Dielectric Effects on Charge-Transfer and Local Excited States in

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Dielectric Effects on Charge-Transfer and Local Excited States in Organic Persistent Room-Temperature Phosphorescence Herim Han, and Eung-Gun Kim Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.9b01364 • Publication Date (Web): 08 Aug 2019 Downloaded from pubs.acs.org on August 8, 2019

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Chemistry of Materials

Dielectric Effects on Charge-Transfer and Local Excited States in Organic Persistent RoomTemperature Phosphorescence Herim Han and Eung-Gun Kim* Department of Polymer Science and Engineering, Dankook University, Yongin, Gyeonggi 16890, Korea *E-mail: [email protected]

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1. INTRODUCTION In the short history of organic electronics, we have witnessed the luminescence in focus alternating between fluorescence and phosphorescence. Polymer fluorescence was first demonstrated in 19901 and, driven primarily by technological interest in advancing organic lightemitting diodes, was soon replaced by organometallic phosphorescence.2 Fluorescence reemerged about a decade ago, thanks to thermally activated delayed fluorescence (TADF),3 which is followed shortly by persistent room-temperature phosphorescence (PRTP).4 Nearly all applications make use of luminescent molecules in a dielectric environment, where they are surrounded by other molecules of either the same type or the host. While it has long been recognized that the dielectric environment could play a role in device performances, new molecular designs by powerful organic synthesis have dominated the development efforts. It is also the notion of an intrinsically narrow range of dielectric constant for organic materials that has contributed to lack of interest. While there is no doubt that synthetic molecular designs will continue to push the limit especially in budding fields such as PRTP,5,6 the role of dielectric media may find renewed interest. In TADF, the charge-transfer (CT) characters of the triplet (T1) and singlet (S1) excited states play the most important role by allowing their energy difference

ST

to be small enough

for the conversion of T1 to S1 (or the reverse intersystem crossing) to be thermally activated. Dielectric effects on the CT states, and thus

ST,

can be significant, as demonstrated

experimentally7 and theoretically.8 A similar level of impact may be expected in PRTP, where an efficient (forward) intersystem crossing, often facilitated by realizing a CT state, is required.9 For instance, embedding PRTP molecules in poly(vinyl alcohol) (PVA) tends to produce a larger


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quantum yield than in poly(methyl methacrylate) (PMMA),10–12 in which PVA has a much greater dielectric constant than PMMA. Understanding the dielectric effects is also important because most of intrinsic photophysical characterizations are carried out in solvents, where increasing the solvent dielectric constant can even flip the ordering of some excited states.13 Density functional theory (DFT) calculations have become a staple in organic synthesis work of designing new emitter and host materials during the organometallic phosphorescence era. By the time it became clear that standard functionals are not suitable for TADF,14 a new family of functionals15 had emerged that can calculate CT excited states very accurately.16,17 The functional, collectively known as the optimally tuned range-separated hybrid (OT-RSH) functional, combines an asymptotically correct functional form (RSH) of the exchange energy at long range with a non-empirical tuning (OT) of the range-separation parameter based on the Koopmans theorem. Further improvements have been added by introducing a fraction of Fock exchange at short range18 and a dielectric constant in the long-range limit.19 The optimal tuning of the short-range Fock fraction ensures accurate quasi-particle spectra,18,20 and the screened exchange allows for consistent dielectric effects whether in explicit crystals19 or in continuum solvation.20–22 OT-RSH also produces accurate optical spectra of organic solids.23 Probably one last remaining challenge within the OT-RSH framework lies in that geometry optimization is not straightforward. The optimal tuning being done on a given geometry means that re-tuning of the parameters is guaranteed on each and every geometry in the course of geometry optimization. While this approach produces excellent gas-phase geometries against experiment,24 ever-changing optimal parameters make it difficult to assess the potential energy surface because total energies calculated using different sets of parameters cannot be compared.25 Furthermore, the re-tuning is not applicable to excited-state geometry


