Mechanism of the Triplet-to-Singlet Upconversion in the Assistant

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On the Mechanism of the Triplet-to-Singlet Upconversion in the Assistant Dopant ACRXTN Christel Maria Marian J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b00060 • Publication Date (Web): 04 Feb 2016 Downloaded from http://pubs.acs.org on February 11, 2016

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The Journal of Physical Chemistry

On the Mechanism of the Triplet-to-Singlet Upconversion in the Assistant Dopant ACRXTN Christel M. Marian∗ Institute of Theoretical and Computational Chemistry, Heinrich Heine University D¨ usseldorf, Universit¨ atsstr. 1, D-40225 D¨ usseldorf, Germany E-mail: [email protected],Phone:+49-211-8113210

∗

To whom correspondence should be addressed

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Abstract In this work, the photophysics of 3-(9,9-dimethylacridin-10(9H)-yl)-9H-xanthen9-one (ACRXTN) has been investigated by combined density functional theory and multi-reference configuration interaction quantum chemical methods. ACRXTN was recently utilized as an assistant dopant in a green emitting organic light-emitting diode (OLED), increasing substantially the external electroluminescence quantum efficiency of the OLED. The efficient triplet-to-singlet upconversion, found experimentally in ARCXTN, cannot be explained solely on the basis of a small singlet-triplet energy gap. We find five interacting electronically excited states in a small energy interval: a charge-transfer excitation (triplet and singlet) from acridine to xanthone, a local xanthone triplet (ππ ∗ ) excitation, and a pair of triplet and singlet states originating from an nπ ∗ excitation on xanthone. On the basis of calculated spin–orbit coupling constants and potential energy profiles, we propose here that the triplet (ππ ∗ ) state mediates the triplet-to-singlet upconversion in ACRXTN and that the carbonyl bond stretching motion plays an essential role in this process.

1

Introduction

Xanthone is well known for its involved solvent- and temperature-dependent photophysics. 1–6 Depending on the experimental conditions, photoexcited xanthone deactivates rapidly to the lowest triplet state or fluoresces brightly. Also, phosphoresence has been observed in apolar media. With regard to excitation energy transfer processes, xanthone has proven to be an efficient triplet-sensitizer. The clue to understanding this wide variation of photophysical properties is the energetic proximity of its low-lying electronically excited singlet and triplet states. 7 The highest occupied molecular orbital (HOMO) of xanthone is a π-type orbital (πH ) and so is the lowest unoccupied molecular orbital (LUMO, πL∗ ). Nevertheless, the S1 and T1 states of isolated xanthone do not originate from a HOMO-LUMO excitation. Rather, T1 results from an excitation out of the ketone oxygen lone-pair orbital (nO ) to the lowest π ∗ 2


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orbital yielding T(nO πL∗ ). Closeby, the T(πH πL∗ ) and S(nO πL∗ ) states are located. The latter states mediate the efficient non-radiative relaxation of the optically bright S(πH πL∗ ) state via internal conversion (IC) and intersystem crossing (ISC) to the T(nO πL∗ ) state, thus explaining the high triplet quantum yield of xanthone in apolar environments. In polar solvents, the nO πL∗ states are strongly blue shifted while the πH πL∗ are slightly red shifted. The differential destabilization of the nO πL∗ states is reinforced in protic solvents. The polarity and proticity of water is sufficient to reverse the order of the πH πL∗ and nO πL∗ states, making xanthone highly fluorescent in aqueous solution. In addition to direct fluorescence, E-type delayed fluorescence was observed in femtosecond time-resolved experiments. 5 The back population of the singlet state was explained by ultrafast ISC from the nearly degenerate T(nO πL∗ ) state that prevails over internal conversion to the lower-lying T(πH πL∗ ). 7 The complexity of the xanthone photophysics is further increased when substituents are introduced that may act as intramolecular donors or acceptors. In this case, low-lying charge-transfer (CT) states will be formed in addition to nπ ∗ and ππ ∗ states. Recently, 3(9,9-dimethylacridin-10(9H)-yl)-9H-xanthen-9-one (ACRXTN, Figure 1) was applied as an assistant dopant in purely organic light-emitting diodes (OLEDs). 8 The idea behind this approach was to use triplet excitons for populating the S1 state of the assistant dopant by reverse intersystem crossing (ReISC). Instead of radiatively decaying by fluorescence, the S1 state transfers its excitation energy by Förster resonance energy transfer (FRET) to a strongly fluorescent organic emitter. Nakanotani et al. 8 could show that the presence of the assistant dopant substantially improved the external electroluminescence (EL) quantum efficiency of the OLED, indicating an internal exciton production efficiency of nearly 100%. The HOMO of ARCXTN is a π-type orbital on the dimethylacridine moiety whereas its LUMO is a π ∗ orbital localized on xanthone. Hence, the lowest electronically excited state is expected to have CT character. But is this really the case? Or do locally excited states bear the palm as it was the case in xanthone itself? Further, with the uncoupled electrons so far apart, spin–orbit interaction is probably very, very small. What is then the mechanism

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behind the efficient (Re)ISC? To answer these questions and to shine light on the triplet-tosinglet upconversion mechanism in ACRXTN, thorough quantum chemical studies beyond simple MO analyses have been carried out in this work.

