fast terms dominate the solvent shifts to the extent that an overall stabilization of the states is observed. Further, the observed stabilization of the CT states is at least 3 times greater that of the XT states. This is expected since XT states lead to relatively weakly polarized electronic densities while CT states (particularly, intermolecular) lead to relatively strongly polarized electronic densities. Consequently, the addition of non-polar solvent results in an overall red-shift in the absorption spectra of the system.

In summary, we have shown that for polymer heterojunction systems such as TFB/FBT, the electronic excited states are highly sensitive to the interfacial stacking orientation between the constituent polymer chains to the extent that slight lateral changes not only shift the energies of the states, but, more importantly, they alters the nature of these excited states altogether. This result underscores the significant influence of interfacial morphology on the electronic properties of composite materials used in the design of optoelectronic devices. In addition, the presence of a low dielectric solvent tend to stabilize the excited states such that an overall red-shift in the absorption spectra is observed.

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Acknowledgements

This work was supported in part by the National Science Foundation and the Robert

A. Welch Foundation.

Competing Interests The authors declare that they have no competing financial interests.

Correspondence

Correspondence and requests for materials should be addressed to ERB. (email: bit-

[email protected]).

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List of Figures 1

Structures of the comonomer subunits dioctylfluorene (F8), benzothiadiazole (BT), bis-N,N-(4-butylphenyl)-bis-N,N-phenyl-1,4-phenylenediamine (PB), and N-(4-butylphenyl)diphenylam (TB). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2

TFB/FBT structures(slightly tilted forward) showing two different orientations of the polymer constitutents. In each, the FBT (top chain) consist of 3 fluorene(F) units and 3 benzothiadiazole(BT) units while the TFB (bottom chain) consist of 3 F units and 2 triarylamine(TB) units. These co-monomer units are labeled with indecies. The eclipsed orientation (2(a)) has the middle F units (F12 and F22) of both chains π-stacked while the staggered orientation (2(b)) has the middle BT of FBT (BT2) and the middle F of TFB (F22) π-stacked. . . . . . . . . . . . . . . . . 20

3

Energy correlation diagram between the gas phase (/G) and solvated (toluene) (/S) lowest excited states in model TFB/FBT calculated by TD-DFT(B3LYP/6-31G(d)). 21

4

Electron-hole density plots of the relevant excited states of model TFB/FBT. The axes represents the electron and hole localizations on the various co-monomer units of FBT and TFB (as labeled in Fig. 2) leading to four possible excitation types: intrachain excitations (FBT∗ , TFB∗ ) and interchain excitations (TFB+ /FBT− , TFB− /FBT+ ) The plots labeled CT and XT correspond to the highlighted states in Fig. 3 while the plots labeled Sx correspond to excited state x. . . . . . . . . . . . . . . . . . . 22

5

Predicted gas phase absorption spectra of model TFB/FBT calculated by (a) TDDFT(B3LYP/6-31G(d)) and (b) CIS(HF/6-31G(d)). The plots involve the 10 lowest states with a 30 meV lineshape broadening. . . . . . . . . . . . . . . . . . . . 23

6

Ground state optimized geometry of Isolated TFB chain at the (a) HF/PM3/631G(d) level and (b) DFT/B3LYP/6-31G(d) level. The PM3 structure show the dihedral between the outer F subunits to be 0◦ relative to the N-N’ line while that of DFT is 108◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

18

BT

F8

* *

*

*

C 4H 9 N

N H17C8

C8H17

S

C 4H 9

*

N

TB

N

*

PB N

*

* C 4H 9

Figure 1: Structures of the comonomer subunits dioctylfluorene (F8), benzothiadiazole (BT), bis-N,N-(4-butylphenyl)-bis-N,N-phenyl-1,4-phenylenediamine (PB), and N-(4butylphenyl)diphenylamine (TB).

19

(a) Eclipsed Orientation

(b) Staggered Orientation

Figure 2: TFB/FBT structures(slightly tilted forward) showing two different orientations of the polymer constitutents. In each, the FBT (top chain) consist of 3 fluorene(F) units and 3 benzothiadiazole(BT) units while the TFB (bottom chain) consist of 3 F units and 2 triarylamine(TB) units. These co-monomer units are labeled with indecies. The eclipsed orientation (2(a)) has the middle F units (F12 and F22) of both chains π-stacked while the staggered orientation (2(b)) has the middle BT of FBT (BT2) and the middle F of TFB (F22) π-stacked.

20

Energy ! eV Eclipsed!S

Eclipsed!G

Staggered!G

Staggered!S

3 2.8 2.6 2.4

XT

XT

2.2 2 1.8

CT

CT

1 2 3 4 5 6 8 Figure 3: Energy correlation diagram between the gas phase (/G)7 and solvated (toluene) (/S) lowest excited states in model TFB/FBT calculated by TD-DFT(B3LYP/6-31G(d)).

21

F23

FBT# ! TFB"

TFB!

F23

TB2

TFB!

