Solvent Polarity Tunes the Barrier Height for Twisted Intramolecular

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Solvent Polarity Tunes the Barrier Height for Twisted Intramolecular Charge Transfer in N-Pyrrolobenzonitrile (PBN) Mercedes Vanessa Bohnwagner, Irene Burghardt, and Andreas Dreuw J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b09115 • Publication Date (Web): 06 Dec 2015 Downloaded from http://pubs.acs.org on December 8, 2015

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The Journal of Physical Chemistry

Solvent Polarity Tunes the Barrier Height for Twisted Intramolecular Charge Transfer in N-Pyrrolobenzonitrile (PBN) Mercedes V. Bohnwagner,∗,†,‡ Irene Burghardt,‡ and Andreas Dreuw∗,† †Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany ‡Institute of Physical and Theoretical Chemistry, Goethe-University, Max-von-Laue-Str. 7, 60438 Frankfurt am Main, Germany. E-mail: [email protected]; [email protected]

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Abstract 4-(1H-pyrrol-1-yl)benzonitrile (PBN) is a typical intramolecular donor-acceptor (D/A) molecule that shows dual fluorescence in weakly polar environments. In this work the underlying photochemical reaction mechanism is investigated theoretically by using high-level ab initio methods including the recently implemented third order algebraic diagrammatic construction of the polarization propagator (ADC(3)). Solvation effects have been considered by using different sophisticated continuum model approaches. Our results conclusively explain all available experimental findings including the effects of excitation wavelength, temperature and solvent polarity. After photoexcitation in gas phase to the bright 2A (S2 , ππ ∗ ) state, PBN relaxes on the 2A state surface until a conical intersection with the energetically close-lying dark 1B (S1 , LE) state is reached. After passing this conical intersection PBN further relaxes on the LE state surface towards a minimum from which emission can occur. In polar environments this picture changes. Then the polar 2B (S3 , CT) state is stabilized and an energy barrier along the twisting coordinate vanishes. As a consequence population of the twisted 2B state minimum becomes the dominating decay channel and red-shifted fluorescence occurs.


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1 Introduction Photoinduced Twisted Intramolecular Charge Transfer (TICT) is an important excited-state mechanism found in numerous donor-acceptor (D/A) molecules. 1–3 It is mediated by rotation around a bond connecting the intramolecular donor and acceptor moieties. This rotation is typically associated with a charge transfer from the donor to the acceptor moiety and leads to the formation of a twisted excited state. 4 The TICT mechanism is often accompanied by an unusual fluorescence behaviour called dual fluorescence. 2 This particular behaviour was the reason why TICT got into the focus of research about 50 years ago. 5 The TICT formation rate is strongly dependent on the solvent’s viscosity and polarity 6–9 A special group of TICT compounds which are of particular interest due to their wide range of applications are so called fluorescent molecular rotors. 9–15 The most common application is their use as fluorescent microviscosity sensors. 9,16,17 2'

H3C

CH3 N

1'

N 1 2

3 4

C

C

N

N

Figure 1: Chemical structures of 4-(Dimethylamino)benzonitrile (DMABN) (left) and 4-(1H-pyrrol-1yl)benzonitrile (PBN) (right) and numbering of atoms in PBN.

A prototype molecular rotor is 4-(Dimethylamino)benzonitrile (DMABN) (Figure 1, left), for which the phenomenon of solvent dependent dual fluorescence has been discovered. 18,19 Besides the so-called ”normal” emission band, a second much weaker red-shifted ”anomalous” emission band appears in the fluorescence spectrum in polar solvents. 20 Today it is known that dual fluorescence in DMABN results from emission from a so-called local excited (LE) state which is populated after photoexcitation as well as from a stabilized intramolecular charge transfer (ICT) state. 1,19,20 Quantum yield, energy and intensity of the fluorescence thereby strongly depend on the solvents polarity and viscosity. 8,21 The role of the solvent in TICT



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dynamics has already been investigated intensively. 7,22–24 The discovery of dual fluorescence in DMABN has triggered numerous experimental and theoretical studies of charge transfer in D/A compounds. 25–34 In the literature, four main models for the stabilization of the ICT state are discussed. These are twisted ICT (TICT), 1 planar ICT (PICT), 35,36 rehybridized ICT (RICT) 37 and wagged ICT (WICT). 38 TICT is today the most popular and most widely accepted one and also effective in DMABN. 39 Dual fluorescence was also found in many other small D/A systems e.g. phenyl pyrroles, 40–42 aryldisilanes 42,43 4-(dimethylamino)benzoic acid methyl ester (DMABME) 44 and in the here investigated compound 4-(1H-pyrrol-1-yl)benzonitrile (PBN) 45–48 (Figure 1, right) which is the pyrrol analogue of DMABN. PBN, in comparison to DMABN, exhibits a higher electron density at the donor moiety due to the pyrrol ring possessing six π -electrons. This should lead to an even more efficient ICT. Even though numerous experimental and theoretical studies of PBN in gas and liquid phase have been carried out to obtain deeper insights into the mechanism of dual fluorescence and its photochemistry, 41,45–57 there remain open questions concerning the involved photochemical processes and the nature of the ICT 41,46,49 as will be outlined below. Cornelissen-Gude et al. 45 were the first to investigate the photochemistry of PBN spectroscopically in liquid and solid phase using solvents of different polarity. At room temperature, one broad absorption band has been observed at around 286 nm (4.33 eV), which was found to be rather insensitive to solvent polarity. This band arises from the dominant 1 La -type state (in the nomenclature of Platt 58 ) as well as the 1 Lb -type state, which is hidden underneath the much stronger 1 La -type band. This result was confirmed by Murali et al. 54 a few years later. In emission spectra recorded at room temperature in polar solvents one broad emission band at around 480 nm (2.58 eV) has also been observed. This emission band has been assigned to a polar CT state. Also these results were confirmed later by Murali et al. 54 Dual fluorescence has been observed only in nonpolar n-hexane solution and frozen ethanol. In frozen ethanol (at 153 K), beside the broad redshifted emission band at around 430 nm (2.88 eV), a second weaker short wavelength emission band has been found at around 320 nm (3.87 eV) which has been assigned to the LE (S2 ) state. It has been further found that the relative intensities of both emission bands and the solvatochromic shift of the red-shifted