2

Methods and computational details

Geometry optimizations were performed by a Kohn-Sham density functional theory (DFT) procedure and time-dependent DFT (TDDFT) for the ground and low-lying excited states, respectively. 9,10 To this end, we used the B3-LYP functional as implemented in the Turbomole program package and the default split valence basis sets with polarization, def-SV(P), from the Turbomole library. 11–13 Test calculations using a larger valence triple-zeta basis with polarization functions, TZVP, 13 showed only minor deviations. Due to the substantially higher computational cost of the latter calculations, we refrained from using the TZVP basis as the standard basis. The effect of a polar, but aprotic solvent (acetonitrile, relative permittivity ǫr ≈ 36 14 ) on the electronic spectrum was mimicked by the conductor-like screening model (COSMO) implemented in the Turbomole package. 15,16 Vertical electronic excitation energies, dipole (transition) moments and oscillator strengths were obtained from subsequent single-point calculations using a combined density functional theory / multi-reference configuration interaction (DFT/MRCI) method. This semiempirical method was originally designed by Grimme and Waletzke 17 as an effective means to predict spectral properties for organic systems. While the method performs very well in general, yielding mean absolute errors for electronic excitation energies below 0.2 eV, 18 it turned out to have some flaws when it comes to weakly interacting bi-chromophoric systems. In the present case, a negative singlet-triplet separation for the charge-transfer state was found. It is caused by an unbalanced treatment of many-open shell configurations in the standard DFT/MRCI Hamiltonian. Throughout this work we employ a newer parameterization of the Hamiltonian, dubbed DFT/MRCI-R, that was especially designed for multi-chromophoric

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systems. 19 In addition to the ground state, 10 excited siglet and 10 excited triplet states were calculated. No symmetry constraints were applied in the calculation. Due to the perpendicular arrangement of the acridine and xanthone rings, the states may nevertheless be classified according to Cs symmetry with the xanthone molecular plane as the mirror plane. For comparison, also single-point calculations were carried out at the level of coupled-cluster theory with approximate treatment of doubles (CC2). For that purpose, we used the parallelized resolution-of-identity (RI)-CC2 implementation in TURBOMOLE. 20,21 The computation of ISC rate constants in Condon approximation requires the electronic spin–orbit coupling matrix elements and overlap of the vibrational wave functions of the involved states. 22 Harmonic vibrational frequencies and normal modes were determined numerically with the program SNF. 23 Electronic spin–orbit matrix elements (SOMEs) between the correlated DFT/MRCI-R wave functions were computed using the SPOCK program developed in our laboratory. 24,25 Herein, an effective one-electron mean-field approximation to the full Breit-Pauli Hamiltonian is utilized. 26 A further simplification is introduced by neglecting all multicenter integrals. The atomic mean-field integrals are calculated with the AMFI program 27 and then transformed to a molecular orbital basis. These approximations introduce errors which are usually lower than 5%, even for purely organic molecules. 28,29 As experience has shown, it is very difficult to converge second-order properties such as phosphorescence probabilities with respect to the number of states included in a perturbation theory scheme. Therefore, multi-reference spin–orbit configuration interaction (MRSOCI) calculations in conjunction with the spin-free DFT/MRCI-R Hamiltonian were carried out. 30 The resulting multiplicity-mixed MRSOCI wave functions can be employed directly in the evaluation of transition moments. Herein, the length form of the electric dipole transition operator, appropriate for spin-forbidden transitions, is utilized. 31

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3

Results and discussion

3.1

Vertical excitation spectra: Vacuum and Solvent

Molecular orbitals (MOs) that are important for the characterization of the electronically excited states are displayed in Figure 2. They can be grouped into three categories: 1. MOs that are localized on the xanthone moiety: nO (Fig. 2(a)), πH−1 (Fig. 2(b)), πL∗ ∗ (Fig. 2(d)), πL+1 (Fig. 2(e)),

2. MOs that are localized on the acridine substituent: πH (Fig. 2(c)), and ∗ ∗ 3. MOs that are delocalized over both rings: πL+4 (Fig. 2(f)), πL+5 (Fig. 2(g)).