F23

FBT# ! TFB"

TFB!

F23

TB2

F22

F22

F22

F22

TB1

TB1

TB1

F21

BT3

F13

FBT!

F21

FBT" ! TFB#

BT3

F13

FBT!

FBT" ! TFB#

BT3

F13

F12

F12

F12

F12

BT2

BT2

BT2

F11

F11

CT

BT1

BT1 F11 BT2 F12 BT3 F13 F21 TB1 F22 TB2 F23 e

F11

XT

BT1


FBT!

FBT" ! TFB#

BT3

BT2

BT1

TFB!

F21 h

FBT" ! TFB#

h

FBT!

h

F13

FBT# ! TFB"

TB2

TB1 F21 h

FBT# ! TFB"

TB2

F11

S4

BT1


S9 BT1 F11 BT2 F12 BT3 F13 F21 TB1 F22 TB2 F23 e

(a) Eclipsed: Gas Phase F23

FBT# ! TFB"

TFB!

F23

TB2

TFB!

F23

FBT# ! TFB"

TFB!

F23

TB2

F22

F22

F22

F22

TB1

TB1

TB1

BT3

F21 F13

FBT!

F21

FBT" ! TFB#

BT3

F13

FBT!

FBT" ! TFB#

BT3

F13

F12

F12

F12

F12

BT2

BT2

BT2

F11

CT BT1 F11 BT2 F12 BT3 F13 F21 TB1 F22 TB2 F23 e

F11 BT1

F11

XT

BT1


FBT!

FBT" ! TFB#

BT3

BT2

BT1

TFB!

F21 h

FBT" ! TFB#

h

FBT!

h

F13

FBT# ! TFB"

TB2

TB1 F21 h

FBT# ! TFB"

TB2


F11 BT1


(b) Staggered: Gas Phase

Figure 4: Electron-hole density plots of the relevant excited states of model TFB/FBT. The axes represents the electron and hole localizations on the various co-monomer units of FBT and TFB (as labeled in Fig. 2) leading to four possible excitation types: intrachain excitations (FBT∗ , TFB∗ ) and interchain excitations (TFB+ /FBT− , TFB− /FBT+ ) The plots labeled CT and XT correspond to the highlighted states in Fig. 3 while the plots labeled Sx correspond to excited state x.

22

Eclipsed

Intensity ! Arb. Units

Staggered

1.8

2

2.4 2.6 Energy ! eV

2.2

2.8

3

3.2

(a) DFT

Eclipsed

Intensity ! Arb. Units

Staggered

3.25

3.5

3.75

4 4.25 Energy ! eV

4.5

4.75

5

(b) CIS

Figure 5: Predicted gas phase absorption spectra of model TFB/FBT calculated by (a) TD-DFT(B3LYP/6-31G(d)) and (b) CIS(HF/6-31G(d)). The plots involve the 10 lowest states with a 30 meV lineshape broadening. 23

(a) HF/PM3/6-31G(d)

(b) DFT/B3LYP/6-31G(d)

Figure 6: Ground state optimized geometry of Isolated TFB chain at the (a) HF/PM3/631G(d) level and (b) DFT/B3LYP/6-31G(d) level. The PM3 structure show the dihedral between the outer F subunits to be 0◦ relative to the N-N’ line while that of DFT is 108◦ .

24

List of Tables 1

(Supplemental Material) Excited state energies (in eV) of model TFB/FBT calculated by TD-DFT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2

(Supplemental Material) Slow and fast contributions to the solvent shifts (in eV) in the excited state energies of model TFB/FBT calculated by TD-DFT. . . . . . . 27

25

Table 1: (Supplemental Material) Excited state energies (in eV) of model TFB/FBT calculated by TD-DFT. Excited State 1 2 3 4 5 6 7 8 9 10

Eclipsed Staggered solvated gas phase solvated gas phase 1.818 1.961 1.787 1.947 2.080 2.236 2.073 2.227 2.394 2.395 2.358 2.358 2.293 2.432 2.292 2.428 2.150 2.589 2.243 2.499 2.620 2.696 2.614 2.660 2.656 2.745 2.626 2.728 2.916 2.913 2.856 2.870 2.931 2.934 2.832 2.892 2.872 2.960 2.944 2.949

26

Table 2: (Supplemental Material) Slow and fast contributions to the solvent shifts (in eV) in the excited state energies of model TFB/FBT calculated by TD-DFT. Excited State 1 2 3 4 5 6 7 8 9 10

Eclipsed slow fast 0.061 -0.204 0.066 -0.221 0.020 -0.022 0.060 -0.199 0.070 -0.509 0.058 -0.134 0.030 -0.119 0.023 -0.020 0.023 -0.025 0.033 -0.121

27

Staggered slow fast 0.073 -0.233 0.073 -0.227 0.030 -0.031 0.060 -0.196 0.082 -0.338 0.050 -0.095 0.048 -0.150 0.041 -0.055 0.050 -0.110 0.028 -0.032