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optimization because the tuning is based on the ionization potential (IP) and HOMO energy, two ground-state properties calculated on a ground-state geometry. It has been shown that standard hybrid functionals such as B3LYP produce excited-state geometries reasonably well,26,27 but their general applicability is limited for obvious reasons.28 Having a high-quality excited-state geometry will be even more vital for a proper description of TADF and PRTP. In previous work on parameter tuning via solvation, we showed that OT-RSH converts to a global hybrid at a certain dielectric constant.20 If OT-RSH is made to behave like a global hybrid under certain dielectric conditions, shouldn’t geometry optimization become straightforward as well? By investigating PTZ-BzPN (phenothiazine bonded to benzophenone), a conformationally bistable molecule with dual PRTP and TADF29 (Scheme 1), we first show that geometry optimization is manageable with only one set of optimal parameters when dielectric effects are taken into account. The calculated geometries and energies, obtained consistently for both the ground and excited states, allow us to shed light on the role of dielectric screening in PRTP and TADF.

quasi-axial (a’) S

N O

quasi-equatorial (e’)

S

N O

Scheme 1. Two conformations, quasi-axial (a’) and quasi-equatorial (e’), of PTZ-BzPN at the 9G> bond bridging the electron-donating PTZ and the electron-accepting BzPN. PTZ-BzPN stands for (4-(10H-phenothiazin-10-yl)phenyl)(phenyl)methanone.


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2. METHODOLOGY 2.1. Computational Procedure. We used the functional form first proposed by Yanai et al.30 to divide the Coulomb operator into short- (SR) and long-range (LR) terms: 1

= SR + LR =

except that (

)=1

1

[ +

(

)]

+

+

(

)

(1)

) was used in place of the more common complementary error

exp(

function as the switching function.31 For a given pair of range Fock exchange, the range-separation parameter

and , where

is the fractional short-

was tuned such that the Koopmans or IP

theorem is achieved as closely as possible by minimizing:16 2

(

) = [HOMO(

) + IP(

)]2 + [LUMO(

) + EA(

)]2

(2)

where HOMO denotes the HOMO energy of the neutral molecule and LUMO the SOMO energy of the anion in neutral geometry. IP and EA are the vertical values of the ionization potential and electron affinity, respectively.

– pairs were chosen such that the correct asymptotic 1/

behavior is obtained at long range:18 +

(3)

=1

The screening effect due to the electron correlation in a dielectric medium is achieved by modifying Equation 3 with an explicit dielectric constant $ to give the asymptotic 1 $ :19 + The tuning of

1

(4)

=$

was carried out in the presence of a continuum solvation model by re-evaluating

Equation 2 with a new

from Equation 4.20

The B88 exchange functional and the correlation functional of B3LYP (0.81 LYP + 0.19 VWN5) were used as the base functionals for OT-RSH, as with the original CAM-B3LYP.30


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B3LYP was also used for a small set of calculations for comparison. Grimme’s dispersion correction with the Becke–Johnson damping function32 was added to both B3LYP and OT-RSH. For OT-RSH, the dispersion correction for CAM-B3LYP was used without modification. The TZP (triple-% with one set of polarization functions) Slater-type orbital basis set was used. The conductor-like screening model (COSMO)33,34 was used for continuum solvation with a solvent radius of 3.28 Å. Relativistic effects were included at two levels using the zeroth-order regular approximation (ZORA), first with self-consistent scalar corrections for the ground and excited states,35 followed by perturbative spin–orbit coupling on the excited states.36 Natural transition orbitals (NTOs) were calculated using the Tamm–Dancoff approximation (TDA). Ground-state geometries were calculated with the highest-possible symmetry whereas no symmetry constraint was imposed during excited-state geometry optimization. All DFT and time-dependent DFT (TDDFT) calculations were carried out using ADF.37 2.2. Transition Rates. Theories of transition rates are well summarized in two recent reviews.38,39 Using the Fermi golden rule, the intersystem crossing (ISC) rate &ISC may be written as: &ISC =

( * + + -2 ) S1 ,SOC T1 .FC

(5a)

where ,SOC is the spin–orbit coupling operator, .FC the Franck–Condon-weighted density of states, and ) the Dirac constant. In the classical limit, .FC at temperature 0 becomes: .FC =

1 1(2ST&B0exp

[

(2ST + 4

2 ST)

42ST&B0

]

(5b)


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where 2ST is the reorganization energy calculated as the energy change in attaining the equilibrium geometry of T1 after vertical transition from S1, 4