Accordingly, the electronic transitions may be characterized as local xanthone excitations (LEX), local acridine excitations (LEA), and charge-transfer (CT) transitions. Table 1 lists the vertical DFT/MRCI-R excitation energies at the electronic ground-state equilibrium. For comparison, also RI-CC2 excitation energies and the corresponding TDDFT values obtained with the B3-LYP functional are given. Since the calculations are performed for an isolated chromophore, these results should be compared with gas-phase spectra or with absorption spectra recorded in apolar hosts. Let us focus on the DFT/MRCI-R results first. In the Franck-Condon (FC) region, the πH → πL∗ excitation gives indeed rise to the lowest singlet and triplet states. The electric dipole transition to the S1 state is weak because it comes along with a charge transfer from the acridine to the xanthone moiety. Hence, the overlap of the orbital densities of the MOs involved in the transition is small. Concomitant with the small orbital density overlap, we find a very small singlet-triplet energy gap 0.06 eV, typical for TADF emitters. Also the next higher-lying singlet state is optically dark. It originates from a local excitation of the carbonyl oxygen lone-pair nO to the πL∗ MO and relates to the first excited singlet state of xanthone in apolar media. In the spectral range between the singlet CT and the Snπ∗ state, we find four further triplet states. The lowest one is a 3 (ππ ∗ ) state of A′ spatial 6


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symmetry dominated by the πH−1 → πL∗ excitation. Closeby, a multiconfigurational 3 (ππ ∗ ) state is found that arises mainly from local acridine excitations. Next comes the 3 (nO πL∗ ) state and an A′ state dominated by the πH−6 → πL∗ excitation. The first optically bright state, 1 (πH−1 πL∗ ), is found 3.83 eV above the electronic ground state in the FC spectrum and relates to lowest Sππ∗ state of xanthone. The order of singlet states is retained in the RI-CC2 calculations. As may be seen in Table 1, the RI-CC2 excitation energies are systematically higher than the corresponding DFT/MRCI-R values by about 0.3-0.4 eV. With small variations this is also true in the triplet manifold where the order of the close-lying 3 (nO πL∗ ) state and the multiconfigurational 3

(ππ ∗ ) states is reversed with respect to DFT/MRCI-R. The tendency that RI-CC2 gives

slightly too high excitation energies has been noted earlier, in particular if a moderate basis set is employed. 32 A completely different picture emerges in the TDDFT(B3-LYP) treatment. While the locally excited 1 (nO πL∗ ) and 1 (πH−1 πL∗ ) states exhibit comparable excitation energies at the TDDFT and DFT/MRCI-R levels, the singlet CT state is found at significantly lower energy in the TDDFT calculations. Hence, the energy gap between the CT state and the locally excited states is substantially increased in the TDDFT description. Moreover, two additional singlet CT states appear below the first optically bright state. The second excited singlet state with an excitation energy of 3.56 eV in the TDDFT treatment is ∗ dominated by the πH → πL+1 excitation. A corresponding state vector is found as the fourth

excited singlet state in the DFT/MRCI-R (4.05 eV) and RI-CC2 (4.30 eV) calculations. The 1 ∗1 πL+ configuration (S4 in TDDFT with an excitation energy singlet CT state with leading πH

of 3.92 eV) is not found amoung the lowest six singlet states in the DFT/MRCI-R and RICC2 calculations. In the triplet manifold, TDDFT finds the second triplet CT state as T7 at 3.51 eV (T8 at 4.23 eV in RI-CC2). In view of these results, great care has to be exercised when TDDFT calculations are employed to aid the experimental assignments for this kind of compounds.

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In polar media, spectral shifts with respect to the gas phase or apolar solutions are expected. Exemplarily, we have carried out calculations for a polar, but non-protic environment with a relative permittivity corresponding to an acetonitrile surrounding of the solute. The presence of the solvent has almost no effect on the ground-state molecular geometry. The only difference is a slight increase of the carbonyl bond by 1 pm (see Table S1 of the supplementary information (SI)). For this reason, we employed gas-phase optimized minimum geometries for the excited states. The vertical excitation energies and static dipole moments obtained at the DFT/MRCI-R level are shown in Table 2. Surprisingly, almost no spectral shift is found for the CT states. The blue shift experienced by the nO π ∗ states is comparatively large, being ≈ 0.20 eV. No general trend can be detected in case of the ππ ∗ states. In the singlet manifold, the Snπ∗ and Sππ∗ states change order in the FC region. Also the order of triplet states is affected by the spectral shifts. The triplet CT state remains the lowest triplet at this geometry, but the polar surrounding pushes the 3 (nO πL∗ ) state above the four 3 (ππ ∗ ) states.