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band depend strongly on the temperature and on the excitation wavelength. Murali et al. 54 report about dual fluorescence in a nonpolar solvent mixture which, however, is only observed at room temperature. The observed vibrational structure of the emission band at around 305 nm vanishes upon cooling. From this result Murali et al. 54 infer that the broad band occurring at longer wavelengths results from emission from a thermodynamically stable CT state while the vanishing vibrational feature results from emission from a less stable LE state which is thermodynamically populated only at higher temperatures. Yoshihara et al. 41 report similar findings. Dual fluorescence has only been observed in alkanes. It has been found that in n-hexane LE and CT emission bands have similar intensities. In more polar solvents, only red-shifted fluorescence has been observed. In gas phase experiments 46 only single emission at around 310 nm has been observed upon excitation up to 2200 cm−1 (0.27 eV) above the 0-0 band. The observed fluorescence with a lifetime of 17 ± 2 ns has been assigned to the S1 (Lb -type) state. In the gas phase absorption spectrum one broad band has been found which is assigned to the S2 (La -type) state. From their results Belau et al. 46 infer only a small energy gap of about 400-500 cm−1 (0.05 - 0.06 eV) between states S2 and S1 . Hence, they suggest that efficient radiationless coupling between S2 and S1 leads to population of and emission from the S1 state. From their gas phase experiments Fuß et al. 47 infer that both S2 (La -type, 2A (in C2 symmetry)) state and the relevant CT state are two locations on the same 2A state potential energy surface. They suggest, that after excitation to the allowed S2 (2A) state two possible relaxation pathways open up: 1) an ultrafast relaxation to the S1 (Lb -type, 1B) state minimum through a conical intersection as already proposed by Belau et al.. 46 2) relaxation from the S2 (2A) state to the CT minimum on the 2A state surface. They further assume that an equilibration between the two minima occurs and that twisting around the central bond and amino-group pyramidalization are two components of the CT reaction coordinate. In order to achieve a better understanding of the experimental findings several theoretical investigations 50,51,53,57,59,60 have been conducted as well, in which mainly semiempirical and DFT methods have been applied so far. In most of these theoretical studies solvation effects on vertical excitation or emission energies are completely neglected or considered by using rather crude models 50 as the Kirkwood-Onsager model. 61–63 However,



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for a fundamental understanding of the phenomenon of dual fluorescence in PBN, high level ab initio computations and the inclusion of solvent effects using more sophisticated solvent models are inevitable. Semiempirical CNDO/s-CI calculations 59 employing two different solvation models predict four energetically low lying TICT states for the C2v symmetric, 90◦ twisted geometry and also a low lying PICT state for the planar conformation. From their results Retting et al. 59 conclude that the observed red-shifted fluorescence is more likely emitted from a TICT state rather than from a PICT state. However, it is emphasised that emission from a PICT state might also become feasible due to stabilization by a polar solvent and thus should not be ruled out. A DFT/MRCI study 50 of the excited states of PBN, in which PBN is assumed to be C2 symmetric, provides two CT states (2B) and (3A) and two allowed ππ ∗ states (1B) and (2A) as the relevant excited states for the TICT mechanism. The CT state (2B) is the S1 state and the allowed ππ ∗ state (2A) is the S3 at the Franck-Condon (FC) geometry. A potential energy surface scan along the twisting coordinate at ground state geometries shows a stabilization of the 1B state (S2 at the FC geometry, µFC = 6.20 D) and the 3A state (S4 at the FC geometry, µFC = 18.48 D) and an increase of the corresponding static dipole moments. At 90◦ the 1B state (µ = 20.1 D) which upon twisting evolves into a CT state is found to be the lowest lying excited singlet state. Based on this result Parusel 50 suggests that the experimentally observed red-shifted fluorescence 45 is due to emission from the 1B-TICT state. Solvation effects on the TICT mechanism have been estimated by using the simple Onsager model. However, in this study excited state geometry relaxation is completely neglected. CASSCF/cc-pVDZ and CASPT2/cc-pVDZ calculations provide two CT minima located on the S2 state (21 A in C2v symmetry) potential energy surface. 51 The S1 state (1B2 in C2v symmetry) is the LE state at CASPT2 level of theory. One of the two 21 A state minima is found to have a 90◦ twisted conformation and the other one is found to be planar. Zilberg et al. report that the TICT state minimum has an anti-quinoid (AQ) geometry i.e. lengthened central benzene bonds and a lengthened central C-N pyrrol bond and possesses a large static dipole moment of about 16 D. The PICT state minimum has a quinoid (Q) geometry i.e. shortened central bonds of the benzene ring and a short C-N pyrrol bond and possesses a smaller static


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dipole moment in the range of 6-13 D. In gas phase, the AQ structure is about 0.63 eV (14.5 kcal/mol ) more stable than the Q structure. Zilberg et al. propose that the ”normal” emission is due to emission from the LE state and that the ”anomalous” emission is due to either the Q or the AQ CT state. However, their results refer to gas phase calculations only and in gas phase the energy of the two CT states is too high for efficient crossing with the LE state. 51 A very recent publication by Minezawa 57 addresses the effects of solvation on the CT states in PBN. The strong dependence of the computed energy profile of ICT states of PBN on the chosen solvation model is emphasized. Absorption and emission spectra of PBN have been calculated at TD-DFT/LC-BLYP/DH+(d) level of theory using the LRFE model for acetonitrile solution, which yielded a bright LE state of A symmetry as S1 , and two dark states S2 and S3 of B symmetry. According to their results in gas phase the TICT (1B) state minimum is spontaneously reached by twisting only. In contrast, LR-RISM-TD-DFT provided a completly different free energy profile for TICT formation being endergonic. However, the LRFE-TD-DFT method predict an exergonic reaction which is in agreement with experimental findings. In view of all these works described above, it is clear that still no common agreement on the involved molecular coordinates or the character of the involved excited states has been reached. The motivation of our work is thus to achieve this understanding of the reaction mechanism of dual fluorescence of PBN in polar solvents.

2 Computational Details The ground state (S0 ) (1A) geometry of PBN has been optimized using the approximate second-order coupled-cluster model (CC2) 64,65 and density functional theory (DFT) in combination with the long-range corrected exchange-correlation functional CAM-B3LYP 66 in conjunction with the correlation-consistent basis set cc-pVTZ. 67–69 For CC2 calculations the resolution-of-the-identity (RI) approximation 65 with the corresponding auxiliary basis set aux-cc-pVTZ 70 has been applied. All ground state geometry optimizations were constrained to C2 symmetry. Vibrational frequency analyses have been performed at the correspond-



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ing level of theory to verify the stationary points as local minima on the potential energy surfaces. For the investigation of twisted ICT, the dihedral angle β (C1’-N-C1-C2) (numbering scheme in Figure 1, right) between pyrrol and benzonitrile moieties was chosen as the reaction coordinate β . A relaxed scan of the S0 potential energy surface along the twisting coordinate β has been carried out at RICC2/cc-pVTZ level of theory. Starting from the equilibrium geometry, β was varied in increments of 10◦ and the geometry was determined by relaxing the remaining degrees of freedom. Vertical excitation energies of the six lowest excited singlet states have been calculated at the S0 state equilibrium geometry obtained at RICC2/cc-pVTZ level of theory. Different excited state methods have been applied: the third-order algebraic diagrammatic construction scheme for the polarization propagator (ADC(3)) 71,72 and the second-order scheme (ADC(2)), 73–75 CC2 linear-response theory, 64,76,77 the perturbative doubles correction to configuration interaction with single substitutions (CIS(D)) method 78,79 and time-dependent density functional theory (TD-DFT) 80,81 using two types of functionals: hybrid BHLYP 82,83 and long-range corrected CAM-B3LYP. 66 For ADC and CC2 linear-response calculations the RI approximation has been employed. All excited state calculations have been performed using the cc-pVTZ and corresponding aux-cc-pVTZ basis set. For our theoretical description of solvation effects we have employed state-specific equilibrium solvation 84 and nonequilibrium, perturbative state-specific (ptSS) and linear-response-type (ptLR) solvation approaches. 85 Solvent effects on vertical excitation energies at the ground state equilibrium geometry have been estimated by using the C-PCM model as implemented in a development version of Q-Chem 4.3 86,87 employing nonequilibrium solvation and the the conductor-like screening model (COSMO) 88 as implemented in Turbomole 6.6 89 employing equilibrium solvation. The parameters of acetonitrile (ACN) (ε =36.6, n=1.344) have been used for comparison with experimental data. Excited state geometries have been optimized at RICC2/cc-pVTZ and TD-DFT/CAM-B3LYP/cc-pVTZ levels of theory. All stationary points were confirmed as local minima or transition states by vibrational frequency analysis at TD-DFT/CAM-B3LYP/cc-pVTZ level of theory. Solvent effects on vertical excitation energies at the corresponding excited state equilibrium geometries have been estimated at ADC(2),