ST

the adiabatic energy change in

going from S1 to T1, and &B the Boltzmann constant. *S1+,SOC+T1-, or the spin–orbit coupling (SOC) matrix element, is calculated on the S1 geometry by adding contributions from all three sublevels: SOC2 = *S1+,SOC+T1-2 = 57 = 1[892*S1+,SOC+T71- + :;2*S1+,SOC+T71-] 3

(5c)

The reverse intersystem crossing (RISC) rate &RISC can be calculated in a similar way, this time with 2ST and SOC from the S1 and T1 potential energy surfaces, respectively. The fluorescence rate &fl, when the Franck–Condon effect is neglected, is written as the Einstein coefficient of spontaneous emission: &fl =

(

AS0

(92 $0? ;@ 2

)( )

3

AS1

where the transition energy

2 S1BS0 S1BS0

S1BS0

and the oscillator strength

(6) S1BS0

are for the vertical S1BS0

transition, and A7 is the degeneracy of state 7. The fundamental constants appearing in the first term are the electron charge 9, vacuum permittivity $0, Planck constant ?, electron mass ;, and speed of light @. The absorption rate &abs is calculated in a similar manner. When the zero-field splitting is small ( F &B0) so that three triplet sublevels are equally populated at room temperature, the overall phosphorescence rate &ph may be simplified as: 1

&ph = 357 = 1&T71 3

(7)

where &T71, denoting the rate for the vertical T1BS0 transition from the i-th sublevel of T1, is obtained similarly using Equation 6.


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3. RESULTS AND DISCUSSION 3.1. Solvation-Mediated Geometry Optimization of the Ground and Excited States 3.1.1. Conformation Dependence of the Optimal RSH Parameters. As shown in Scheme 1, PTZ-BzPN has two stable conformations around the rotatable bond between the PTZ and BzPN units.29 With a torsion defined by the angle between the mirror plane cutting PTZ in half and the molecular plane of the neighboring phenylene, the quasi-axial conformation is found at 90° (denoted as a’) and the quasi-equatorial at 0° (denoted as e’). The puckered structure of PTZ due to a large sulfur atom (thus two long C—S bonds) makes the (a’)-conformation possible. The large torsional change between two conformations is accompanied by a significant rearrangement of electron density in the HOMO (Figure 1). As a result, (a’) and (e’) have two different sets of OT-RSH parameters (

H

,

H

) as if they were two different molecules (Table 1).

This creates two parallel potential energy surfaces for the ground state, with the accuracy of a particular geometry being determined by which surface it is on, as illustrated in Figure 2 for the isolated molecule. As for the MO energies, using the OT-RSH parameters of one conformer to calculate the other can lead to an error as large as 0.08 eV (Table 2.1).


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(a’)-PTZ-BzPN

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(e’)-PTZ-BzPN

HOMO

LUMO

Figure 1. Conformational bistability at the donor–acceptor linkage of PTZ-BzPN and its impact on the frontier orbitals. Data shown are at $ = 5.

Table 1. Conformation dependence of the OT-RSH parameters ( different dielectric constants $. $ 3

* * *

4

* *

5

* *

7

* a

H

(a’) 0.27 0.201 0.26 0.205 0.26 0.205 0.26 0.205

(e’) 0.28 0.214 0.28 0.214 0.27 0.218 0.27 0.218

H

,

H a

) of PTZ-BzPN at

Difference 0.01 0.013 0.02 0.009 0.01 0.013 0.01 0.013

in J0 1, where J0 is the Bohr radius.


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( *, *) of (a’)

3439.99

0.03 3440.02

( *, *) of (e’)

4.71

4.71

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 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


’

3444.70

0.03

3444.73

(a’)

(e’)

Structural Coordinate

Figure 2. Schematic of the ground-state potential energy surfaces calculated by two different sets of OT-RSH parameters ( H , H ), one tuned for (a’) and the other for (e’). Each curve consists of a region covered accurately by a given set of parameters (solid) and a region with uncertainty (dotted). Energies shown are actual values calculated for PTZ-BzPN in the isolated state.

Table 2. MO and transition energies of PTZ-BzPN and the errorsa incurred when calculating one conformation by using the OT-RSH parameters of the other (all energies are in eV). (1) S0 in the isolated state Modelb Conformer (a') RSH//B3LYP (e') (a') RSH//RSH (e')

HOMO G?&

Dielectric Effects on Charge-Transfer and Local Excited States in

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