3.2

Adiabatic Energies and Luminescence Properties

It is quite obvious that the minima of the excited state potential energy surfaces have to be investigated in order to understand the photophysical processes a species may undergo after electronic excitation, be it optically by photons or electrically by excitons. 3.2.1

The CT states

The geometry parameters of the singlet and triplet CT minima differ only slightly from those of the electronic ground state. Upon excitation, the C3 -N bond connecting acridine with xanthone is elongated from 143 pm to 146 pm. The bond lengths in the central acridine ring change by ±2 pm while the two outer rings are unaffected. In the xanthone nuclear frame, only the ring attachend to acridine and the central ring experience bond length changes by more than 1 pm. In particular, the C3 -C4 bond and the carbonyl bond are extended by 8


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about 3 pm. For further details see Table S1 in the SI. The relaxation of the nuclear arrangement in the singlet CT state is accompanied by a small energy release yielding an adiabatic excitation energy of 2.96 eV. Simultaneously, the ground-state potential rises by 0.19 eV. The calculated vertical emission energy of 2.77 eV is only slightly higher than the value (2.53 eV) estimated from the peak wavelengths of the fluorescence emission of ACRXTN codeposited with 1,3-bis(N-carbazolyl)benzene (mCP) host material in film. 8 The oscillator strength for this transition is very weak (≈ 5 × 10−5 ), corresponding to a fluorescence lifetime of about 20 µs. The geometry and wave function characteristics are almost identical at the singlet and triplet CT minima (see Tables S1, S3, and S4 of the SI). We determine the probability for radiative decay of the triplet CT state by phosphorescence to be very small with an average rate of ≈ 5 s−1 . The discussion of possible (Re)ISC mechanisms will be postponed to Section 3.3. 3.2.2

The (nO πL∗ ) states

The (nO πL∗ ) excitations are well localized on xanthone. While the C9 =O bond stretches by 9 pm to 131 pm in the (nO πL∗ ) excited states, the neighboring C9 -C9a and C9 -C8a bonds (for atom labeling see Figure 1) adopt more double bond character and shrink by 5 pm to 143 pm. All other bond lengths change by less than 1 pm (see Table S1 of the SI). Geometry relaxation in the Snπ∗ state reverses the order of states with respect to the FC point. At the Snπ∗ minimum, the Snπ∗ and singlet CT wave functions are substantially mixed. The singlet state dominated by the (nO πL∗ ) configuration is the lower one with an adiabatic excitation energy of 3.20 eV. The state with predominantly singlet CT character is located only 0.05 eV higher in energy at this geometry (see Table S5 of the SI). Due to the substantial C9 =O bond stretch, the electronic ground-state energy is higher here than at the singlet CT minimum. The vertical emission wavelength at the Snπ∗ minimum amounts to 442 nm (2.80 eV).

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The Tnπ∗ potential energy surface runs essentially parallel to the one of Snπ∗ . It exhibits an adiabatic excitation energy of 3.04 eV, 0.16 eV below the corresponding singlet. With at least three closely spaced low-lying triplet states, the course of the potential energy is, however, more complicated than in the singlet manifold. Within the error bounds of the method, the Tnπ∗ state and the lowest Tππ∗ state are degenerate at the Tnπ∗ minimum (∆E < 200 cm−1 ). The triplet CT state is the third triplet state at the Tnπ∗ minimum, approximately 0.14 eV above the Tππ∗ state. For further details see Table S6 of the SI. Why could the proximity of these states be important for the photophysics? Not only the singlet and triplet CT states have tiny SOMEs. Also the spin–orbit interaction between the Tnπ∗ and Snπ∗ states is negligibly small (see Table S10 of the SI). The largest SOME (−0.080i cm−1 ) is found for the y component of the spin–orbit coupling Hamiltonian at the Snπ∗ minimum. According to El-Sayed’s rules, 33 large SOMEs are to be expected if the magnetic moments of the involved MOs differ. In agreement with this simple rule of thumb, the Tππ∗ state couples strongly to the Snπ∗ state. As the two lowest singlet-excited wave functions are heavily mixed, both exhibit substantial spin–orbit interaction with the Tππ∗ state. (SOMEs of −15.005i, −31.230i, and −8.202i cm−1 for the x, y, and z components of the lower one and 12.198i, −24.479i, and 6.494i cm−1 for the x, y, and z components of the upper one, respectively). At the Tnπ∗ minimum, the singlet wave functions are slightly less mixed than at the Snπ∗ minimum (compare Tables S5 and S6 of the SI). Adiabatically, the Tnπ∗ state is found at 3.04 eV, 0.14 eV above the triplet CT minimum and only 0.08 eV above the singlet CT minimum. Tnπ∗ is the only triplet with a sizeable phosphorescence probability (≈ 425 s−1 . The computed vertical phosphorescence emission energy of 2.61 eV) is a bit higher than the value of 2.47 eV estimated from the measured peak maximum. 8 The phosphorescence borrows its intensity mainly from the bright Sππ∗ →S0 transition, yielding an averaged phosphorescence lifetime of about 2.3 ms in Condon approximation.

