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# Unraveling the orientation of phosphors doped in organic semiconducting layers

## Abstract

Emitting dipole orientation is an important issue of emitting materials in organic light-emitting diodes for an increase of outcoupling efficiency of light. The origin of preferred orientation of emitting dipole of iridium-based heteroleptic phosphorescent dyes doped in organic layers is revealed by simulation of vacuum deposition using molecular dynamics along with quantum mechanical characterization of the phosphors. Consideration of both the electronic transitions in a molecular frame and the orientation of the molecules at the vacuum/molecular film interface allows quantitative analyses of the emitting dipole orientation depending on host molecules and dopant structures. Interactions between the phosphor and nearest host molecules on the surface, minimizing the non-bonded van der Waals and electrostatic interaction energies determines the molecular alignment during the vacuum deposition. Parallel alignment of the main cyclometalating ligands in the molecular complex due to host interactions rather than the ancillary ligand orienting to vacuum leads to the horizontal emitting dipole orientation.

## Introduction

The orientation of molecules in molecular films dictates their electrical and optical properties such as charge mobility1, 2, birefringence3, absorption4, emission5, ionization potential6, and dielectric7 and ferroelectric properties8. Therefore, understanding and control of molecular orientation in organic films have been a research topic with central importance in organic electronics and photonics, including the fields of liquid crystals9, organic field effect transistors10, and organic photovoltaics11. In organic light-emitting diodes, the molecular orientation of emitter embedded in the emissive layer has been an issue to enhance the outcoupling efficiency of light pursuing the horizontal alignment of the emitting dipole moment3, 12,13,14,15,16,17,18,19,20,21.

Interestingly enough, it is only in recent years has attention turned to the orientation of emitting dipoles of iridium-based phosphors, the most verified light-emitting dyes with high photoluminescence quantum yield and variety of chromatic spectrum as doped in the emissive layers; probably because their iridium-centered spherical shape and the amorphous surrounding nature in the emissive layers are far from having strong molecular alignments. Recently, some heteroleptic Ir complexes exhibiting efficient electroluminescence in organic light-emitting diodes are reported to possess preferred horizontal emitting dipole orientations (EDOs)13,14,15,16, 18,19,20. However, it was difficult to assert the reason why the spherical-shaped phosphors have a propensity toward preferred molecular alignment in the emissive layers. A few mechanisms have been proposed to explain the preferred molecular orientation of the Ir complexes doped in vacuum-deposited organic semiconducting layers: molecular aggregation of the dopants leading to randomizing their orientation by suppressing the intermolecular interaction between the dopant and host molecules22, strong intermolecular interactions between electro-positive sides of the dopant, and the electro-negative host molecules promoting parallel alignment of the N-heterocycles of Ir complexes by forming host-dopant–host pseudo-complex mainly participating in 3MLCT transition16, 23, and π–π interactions between the dopant and host molecules on the organic surface bringing alignment of aliphatic ligands to the vacuum side20, 24. Currently, it is not very clear which mechanism most comprehensively describes the origin of the preferred EDO of the heteroleptic iridium phosphors. Moreover, the models are too oversimplified to describe the EDO values quantitatively, which depend on structures of the phosphors and host molecules23. Therefore, the molecular configurations and the interactions responsible for the EDOs of Ir complexes should be established by atomic-scale simulation of the Ir complexes interacting with host molecules during film fabrication.

In this paper, we carefully examine the vacuum deposition process of phosphors on organic layers using a combination of molecular dynamics (MD) simulations and quantum mechanical analyses. The triplet EDO of heteroleptic Ir complexes doped in organic layers is studied with systematic variations of the molecular structures of both host and dopant. Theoretical prediction of EDO from simulated deposition process reveals excellent quantitative agreement with experimental observations, reproducing the anisotropic molecular orientations of heteroleptic Ir complexes in the emissive layers. In-depth analysis indicates that the molecular orientation originates from the coupling of the cyclometalated main ligand participating in the optical transition with neighbor host molecules rather than from the alignment of aliphatic ancillary ligand toward the vacuum. Close observation of the simulation results indicates that non-bonded interaction energy has a critical influence on the molecular orientation during the deposition.

