Climbing up the Ladder: Intermediate Triplet States Promote the

Article pubs.acs.org/JPCC

Climbing up the Ladder: Intermediate Triplet States Promote the Reverse Intersystem Crossing in the Efficient TADF Emitter ACRSA Igor Lyskov and Christel M. Marian* Institute of Theoretical and Computational Chemistry, Heinrich Heine University Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany S Supporting Information *

ABSTRACT: It is usually assumed that the reverse intersystem crossing (rISC) in organic TADF emitters occurs at the microsecond time scale. However, the underlying dynamics can be enhanced in the presence of low-lying nπ* states as stipulated by the El-Sayed rule. Here, we report a theoretical study of the short-time quantum dynamics of the ACRSA dye in different solvents following the electrical excitation. The wave packet propagation in multidimensional excited state potentials reveals the intersystem crossing (ISC) rate to be one or 2 orders of magnitude faster compared to the rISC process depending on the environment. Upon the molecular geometry distortions, the system rapidly converts the initial vibrational density to the valence excited-state potentials with subsequent change of spin state owing to spin−orbit interaction. We show that a local triplet ππ* state, residing on the acceptor moiety, mediates the nonradiative passage from triplet to singlet, thus increasing the quantum yield of light harvesting in OLED. This tandem interplay of vibronic and spin−orbit interactions favors the rISC to occur at the subnanosecond regime in ACRSA.

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INTRODUCTION Organic light-emitting diodes (OLEDs) based on thermally activated delayed fluorescence (TADF) arouse great interest due to their potentially high yield of electroluminescence, flexibility for synthesis and low fabrication cost compared to the traditional metal−organic emitters.1−5 Conventional TADF molecules represent bi- or multichromophoric systems consisting of weakly coupled donor and acceptor subunits that undergo a charge transfer (CT) process upon exciton generation. The donor and acceptor subunits are covalently linked in such a way that the respective π systems are (nearly) orthogonal, either by twisted single bonds or by a spirojunction. An electron−hole recombination in the emissive layer of the OLED forms 25% of singlet and 75% of triplet excitons with equal population of the respective sublevels as imposed by spin statistics. Contrary to the dyes containing heavy elements, where radiation emission originates from the triplet manifold owing to phosphorescence,6 the light harvesting transition in TADF is assigned to fluorescence. The initially populated singlet density relaxes rapidly to the S1 minimum and produces the prompt component of the fluorescence signal. Because molecular triplet excited states and the singlet ground state are coupled only weakly by electric dipole interaction, phosphorescence is not a competitive decay mechanism at room temperature in metal-free compounds. In the presence of spin− orbit (SO) interaction, the initial triplet density rather undergoes reverse intersystem crossing (rISC) to the excited singlet, which causes a delayed fluorescence thereupon. In this © 2017 American Chemical Society

spirit, the quantum yield of light emission in TADF is given by the sum of these two individual fluorescence components, which formally define the quality of a dye on a whole. Due to the small spatial overlap between the electron and hole densities of the CT exciton, the exchange interaction together with correlation effects split corresponding singlet and triplet energies by ∼0.1 eV. Such a small energy gap appears to be an important condition for efficient rISC, which can actually be activated thermally.4 However, the SO interaction between the singlet CT state and any of the triplet CT sublevels is typically negligibly small,7 which hampers the direct spin-forbidden transition and thus reduces the potentially high quantum yield of emission. This transition can be mitigated by considering local donor or acceptor triplet ππ* states, also called Frenkel excitons, which are energetically stabilized compared to their singlet counterparts and, therefore, are in a close proximity to the CT state.5 Important to note here, that the relative energy difference of the CT and local triplet excitons can be manipulated by doping a dye into matrices with different polarity.4,8 The small energy spacing results in pronounced vibronic interaction between the states of same spin symmetry induced by molecular geometry deformation as a consequence of second-order Jahn−Teller effects. This leads to the second critical determining factor of TADF, namely, the rate of energy Received: June 23, 2017 Revised: August 30, 2017 Published: September 6, 2017 21145

DOI: 10.1021/acs.jpcc.7b06187 J. Phys. Chem. C 2017, 121, 21145−21153

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The Journal of Physical Chemistry C

evolution of the dye under isolated conditions and in apolar media.

dissipation into low-lying locally excited states owing to vibronic coupling.4,7−11 In this sense, efficient rISC is brought about by vibronic and SO interactions of the low-lying Frenkel and charge transfer excitons. The rISC process in PTZDBTO2, as an example of a prototypical organic TADF dye, was recently investigated by means of quantum nuclear dynamics.9 As a result of strong vibronic interaction, even small SO-coupling of 2 cm−1 impels vibrational energy transfer from triplet to singlet in the microsecond time regime. It was also pointed out before that in the ACRXTN dye, which possesses a lone electron pair, large SO coupling is found between the locally excited states of the acceptor12 in accordance with the El-Sayed rule.13 In this case, the corresponding excited nπ* states are in energetic proximity to the CT states and, therefore, can be easily accessed. This necessitates to consider nπ* states as intermediates in TADF, which is supposed to open a new subnanosecond route of rISC. However, to our knowledge, no studies describing the rate constants of this process have been published so far. Understanding the photophysical properties of dyes with lowlying nπ* states will help in designing the ideal candidates with desirable properties to be utilized in the role of TADF dopants. 10-Phenyl-10H,10′H-spiro[acridine-9,9′-anthracen]-10′-one, hereinafter referred to as ACRSA (Figure 1), is one of the few