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3.2.3

The (πH−1 πL∗ ) states

The minimum geometry of the 21 A′ state, as obtained from TDDFT calculations using the B3-LYP functional, differs only marginally from that of the singlet CT state (see Table S1 of the SI). The wave function has substantial multiconfigurational character. Besides the leading (πH−1 πL∗ ) configuration (with a squared coefficient of about 52% at the DFT/MRCIR level and of about 80% at the TDDFT level), the wave function exhibits large contributions (squared coefficient of about 21% at the DFT/MRCI-R level and about 14% at the TDDFT level) from the (πH−3 → πL∗ ) excitation (see Table S7 of the SI). The different compositions of the wave functions in these methods may explain why the adiabatic excitation energy of 3.83 eV, obtained as the difference of the DFT/MRCI-R energies at the (TD)DFT optimized minima, is identical to the vertical excitation energy of 3.83 eV at the ground state minimum. The minimum of the triplet-coupled (πH−1 → πL∗ ) excitation could not be reached with TDDFT. The calculation stops at a crossing point between the two lowest 3 A′ states. We therefore optimized the geometry at the level of unrestricted DFT imposing symmetry constraints. It was also possible to optimize the state geometry with TDDFT in acetonitrile solution. The two nuclear arrangements are practically identical. We present here the results of the DFT/MRCI-R calculations at the UDFT minimum. The nuclear arrangement in the Tππ∗ minimum closely resembles the Tnπ∗ minimum geometry (see Table S1 of the SI). The Tππ∗ state is the lowest state here. It has an adiabatic energy of 3.04 eV (see Table S8 of the SI). The probability for phosphorescence from the T1 minimum is very low. The rate of 0.7 s−1 is typical for a 3 (ππ ∗ ) state. Only slightly higher in energy, two triplet states are located which are nearly 1:1 mixtures of triplet CT and Tnπ∗ character. The upper one is practically degenerate with the singlet CT state. Even slight solvent effect can tune these state into resonance. Also the singlet CT and Snπ∗ wave functions are mixed, but to a much lesser extent than the corresponding triplet states.

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3.3

(Reverse) Intersystem Crossing Mechanism

The energetic proximity and the mutual couplings of the five lowest electronically excited states (singlet CT, triplet CT, Tππ∗ ,Tnπ∗ , Snπ∗ ) makes the photophysics of ACRXTN very involved. Due to the complexity of the system of coupled equations, a quantitative determination of non-radiative transition rates was not possible. The geometry parameters of the singlet and triplet CT minima are almost identical, i.e., singlet and triplet CT are nested states, about 0.06 eV apart. This situation corresponds to the weak coupling limit of Englman and Jortner. 34 In this case, the probability of radiationless transition decreases exponentially with increasing energy gap. However, the electronic SOMEs between the singlet and triplet CT states are tiny. Their sum of squares, which is the decisive quantitity, is very small, i.e., ≈ 10−3 cm−2 (for details see Table S9 of the SI). Hence, it seems that the energetic proximity of the two CT states alone is not sufficient to explain a fast equilibration of the singlet and triplet populations. From the above discussion it becomes clear that simple Condon-type approximations for computing (Re)ISC rate constants are not appropriate and that spin-vibronic coupling has to be invoked. 22 The vibrational mode with the largest displacement is the C=O stretching mode. Since it drives the potential energy surfaces of the low-lying excited states towards various intersections, it is considered to be the major promoting mode. DFT/MRCI-R energy profiles of the low-lying excited states along a linearly interpolated path connecting the singlet CT and Snπ∗ states are shown in Figure 3. Herein, the singlet CT minimum corresponds to R=0 and the Snπ∗ minimum to R=1. The singlet CT and Tππ∗ potential energy curves are seen to cross each other approximately at R=0.6, only 0.11 eV above the adiabatic minimum of the singlet CT state. They exhibit substantial spin–orbit interaction (SOMEs of −1.526i, −3.875i, and 0.962i cm−1 for the x, y, and z components of the Hamiltonian). Also the triplet CT and Tππ∗ interact via spin-orbit coupling (x: −2.806i, y: 6.487i, z: −1.649i cm−1 ) in addition to non-adiabatic coupling. From the course of the potential energy curves and the knowledge of the coupling matrix elements, the following 12


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picture emerges. In apolar media, the S1 potential energy surface of ACRXTN exhibits at least two minima, the global minimum with CT electronic structure and a local minimum originating from a local (nO → πL∗ ) excitation on xanthone. We expect to find two or three minima on the lowest triplet exicted-state surface, with the triplet CT minimum being the global minimum. The second minimum on the T1 surface exhibits Tππ∗ electronic structure. According to our calculations, it is nearly degenerate with the Tnπ∗ minimum in apolar media. In the CT potential well, the singlet-triplet splitting is small enough to enable, at least in principle, the thermally activated ReISC from the triplet to the corresponding singlet. However, the direct spin–orbit coupling between the states is too small to make this process efficient. The carbonyl stretching vibration drives the system through a crossing with the Tππ∗ state which mediates the coupling of the CT states and allows for an equilibration of the singlet and triplet CT populations. In polar media, the (nO π ∗ ) states are blue-shifted whereas the Tππ∗ state experiences a slight red shift. Hence, we expect a double minimum situation on the lowest triplet exictedstate surface. In contrast, only one minimum with CT character is expected on the lowest singlet excited state potential energy surface. The Tππ∗ state continues to be doorway state mediating the Re(ISC) of the singlet and triplet CT states.