## Results

### Modeling of emitting dipole orientation

The simulation method for obtaining EDO of an emitter in the vacuum-deposited layer is schematically illustrated in Fig. 1a. First, the transition dipole moment (TDM) vector in the molecular frame (m x -, m y -, and m z -axes) was determined by quantum mechanical calculations after optimization of molecular geometry. For iridium-based phosphors, spin-orbit-coupled time-dependent density functional theory (SOC-TDDFT) was employed for the calculation of the triplet TDM vectors for phosphorescence. Second, vacuum deposition of the emitting molecules on organic surfaces was simulated using MD. Finally, the TDM vectors in the molecular axis in each frame of MD were transformed to the vectors in the laboratory axis (n x -, n y -, and n z -axes) by rotation matrix method (Fig. 1b). We determine φ C and φ L as the angle between m z and n z axes and the angle between the TDM vector of the emitter and n z axis, representing the molecular orientation and the EDO against the vertical direction in the laboratory axis, respectively. The ratio of the horizontal (TDMH) to the vertical transition dipole moment (TDMV) follows the trigonometric relationship:

$${\rm{TD}}{{\rm{M}}_{\rm{H}}}\!:\!{\rm{TD}}{{\rm{M}}_{\rm{V}}} = \mu _0^2{\sin ^2}{\varphi _L}\!:\!\mu _0^2{\cos ^2}{\varphi _L},$$
(1)

where μ 0 is the magnitude of the dipole moment and squares of the components indicate the intensity of the transition (emission intensity). The EDO describes an average fraction of the horizontal and vertical dipole moment of whole emitters embedded in the emissive layer. An ensemble average of the horizontal dipole moment gives the fraction of horizontal emitting dipole moment in the emissive layer (Θ) as a parameter of the EDO by

$$\Theta = \left\langle {{{\sin }^2}{\varphi _L}} \right\rangle .$$
(2)

Details about the rotation matrix and the vector transformation are given in Methods section.

The deposition simulation was performed by dropping a target molecule onto organic substrates under vacuum followed by thermal equilibration at 300 K as shown in Fig. 1c. The simulations were performed using the Materials Science Suite (Version 2.2) released by Schrödinger Inc.25 Force field of OPLS_200526 and periodic boundary conditions were used for the MD simulations. Organic substrates were prepared by packing of 256 host molecules at 300 K and 1 atm. The simulated substrates have random molecular orientations and similar densities as the experimental results. Detailed steps of preparation of the substrates are given in Supplementary Fig. 1 and Supplementary Note 1. One of the challenges of a single-trajectory-based MD analysis for orientation during deposition is that the time scale needed to observe the entirety of lateral degrees of freedom for a single molecule is much longer than that of a typical MD simulation. As such, we introduced 50 independent deposition events per dopant, instead of relying upon a single MD trajectory for each. About 50 target dopant molecules were distributed in the vacuum slab of the periodic substrate model at un-overlapped locations with different orientations for the deposition simulation. Each target molecule was individually dropped onto the substrate under vacuum at 300 K. Translational motion of the host molecules at the bottom of the substrate was restrained in order to avoid the drift of the system. The deposition simulation used an NVT ensemble for a duration of 6000 ps with a time step of 2 fs and configurations of the system were recorded every 6 ps. One example of the process is shown in Supplementary Movies 1 and 2. Finally, EDOs of the phosphors and the molecular angles (φ C ) were analyzed using Eq. (1) from the configurations. The analysis is based upon an assumption that the characteristic time to determine the orientation of dopants is in the same scale of which the intermolecular interaction converges after the deposition of a dopant.

### Materials

Chemical structures of the materials used in this study are depicted in Fig. 2a, b. Three heteroleptic iridium complexes of Ir(ppy)2tmd, Ir(3′,5′,4-mppy)2tmd18, and Ir(dmppy-ph)2tmd19 possessing high Θ values were adopted to investigate the effect of the phosphor molecular structure. The molecular C 2 symmetry axis toward the center of the ancillary ligand from the origin located at the Ir atom was set as m z , the orthogonal vector to m z normal to the molecular Ir-O-O plane was set as m x , and m y was determined by a cross product of m z and m x in the dopants. The triplet TDM vectors of the three Ir complexes align along the direction of the iridium atom to the pyridine rings by 3MLCT as displayed in Fig. 2a. Coordinates of the TDM vectors of Ir(ppy)2tmd, Ir(3′,5′,4-mppy)2tmd, and Ir(dmppy-ph)2tmd were $$\left[ {{\varphi _M} = {\rm{88}}^\circ ,\theta {\rm{ = 147}}^\circ } \right],$$ $$\left[ {{\varphi _M} = {\rm{89}}^\circ ,\theta {\rm{ = 141}}^\circ } \right],$$and [φ M  = 89°, θ = 156°], respectively, indicating that the substituents at the 4-position of the pyridine of the main ligands do not change the direction of triplet TDM vectors much.