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COMPUTATIONAL DETAILS The electronic ground state (GS) geometry of ACRSA (C2v symmetry) was obtained by density functional theory, employing the semilocal B3LYP17 functional and the split valence atomic orbital basis set def-SV(P)18 as implemented in the Turbomole19 package. For treating environment effects on the excited state energies, we made a use of the continuum solvation model COSMO.20 The redesigned semiempirical DFT/MRCI-R21 method was employed for computations of excited state properties in conjunction with the tight set of empirical parameters allowing faster energy convergence with respect to the truncation of the configuration space. Furthermore, we tested the sensitivity of the DFT/MRCI-R vertical excitation energies with regard to the atomic orbital basis. The vertical energy variance of the relevant states does not exceed a value of 0.05 eV when going from SV(P) to a primitive-rich augmented cc-pVTZ basis (see Table S1 in the Supporting Information). Therefore, we used the smaller SV(P) basis for solving the electronic part of the problem throughout this paper. Spin−orbit matrix elements between electronic wave functions were computed with the SPOCK module,22,23 replacing the two-electron part of the Breit-Pauli spin−orbit operator by a mean-field approximation. The quantum dynamics were performed with the MCTDH24,25 package, the calculation setup of which is given in the next sections. Emission spectra were determined using a Fourier transform approach as implemented in the VIBES program.26 The Fourier transformations of the time-correlation functions were performed using a Gaussian damping function of 50 cm−1 width at half-maximum. Vibrational frequencies and normal modes were obtained by numeric differentiation of (TD)DFT gradients employing SNF.27 Because the S1 →S0 electric dipole transition is symmetry forbidden in Franck−Condon approximation, vibronic interaction was included in a Herzberg− Teller coupling model.28 The derivative couplings were determined numerically at the DFT/MRCI-R level of theory. To this end, the molecule was distorted from the S1 minimum geometry along all a2, b1, and b2 normal modes by ±0.05 units in dimensionless normal coordinates. Fluorescence rate constants were obtained by numerical integration of the spectral intensities.

Figure 1. Chemical structure of ACRSA.

spiro compounds known to exhibit efficient TADF.14−16 This bichromophoric system consists of weakly coupled donor and acceptor moieties, which are covalently linked by a spirojunction in such a way that the respective π systems are orthogonal. The TADF in ACRSA was assumed to originate from a charge-transfer transition as supported by density functional theory (DFT) calculations, showing that the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) reside on different molecular parts.14 While the HOMO is located mainly on the acridinium moiety, the LUMO is centered predominantly on the anthracenone moiety. Using ACRSA as a blue-green emitter, a high-performance third-generation organic lightemitting diode was achieved.14 Also, more recently, ACRSA was utilized as assistant dopant in a hyperfluorescent OLED in which the TADF dye does not luminesce itself but rather transfers its excitation energy to a strongly fluorescent partner by a Förster mechanism.15 This work aims to show the effect of energetically low-lying nπ* electronic states on the efficiency and rate of ISC and rISC in ACRSA. Here, we present the results of wave packet propagation in the picosecond time regime among multidimensional excited-state potential energy surfaces following electrical exciton generation. By going beyond the Born−Oppenheimer limit in constructing a time-dependent spin-vibronic Hamiltonian, we will arrive at a comprehensive picture of spin state

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RESULTS AND DISCUSSIONS Vertical Energies and Electronic Structure of Excited States. Within an energy interval of 0.3 eV, six electronically excited states (two singlets and four triplets) are found in the gas phase. Among them are two states of A2 symmetry in each multiplicity aroused by linear combinations of dark CT and nπ* configurations. The remaining two triplets 13B2 and 13A1 stem from Frenkel excitons on the acridine π2π2* and anthracenone π 1 π 1* moieties, correspondingly. As mentioned in the Introduction, the spectral position of the CT states, which possess large static dipole moments, and the remaining locally excited states depend to a large extent on the environment. The relative energy differences are of a great importance for the kinetic properties of the TADF dye.9 In the scope of this paper, we investigate the photophysical properties of ACRSA in vacuum, apolar toluene (ϵ = 2.38) and polar acetonitrile (ϵ = 21146


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introduced a versed assumption constituting that, due to the small overlap of exciton densities and 1/r3 dependence of the spin−orbit Hamiltonian on the interparticle distance, the SO matrix elements of the CT and ππ* states are zero and that thus the entire LS-amplitude in the adiabatic basis originates from the interaction of the local ππ* and nπ* states. By solving a system of trivial equations, this assumption allows us to estimate the vertical energies of the coupled states and the magnitudes of their vibronic coupling at the FC point as tabulated in Table 2. The coupling constants in vacuum are λ012

37.5) solutions. In order to better illustrate the effect of different environments on the excited state energies, we split ACRSA into its constituent fragments, i.e., acridinium and anthracenone moieties (acr. and ant.). Inspection of Table 1 Table 1. DFT/MRCI Vertical Excitation Energies E (eV) of Low-Lying Electronic States in Vacuum (vac), Toluene (tol), and Acetonitrile (acn) of ACRSA and Its Isolated Anthracenone (fr. ant.) and Acridinium (fr. acr.) Fragmentsa system

state

character

E (vac)

E (tol)

E (acn)

ACRSA

11A2 21A2 13A2 23A2 13B2 13A1 11A2 13A2 13A1 13B2

nπ*1 + π2π*1 nπ1* − π2π1* nπ1* + π2π1* nπ*1 − π2π*1 π2π2* π1π1* nπ*1 nπ*1 π1π1* π2π2*

3.41 3.56 3.24 3.40 3.31 3.38 3.54 3.27 3.35 3.31

3.32 3.61 3.22 3.45 3.34 3.33 3.63 3.43 3.41 3.35

3.21 3.71 3.12 3.55 3.32 3.44 3.73 3.54 3.41 3.32

fr. ant.

fr. acr.