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TDA/CAM-B3LYP and TD-DFT/CAM-B3LYP levels of theory in conjunction with the cc-pVTZ basis set, employing equilibrium solvation using two different models: COSMO as implemented in Turbomole 6.6 and Orca 3.0.1 90 as well as the C-PCM 91 model employing perturbative state-specific (ptSS) and linearresponse-type (ptLR) corrections 85 as implemented in a development version of Q-Chem 4.3. 86,87 In order to investigate the TICT mechanism, a relaxed scan of the bright 2A state potential energy surface along the twisting coordinate β has been performed first in gas phase at RICC2/cc-pVTZ level of theory. Starting from the equilibrium dihedral angle β2A = 12.9◦ , β was varied in increments of 10◦ and the geometries were constrained to C2 symmetry. Along this scan TD-DFT/CAM-B3LYP/cc-PVTZ and ADC(2)/cc-pVTZ single point calculations were carried out to obtain vertical excitation energies for the relevant excited states. The influence of polar solvents on the energy profile of the relevant CT state has been studied by employing state-specific equilibrium solvation at TD-DFT/CAM-B3LYP/cc-PVTZ/C-PCM and ADC(2)/cc-pVTZ/COSMO and C-PCM level of theory, respectively, using the parameters of ACN. All RICC2 and CIS(D) calculations have been performed using Turbomole 6.3.1. 92 Vertical excitation energies at ADC(2), ADC(3) and ADC(2)/C-PCM level of theory have been computed using the Q-Chem 86,87,93 package versions 4.2.0 and 4.3.0. For the computation of vertical excitation energies at TD-DFT/CAMB3LYP, TD-DFT/CAM-B3LYP/C-PCM and TD-DFT/BHLYP level of theory Gaussian 09 Rev D01. 94 has been used.

2.1 Ground state properties of PBN The ground state geometry of PBN is C2 symmetric with the C2 rotation axis passing through the cyano group (CN) and the nitrogen atom of the pyrrol ring (Figure 1, right). At the theoretical level of RICC2/ccpVTZ the rings are planar but twisted against each other by an equilibrium dihedral angle of βS0 =32.5◦ . ˚ N − C1 = 1.404 A, ˚ C1 − C2 = 1.400 A, ˚ ˚ C1′ − N = 1.383 A, With bond lengths of C2′ − C1′ = 1.379 A, C2 − C3 = 1.389 A˚ and C3 − C4 = 1.402 A˚ (numbering scheme in Figure 1) the rings show the typical alternating bond length pattern of aromatic compounds. 95 At DFT/CAM-B3LYP/cc-pVTZ level of theory an equilibrium dihedral angle of βS0 = 31.4◦ is obtained. The bond lengths C2′ −C1′ , C1′ − N, C1 −C2 , C2 − 9 ACS Paragon Plus Environment


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˚ respectively, compared to the RICC2 C3 , C3 − C4 are shortened by only 0.006, 0.007, 0.009 and 0.011 A, optimized structure indicating that the geometries are very similar for both methods. The slightly twisted orientation in the ground state results in a less effective π -conjugation between the rings as compared to a ˚ an intermediate length between a single planar structure, yielding a central N-C1 bond length of 1.404 A, and a double bond. 96 In the ground state, PBN has a static dipole moment µ0 of 3.4 D and 3.8 D along the z axis at RICC2/cc-pVTZ and CAM-B3LYP level of theory, respectively. The ring-ring torsion calculated at RICC2/cc-pVTZ level of theory is characterized by a flat potential which is symmetric around the planar (β = 0◦ ) conformation. The potential has two barriers: a small barrier of 0.05 eV (1.15 kcal/mol ≈ 2kB T ) for the planar transition state, and a higher barrier of 0.13 eV (2.99 kcal/mol) for the perpendicular transition state (β = 90◦ ) and two local minima corresponding to two ’static’ enantiomers (δ and λ ) with β = 32.5◦ and β = −32.5◦ , respectively. The interconversion between the two enantiomeric conformers at room temperature (298.15 K) is extremely fast, with a rate constant k of k = 8.12∗ 1011

1 s

(corresponding to a

half life of 80 ps) using the simple Arrhenius equation for an estimate. Thus, the enantiomers can not be isolated under experimental conditions at room temperature. The ring-ring torsion around 90◦ , however, is slightly hindered with k = 4.67∗ 1010 1s (corresponding to a half life of 0.46 ns). Our ground state calculations confirm earlier DFT/MRCI results by Parusel et al. 50

2.2 Vertical excited states of PBN Vertical excitation energies and properties of the energetically low lying excited singlet states of PBN have been calculated at the equilibrium ground state geometry obtained at RICC2/cc-pVTZ level of theory. Results for the first four excited singlet states obtained at ADC(3), RICC2, ADC(2), CIS(D), TD-DFT/BHLYP and TD-DFT/CAM-B3LYP levels of theory are summarized in Table 1, because only these four states are relevant for the investigated ICT mechanism. For the nomenclature of the excited states irreducible representations will be used independently of the energetic order of the states. According to ADC(3), ADC(2), RICC2 and CIS(D) calculations, the lowest excited singlet state (S1 ) is a dark ππ ∗ state. The S1 state belongs to the B irreducible representation of C2 and will be named 1B 10 ACS Paragon Plus Environment

