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C: Physical Processes in Nanomaterials and Nanostructures

Theoretical Study of the Intramolecular Localization and Migration of a Triplet Exciton in the #-NPD Molecule Ilya D. Krysko, Alexandra Yakovlevna Freidzon, and Alexander A. Bagaturyants J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b10726 • Publication Date (Web): 29 Mar 2019 Downloaded from http://pubs.acs.org on March 29, 2019

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The Journal of Physical Chemistry

Theoretical study of the intramolecular localization and migration of a triplet exciton in the N,N′-Di(1naphthyl)-N,N′-diphenyl-(1,1′-biphenyl)-4,4′diamine (α-NPD) molecule Ilya D. Kryskoa,b, Alexandra Y. Freidzona,b, Alexander A. Bagaturyantsa,b,*

a

National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoye shosse 31, Moscow 115409, Russia

b

Photochemistry Centre of Federal Scientific Research Centre “Crystallography and

Photonics” of Russian Academy of Sciences”, Russia, 119421, Moscow, Novatorov 7a

∗ Corresponding author

Email: [email protected]

KEYWORDS: OLED, α-NPD, triplet states, exciton, lifetime, quantum chemical calculation 1

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Abstract: The intramolecular localization and migration of a triplet exciton in the N,N′Di(1-naphthyl)-N,N′-diphenyl-(1,1′-biphenyl)-4,4′-diamine (α-NPD) molecule is studied by the XMCQDPT/CASSCF method. Energy profiles corresponding to linear interpolations between different localized states show that the barriers between minima are comparable with the vibrational energies of the soft modes corresponding to the transition of one structure to another. The triplet exciton lifetimes and characteristic migration times are estimated. It is shown that the intramolecular migration is three orders of magnitude faster than the main triplet decay process in α-NPD, namely, nonradiative deactivation. Therefore, at room temperature, the excitons can freely migrate over the molecule and become effectively delocalized during their lifetime.

1. Introduction Investigation of new electroluminescent materials and their use as emitting layers for creating effective organic light-emitting diodes (OLED) is an urgent problem of current applied physics and chemistry. OLEDs are thin-film multilayer devices consisting of layers of several organic semiconductors. When a voltage is applied to the device, 2


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charge carriers (electrons and holes) are injected into the light-emitting layer, where they recombine to form excitons, which decay with light emission. The efficiency, kinetics, and the very possibility of these processes depend on the positions of the energy levels of the materials of layers that constitute the structure of the device. For the development of new, more efficient materials for OLEDs, it is useful to determine correlations between the composition, structure and functional properties of the initial compounds on one side and the properties of the corresponding OLED layers on the other. Phosphorescence provides a way for efficient utilization of electrogenerated triplet excitons

[1,

2].

Although

pure

organic

molecules

do

not

exhibit

efficient

phosphorescence, organometallic complexes, especially those containing platinum group metals, can efficiently phosphoresce at room temperature. OLEDs utilizing phosphorescence are called phosphorescent OLEDs (PhOLEDs).

3



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N

N

Figure 1. α-NPD Structure The use of N,N′-Di(1-naphthyl)-N,N′-diphenyl-(1,1′-biphenyl)-4,4′-diamine (α-NPD) (Figure 1) as a host for phosphorescent dopants based on iridium complexes [3, 4] suggests a resonance between the triplet levels of the host and the triplet levels of the dopant (Figure 2). At the same time, the energy gap between the host and the dopant should be sufficiently large to suppress both the electron and energy paths of exciton back-transfer from the emitting dopant to the host material [5].

4


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Figure 2. Level alignment for efficient triplet energy transfer from host to dopant. In this connection, the problem of reliable theoretical estimation of the position of the triplet levels in the molecules comprising both the host and the dopant becomes urgent. The experimental value for the triplet energy of α-NPD is Eexp = 2.26 eV [6, 7] The long lifetime of triplet excitons theoretically allows them to migrate over considerable distances and leave the recombination zone. To suppress this process and confine the excitons in the recombination zone, a typical diode architecture with phosphorescent emitters, as distinct from fluorescent ones, requires one more auxiliary hole-blocking layer, and the energy levels of the host should be somewhat higher to localize the excitons on the dopant [8].