Table 2. Nonadiabatic State Energies and Coupling Constants E (eV) of ACRSA at the Ground State Geometry in Vacuum, Toluene, and Acetonitrile

The set of (n,π1,π1*) orbitals resides on anthracenone the moiety and (π2,π2*) on the acridinium moiety.

a

reveals that the monomeric energies of valence triplet ππ* states exhibit small change in different solvents. They both rise up only by hundredths of an electronvolt going from vacuum to the high-permittivity medium acetonitrile. Almost exactly the same energy shift is seen for 13B2 in ACRSA. By contrast, the energies of 13A1 in ACRSA do not follow the trend of the monomer calculation. We recall, however, the fact that an environment stabilizes also the second lowest triplet CT exciton of A1 symmetry, which in turn changes the adiabatic energy of the π1π1* state in ACRSA. The computed blue shifts in toulene are 0.09 eV for singlet and 0.16 eV for triplet, and even more pronounced in acetonitrile  0.19 eV for singlet and 0.27 eV for triplet nπ* state. Contrary to the local ππ* states, the implicit solvation vastly influences the DFT/MRCI energies of the nπ* states computed for anthracenone fragment. Similar trends have been observed in many aromatic ketones.29−33 Bearing in mind the fact that the higher dielectric constant of a solvent the lower CT state relative to its energy position in vacuum, one can notice in Table 1 a similar behavior of first and second mixed adiabatic states in ACRSA. Because an electron and its conjugated hole of 13B2 and 13A1 excitons are situated mostly either on one or the other chromophore, we will assume that, at the ground state geometry, there is no need to employ a diabatization procedure to adapt them to the MCTDH protocol. This is distinctively different for the adiabatic A2 states, however. The strong mixture of configurations in the 1A2 and 2A2 wave functions and their small energy splitting for both singlet and triplet multiplicities indicates that the two underlying nonadiabatic states interact with nonzero strength at the Franck−Condon (FC) center. At this point, we exploit the spin−orbit (SO) properties of the DFT/MRCI wave functions to arrive at a quasidiabatic (called nonadiabatic hereinafter) state representation and estimate the magnitude of vibronic coupling among them at the molecular GS. Analysis of the pairwise SOinteraction of the adiabatic wave functions reveals a pronounced LzSz coupling between first and second 1/3A2 states and the triplet 13A1 locating on the anthracenone moiety (see Table S3 in the Supporting Information). Herein, we

sym.

type

E (vac)

E (tol)

E (acn)

11A2 21A2 13A2 13B2 13A1 23A2

c.t./ππ* ant./nπ* c.t./ππ* acr./ππ* ant./ππ* ant./nπ* λ012 λ034 bz

3.452 3.519 3.355 3.306 3.376 3.290 0.071 0.075 0.0035

3.336 3.593 3.253 3.343 3.332 3.419 0.075 0.080 0.0036

3.223 3.704 3.137 3.329 3.444 3.535 0.074 0.079 0.0035

= 0.071 eV − between the two singlet A2 states, λ034 = 0.075 eV − between two the triplet A2 states, and very similar values were found in toluene and acetonitrile. As expected, the CT exciton energies are shifted down and the nπ* excitons are shifted energetically up by the presence of the environment, which is in agreement with the monomer results. The nonadiabatic and adiabatic state densities in vacuum are shown in Figure 2. The density difference plots pictorially show that the resulting nonadiabatic A2 states have a plain character of either CT or nπ* excitons. Consequently, the corresponding z-components of the SO matrix in nonadiabatic states representation are determined to be az = −27.4i cm−1 between 3(nπ*) and 3(ππ*) and bz = −28.6i cm−1 between 1(nπ*) and 3(ππ*) in vacuum. Note that az and bz are reduced to zero for some triplet spin components due to the selection rules imposed by the spin double group. All nonvanishing coupling terms at the FC point are graphically depicted in Figure 3. Before elaborating on Jahn−Teller effects, let us recognize that all other SO-terms do not exceed 1.5 cm−1 and, therefore, by analogy to the PTZ-DBTO2 dye, contribute to the population transfer at the nanosecond time scale, which is beyond the time scope of our actual work. Also, these neglected x- and y-components of the spin−orbit Hamiltonian drive the spin relaxation dynamics and are responsible for the population equilibration among the triplet sublevels. In this work we disregard the role of ms= ± 1 sublevels in the shorttime ISC processes and do not consider them in our vibronic model. Molecular Vibrations. Because the equilibrium GS geometry arranges the nuclear framework in the C2v point group, all vibrational modes transform under a1, a2, b1 and b2 representations. In this work, symmetry-adapted internal coordinates qi as computed in the limit of harmonic approximation are used to characterize the nuclear displacements and electronic PESs along them. We briefly discuss important normal distortions, which induce intra- and interstate 21147