Diphenyl-4-triphenylsilyphenyl-phosphineoxide (TSPO1), 1,4-bis(triphenylsilyl)benzene (UGH-2), and 4,4′-bis(N-carbazolyl)-1,1′-biphenyl (CBP) were selected as host materials to investigate the effect of ground state dipole and conjugation length of the host on the EDO. TSPO1 has large permanent dipole moment due to the polar phosphine oxide group and the asymmetric structure, while UGH-2 and CBP molecules have small ground state dipole moments compared to TSPO1 due to the symmetric structures and the less polar groups. On the other hand, CBP has longer conjugation length than UGH-2 and TSPO1, indicating that CBP has a larger polarizability than UGH-2.

Experimentally, Ir(ppy)2tmd exhibited the Θ values of 0.60, 0.75, and 0.78 when doped in the UGH-2, CBP, and TSPO1 layers, respectively. Ir(3′,5′,4-mppy)2tmd and Ir(dmppy-ph)2tmd doped in TSPO1 layers have enhanced horizontal dipole orientation with the Θ values of 0.80 and 0.86, respectively (Supplementary Fig. 2, Supplementary Note 2, and ref. 23).

### Simulation results

The simulated variations of the orientation of the TDMH and C 2 axis of the dopants with time on the different hosts are displayed in Supplementary Fig. 3 for 50 depositions for each system. The orientation of the phosphors was stabilized after certain time for some molecules, but fluctuated continuously for other molecules.

Figure 3a exhibits the histograms of the EDO resulting from the deposition simulation. The blue lines represent the probability density of TDMH ($${\sin ^2}{\varphi _L}$$, derivation in Methods section) of an arbitrary vector. The green lines exhibit the deviations of the population from the random distribution. The simulated Θ values of Ir(ppy)2tmd were 0.63, 0.72, and 0.74 on the UGH-2, CBP, and TSPO1 substrates, respectively. Ir(3′,5′,4-mppy)2tmd and Ir(dmppy-ph)2tmd on TSPO1 substrates have the Θ values of 0.76 and 0.82, respectively. In addition, the simulation was performed for Ir(ppy)3, a homoleptic complex exhibiting isotropic EDO when doped in CBP as a refs 14, 23. The distribution of the emitting dipole moment of Ir(ppy)3 was close to the random distribution with a simulated Θ value of 0.67 and random orientation of the C 3 symmetry axis of the molecule (Supplementary Fig. 4; Supplementary Note 3). The simulated EDOs match well with the experimental results as compared in Table 1, verifying that the MD simulation describes the vacuum deposition adequately. The results show that Ir(ppy)2tmd in UGH-2 has larger molecular population with vertical TDM at the expense of reduced population with horizontal TDM compared to the random distribution (Θ = 0.67). Higher Θ values are obtained when population of molecules possessing high TDMH is getting larger with the reduced population with low TDMH.

The orientation of the C 2 axes of the phosphors on the organic layers is shown in Fig. 3b to find out if alignments of the aliphatic ancillary ligands have any correlation with EDO, for instance, if the horizontal EDO results from the vertical alignment of ancillary ligands with respect to the substrate20, 24. One expects that the distribution function follows $$\sin {\varphi _c}$$ (blue line) if the orientation is random. We can extract several interesting results from Fig. 3b. First, the orientation of the ancillary ligand of the Ir complexes has broad distributions for all the deposited films. Second, host effect on EDO is independent of alignments of the ancillary ligand. The total distribution of the C 2 axis of Ir(ppy)2tmd is similar on the UGH-2, CBP, and TSPO1 layers with the average φ C of 70°, but the EDO on UGH-2 host is different from the EDOs on other two hosts. Third, the orientation of the C 2 axes of Ir(3,5′,4-mppy)2tmd and Ir(dmppy-ph)2tmd on TSPO1 are more random (closer to $$\sin {\varphi _c}$$) even though they possess higher Θ values than Ir(ppy)2tmd. The random distributions are observed even in the region with high horizontal alignment of the emitting dipole moment (green regions in the stacked histogram with 0.95 ≤ TDMH ≤ 1). Fourth, the dopant molecules with vertical TDM (red regions in the stacked histogram with 0 ≤ TDMH ≤ 0.3) have φ C close to 90° for all the system, indicating that the ancillary ligands align parallel to the surface. All the results show that there is little correlation between the orientation of TDMs and alignment of the ancillary ligands.