5



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In the theoretical modeling of materials for organic electronics, relatively simple and resource-saving single-reference methods, such as Hartree–Fock and DFT, are commonly used. However, it is known that these methods do not accurately reproduce the triplet state energies and can result in different errors for states of different nature, which complicates a comparison of energy levels of different molecules [9]. Multiconfiguration methods require more computational efforts; however, they enable a systematic improvement in the quality of calculations. For example, multireference calculations made by our group demonstrate excellent accuracy and reliability in predicting the energy and localization of the triplet states in different lanthanide(III) complexes [10–12], charge localization in Be(II) complexes [13, 14], and charge and exciton localization in purely organic OLED hosts [15]. Thus, although multireference calculation of large molecular systems is feasible, a balance between the computational costs and the accuracy of the calculation is necessary. Exciton migration across the host layer is an important process in OLED operation. Here, we focus on the process of intramolecular exciton migration and leave the intermolecular process for a further study.

6


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Compounds such as α-NPD consist of several incompletely conjugated aromatic fragments. This can lead to the localization of excitons or charge carriers on individual fragments (Figure 3). Thermal vibrations and local electric fields from the neighboring molecules can result in an exciton hop from one intramolecular site to another, which can facilitate or inhibit intermolecular hopping.

Figure 3. Sites of possible exciton localization. It is known that density functional theory suffers from the so-called “delocalization error”, resulting in an overestimation of electron density delocalization [16–18]. Thus, it is demonstrated in Ref. [19] how the weight of HF exchange in the density functional affects the calculated energy profile of a dye having both locally excited and TICT states. The results of Ref. [19] are benchmarked against a multireference calculation.

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Nevertheless, localized polaron or exciton states can be obtained using rangeseparated functionals, such as CAM-B3LYP [9], and special schemes, such as constrained DFT [20]. Moreover, our preliminary calculations of α-NPD show that localized exciton states can be obtained even with global hybrid functionals, such as PBE0, B3LYP, or BHHLYP, when geometry optimization is started with pre-deformed geometries (see below). Unfortunately, the above-mentioned problem of inaccuracy of the calculated states depending on their nature still remains, being especially important for triplets. At the same time, we have previously shown using multireference methods [10–15] that excitons and excess charges are most frequently localized on individual fragments of very different molecules with incompletely conjugated or even independent fragments. In this paper, we calculate the energies of the lowest triplet states of the α-NPD molecule by the XMCQDPT/CASSCF [21] method and investigate the intramolecular localization and migration of the triplet exciton in the α-NPD molecule.

2. Methods of calculations

8


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Preliminary calculations were performed using the restricted closed-shell and openshell Hartree–Fock (RHF and ROHF, respectively) methods, the CIS method, the restricted closed-shell and open-shell DFT (R-DFT and RO-DFT, respectively) methods, and the TDDFT (in the Tamm–Dancoff approximation) methods with the PBE0, B3LYP, BHHLYP, and CAM-B3LYP functionals. The triplet state geometries were first optimized by CIS with state tracking to obtain the pre-deformed geometries for further ROHF or RO-DFT optimizations. The triplet exciton localizations corresponded to the localization of the singly occupied MOs. All multireference calculations were performed using the 6-31(d,p) basis set according to the flowchart shown at Figure 4.

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Figure 4. Flowchart of XMCQDPT/CASSCF calculation Geometries of the ground singlet and excited triplet states were optimized by the SSCASSCF(8,8)1 method without symmetry restrictions. The wave functions of the singlet ground state and excited triplets were obtained by SA(5)-CASSCF(8,8)2 for each of the found geometries to obtain the energies of S0 and four triplet states simultaneously. For each geometry, the energies of these states were refined by the XMCQDPT2 method. The triplet exciton localization was determined from the localization of the singly

1

State-specific CASSCF of 8 electrons on 8 orbitals

2

State-averaged over 5 states CASSCF of 8 electrons on 8 orbitals 10


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occupied natural orbitals. Alternatively, the geometries were optimized by R(O)HF and R(O)-DFT with the corresponding functionals, and the triplet energies were calculated by ΔSCF (ΔDFT) or TDDFT (in the TDA version). For the energy profiles, we used the linear interpolation technique developed in [13]. The FireFly program package [22] partially based on GAMESS [23] was used in the calculations. The normal modes responsible for the transition from one localized state to another (reorganization modes) were calculated according to the Lax model [24, 25] utilizing the time-domain formalism and the multi-mode harmonic oscillator model [2630–31]. For the purposes of analysis and interpretation, the calculated spectra were deconvoluted into components corresponding to hard and soft modes according to the procedure developed in [282930–31]. The hessians and gradients of the triplet states required in these calculations were calculated by CIS. The spin-orbit interaction was calculated using the full two-electron Pauli–Breit operator by spin-orbit CASSCF (SO-CASSCF) [32–34] using the GAMESS-US program [23].