4

Conclusion

We have investigated the low-lying electronically excited states of the assistant dopant ACRXTN by means of high-level quantum chemical multi-reference methods including spin– orbit coupling. The results of the calculations support the conclusion drawn by the experimentalists 8 that the first excited singlet and triplet states are charcterized by charge-transfer excitations from the acridine to the xanthone moiety with a singlet-triplet gap of about 0.06 eV. The picture is by far more complicated, however, than a simple frontier MO analysis

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suggests. In addition to the singlet and triplet CT states, the DFT/MRCI-R calculations reveal three further low-lying excited states, a pair of Tnπ∗ and Snπ∗ states and a Tππ∗ state that correspond to local excitations on the xanthone moeity. Their equilibrium molecular structures are characterized by a substantial elongation of the C=O bond and a concomitant shortening of the neighboring C-C bonds. Their minima constitute additional local minima on the S1 or T1 potential energy surfaces, respectively. The singlet-triplet splitting of the CT states (0.06 eV) obtained in this work agrees very well with the experimental estimates. It is sufficiently small to enable, at least in principle, the thermally activated ReISC from the triplet to the corresponding singlet which is essential for thermally activated delayed fluorescence. Also the role of ACRXTN as an assistant dopant in metal-free OLEDs depends upon this process because triplet-to-singlet upconversion is required before the excitation energy is transferred by FRET to the emitter. We find the direct spin–orbit coupling between the CT states to be by far too small to explain the efficient triplet-to-singlet upconversion observed in experiment. Instead, we propose the following mechanism. Spin–orbit coupling between the singlet and triplet CT states is mediated by an energetically close-lying triplet state with leading πH−1 → πL∗ character. The main promoting mode, driving the system through a crossing with the Tππ∗ and the closeby Tnπ∗ and Snπ∗ states, is the carbonyl stretching vibration.

5

Acknowledgements

The author thanks Dr. Vidisha Rai-Constapel for technical assistance and Dr. Martin Kleinschmidt for valuable discussions. Financial support by the Deutsche Forschungsgemeinschaft through MA 1051/12-1 is gratefully acknowledged.

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Supporting Information Available Geometry parameters of all optimized states, calculated ground- and excited-state properties at all minima as well as SOMEs at selected points. This material is available free of charge via the Internet at http://pubs.acs.org/.

References (1) Pownall, H. J.; Huber, J. R. Absorption and Emission Spectra of Aromatic Ketones and their Medium Dependence. Excited States of Xanthone. J. Am. Chem. Soc. 1971, 93, 6429–6436. (2) Connors, R. E.; Christian, W. R. Origin of the Unusal Triplet-State Properties of Xanthone. J. Phys. Chem. 1982, 86, 1524–1528. (3) Cavaleri, J. J.; Prater, K.; Bowman, R. M. An Investigation of the Solvent Dependence on the Ultrafast Intersystem Crossing Kinetics of Xanthone. Chem. Phys. Lett. 1996, 259, 495–502. (4) Ley, C.; Morlet-Savary, F.; Fouassier, J. P.; Jacques, P. The Spectral Shape Dependence of Xanthone Triplet–Triplet Absorption on Solvent Polarity. J. Photochem. Photobio. A 2000, 137, 87–92. (5) Heinz, B.; Schmidt, B.; Root, C.; Satzger, H.; Milota, F.; Fierz, B.; Kiefhaber, T.; Zinth, W.; Gilch, P. On the Unusual Fluorescence Properties of Xanthone in Water. Phys. Chem. Chem. Phys. 2006, 8, 3432–3439. (6) Satzger, H.; Schmidt, B.; Root, C.; Zinth, W.; Fierz, B.; Krieger, F.; Kiefhaber, T.; Gilch, P. Ultrafast Quenching of the Xanthone Triplet by Energy Transfer: New Insight into the Intersystem Crossing Kinetics. J. Phys. Chem. A 2004, 108, 10072–10079. (7) Rai-Constapel, V.; Etinski, M.; Marian, C. M. Photophysics of Xanthone: A Quantum Chemical Perusal. J. Phys. Chem. A 2013, 117, 3935–3944. 15