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Figure 2. Ground and excited-state density differences of ACRSA. Red and blue colors denote electron and hole density localization, respectively.

molecular symmetry to Cs with the preserved mirror plane orthogonal or coplanar to the acridinium fragment, respectively. Consequently, b1 modes mediate a coupling between 13B2 and 3 A2 states, and b2 modes mediate a coupling between 13B2 and 3 A2 states. In this case, we define nonadiabatic 1D PES of the states, the wave functions of which are transformed under the identical irreducible representation upon either a2, b1, or b2 deformation, as topologically nested curves and shifted with respect to each other by the constant energy interval consistent with the energy gap at the FC center. Therefore, the curvature of adiabatic PESs along the aforementioned nontotally symmetric distortions is solely defined by the interstate coupling parameters. To lowest order, the interstate coupling strength λnmj between two electronic states n and m along a coordinate qj is described as a function linearly dependent on the coordinate:

Figure 3. Graphical representation of nonzero spin−orbit (az and bz) and vibronic (λ012 and λ034) interactions between low-lying states of ACRSA at the GS geometry.

vibronic coupling and which are used thereafter for solving the electron−nuclear dynamics problem. The Franck−Condon active modes a1 retain the molecular C2v symmetry so that they tune the relative energy position of all six excited states. The nonadiabatic one-dimensional (1D) excited state profiles along the a1 distortions were described by shifted frequency-modified harmonic potentials: ωj unn(qj) = − qj2 + γnj(1)·qj + γnj(2)·qj2 2 where qj is a normal molecular displacement in dimensionless units and ωj its characteristic harmonic frequency of the GS potential. Let us stress that the a1 deformations modulate the vibronic coupling between nonadiabatic A2 states as imposed by symmetry constraints, which is taken into account by adding the displacement-dependent offdiagonal energies into the Hamiltonian. The second class of distortions are nontotally symmetric, so-called, coupling modes. The a2 Jahn−Teller distortions reduce the C2v symmetry to C2 and leave A2 and A1 states in the A irreducible representation allowing them to interact. At the same time, the b1 or b2 modes reduce the

0 1 λnmj(qj) = λnm + λnmj ·qj

where λ0nm is a coupling constant at the GS geometry. The (2) 1 entire set of PES parameters γ(1) nj , γnj and λnmj is subject to sequential iterative optimizations minimizing the polynomial regression error to fit the precomputed DFT/MRCI state energies. In this sense, the diagonalization of the parametrized nonadiabatic potential energy matrix regains the adiabatic energies which were subsequently compared with DFT/MRCI results to represent them optimally at every point qj. While the geometry of the CT state minimum as optimized within TDDFT theory does not change significantly with respect to the geometry of the GS, the relaxation of the nπ* state extends the CO bond distance from 1.22 to 1.31 Å in all environments, stabilizing the nπ* state energy by ∼0.3 eV. The aforementioned bond elongation is solely represented by

Figure 4. One-dimensional q138 cut through excited PESs of ACRSA in different environments. 21148


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The Journal of Physical Chemistry C the high-energy normal mode with harmonic frequency ω138 = 1763 cm−1 in vacuum, ω138 = 1751 cm−1 in toluene and ω138 = 1732 cm−1 in acetonitrile. Figure 4 displays distinctively different pictures of 1D PESs along q138 for the different environments. In vacuum, the 3(ππ*) and 1(nπ*) potentials dive below the initially populated CT excitons upon the nuclear displacement. The energy difference between the minima of the 3 (CT) and 3(ππ*) PESs is 0.06 eV and between the minima of the 3(CT) and 1(nπ*) is 0.1 eV. Futhermore, the potential curve crossings are in the vicinity of the FC center and are energetically lower than the CT energy at q138 = 0. In contrast, toluene does not stabilize the energy of the ππ* Frenkel excitons relative to the 3(CT) state minimum. The q138 distortion aligns the minima of the 3(ππ*) and 1(nπ*) PESs almost at a resonance energy. In contrast to the vacuum case, we observed a small energy barrier of 0.02 eV between the triplet CT energy at the FC point and the crossing coordinates of the 3(ππ*) and 1(nπ*) 1D surfaces. This barrier is, however, much higher for ACRSA dissolved in acetonitrile ∼0.4 eV, and >1.0 eV for climbing up to the crossing of the triplet CT and 3 (ππ*). Such a drastic change of these key features of the PESs is obviously due to the environmental effect on the exciton energies at the FC center, since not a big difference in optimized PES parameters γ(1), γ(2), and λ1 was found for various solvents along q138 distortions. In addition, our vibronic Hamiltonian encompasses the q23 mode of a1 symmetry with ω38 = 381 cm−1. This mode causes an in-plane deformation of the acridinium fragment of ACRSA where a bunch of lowenergy barriers of the PES crossings was detected near the FC point in vacuum. Based on a preliminary comparative analysis of λ1nmj in vacuum, we comprise two normal modes of a2 symmetry, two modes of b1 symmetry and one mode of b2 symmetry into the vibronic Hamiltonian as documented in Table S4 of the Supporting Information.34 Their counterparts were identified in COSMO calculations and induced interstate coupling constants were estimated for ACRSA in toluene and acetonitrile. It appears important to consider low energy coupling modes, for example, a spiro twisting vibration q5 of a2 symmetry with ω5 = 60 cm−1 in vacuum. Their inclusion is motivated by the fact that the population upconversion and thus the complete rISC kinetics crucially rely on the energy supply either in its thermal or kinetic form, which can be borrowed from the potential energy component of the underlying Hamiltonian. Hence, due to the small energy spacing, excited vibrational levels of the ω5 mode can be populated which potentially enhances the population transfer from the triplet CT to the rISC productive 13A1 state. The complete set of 1D PES incorporated into the vibronic Hamiltonian is found in Figure S2 of the Supporting Information.34 By the end, we shall characterize a change of SO interaction in the nonadiabatic basis along the nuclear displacements. Let us consider, for example, the vivid LzSz-coupling between the 13A1 state and the singlet A2 states along q38 (Figure 5b). As it was discussed in the beginning of this chapter, the 3(nπ*) gauges the adiabatic-nonadiabatic transformation t of the A2 states. Figure 5a illustrates the outcome of this transformation as applied to the canonical basis of DFT/MRCI wave functions (black circles are the corresponding energies) leading to two fitted nonadiabatic 1D PES (colored curves). At each coordinate q38, the rotation matrix t was set in such a way, that the back-transformed adiabatic energies (gray curves) match best the precomputed adiabatic data. Thus, in order to