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delocalized MO to a MO localized on the benzonitrile moiety. Thus, this ππ ∗ state acquires certain CT character explaining its relatively large static dipole moment of 11 D at RICC2 and ADC(2) levels. For the 2A state excitation energies of 4.81, 4,82, 4.76, 5.31, 4.82 and 4.88 eV are obtained at ADC(3), RICC2, ADC(2), CIS(D), TD-DFT/CAM-B3LYP and TD-DFT/BHLYP levels of theory, respectively. This state can be assigned to the experimentally observed allowed La -type transition. 45–47 ADC, RICC2 and CIS(D) levels of theory provide an S3 state with CT character possessing B symmetry hereinafter named 2B. The 2B state is characterized exclusively by the HOMO → LUMO excitation (Figure 2) exhibiting very small oscillator strength. The localized nature of HOMO and LUMO results in a large static dipole moment of 17-18 D at RICC2 and ADC(2) levels, respectively. For the 2B state ADC(3), RICC2, ADC(2), CIS(D), TD-DFT/CAM-B3LYP and TD-DFT/BHLYP levels of theory predict excitation energies of 5.06, 4.93, 4.93, 5,46, 4.78 and 4.81 eV, respectively. TD-DFT seems to underestimate the excitation energy of the 2B state slightly. The S4 state obtained at ADC, RICC2, TD-DFT/CAM-B3LYP and TD-DFT/BHLYP levels of theory possesses A symmetry. It is mainly a HOMO → LUMO+1 transition (75% at ADC(3) level of theory) (Figure 2). Again, the localized character of the involved MOs results in a substantial CT character and a large static dipole moment of 17-19 D at RICC2 and ADC(2) levels, respectively. This state will be named 3A state. The 3A state also has only a very small oscillator strength. For the 3A state excitation energies of 5.52, 5.67, 5.54 and 5.58 eV are obtained at RICC2, ADC(2), TD-DFT/CAM-B3LYP and TD-DFT/BHLYP levels of theory, respectively. In general, the results obtained via traditional linear-response TD-DFT are in good agreement with those obtained at RICC2 and ADC levels of theory. One striking difference, however, is that at the FC geometry, the energetic order of the two states 1B (LE) and 2B (CT) is interchanged at TD-DFT level as compared to the RICC2 and ADC levels. In order to examine whether the lowering of the 2B (CT) state energy can be related to the electron-transfer self-interaction error in TD-DFT and the missing integer discontinuity in the functionals 97,98 the amount of HF exchange in CAM-B3LYP was varied. In CAM-B3LYP the contribution of HF exchange is incorporated by two parameters α and β , i.e. 19% HF exchange at short-range


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(α = 0.19) and 65% HF exchange at long-range (α + β = 0.65). 66 Our study reveals that vertical excitation energies of the two CT states 2B and 3A strongly depend on the amount of HF exchange. When going from

α = 0.00 to α = 0.65 they are increased by 0.65 eV and 0.90 eV, respectively. In contrast, those of the 2A (ππ ∗ ) and 1B (LE) states are less affected. They are increased only by 0.33 eV and 0.47 eV, respectively. For 30% HF exchange at short-range (α = 0.30) and more, the energetic order of 2B (CT) and 2A (ππ ∗ ) is interchanged. With full (100%) HF exchange at long-range (α + β = 1.00) and no short-range contribution (α = 0.00) the energetic order of the first three lowest excited states changes again: 2A (S1 ) and 1B (S2 ) states become energetically almost degenerate. Vertical excitation energies are 4.95 eV and 4.99 eV, respectively. And the 2B (CT) state becomes the S3 state, i.e. the energetic order of the states is the same as at ADC and RICC2 levels. This behavior of the excitation energies demonstrates that the underestimation of the excitation energies of the 2B (CT) state observed for TD-DFT/BHLYP and TD-DFT/CAM-B3LYP is indeed due to the aforementioned electron-transfer self-interaction error and hence artificial. The results for the two states with A symmetry S2 and S4 agree among all methods but CIS(D). The S4 state at CIS(D) level has B symmetry and no CT character. All applied methods, except for CIS(D), provide nearly degenerate vertical excitation energies for the first three excited singlet states and a very small energy gap ∆E1B,2A between 1B (ππ ∗ ) and 2A (ππ ∗ ) (∆E1B,2A of only 0.06 eV at RICC2/cc-pVTZ and 0.23 eV at ADC(3) level of theory), indicating a strong mixing of these states. The vertical excitation energies of the 1B (S1 ) and 2A (S2 ) states obtained at the ADC and RICC2 levels of theory in gas phase are in very good agreement with gas phase absorption measurements of PBN. These measurements, taken at 80 C◦ , show one broad absorption band centered at 4.59 eV 47 which is assigned to the La -type (S2 ) state and a weak precursor at longer wavelengths which is assigned to the Lb -type (S1 ) state. 46,47 Jet cooled measurements provide the 0-0 band at 4.27 eV. 46 To get a first estimate of the extent to which solvent effects are involved in the stabilization of the relevant excited states, i.e. 1B (LE), 2A and 2B (CT), and how much they may affect emission energies, vertical excitation energies have been computed using ADC(2)/cc-pVTZ employing a state-specific equilibrium solvation method i.e. COSMO. For this initial test, the equilibrium ground state geometry obtained



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at RICC2/cc-pVTZ level of theory and the parameters of ACN have been used for the solvation model. To obtain corrected vertical excitation energies the image charges of the COSMO model are equilibrated with respect to the corresponding states. The vertical energy separations to the other states were corrected for the fast response part of the reaction field. For comparison, first the ground state has been used to equilibrate the solvent model yielding solvation corrected excitation energies. In a second step the image charges are equilibrated with respect to the excited states and vertical excitation energies are recalculated. The difference in excitation energies then reveals the pure contribution of the fast solvent response to the Stokes Shift at fixed geometry (Table 2). Table 2: Comparison of vertical excitation energies ∆E (in eV) of the relevant singlet excited states obtained at ADC(2)/cc-pVTZ, ADC(2)/cc-pVTZ/COSMO and ADC(2)/cc-pVTZ/ptSS-PCM levels of theory. Vertical excitation energies in gas phase and solvent-corrected vertical excitation energies, static dipole moments µ (relaxed) (in Debye) and solvent shifts ∆∆Esol a and ∆∆E(in eV) are given.b State 1B 2A 2B

ADC(2)gas ∆E µ 4.74 5.5 4.76 10.4 4.93 16.0

ADC(2)COSMO ∆E µ 4.80 5.7 4.65 11.2 4.77 16.8

ADC(2)COSMO ∆E µ 4.76 7.8 4.50 13.2 4.50 18.1

wrt 1B ∆∆Esol -0.04 -0.15 -0.26

ADC(2)COSMO ∆E µ 4.60 13.2 4.12 17.7 3.90 21.8

wrt 2A ∆∆Esol -0.20 -0.53 -0.86

ADC(2)COSMO ∆E µ 4.40 17.2 3.82 20.0 3.41 23.5

wrt 2B ∆∆Esol -0.40 -0.83 -1.35

ADC(2)ptSS-PCM ∆E ∆∆E 4.79 +0.05 4.66 -0.20 4.60 -0.24

a ∆∆E sol

is the difference between vertical excitation energies in solution within COSMO solvation when the reaction field is equilibrated with respect to the ground state density and with respect to the respective excited state density b ∆∆E is the difference between the vertical excitation energies computed in gas phase and with the C-PCM solvent model.