## Discussion

The size of the substrates turns out to be large enough to simulate the vacuum deposition of the phosphorescent dyes adequately, as confirmed by the similar results obtained on a larger substrate consisting of 1024 molecules (Supplementary Fig. 5; Supplementary Note 4). The computation of the autocorrelation times of the molecular angles for the 50 independent depositions for each phosphorescent molecule verifies that the number of events sampled during the deposition (the simulation time and the number of the deposition events) is large enough to validate the MD simulation of the vacuum deposition process (Supplementary Fig. 6; Supplementary Note 5).

The aggregation effect of the Ir complexes is neglected in the MD simulation by depositing each target molecule on an organic substrate at a time and by repeating for 50 molecules deposited on different positions of the organic substrates. The very good consistency of the simulated EDO and experimental values indicates that aggregation is not a necessary condition for the alignment of heteroleptic Ir complexes.

Alignment of aliphatic ligands of heteroleptic Ir complexes to vacuum (model 3) is not required for preferred horizontal EDO either as shown in Fig. 3. A much larger portion of the aliphatic ligand (‒tmd group) of Ir(ppy)2tmd molecules align to the vacuum side (0° < φ C  < 90° in Fig. 3b) than Ir(3′,5′,4-mppy2)tmd and Ir(dmppy-ph)2tmd molecules. However, the Θ value of Ir(ppy)2tmd is much lower than Ir(3′,5′,4-mppy)2tmd and Ir(dmppy-ph)2tmd. These results are the reverse direction from the prediction based on the model and clearly demonstrate, therefore, that alignment of aliphatic ligands to the vacuum side is not a necessary condition for the alignment of EDO in heteroleptic Ir complexes. The reason why it is not required can be understood from the following consideration.

The relationship between the orientation of molecules and emitting dipole moment can be easily figured out using schematic molecular orientations of a heteroleptic Ir complex shown in Fig. 4. The C 2 axis is toward the ancillary ligand (dark blue arrows) and the TDM vector (red arrows) is approximately along the direction from the iridium center to one of the pyridine rings. The alignment of iridium-pyridines determines the orientations of TDM for Ir(ppy)2tmd, Ir(3′,5′,4-mppy)2tmd, and Ir(dmppy-ph)2tmd. Figure 4 shows five configurations with different rotation angles of the C 2 axis for the horizontal TDM and one configuration for the vertical TDM. Rotation of the C 2 axis from the vertical to the horizontal direction can result in the horizontal TDM as long as the TDM is located on the horizontal plane (substrate) with an arbitrary orientation of the ancillary ligand. In other words, horizontal EDO is possible no matter which direction of the ancillary ligand aligns, either toward vacuum or film. On the other hand, the vertical TDM is obtained only when the pyridine rings are aligned perpendicular to the substrate. It accompanies horizontal alignment of the C 2 axis (φ C ~90°) on the configuration. This consideration is consistent with the simulation results in Fig. 3.

The distributions of the ancillary ligand can be partly explained by analyzing the differences in Hildebrand solubility parameters (δ) of the phosphor and host molecules. Predicted solubility parameters of the molecules are 16.2 (UGH-2), 18.5 (CBP), 17.2 (TSPO1), 15.3 (Ir(ppy)3), 14.7 (Ir(ppy)2tmd), 13.8 (Ir(3′,5′,4-mppy)2tmd), and 14.4 MPa1/2 (Ir(dmppy-ph)2tmd), respectively, calculated from OPLS_2005 NPT MD by the equation:27

$$\delta = {\left( {\frac{{\Delta {E_v}}}{{{V_{\rm{m}}}}}} \right)^{1{\rm{/}}2}},$$
(3)