Figure 5. (a) circles: computed relative 11A2 and 21A2 state energies along q38 coordinate; gray: adiabatic PES of 11A2 and 21A2 states; colored: nonadiabatic PES. (b) circles: computed z-compotent of spin−orbit operator between adiabatic 11A2/21A2 and 13A1 states; triangles: z-component of spin−orbit operator between nonadiabatic states.

obtain spin−orbit coupling terms in the rotated basis, the transformation t has to be applied accordingly at every point of q38: t−1Rit where Ri stands for the precomputed ith Cartesian component of the SO matrix in the adiabatic representation. As a result of this transformation, we found that in most cases the molecular distortions do not change significantly the magnitude of the SO-interaction at the FC center (see Figure 5b), unless energetically higher lying states are brought into the play upon the nuclear displacements of large amplitudes. For the sake of simplicity, the SO-coupling terms are kept constant in regard to their values at the ground state geometry (Table 2). Let us point out that the magnitudes of the SO interaction between the adiabatic states at q38 ≈ −0.8 are equivalent. This can come about only when the amplitudes of the base electron configurations (nonadiabatic wave functions) enter the DFT/ MRCI vectors in half-by-half ratio, and, hence, the nonadiabatic energies are expected to be equal at this point. This is really the case, as seen in Figure 5a, which corroborates the good quality of the employed spin−orbit adapted diabatization scheme. MCTDH Setup. Finally, we start composing the Hamiltonian which is used in the MCTDH production runs. The multidimensional PES was constructed with the help of the linear vibronic coupling model,35 representing a linear sum of 1D surfaces along seven degrees of freedom. Assigning the diagonal elements H11, H22, H33, H44, H55, and H66 to the PESs corresponding to the nonadiabatic 11A2, 21A2, 13A2, 23A2, 13B2, and 1 3 A1 electronic states, the resulting spin-vibronic Hamiltonian reads: 21149


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The Journal of Physical Chemistry C H=E−

∑ j

⎞ ωj ⎛ ∂ 2 2⎟ ⎜ − +U q 1 j ⎟ 6×6 2 ⎜⎝ ∂qj2 ⎠

⎡ ϵ λ0⎤ 1 12 ⎥ E[12] = ⎢ E = ⎢⎣ λ 0 ϵ ⎥⎦ [26] 12 2

Results of Quantum Dynamics. The initially excited wave packet was propagated in the constructed six-state-seven-mode potential manifold for 100 ps. Figure 6 shows the population evolution of the singlet excited states of ACRSA. The populations of the triplet excited states are documented in Figure S3 in the Supporting Information.34

⎡ ϵ b† ⎤ ⎢ 2 z⎥ ⎢⎣ b ϵ ⎥⎦ 6 z

⎡ ϵ λ0 ⎤ ⎡ ϵ5 0 ⎤ 3 34 ⎥ ⎥ E[34] = ⎢ E[56] = ⎢ ⎢λ 0 ϵ ⎥ ⎣ 0 ϵ6 ⎦ ⎣ 34 4 ⎦ U[nn] =

∑ (γnj(1)·qj + γnj(2)·qj2) j

U[nm] =

1 ·qj ∑ λnmj

(1)

j

where index j runs over all seven degrees of freedom. The first matrix E, nonvanishing elements of which are shown in the E[nm] submatrices, is built from vertical excitation energies ϵ and interaction terms at the GS geometry in accordance with Figure 3 and Table 2. The second matrix lists kinetic components of all incorporated nuclear degrees of freedom and their conjugated harmonic potentials in the electronic ground state. The third matrix U contains corrections for harmonic frequencies γ(2) nj adopted for excited states, as well as intraγ(1) and interstate λ1nmj coupling terms induced by nuclear nj distortions qj among the six considered electronic states. The Hamiltonian H for the six-state system was treated within the fully quantal, time-dependent scheme of wave packet propagation as formulated in MCTDH. In the MCTDH25,36 scheme, the wave function which describes the molecular dynamics of a system with f degrees of freedom is written as a linear combination of Hartree products as follows: Ψ(q1 ,..., qf , t ) =

n1

nf

j1

jf

f

∑ ... ∑ A j ... j (t ) ∏ ϕj(k)(qk , t ) 1

f

k=1

Figure 6. Time-dependent population of the singlet excited states of ACRSA in vacuum, toluene, and acetonitrile following the triplet CT exciton formation.