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The triplet exciton lifetime was calculated using the Fermi golden rule for the nonradiative relaxation constant 𝑘𝑛𝑟 =

1 𝜏𝑛𝑟

=

2𝜋|⟨𝑆0│𝐻𝑆𝑂│𝑇1⟩| ℎ Δ𝐸𝑆𝑇

2

, while the radiative relaxation

constant was calculated by the following equation [35]: 1

𝑘𝑟 = 𝜏𝑝ℎ𝑜𝑠𝑝ℎ =

(|

64𝜋4𝜈3 3ℎ𝑐3

∑𝑟

⟨𝑆𝑘│𝐻𝑆𝑂│𝑇𝑟1⟩ 𝐸𝑇1 ― 𝐸𝑆𝑘

|

2

|

|⟨𝑆0│𝑒𝑟│𝑆𝑘⟩|2 + ∑𝑚∑𝑛

⟨𝑆0│𝐻𝑆𝑂│𝑇𝑛𝑚⟩ 𝐸𝑆0 ― 𝐸𝑇𝑛

𝑚

| |⟨𝑇 │𝑒𝑟│𝑇 ⟩| ) (1) 2

2

𝑛 𝑚

1

where r and n denote sublevels of the triplet states T1 and Tm, 𝑒𝑟 is the dipole operator,

⟨𝑆0│𝑒𝑟│𝑆𝑘⟩ and ⟨𝑇𝑛𝑚│𝑒𝑟│𝑇1⟩ are transition dipoles between singlets and triplets, ⟨𝑆𝑘│𝐻𝑆𝑂│𝑇𝑟1⟩ and ⟨𝑆0│𝐻𝑆𝑂│𝑇𝑛𝑚⟩ are spin-orbit coupling matrix elements governing the intensity borrowing by the T1→S0 transition from the Sk→S0 and T1→Tm transitions, and 𝐸𝑇1 ― 𝐸𝑆𝑘 and 𝐸𝑆0 ― 𝐸𝑇𝑛𝑚 are the corresponding energy gaps. The exciton migration constant was calculated using the Marcus equation

𝑘=

― 2𝜋 2 1 ℏ 𝑉 4𝜋𝜆𝑘𝐵𝑇𝑒

(Δ𝐺 + 𝜆)2 4𝜆𝑘𝐵𝑇

(2),

where V is the hopping integral taken as half the minimum gap between the two triplet surfaces, T1 and T2; λ is the reorganization energy for triplet exciton migration calculated as the energy gap between T1 and T2 states at the minimum of the T1 profile; and ΔG is the T1 energy difference between the two sites of exciton localization (say, naphthyl A and biphenyl). On the other hand, exciton migration can be considered as an isomerization reaction of the triplet α-NPD molecule associated with barrier crossing and molecular reorganization (Figure 5). This process takes place on a single potential energy surface. Therefore, the corresponding

rate constant can be calculated by the Arrhenius equation 𝑘 = 𝑘0𝑒

12


𝐸𝑎 𝐵𝑇

―𝑘

with the pre-

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exponential factor k0 taken equal to the frequency of the reorganization mode [36, 37, 38] and the activation energy Ea taken at the barrier top on the T1 surface. The barrier height can be found from the energy profile, and the frequency of the reorganization mode used as a pre-exponential factor can be found after considering the contributions of normal modes to the reorganization energy (the soft mode with the largest contribution is taken as the reorganization mode). Because, under certain assumptions, the Marcus formula can be derived from the Arrhenius equation [39], a good agreement between the rate constants calculated using the Marcus and Arrhenius equations is quite reasonable. All the parameters used in the calculations of the rate constant k are given in Supporting Information, Table S2.