where ΔE v is the internal energy change of vaporization, and V m is the molar volume, respectively. In general, the differences in the solubility parameters (Δδ) between two components in a chemical mixture can be an indicator of the degree of miscibility, with smaller and larger values of Δδ indicating more and less miscible, respectively. In this work, the host and the phosphor Δδ are much less than 7 MPa1/2, suggesting that all the phosphors are miscible with the hosts28. However, Δδ’s between Ir(ppy)3 and the hosts are smaller than between Ir(ppy)2tmd and the hosts. Since the difference comes from the ppy and tmd groups, it follows that the tmd group is less miscible in the host substrates than the main ligand ppy group, which explains the orientation of the aliphatic ancillary ligand toward vacuum side for Ir(ppy)2tmd. On the other hand, the difference in the solubility parameters among Ir(ppy)2tmd, Ir(3′,5′,4-mppy)2tmd, and Ir(dmppy-ph)2tmd comes from the difference in main ligands. The reduced solubility of Ir(3′,5′,4-mppy)2tmd and Ir(dmppy-ph)2tmd indicates that both 3′,5′,4-mppy and dmppy-ph groups are less miscible to the host than ppy of Ir(ppy)2tmd and less preference to attachment to the substrate compared to the ppy group. Therefore, the orientations of the ancillary ligand of the two phosphors are more randomized during the deposition, consistent with the simulated distributions in Fig. 3b.

Non-bonded interaction energy is calculated as a summation of van der Waals and Coulomb interaction energies from the MD simulation to investigate if the intermolecular interaction between the phosphor and neighbor host molecules is responsible for the spontaneous molecular alignments of the phosphors on the surfaces. Figure 5a depicts the correlation between non-bonded interaction energy and orientation of the emitting dipole moment of the phosphors in the five different host-dopant systems. Distributions of the non-bonded interaction energy are given in Supplementary Fig. 7. There is a broad energy trap of ~3 kcal/mol in the region of TDMH = 0.1−0.5 for Ir(ppy)2tmd on the UGH-2 host and the energy increases with further increasing of TDMH, thereby resulting in rather a vertical EDO compared to random orientation because the population of TDMH is expected to be concentrated in the regions of low (large) non-bonded interaction energy. On the other hand, non-bonded interaction energies of Ir(ppy)2tmd on CBP and TSPO1 layers, and the energies of Ir(3′,5′,4-mppy)2tmd and Ir(dmppy-ph)2tmd on TSPO1 are lowered as TDMH increases. As a result, molecular alignment with horizontal TDM is energetically preferred when they are deposited onto the organic semiconducting layers. Furthermore, much lower energies were obtained from Ir(3′,5′,4-mppy)2tmd and Ir(dmppy-ph)2tmd than Ir(ppy)2tmd on the TSPO1 layer, indicating that the increased EDOs are also related to the stabilization by neighbor molecules. The calculated non-bonded interaction energy and the statistical results indicate that the host–dopant interaction plays a pivotal role in orienting heteroleptic Ir complexes and the force applies to the alignment of the iridium–pyridine bonds of the phosphors toward the horizontal direction.

The type and magnitude of the non-bonded interactions are different for different phosphors and hosts, leading to different EDOs. The separated vdW and Coulomb energies as a function of the molecular orientation are depicted in Fig. 5b, c. The vdW energies in CBP:Ir(ppy)2tmd, TSPO1:Ir(ppy)2tmd, TSPO1:Ir(3′,5′,4-mppy)2tmd, and TSPO1:Ir(dmppy-ph)2tmd systems decrease, whereas the energy in UGH-2:Ir(ppy)2tmd increases as the ratio of the horizontal transition dipole moment (TDMH) increases. For a polar host molecule of TSPO1, Coulomb energies of the phosphors are lowered as TDMH increases. The variation of vdW energy depending on the molecular orientation was 3–5 kcal/mol, which is larger than the variation of Coulomb energy of 0–1 kcal/mol. The results indicate that vdW interactions (dipole-induced dipole and induced dipole-induced dipole interactions) between the aromatic ligands and the nearest host molecules are the main mechanism contributing to the molecular alignment of the phosphors. The Coulomb interaction helps further alignments of the phosphors if polar host materials are employed. For instance, Ir(ppy)2tmd and Ir(3′,5′,4-mppy)2tmd have a quadrupole composed of two dipoles from pyridines (δ+ charge) to Ir atom (2δ− charge). If there is a dipole in host molecule (i.e., TSPO1), dipole and quadrupole interaction [‒P = Oδ and δ+H(pyridine)] anchors one phosphor molecule to two host molecules, leading to a rather horizontal orientation of iridium–pyridines bond of the phosphors, which is approximately parallel to the TDM. In contrast, if host molecule has the positive surface potential (i.e., δ+(phenyl)3-Si-phenyl-Si-(Phenyl)3 δ+ in UGH-2), there must be a repulsive force between pyridine of phosphors and host molecules so that pyridine ring must be pushed to vacuum. Dispersion force between the conjugated phenyl substituents of Ir(dmppy-ph)2tmd and nearest neighbors anchors the pyridines onto the surface as well and lowers the energy with the molecular long axis lying on the surface. Meanwhile, random EDO of Ir(ppy)3 is attributed to three intermolecular interaction sites, resulting in random orientation of the molecule.