k

(2)

Here q1,...,qf are a set of the nuclear coordinates, Aj1...jf denote the time-dependent expansion coefficients, and ϕ(k) jk (qk,t) are a set of time-dependent single-particle functions. To reduce the computational time demands, seven degrees of freedom were grouped together into three generalized MCTDH-particles and the multiset formalism for building the vibrational wave functions of each electronic state was employed. The timedependent single-particle functions of each combined degree of freedom were described by the Hermite DVR. The complete information about the MCTDH basis is found in Table S4 in the Supporting Information.34 At first, the vibrational wave function was relaxed in the harmonic ground state potentials. Then the resulting wave packet was lifted vertically upward to the position of the triplet CT potential with zero kinetic momentum, thereby mimicking an electrical generation of the triplet exciton. Subsequently, the wave packet evolves in time on the seven-dimensional potential energy surfaces of six coupled electronic states in the absence of energy dissipation and spin relaxation among the triplet sublevels. We carried out three MCTDH propagations by incorporating different PESs in to the Hamiltonian (1) as calculated for vacuum, toluene, and acetonitrile and by utilizing slightly modified bases for the MCTDH wave functions.

According to the model Hamiltonian, the SO interaction bz between the locally excited 1(nπ*) and 3(ππ*) states on the acceptor moiety of ACRSA is the only productive channel for population of the singlet states. Hence, for rISC to occur, the initial vibrational density must ladder up at first to the 13A1 potential, which is facilitated by activities of a2 molecular distortions. As seen from Figure S3, within the first picosecond the anthracenone’s triplet ππ* PES gains 10% and 7% of the initial population for ACRSA in vacuum and in toluene, correspondingly. In acetonitrile, the 3(ππ*) population curve stabilizes much longer and straightens out only after 40 ps of the propagation time. After the wave packet density has been accommodated on the 13A1 surfaces, the singlet nπ* population begins rising up. Within the framework of our Hamiltonian, a time span of 50 ps is enough to complete the rISC process originating from the ms = 0 sublevels with a yield of 10% for the vacuum case and 5% for toluene as Figure 6 displays. Hereinafter, the singlet populations changes insignificantly in time. Because the minima of the singlet CT and nπ* PESs are almost isoenergetic in toluene, the entire singlet wave packet density is distributed equally among their surfaces. The ACRSA excited state dynamics in acetonitrile environment is much 21150


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constant krISC was retrieved to be 3.50 × 109 s−1 in vacuum, 2.30 × 109 s−1 in toluene at 0 K. These are quite ordinary values for El-Sayed allowed transitions, which are translated into lifetime constants of the triplet ms = 0 component of 290 and 430 ps, correspondingly. The same order of krISC, i.e., 109 s−1, was previously deduced from measurments of a number of TADF dyes.37 Therein, the authors ascribe this enhancement of the rISC constant to the presence of low-lying triplet and singlet nπ* states and propose a TADF mechanism, which embraces five electronic states. However, usually such high krISC is not determined in experiments due to the fact that these types of emitters are studied by doping them into polar host materials or in solid film. A polar environment destabilizes nπ* energies and stabilizes CT exciton energies, by that deteriorating the efficient rISC pathway. In this sense, a dye demonstrates photophysical properties similar to regular conjugated π-system emitters.38−41 Thus, our estimated krISC and kISC values for ACRSA in acetonitrile (2.61 × 107 s−1 and 4.59 × 108 s−1) are not much different from corresponging values in the related ACRFLCN molecule with altered acceptor fragment for which a value of kISC = 7.4 × 107 s−1 was reported.16 A recent B3LYP study42 of the ACRSA dye relies on the semiclassical Marcus approach for calculating the rISC and ISC rates between singlet and triplet CT states which are mediated by SO coupling of 0.05 cm−1. The rates were found to be 1.29 × 104 s−1 and 6.10 × 104 s−1, which are of course reasonable in the absence of the intermediates. This is, likely, due to the well-known methodological deficiency of semilocal DFT functionals lacking a balanced description of CT and locally excited states leading to an artificial overstabilization of CT energies.43 Therefore, using TDDFT optimized potentials, the decisive role of valence excited states in the rISC mechanism can easily be overlooked. Overall, the underlying vibronic and SO couplings among local and CT excitons yield fast formation of singlet excitons as mitigated by the thermodynamical factors. The resulting singlet density causes then the delayed component of electroluminescence. The authors of ref 42 assign the light emission to occur from the second conformer of ACRSA being a result of a twist of the phenyl ring. The distorted system gains nonzero oscillator strength, yielding a radiation rate of kF = 1.81 × 105 s−1 in gas phase. However, DFT predicts the energy barrier between the conformers on the CT surface to be as large as 1 eV, and thus this emissive mechanism is hardly possible. Although the emission from 1A2 states in the C2v symmetric conformer is dipole forbidden they can couple to the optically bright higher-lying states by virtue of vibronic forces, thus borrowing nonzero oscillator strength in the second-order perturbative ansatz. Fluorescence rate constants were computed for ACRSA in vacuum, toluene, and acetonitrile at room temperature. The most active Herzberg−Teller coupling modes are found in the a2 and b1 irreducible representations. Modes q20 (ω20 = 309 cm−1) and q36 (ω36 = 571 cm−1) represent a2symmetric out-of-plane distortions of the acridine and anthracenone moieties which couple S1 to close-by bright 1A1 states. Modes q91 (ω91 = 1111 cm−1) and q106 (ω106 = 1251 cm−1) correspond to b1-symmetric in-plane deformations of the anthracenone moeity which couple S1 to close-by bright 1B2 states. Fluorescence emission from the S1 state is seen to proceed on the microsecond time scale (Table 3). In Herzberg−Teller approximation fluorescence rate constants of kF = 1.4 × 106 for vacuum, kF = 1.1 × 106 for toluene solution, and kF = 0.9 × 106 for acetonitrile solution are obtained.