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(8) Nakanotani, H.; Higuchi, T.; Furukawa, T.; Masui, K.; Morimoto, K.; Numata, M.; Tanaka, H.; Sagara, Y.; Yasuda, T.; Adachi, C. High-Efficiency Organic Light-Emitting Diodes with Fluorescent Emitters. Nat. Commun. 2014, 5, 4016–4022. (9) TURBOMOLE, a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989-2007, TURBOMOLE GmbH, since 2007; available from http://www.turbomole-gmbh.com as of July 2015. (10) Furche, F.; Ahlrichs, R. Adiabatic Time-Dependent Density Functional Methods for Excited State Properties. J. Chem. Phys. 2002, 117, 7433–7447. (11) Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648–5652. (12) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. 1988, B 37, 785–789. (13) Schäfer, A.; Huber, C.; Ahlrichs, R. Fully Optimized Contracted Gaussian Basis Sets of Triple Zeta Valence Quality for Atoms Li to Kr. J. Chem. Phys. 1994, 100, 5829–5835. (14) Barthel, J.; Buchner, R. High Frequency Permittivity and its Use in the Investigation of Solution Properties. Pure & Appl. Chem. 1991, 63, 1473–1483. (15) Klamt, A.; Sch¨ uu ¨rmann, G. COSMO: A New Approach to Dielectric Screening in Solvents with Explicit Expressions for the Screening Energy and its Gradient. J. Chem. Soc., Perkin Trans. 2 1993, 5, 799–805. (16) Schäfer, A.; Klamt, A.; Sattel, D.; Lohrenz, J. C. W.; Eckert, F. COSMO Implementation in TURBOMOLE: Extension of an Efficient Quantum Chemical Code Towards Liquid Systems. Phys. Chem. Chem. Phys. 2000, 2, 2187–2193. (17) Grimme, S.; Waletzke, M. A Combination of Kohn–Sham Density Functional Theory

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and Multi-Reference Configuration Interaction Methods. J. Chem. Phys. 1999, 111, 5645–5656. (18) Silva-Junior, M. R.; Schreiber, M.; Sauer, S. P. A.; Thiel, W. Benchmarks for Electronically Excited States: Time-Dependent Density Functional Theory and Density Functional Theory Based Multireference Configuration Interaction. J. Chem. Phys. 2008, 129, 104103. (19) Lyskov, I.; Kleinschmidt, M.; Marian, C. M. Redesign of the DFT/MRCI Hamiltonian. J. Chem. Phys. 2016, 144, 034104. (20) Hättig, C.; Weigend, F. CC2 Excitation Energy Calculations on Large Molecules Using the Resolution of the Identity Approximation. J. Chem. Phys. 2000, 113, 5154–5161. (21) Hättig, C.; Hellweg, A.; Köhn, A. Distributed Memory Parallel Implementation of Energies and Gradients for Second-Order Møller-Plesset Perturbation Theory with the Resolution-of-the-Identity Approximation. Phys. Chem. Chem. Phys. 2006, 8, 1159– 1169. (22) Marian, C. M. Spin–orbit Coupling and Intersystem Crossing in Molecules. WIREs Comput. Mol. Sci. 2012, 2, 187–203. (23) Neugebauer, J.; Reiher, M.; Kind, C.; Hess, B. A. Quantum Chemical Calculation of Vibrational Spectra of Large Molecules — Raman and IR spectra for Buckminsterfullerene. J. Comput. Chem. 2002, 23, 895–910. (24) Kleinschmidt, M.; Tatchen, J.; Marian, C. M. Spin–Orbit Coupling of DFT/MRCI Wavefunctions: Method, Test Calculations, and Application to Thiophene. J. Comput. Chem. 2002, 23, 824–833. (25) Kleinschmidt, M.; Marian, C. M. Efficient Generation of Matrix Elements for OneElectron Spin–Orbit Operators. Chem. Phys. 2005, 311, 71–79. 17



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(26) Hess, B. A.; Marian, C. M.; Wahlgren, U.; Gropen, O. A Mean-Field Spin–Orbit Method Applicable to Correlated Wavefunctions. Chem. Phys. Lett. 1996, 251, 365– 371. (27) Schimmelpfennig, B. Atomic Mean-Field Integral (AMFI) Program. University of Stockholm, 1996. (28) Tatchen, J.; Marian, C. M. On the Performance of Approximate Spin–Orbit Hamiltonians in Light Conjugated Molecules: The Fine-Structure Splitting of HC6 H+ , NC5 H+ , and NC4 N+ . Chem. Phys. Lett. 1999, 313, 351–357. (29) Danovich, D.; Marian, C. M.; Neuheuser, T.; Peyerimhoff, S. D.; Shaik, S. Spin–Orbit Coupling Patterns Induced by Twist and Pyramidalization Modes in C2 H4 : A Quantitative Study and a Qualitative Analysis. J. Phys. Chem. A 1998, 102, 5923–5936. (30) Kleinschmidt, M.; Tatchen, J.; Marian, C. M. Spock.CI: A Multireference Spin-Orbit Configuariation Interaction Method for Large Molecules. J. Chem. Phys. 2006, 124, 124101. (31) Marian, C. In Reviews In Computational Chemistry; Lipkowitz, K., Boyd, D., Eds.; 2001; Vol. 17; pp 99–204, Wiley-VCH, Weinheim (2001). (32) Schreiber, M.; Silva-Junior, M. R.; Sauer, S. P. A.; Thiel, W. Benchmarks for Electronically Excited States: CASPT2, CC2, CCSD, and CC3. J. Chem. Phys. 2008, 128, 134110. (33) El-Sayed, M. A. The Triplet State: Its Radiative and Nonradiative Properties. Acc. Chem. Res. 1968, 1, 8–16. (34) Englman, R.; Jortner, J. Energy Gap Law for Radiationless Transitions in Large Molecules. Mol. Phys. 1970, 18, 145–164.