The solvent-corrected vertical excitation energy of the bright 2A state of 4.65 eV is in good agreement with the experimentally observed absorption maximum at 35180 cm−1 (4.36 eV). 55 Independent on the excited state to which the image charges are equilibrated, a strong red-shift of the vertical excitation energy of the 2B (CT) state is obtained in comparison to the vertical energy obtained when the image charges are equilibrated with respect to the ground state density. When the image charges are equilibrated with respect to the bright 2A state, the red-shift of vertical excitation energy of the CT state is already so pronounced that the energetic order of bright 2A and 2B (CT) state changes: the 2B (CT) state becomes the lowest excited state. In contrast to that, vertical excitation energies of 1B (LE) and bright 2A states are shifted very little. In comparison to the gas phase results, the dipole moments are generally enhanced. From these results we can conclude that already the fast electronic solvent response has a strong influence on the stabilization of the 2B (CT) state and thus on the energetic order of the excited states at the FC geometry. In the gas phase, 14 ACS Paragon Plus Environment

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the energy of the 2B state is too high for efficient crossing with the bright 2A state, while in polar solvents the polar CT state is stabilized so that crossing becomes feasible.

2.3 Structural relaxation in the excited states To consider geometric relaxation effects, geometries of all relevant excited states were optimized at RICC2 (Figure 3) and TD-DFT/CAM-B3LYP level of theory in C2 symmetry using the cc-pVTZ basis set. For each stationary point a vibrational frequency analysis has been carried out at TD-DFT/CAM-B3LYP/cc-pVTZ level of theory in order to verify its identity as local minimum or transition state (TS). 24

00

1.4

25

N 1.386

N

C

1.4

02

3

1.4

1.430

94

1.4

38

N

0

1.37

1.3

1.389

9

1.37

1.

1.404

S0

C

N

C

N

1BMin

1.4

31

7

43

1.

N

43

5 C

N

1.333

1.374 1 4 .4

44

1.

28

4

48

N

1.373

1.

1.

1.37 0

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2BMin

2AMin

Figure 3: Schematic representation of the bond length pattern in the equilibrium geometries of ground (S0 ), 1B (LE), 2A (ππ ∗ ) and 2B (CT) states obtained at RICC2/cc-pVTZ level of theory.

2.3.1

The dark 1B (LE) state:

Symmetry-constrained geometry optimizations (PBN is constrained to C2 symmetry) of the dark 1B (LE) state performed at RICC2/cc-pVTZ and TD-DFT/CAM-B3LYP/cc-pVTZ levels of theory converge to a local minimum (1BMin ) which is more planar than the ground state minimum structure. The 1BMin minimum has been confirmed by vibrational frequency analysis to have no imaginary frequencies. RICC2 and TD-DFT/CAM-B3LYP levels predict nearly identical equilibrium geometries of the 1B state. The TD-DFT/CAM-B3LYP optimized structure is slightly more planar than the RICC2 optimized one as the corresponding ring-ring torsion angles are 18.9◦ and 20.8◦ , respectively. In general DFT methods tend to favor delocalized solutions, thus geometry optimizations prefer more planar geometries. 99–104 Compared to the ground state equilibrium geometry, the bond C2′ −C1′ and its symmetry equivalent, as well as the central 15 ACS Paragon Plus Environment


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N −C1 bond (numbering scheme in Figure 1, right) are shortened in the 1BMin geometry, while symmetry equivalent bonds C1′ − N and the C −C bonds of the benzene ring are elongated (Figure 3). The static dipole moment of PBN in the 2B state is slightly increased as compared to the one of the ground state. Total excited state energies, excitation energies and excited state properties for the first four excited singlet states calculated at RICC2/cc-pVTZ level of theory at the 1BMin geometry are summarized in Table 3. TDDFT/CAM-B3LYP provides the same state order with vertical excitation energies of the 1B, 2A and 2B states of 4.57, 4.59 and 4.85 eV, respectively. Table 3: Vertical excitation energies ∆E, oscillator strengths (in parenthesis), total excited state energiesa , static dipole moments µ and dominant molecular orbital contributions of the four lowest excited singlet statesb obtained at RICC2/cc-pVTZ level of theory at the 1BMin geometry c geometry are given. State 1B

∆E [eV] 4.35(0.01)

Etotal [eV] 4.56

µ [D] 6.1

2A 2B 3A

4.59(0.66) 4.99(0.01) 5.39(0.14)

4.80 5.20 5.60

9.7 16.3 17.8

MOs H-1>L+1 (ππ ∗ ) (73) H-2>L (local ππ ∗ ) (22) H-1>L (ππ ∗ ) (88) H>L (CT) (96) H>L+1 (CT) (97)

a Relative

to the S0 state equilibrium geometry obtained at RICC2 level of the state and the squared value of the wave function expansion coefficient (in percent) are given in parenthesis. c Obtained at RICC2 level of theory b Character

Emission energies from the 1B state in gas phase obtained at RICC2, ADC(2) and TD-DFT/CAMB3LYP levels of theory are 4.35, 4.33 and 4.57 eV, respectively. Our gas phase results agree well with gas phase fluorescence measurements 46,52 of isolated PBN which show only a single emission band at around 305 nm (4.07 eV) with an emission decay time of 17 ± 2 ns, 46 which is assigned to the Lb -type state. 2.3.2

The bright 2A (ππ ∗ ) state:

Symmetry-constrained geometry optimizations of the bright 2A (ππ ∗ ) state in C2 symmetry performed at RICC2/cc-pVTZ and TD-DFT/CAM-B3LYP/cc-pVTZ levels of theory both converge to a nearly planar 16 ACS Paragon Plus Environment

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minimum structure (2AMin ). This structure has been confirmed as a local minimum on the PES by vibrational analysis. No imaginary frequencies were found. The ring-ring torsion angle β has values of 12.9◦ and 8.6◦ at the RICC2 and TD-DFT/CAM-B3LYP levels of theory, respectively. Energies and excited state properties of the first four excited singlet states calculated at RICC2/cc-pVTZ level of theory at the 2AMin geometry are summarized in Table 4. The total energy of 2AMin obtained at RICC2/cc-pVTZ level of theory is 4.60 eV (relative to the ground state equilibrium geometry). Hence, the energy of the 2A state minimum (2AMin ) is 0.04 eV above 1BMin (E1BMin = 4.56 eV). The emission energy from the 2A state in gas phase is 4.40 eV at RICC2/cc-pVTZ level (Table 4). In the course of the constrained geometry optimization, symmetry equivalent bonds C1′ − N, C1 −C2 as well as C3 −C4 (numbering scheme in Figure 1, right) are elongated (Figure 3). On the contrary, symmetry equivalent bonds C2′ −C1′ and C2 −C3 and the central N −C1 bond are shortened. Hence, 2AMin can be described as the quinoid structure, which was previously suggested. 48,51 Unconstrained geometry optimization of PBN in the 2A (S2 ) state at RICC2/cc-pVTZ level does not usually converge to a stationary point. In the course of the optimization the symmetry equivalent C1′ − N bonds are ˚ the central N − C1 bond is shortened by about 0.02 A˚ (numbering scheme in elongated by about 0.02 A, Figure 1, right) and the pyrrol ring is tilted driving the system towards a surface crossing between the 2A (S2 ) and 1B (S1 ) states. However, since RICC2 is a single-reference method a close lying 2A-1B conical intersection can only be inferred and its energetic location can only be estimated from this result. In the following, the geometry in which the two states are energetically almost degenerate (∆E = 0.004 eV) will be named approximate intersection geometry. The angle θ (N −C1 −C4) (numbering scheme in Figure 1, right) which describes the bending of the pyrrol ring out of the benzene plane changes from 180◦ at the FC geometry to 175◦ in the approximate intersection geometry. Hence, the out-of-plane bending mode is one coordinate active in reaching the conical intersection to the 1B (S1 ) state minimum. The total energy of the approximate intersection geometry (relative to the ground state equilibrium geometry) is 4.66 eV. Thus, this geometry lies only about 0.06 eV above the total energy of 2AMin . This result agrees well with gas phase fluorescence measurements, 46 which suggest an ultrafast internal conversion between the bright S2



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(La -type) and the dark S1 (Lb -type) state.