slower than in vacuum and toluene. Only 2% of the evolving wave packet is attributed to the singlet PESs after 0.25 ns and their population keeps rising up. Such a variation of the rISC yield can be understood by addressing to the decisive PES features along the CO stretching shown in Figure 4. As already discussed, the initial wave packet needs a vast quantity of free energy to overcome such large thermodynamic barriers for efficient rISC in acetonitrile. Thereby, the vibrational density transfer from the triplet CT to the valence states occurs solely by stationary tunneling, stipulating a slow increase of the singlet populations. According to second-order perturbation theory, the rISC rate depends on the energy gap between intermediate 3(ππ*) and the final 1(nπ*) state, thus reducing the energy requirement for the transfer.10 In this regard, despite large SO interaction, the rISC time scale of ACRSA in acetonitrile is comparable with organic emitters in which n orbitals are absent. The barrierless wave packet passage toward the singlet potentials through the triplet CT and 3(ππ*) crossing and the 3(ππ*) and 1(nπ*) crossing in vacuum favors the rISC dynamics in comparison with toluene environment. Based on this fact, one can assume that the rISC rate constant in vacuum is temperature independent and that the delayed fluorescence originates from the nonthermal component of the triplet wave packet. The successive transition from triplet CT to the singlet nπ* in toluene involves a small barrier of 0.02 eV. This small activation energy can indeed be brought about by thermal supply. Alternatively, which is more likely, the barrier height can be reduced by displacement along the q 23 coordinate. We, however, stress here that an effect of temperature on the rISC process in ACRSA solute in different environments must be studied in detail and quantitatively assessed, which is the subject of our forthcoming research. At this instance, we suppose that the rate of 3(CT) ⇝ 3(ππ*) internal conversion is much higher than the rate of the ensuing 3 (ππ*) ⇝ 1(nπ*) transition in vacuum and toluene. Based on this assumption, the transition dynamics and the quantum yield of singlet formation can be described by a balanced trade-off between rISC krISC and ISC kISC processes: k rISC

Tall ←→ Sall kISC

where Tall and Sall are the combined populations of the triplet and singlet states, respectively. The analytical solution for the simplified kinetic equation reads: [Sall] =

k rISC (1 − e−(krISC+ kISC)t ) 3(k rISC + kISC)

(3)

with an equilibrium singlet concentration of krISC/3(krISC + kISC) at t → ∞. The scaling factor of 1/3 is introduced because we have propagated only the third part of the total triplet density which is allocated for ms = 0. The expression 3 was used for fitting of the MCTDH results to give an estimate for the rISC and ISC rates documented in Table 3. The reaction Table 3. RISC krISC, ISC kISC, and Fluorescence kF Rate Constants (s−1) in Acrsa Solute in Vacuum, Toluene and Acetonitrile

vac tol acn

krISC (0 K)

kISC (0 K)

kF (300 K)

3.50 × 109 2.30 × 109 2.61 × 107

1.09 × 1011 1.36 × 1011 4.59 × 108

1.4 × 106 1.1 × 106 0.9 × 106 21151



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Comparing these results with the rate constants for ISC and rISC in vacuum and toluene, we find that the fluorescence occurs on a time scale of 3 orders of magnitude slower. The initial triplet vibrational density is rapidly spread over the singlet and triplet potentials toward its stationary distribution with subsequent activation of light emission. It may be concluded that in vacuum and toluene environment the kF is the rate-determining step for harvesting of delayed fluorescence which originates from ms = 0 triplet density. This, however, might be controversial for ms= ± 1 components, since the triplet-to-singlet transition dynamics is not expected to be fast. The computed rate constant for toluene compares well with the experimental results of 175 ns for the transient decay time of emissive state.14 One should note thatapart from the fluorescencethe depletion of the 1(CT) state incorporates also the population decay owing to the ISC, and therefore the actual experimental fluorescence time kF is somewhat longer than 175 ns. In polar aprotic environments such as acetonitrile, the decay kinetics is more involved. In this case, the three rate constants are comparable and it seems difficult to unambiguosly assign the rate-determining transition.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +49-211-8113209. Fax: +49-211-8113446. ORCID

Christel M. Marian: 0000-0001-7148-0900 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful to Deutsche Forschungsgemeinschaf t (DFG) for financial support through project MA1051/17-1. REFERENCES