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Table 1: Vertical absorption ∆Eabs and emission ∆Eem energies (eV) as well as adiabatic excitation energies ∆Eadia (eV) of ACRXTN. The electric dipole moments µ (Debye) and oscillator strengths f(r) were computed at the groundstate minimum. State

11 A′ 11 A′′ 21 A′′ 21 A′ 13 A′′ 13 A′ 23 A′′ 33 A′′

Electronic structure

(0.93) GS CT (0.80) πH → πL∗ LEX (0.76) nO → πL∗ LEX (0.70) πH−1 → πL∗ ∗ CT (0.79) πH → πL+1 LEX (0.63) πH−1 → πL∗ (0.10) πH−6 → πL∗ ∗ LEA (0.45) πH → πL+4 ∗ (0.18) πH → πL+5 ∗ LEX (0.67) nO → πL

DFT/ MRCI-R 0.00 3.09 3.61 3.83 3.03 3.25

∆Eabs RICC2 0.00 3.41 3.91 4.21 3.41 3.77

∆Eadia

3.35

3.73

3.18

—

—

2.54

—

3.42

3.63

3.17

3.04

2.61

1.96

—

TDDFT B3-LYP 0.00 2.50 3.60a 3.92b 2.50 3.13

∆Eem µ DFT/ MRCI-R — — 2.58 2.96 2.77 22.05 3.20 2.80 1.93 3.60 3.83 3.68 2.90 2.71 21.71 3.04 2.67 3.28

a

S3 state; S2 (3.56 eV) is a CT state in TDDFT(B3-LYP) calculation, found as S4 at 4.05 eV (DFT/MRCI-R) and at 4.30 eV in RI-CC2 b

S5 state; S4 (3.92 eV) is a CT state in TDDFT(B3-LYP) calculation, not found among the lowest six excited singlet states in DFT/MRCI-R and RI-CC2.

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f(r)

— 4 × 10−5 < 10−5 0.13442 — —


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Table 2: Vertical DFT/MRCI-R absorption energies ∆Eabs and electronic structures at the B3-LYP optimized ground-state minimum in acetonitrile. State 11 A′ 21 A′′ 21 A′ 11 A′′ 13 A′′ 13 A′ 23 A′′ 23 A′ 33 A′ 23 A′′

Electronic structure (0.92) GS CT (0.79) πH → πL∗ LEX (0.72) πH−1 → πL∗ LEX (0.74) nO → πL∗ CT (0.80) πH → πL∗ LEX (0.73) πH−1 → πL∗ ∗ LEA (0.50) πH → πL+4 ∗ (0.18) πH → πL+2 LEX (0.45) πH−6 → πL∗ (0.10) πH−7 → πL∗ LEX (0.45) πH−7 → πL∗ LEX (0.77) nO → πL∗

20

∆Eabs (eV) 0.00 3.11 3.76 3.81 3.05 3.20 3.39

µ (Debye) 3.84 23.00 5.16 1.55 22.70 5.08 3.75

3.54

3.99

3.61 3.62

4.65 1.52


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1'

2' 3'

9'a

4'

9' 10'

8'a 8' 7' 6'

4'a N

10'a 5'

4a 3 2

4 1 9a

ACRXTN

O

10a

10

5 8

9

6 7

8a O

Figure 1: Chemical structure and atom labeling of ACRXTN

21



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(a) nO

(b) πH−1

Page 22 of 24

(c) πH

∗ (d) πL

∗ (e) πL+1

∗ (f) πL+4

∗ (g) πL+5

Figure 2: Frontier orbitals at the optimized ground-state geometry (isovalue=0.03)

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4 Energy (eV)

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3.8 3.6 3.4 3.2 3 2.8 0

0.2 0.4 0.6 0.8 Reaction Coordinate

1

Figure 3: DFT/MRCI-R energy profiles along a linearly interpolated path connecting the singlet CT minimum (R=0.0) and the minimum of the S(nO π ∗ ) state (R=1.0). Solid lines: singlets; dahed lines: triplets; triangles: CT states, circles: nO πL∗ states; squares: ππ ∗ states with leading πH−1 πL∗ term; crosses and stars: ππ ∗ states resulting from positive and negative ∗ ∗ linear combinations of πH πL+4 and πH πL+5 .

23



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TOC Figure

N

O

3 ∗ nπ 3ππ∗

1

1

3

CT CT

3 ACRXTN

C O

O

24


CT 3nπ∗ 3 ∗ CT ππ

Mechanism of the Triplet-to-Singlet Upconversion in the Assistant

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