Table 4: Vertical excitation energies ∆E, oscillator strengths (in parenthesis), total excited state energies,a static dipole moments µ and dominant molecular orbital contributions of the four lowest excited singlet statesb at the 2AMin geometryc . State 2A 1B

∆E [eV] 4.40(0.77) 4.55(0.01)

Etotal [eV] 4.60 4.75

µ [D] 8.6 5.7

2B 3A

4.92(0.01) 5.82(0.14)

5.12 6.02

16.1 16.5

MOs H>L (ππ ∗ ) (89) H>L+1 (CT) (68) H-2>L (local ππ ∗ ) (25) H>L (ππ ∗ ) (94) (ππ ∗ ) (89)

a (Relative

to the S0 state equilibrium geometry obtained at RICC2 level) of the state and the squared value of the wave function expansion coefficient (in percent) are given in parenthesis. c Obtained at RICC2 level of theory. b Character

Vertical excitation energies of the relevant singly excited states have been computed at the 2AMin geometry at RICC2, ADC(2), TD-DFT/CAM-B3LYP and TDA/CAM-B3LYP levels of theory in conjunction with the cc-pVTZ basis set. The ADC(2) results agree very well with the RICC2 results which are summarized in Table 4. The respective ADC(2) excitation energies for states 2A, 1B, 2B and 3A are: 4.31, 4.52, 4.92 and 5.86 eV. At TD-DFT/CAM-B3LYP/cc-pVTZ and TDA/CAM-B3LYP/cc-pVTZ levels of theory excitation energies of 4.37, 4.78, 4.72, 5.89 eV and 4.57, 4.80, 4.89 and 5.93 eV are obtained, respectively. Comparing these energies with those obtained at RICC2 and ADC(2) levels reveals that i) the agreement of TD-DFT/CAM-B3LYP with RICC2 is very good for states 2A and 3A ii) TDA/CAM-B3LYP overestimates the excitation energies of states 2A, 1B and 3A, but yields the same state order as RICC2 and ADC(2). In contrast, for TD-DFT/CAM-B3LYP states 1B and 2B are interchanged. To estimate solvation effects on the 2B (CT) state energy in the 2AMin geometry and also on the emission energy of the 2A state, vertical excitation energies of the relevant excited singlet states have been recomputed at TDA/CAM-B3LYP/cc-pVTZ/COSMO, ADC(2)/cc-pVTZ/COSMO and ADC(2)/cc-pVTZ/C-PCM levels of theory (Table 5). For the C-PCM calculation the recently implemented ptSS-PCM and ptLR-PCM approaches 85 have been employed. In the ADC(2)/cc-pVTZ/COSMO calculation the solvent reaction field 18 ACS Paragon Plus Environment

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has been equilibrated with respect to the charge density of the 2A state. Again the parameters of ACN have been used for the solvent models. All applied levels of theory predict a strong downshift of vertical excitation energies of the two CT states 2B and 3A (of about 0.3 − 0.7 eV) (indicated by a negative sign for the energy difference (∆∆E)). ADC(2)/cc-pVTZ/COSMO yields the most pronounced red-shift of the vertical excitation energy of the relevant 2B (CT) state. On the contrary, vertical excitation energies of the two ππ ∗ transitions 2A and 1B are hardly influenced by application of a solvent model. While the 2A state energy is also slightly shifted downwards, the COSMO approach predicts an upshift of the excitation energy of the 1B (LE) state. In contrast, both ptLR- and ptSS-C-PCM approaches predict a slight downshift of its excitation. Solvent-corrected vertical excitation energies of the 2A state obtained at TD-DFT/CAM-B3LYP/COSMO, ADC(2)/COSMO and ADC(2)/C-PCM levels of theory are: 4.54, 3.96 and 4.23 eV, respectively. The emission energy obtained at ADC(2)/COSMO level of 3.96 eV is in best agreement with fluorescence experiments in liquid phase. 56 In ACN solution two emission bands are observed one band at about 350 nm (3.54 eV) and a red-shifted band at about 480 nm (2.58 eV). 56 Comparison of the ptLR and ptSS contributions for the different excited states reveals the importance of inclusion of ptSS correction terms to assure a physically meaningful description of solvent stabilization of CT states as also reported in a recent theoretical study of solvatochroism of nitroaromatics. 85 This is mainly because the state-specific (SS) approach explicitly takes into account the electron densities of the respective states, i.e. the difference density is used to compute the correction energy. In the case of linear-response corrections the transition density is used and then, the Coulombic interaction of electron and hole remains unscreened. 84 Table 5: Gas phase (∆Egas ) and solvent-corrected (∆Esol ) excitation energies (in eV) of the first four lowest excited states and solvent shifts (∆∆E) (in eV) calculated at TDA/CAM-B3LYP/cc-pVTZ and ADC(2)/cc-pVTZ levels of theory at the 2AMin geometrya employing COSMOb and C-PCM solvation. State 2A 1B 2B 3A

CAM-B3LYP ∆Egas 4.57 4.80 4.89 5.93

CAM-B3LYP/COSMO ∆Esol ∆∆E 4.54 -0.03 4.89 +0.09 4.46 -0.43 5.60 -0.33

ADC(2) ADC(2)/COSMO ∆Egas ∆Esol, wrt 2A ∆∆E 4.31 3.96 -0.35 4.52 4.54 +0.02 4.92 4.22 -0.70 5.86 5.25 -0.61

∆Esol, ptSS 4.23 4.57 4.57 5.60

a Obtained b For

ADC(2)/C-PCM ptLR correction ptSS correction -0.46 -0.03 -0.02 -0.01 -0.05 -0.25 -0.06 -0.27

at RICC2 level of theory TDA/CAM-B3LYP/COSMO the linear response approach and for ADC(2)/COSMO calculations the state-specific approach has been employed.