(1) Adachi, C. Third-Generation Organic Electroluminescence Materials. Jpn. J. Appl. Phys. 2014, 53, 060101. (2) Wong, M. Y.; Zysman-Colman, E. Purely Organic Thermally Activated Delayed Fluorescence Materials for Organic Light-Emitting Diodes. Adv. Mater. 2017, 29, 1605444. (3) Im, Y.; Kim, M.; Cho, Y. J.; Seo, J.-A.; Yook, K. S.; Lee, J. Y. Molecular Design Strategy of Organic Thermally Activated Delayed Fluorescence Emitters. Chem. Mater. 2017, 29, 1946−1963. (4) Yang, Z.; Mao, Z.; Xie, Z.; Zhang, Y.; Liu, S.; Zhao, J.; Xu, J.; Chi, Z.; Aldred, M. P. Recent Advances in Organic Thermally Activated Delayed Fluorescence Materials. Chem. Soc. Rev. 2017, 46, 915−1016. (5) Dias, F. B.; Penfold, T. J.; Monkman, A. P. Photophysics of Thermally Activated Delayed Fluorescence Molecules. Methods Appl. Fluoresc. 2017, 5, 012001. (6) Baryshnikov, G.; Minaev, B.; Ågren, H. Theory and Calculation of the Phosphorescence Phenomenon. Chem. Rev. 2017, 117, 6500− 6537. (7) Marian, C. Spin-Orbit Coupling in Molecules. In Reviews In Computational Chemistry; Lipkowitz, K., Boyd, D., Eds.; Wiley-VCH: Weinheim, Germany, 2001; Vol. 17, pp 99−204. (8) Etherington, M. K.; Gibson, J.; Higginbotham, H. F.; Penfold, T. J.; Monkman, A. P. Revealing the Spin-Vibronic Coupling Mechanism of Thermally Activated Delayed Fluorescence. Nat. Commun. 2016, 7, 13680. (9) Gibson, J.; Monkman, A. P.; Penfold, T. J. The Importance of Vibronic Coupling for Efficient Reverse Intersystem Crossing in Thermally Activated Delayed Fluorescence Molecules. ChemPhysChem 2016, 17, 2956−2961. (10) Gibson, J.; Penfold, T. J. Nonadiabatic Coupling Reduces the Activation Energy in Thermally Activated Delayed Fluorescence. Phys. Chem. Chem. Phys. 2017, 19, 8428−8434. (11) Nobuyasu, R. S.; Ren, Z.; Griffiths, G. C.; Batsanov, A. S.; Data, P.; Yan, S.; Monkman, A. P.; Bryce, M. R.; Dias, F. B. Rational Design of TADF Polymers Using a Donor−Acceptor Monomer with Enhanced TADF Efficiency Induced by the Energy Alignment of Charge Transfer and Local Triplet Excited States. Adv. Opt. Mater. 2016, 4, 597−607. (12) Marian, C. M. Mechanism of the Triplet-to-Singlet Upconversion in the Assistant Dopant ACRXTN. J. Phys. Chem. C 2016, 120, 3715−3721. (13) El-Sayed, M. A. The Triplet State: Its Radiative and Nonradiative Properties. Acc. Chem. Res. 1968, 1, 8−16. (14) Nasu, K.; Nakagawa, T.; Nomura, H.; Lin, C.-J.; Cheng, C.-H.; Tseng, M.-R.; Yasuda, T.; Adachi, C. A Highly Luminescent SpiroAnthracenone-Based Organic Light-Emitting Diode Exhibiting Thermally Activated Delayed Fluorescence. Chem. Commun. 2013, 49, 10385−10387. (15) 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. (16) Méhes, G.; Nomura, H.; Zhang, Q.; Nakagawa, T.; Adachi, C. Enhanced Electroluminescence Efficiency in a Spiro-Acridine De-

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CONCLUSIONS In this paper we have described the ISC mechanism supervening the exciton formation in ACRSA solute in environments of different permittivity. By constructing the spin-vibronic Hamiltonian for the wave packet propagation among six electronic potentials of close-lying excited states with unique inter- and intra state coupling parameters for each solvent, we arrived at a detailed physical picture of the exciton dynamics. By virtue of the strong spin−orbit interaction, initially populated triplet CT density undergoes a rapid passage to singlet PESs mediating the population of Frenkel excitons locating on the acceptor fragment of ACRSA. The depopulation time of the CT states in ACRSA occurs in the picosecond regime in vacuum and in apolar toluene, whereas it proceeds in the nanosecond regime in the polar solvent acetonitrile. To this end, we affirm that triplet-to-singlet decay is driven by vibronic and spin−orbit forces and crucially relies on the thermodynamic features of the excited PESs. Clearly, the low-lying nπ* states significantly speed up the rISC transition compared to the TADF emitters where only ππ* excitons are energetically accessible. The fluorescence in ACRSA proceeds in a Herzberg−Teller regime. Our calculations reveal microsecond lifetime for the emissive state which changes insignificantly with varying solvent. The rate-determining step for the harvesting of the delayed fluorescence is assigned to the fluorescence itself which is 3 orders of magnitude slower than the rate constant for triplet−singlet density transfer in vacuum and toluene environments.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b06187. Vertical excitation energies, spin−orbit coupling matrix, MCTDH basis, molecular orbitals, potential energy surfaces and time evolution of excited state populations in ACRSA (PDF) 21152


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