3. Results and Discussion 3.1. Localized states The optimal geometry of the ground state of the α-NPD molecule is symmetric (C2 group). The triplet states are open-shell states; therefore, they are subject to the pseudo Jahn–Teller effect, namely, spontaneous symmetry breaking in polyatomic systems (molecules and solids), which occurs even in nondegenerate electronic states under the

13



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influence of sufficiently low-lying excited states of an appropriate symmetry [40]. Therefore, our model should include the possibility of such symmetry breaking. The results of preliminary calculations are shown in Supporting Information, Figs. S1S4. We managed to obtain the localized triplet states both using CIS, ROHF, and RODFT with global hybrid PBE0 (25% HF exchange), B3LYP (20% HF exchange), and BHHLYP (50% HF exchange) and range-separated CAM-B3LYP functionals. Singly occupied orbitals shown in Fig. S4 for RO-CAM-B3LYP calculations are similar to those obtained by RO-PBE0 and ROHF. Nevertheless, the calculated triplet energies in the optimized geometries were found to be unsatisfactory: all methods except for TDACAM-B3LYP underestimate the triplet energies to different extent, while the latter severely overestimates them. Surprisingly, the energies of naphthyl-localized triplets obtained by ΔCAM-B3LYP are almost the same as those obtained by ΔDFT with global hybrids, while the energy of the biphenyl-localized triplet is close to that obtained by XMCQDPT/CASSCF. Unfortunately, the gap between the T1 and T2 states, which is required for the estimation of the triplet migration rate, can be calculated only by TDDFT (or TDA-DFT) or CIS, which give wrong triplet energies. Hence, the reliability of DFT-

14


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based methods is questionable and requires a careful choice of the DFT functional verified by alternative experimental or computational methods. The geometry optimization of the triplet states of α-NPD by SS-CASSCF led to the geometry changes shown in Table S1 (see Supporting Information) and Figure 5. One can see that the geometry changes correlate with the localization of singly occupied orbitals and definitely indicate exciton localization on either naphthyl A, biphenyl, or naphthyl B (Figure 6). The phenyl rings are not involved in the triplet exciton states.

15



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Figure 5. Geometry changes in the triplet states with respect to the ground state geometry. Red lines indicate bond elongation and blue lines show bond shortening.

Figure 6. Localization of singly-occupied orbitals in the three lowest triplet states.

16


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The energies of phosphorescence emission from each of the localized states are 2.36–2.38 eV (Figure 7), which is only 0.10–0.12 eV higher than the experimental value.

Figure 7. Energies of the localized states calculated by the XMCQDPT/CASSCF method.

3.2. Intramolecular migration of triplet exciton The energy profiles for the exciton migration from naphthyl A to naphthyl B were studied by the linear interpolation of internal molecular coordinates from one geometry to the other. Two migration paths were considered: direct hopping from naphthyl A to naphthyl B (Path 1) shown in Figure 8 and migration via intermediate localization on biphenyl (Path

17



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2) shown in Figure 9. It was found that both paths involve very low energy barriers (~3 kcal/mol). The difference between two paths is in the electronic and geometrical structure of intermediate points. Path 1 proceeds through a point close to the conical intersection point between T1 and T2 states localized on naphthyl A and naphthyl B, respectively, while Path 2 involves two avoided crossing points between states localized on naphthyl and biphenyl, and the T1–T2 gaps at the midpoints are non-negligible. The unpaired electron density along Path 1 is localized on each respective naphthyl in all points of the energy profile. The only point where it is delocalized on two naphthyls is the midpoint of the path.

18


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Figure 8. Direct hopping from naphthyl A to naphthyl B (Path 1). The unpaired electron density shows the localization of the triplet exciton.

a

b

Figure 9. (a) Migration via intermediate localization on biphenyl (Path 2); (b) enlarged view of the avoided crossing region in the rectangle. The unpaired electron density shows the localization of the triplet exciton. 19



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The normal modes responsible for the transfer from one localized state to another (reorganization modes) were found with the use of the Lax model. The diagram (Figure 10) shows the modes that contribute most to the total reorganization energy of the process. Note that, in addition to the bond length redistribution (hard modes of 1200– 1700 cm–1, Figure 11) Path 2 includes soft modes (

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