∆∆E -0.08 +0.05 -0.35 -0.26


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2.3.3

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The 2B (CT) state:

Symmetry-constrained geometry optimizations (geometry is constrained to C2 symmetry) of the 2B (CT) state at RICC2/cc-pVTZ and TD-DFT/CAM-B3LYP/cc-pVTZ levels of theory converge to a transition state (TSCT ). Vibrational analysis performed at TD-DFT/CAM-B3LYP/cc-pVTZ level provides one imaginary frequency of -69.9 cm−1 for the TSCT state geometry. The corresponding eigenvector activates a bending of the pyrrol ring. In the TSCT state geometry the dihedral angle β is 90.2◦ at RICC2/cc-pVTZ level and 90.0◦ at CAM-B3LYP/cc-pVTZ level of theory, respectively. Full geometry optimizations of the 2B state at RICC2/cc-pVTZ and TD-DFT/CAM-B3LYP/cc-pVTZ level predict a C1 symmetric minimum structure (2BMin ) with 90.0◦ twisted ring planes and a tilted pyrrol ring (Figure 3). Both geometries are almost identical. The 2BMin structure (Figure 3) was confirmed as a local minimum on the PES by vibrational analysis; only real frequencies were obtained. In the course of the geometry optimization i) a bending of the pyrrol ring ii) quinoidization of the benzonitrile group i.e. a shortening of the two central C-C bonds in the benzene ring and elongation of the other four C-C bonds and iii) a bond length reversal in the pyrrol ring occur. Additionally, the central N −C1 bond is significantly increased. Thus, facile rotation around the central bond is possible. Our results concerning the structure of the emissive CT state contrasts earlier studies, 51,54 which report an antiquinoid structure of the possible TICT state possessing A symmetry. The dihedral angle β is 112.1◦ at RICC2/cc-pVTZ and 105.5◦ at TD-DFT/CAM-B3LYP/cc-pVTZ level of theory. Both levels predict the same tilt angle θ (N − C1 − C4) (numbering scheme in Figure 1, right) of 158.1◦ . Geometric relaxation stabilizes the energy of the 2B state by about 0.61 eV (14.08 kcal/mol). RICC2/cc-pVTZ level of theory predicts the 2B state to be the lowest-lying local minimum (Etot,2BMin = 4.32 eV) on the S1 state surface compared to the other two minima (Etot,2AMin = 4.60 eV and Etot,1BMin = 4.56 eV). Gas phase emission energies from the 2B state obtained at RICC2, ADC(2) and TD-DFT/CAMB3LYP levels of theory are 3.07, 3.04 and 2.94 eV, respectively. Compared to wavefunction-based methods, TD-DFT underestimates the excitation energy of this CT state. Our results show, that twisting is not the only important coordinate alone involved in formation of a stable TICT state. Instead, stretching modes e.g quinoidization of the benzonitrile group and bending of the pyrrol ring are also involved. Vertical excitation 20 ACS Paragon Plus Environment

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energies and excited state properties of the first three lowest excited singlet states at the 2BMin geometry obtained at RICC2/cc-pVTZ level of theory are summarized in Table 6. Table 6: Vertical excitation energies ∆E, oscillator strengths (in parenthesis), total excited state energies, static dipole moments µ and dominant molecular orbital contributions of the three lowest excited singlet statesa obtained at RICC2/cc-pVTZ level of theory at the 2BMin geometry. State S1 (2B) S2 (2A) S3 (1B)

∆E 3.07(0.00) 4.19(0.01) 4.65(0.01)

Etotal 4.32 5.44 5.90

µ 16.1 11.8 6.3

MOs H > L (CT) (95) H-1 > L (CT) (82) H-3 > L (local ππ ∗ ) (65) H-2 > L+1 (local ππ ∗ ) (21)

a Relative

to the S0 state equilibrium geometry obtained at RICC2 level. of the state and the squared value of the wave function expansion coefficient (in percent) are given in parenthesis. c Obtained at RICC2 level. This geometry is C symmetric, therefore, the irreducible representations are given in 1 parenthesis. b Character

Beside the lowest lying CT (HOMO → LUMO) S1 (2B) state, there is a second low lying CT (HOMO1 → LUMO) S2 (2A) state present at this 2BMin geometry. This CT state evolves out of the bright 2A (HOMO-1 → LUMO) state along the twisting coordinate because HOMO-1 in the C2 symmetric FC geometry is a linear combination of HOMO-1 and HOMO-2 in the C1 symmetric equilibrium geometry of the 2B state. HOMO, LUMO and LUMO+1 remain the same as in the FC geometry. The S3 state corresponds to the dark 1B (LE) state. Solvation effects on the emission energy of the 2B state have been estimated by employing state-specific equilibrium solvation using C-PCM as implemented in Gaussian 09 and COSMO as implemented in Turbomole V 6.6. For the solvent model, the parameters of ACN have been used. The state-specific approach has been chosen because it was shown in previous studies that the linear-response formalism tends to fail correcting excitation energies of CT states, as already mentioned above. 57,84 Vertical excitation energies of the lowest singly excited states have thus been recomputed at the 2BMin structure at TD-DFT/CAMB3LYP/cc-pVTZ/C-PCM and ADC(2)/cc-pVTZ/COSMO levels of theory. In the case of state-specific equilibrium solvation calculations the solvent reaction field is equilibrated with respect to the 2B state density. The respective solvent-corrected vertical excitation energies are 1.57 and 1.42 eV. With respect 21 ACS Paragon Plus Environment


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to the gas phase excitation energies (3.04 and 2.94 eV), the solvent corrected excitation energies of the 2B state are strongly downshifted. The solvent-corrected emission energy is 1.72 eV at ADC(2)/COSMO level of theory. It has been computed as the difference between the equilibrium total energy of the 2B state and the non-equilibrium total energy of the ground state in the reaction field equilibrated for the 2B state. The computed emission energy is in fair agreement with experimental emission energies of the CT state which are 460 nm 54 (2.69 eV) and about 480 nm 56 (2.58 eV). The computed red-shift is 2.94 eV at ADC(2)/cc-pVTZ/COSMO level of theory. For comparison with the experimentally obtained red-shift, it is computed with respect to the solvent-corrected vertical excitation energy of the 2A state at the ground state geometry obtained by employing state-specific, equilibrium solvation equilibrating the reaction field with respect to the ground state density. The computed red-shift is larger as the experimentally obtained Stokes’ shift of 13104 cm−1 54 (1.6 eV). Both, solvent-corrected emission energy and red-shift are overestimated at ADC(2)/COSMO level of theory. Nevertheless, the expected and experimentally observed trend is well reproduced.

2.4 TICT formation mechanism To relate the identified equilibrium structures of the different electronic states to the experimentally observed occurrence of red-shifted fluorescence under different conditions, the reaction paths connecting these structures need to be investigated. The focus lies on the formation of the TICT equilibrium structure of the 2B state. Therefore, a possible reaction pathway leading from the bright 2A state minimum to the TICT (2BMin ) state minimum is searched. At first a relaxed gas phase scan along the twisting coordinate β of the 2A state PES has been performed at RICC2/cc-pVTZ level of theory (Figure 4). This scan yields a direct pathway from the FC structure to the flat 2A state minimum at 13◦ (Figure 4). The 2A state has a maximum at 90.0◦ corresponding to an energy barrier of 0.39 eV (8.99 kcal/mol) along the twisting coordinate. This increased rotational barrier can be explained by the partial double bond character of the central N −C1 bond of PBN in the 2A state. The potential energy curve of the 2B (CT) state has a flat local minimum at 43◦ and a maximum at 13◦ . Along the twisting coordinate an avoided crossing between the two states of B 22 ACS Paragon Plus Environment

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investigated by increasing the amount of HF exchange gradually. Indeed, the 2B state was shifted upwards in energy corroborating the effect of the ET-SI error: At 13◦ 2A (ππ ∗ ), 2B (CT) and 3A (CT) states are shifted upwards by 0.24, 0.58 and 0.95 eV, respectively. The energy difference between the shifts of 2A and 2B states is 0.34 eV. The energy shift of the CT states is equally large as in the FC geometry. At 73◦ , 83◦ and 93◦ the 2A state is shifted upwards by 0.55, 0.70 and 0.77 eV, respectively, while the 2B state is shifted by 0.80, 0.81 and 0.82 eV, respectively. The reason why the energy shift of the 2A (HOMO-1 → LUMO) state becomes more pronounced in twisted conformations is that HOMO-1 and LUMO decouple during rotation i.e. the contribution on the benzonitrile (of HOMO-1) and the pyrrol moiety (of LUMO), respectively, vanishes such that the 2A state evolves into a pure CT state. This decoupling leads to a more pronounced CT character of the 2B (HOMO → LUMO) state. Hence also the effect of the ET-SI error becomes more pronounced. This result is highly significant for the investigation of energy profiles of CT states along twisting coordinates when using TD-DFT and should be kept in mind when undertaking such computations. 105 However, even though the 2B (CT) excitation in PBN seems to suffer from the ET-SI error and its vertical excitation energy is underestimated by TD-DFT, also at this level of theory there is no pronounced stabilization of its energy along the twisting coordinate and no TICT state minimum is found.

To investigate solvent effects on the PES of the 2A and 2B states, single point calculations have been carried out along the previously calculated relaxed PES of the 2A and 2B states, respectively (Figure 6). Vertical excitation energies of the four lowest excited singlet states have been recalculated at ADC(2)/ccpVTZ/COSMO level of theory using state-specific, equilibrium solvation. Hereby, the solvent charges are equilibrated either for the 2A state or 2B state, respectively. For the solvent model, again the parameters of ACN have been used. Along the relaxed scan of the 2A state, the 2A state is the lowest excited state at small twisting angles. However, the energy barrier present in the gas phase along the twisting coordinate disappears when the COSMO model for ACN solution is used, and PBN can twist barrierless and reach a crossing between the 2A and 2B states at 43◦ . Once the 2B state is reached, the optimized geometry of this state (2BMin )




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frozen ethanol and medium polar solvents dual fluorescence is observed, while in strongly polar solvents only red-shifted fluorescence is observed. 45,52,54,56 In addition, the relative intensities of the dual fluorescence bands depends on the temperature and excitation wavelength suggesting the existence of an energy barrier for red-shifted fluorescence to occur. 45 The red-shifted emission band has been assumed to arise from the emission from a polar twisted CT (TICT) state while for the so called ”blue” band it is assumed that it arises due to emission from a locally excited (LE) state. In this work the photochemical mechanism underlying the experimentally observed fluorescence phenomena of PBN has been investigated theoretically with a focus on the intramolecular CT states. For these investigations different levels of theory have been employed including high-level ab initio methods such as RICC2, ADC(2) and ADC(3). Solvent effects on transition energies of the relevant excited states of PBN have been described within the conductor-like polarizable continuum model (C-PCM) and the conductorlike screening model (COSMO) to enable a better comparison with experiment. PBN has a linear equilibrium geometry with C2 symmetry in the ground state in which the rings are slightly twisted towards one another. To reach an orthogonal conformation a torsional barrier of only about 0.13 eV (3 kcal/mol) has to be overcome. Hence, rotation around the central C-N bond, though not free, is quite facile. All applied levels of theory predict the S1 state of PBN to be a local ππ ∗ state with low CT character exhibiting B symmetry, here named 1B. This state can be assigned to the Lb -type (LE) state observed in experiment. The S2 state is predicted to be the spectroscopically accessible excited state possessing A symmetry, here named 2A. This state can be assigned to the so called ”bright” La -type state observed in experiment. The lowest lying CT state of PBN is the S3 state at RICC2, ADC(2) and ADC(3) levels of theory and the S1 state at the applied TD-DFT levels of theory. All levels predict this CT state to exhibit B symmetry, hence, here named 2B. In PBN these three relevant excited states: 1B (LE), bright 2A and 2B (CT) lie energetically very close together in accord with experiment. To find a possible pathway leading from the bright 2A (ππ ∗ ) state minimum to a 2B (TICT) state minimum, a relaxed scan of the PES of the 2A state along the twisting coordinate has been performed in gas phase and treating solvation with the above mentioned solvent models. Based on our calculations the following




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lowest in energy and the twisted CT equilibrium structure of the 2B state is adopted. The occurrence of red-shifted fluorescence is directly connected with the ability to reach the 2B TICT minimum. Summarizing, in gas phase and non-polar solvents, 2A and 2B states are not sufficiently stabilized and an energy barrier for twisting exists such that only single emission from the 1B (LE) state occurs. With increasing polarity of the solvent, both the 1B (LE) and 2A states, the latter exhibiting a larger static dipole moment, are stabilized and the energy barrier shrinks. Hence, already in n-hexane dual fluorescence may occur, but, the red-shift of the CT state emission band is not pronounced in this case. In solvents of medium polarity, the stabilization of both 2A state and 2B states becomes more distinct such that the emission bands are more separated and the red-shift is more pronounced. In polar solvents, the stabilization of the polar 2B (CT) state is so pronounced that the energy barrier disappears and only red-shifted fluorescence occurs.

4 Acknowledgements MVB gratefully acknowledges scientific discussions with Dr. Matthias Ruckenbauer and Dr. Felix Plasser. Additionally MVB acknowledges the Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences for their support.

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25

C

1.430

1.4

3

02

38

1.4

1.

N

C

N

C

N

1BMin

1.4

31

1.

N

43

1.333 C N ACS Paragon Plus Environment

5

2AMin

1.374 1 4 .4

4 .4

4 48

N

1.373

1.37 0

37

4 1.

1.

1 2 3 4 5 6 7 8 9 10 11 12

70 The Journal of Physical 1.3Chemistry

94 1.3

1.389

9 1.37

1

2BMin

28

3.0 6.5

Page 45 of 48

Relative energy [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


6.0

5.5 2.0

5.0

1.0 4.5

0.0 0

20 2A@2A 2A@2B

40 1B@2A 1B@2B

60

80

100

2B@2A 3A@2A ACS Paragon Plus Environment 2A@S0 1B@S0

Twisting angle β [°]

120 4A@2A 2B@S0

140

160 S0@2A 3A@S0

180 2B@2B 4A@S0


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

Page 46 of 48

HOMO

HOMO-1

LUMO

HOMO-2 LUMO+1


HOMO-3

6.5

Page 47 of 48

Relative energy [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


6.0 5.5

5.0 4.5 4.0 3.5 3.0 2.5 2.0 0

20 2B@2B

3A@2B

40

60

1B@2B 2A@2A ACS Paragon2A@2B Plus Environment

Twisting angle β [°]

80 2B@2A

1B@2A

100 3A@2A


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


Page 48 of 48

Solvent Polarity Tunes the Barrier Height for Twisted Intramolecular

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