Figure 6a–c exhibit the representative molecular behaviors of phosphors and nearest host molecules during the deposition out of 50 cases (Supplementary Fig. 3) with different host–dopant combinations of UGH-2:Ir(ppy)2tmd, TSPO1:Ir(ppy)2tmd, and TSPO1:Ir(dmppy-ph)2tmd, respectively. Large vibrations, rotations, and diffusions of Ir(ppy)2tmd on the surface of the UGH-2 layer without lowering the energy were observed in the trajectory shown in Fig. 6a. The perpendicular alignment of pyridines occasionally formed on the surface resulted in vertical emitting dipole moment in average. On the other hand, a hydrogen atom at one of pyridines of Ir(ppy)2tmd faced toward an oxygen atom of TSPO1 with the −P = O··H(pyridine) distance around 0.4 nm at t = 2472 and 4560 ps, thereby the parallel alignment of the Ir-pyridines of Ir(ppy)2tmd to the surface. Larger quadrupole moment of Ir(3′,5′,4-mppy)2tmd than that of Ir(ppy)2tmd increased the strength of quadrupole–dipole interaction and resulted in enhancement of fraction of the horizontal dipole compared to Ir(ppy)2tmd. The horizontal EDO of Ir(ppy)2tmd in CBP could be understood by the dipole inducement in carbazole groups of CBP when the positive pole of pyridine approaches, but the interaction strength for the iridium−pyridines alignment between Ir(ppy)2tmd-CBP is smaller than that between Ir(ppy)2tmd−TSPO1. Compared to the former cases, the picture of Ir(dmppy-ph)2tmd shown in Fig. 6c is rather simple. The phosphor deposited onto the TSPO1 layer was stabilized after short time of deposition to the one with the horizontal iridium-pyridine-phenyl alignment and maintain the configuration. The much lower (larger) non-bonded interaction energy of Ir(dmppy-ph)2tmd in Fig. 5a restrained rotation of the molecule and the molecular configurations are easily fixed on the surface, resulting in much enhancement of horizontal EDO was achieved by the substitutions.

The origin of the molecular orientation and EDO of doped heteroleptic iridium complexes in vacuum-deposited organic layers is investigated using MD simulations and quantum mechanical analyses in direct comparison with experimental observation. Careful analyses of the simulation results revealed that molecular alignments of the phosphors are spontaneous by local electrostatic and van der Waals interaction with nearest host molecules interacting in a smaller scale than a molecule. The orientation of the TDM vector of the phosphors on the organic surfaces follows the direction of the ligand mainly participating in optical transition, such as pyridines in ppy, in the molecular alignment, whereas the alignment of ancillary ligand does not have a direct correlation with the EDO. Attractive interactions between pyridines of a phosphor and CBP (quadrupole-induced dipole interaction) or TSPO1 (quadrupole–dipole interaction) anchor the phosphor onto host molecules with the parallel iridium-pyridine alignment, thereby increasing the horizontal EDO. Ir(3′,5′,4-mppy)2tmd has larger quadrupole moment than Ir(ppy)2tmd resulted in further molecular alignment for the horizontal emitting dipole moment. The increase of the dispersion force along the direction of TDM was also effective on control of the molecular orientation for the horizontal EDO with lowered non-bonded interaction energy.

## Methods

### Quantum mechanical calculations and molecular dynamics simulations

Density functional theory (DFT) was used to obtain molecular geometries and electrostatic potentials of host and phosphors. Triplet TDMs of the same phosphors from T 1 to S 0 were also calculated via SOC-TDDFT. The DFT and SOC-TDDFT calculations and the follow-up analyses were performed with Schrodinger Materials Science Suite25 along with the quantum chemical engine, Jaguar29. A TDM having the largest oscillator strength among the three degenerated states of T 1 level (T x , T y , and T z ) obtained from the density functional calculations was used in this study as a representative TDM. All MD simulations were performed by Desmond30, 31, a MD engine implemented in the Schrodinger Materials Science Suite. Equilibration simulations prior to deposition were performed in NPT ensembles, where pressure and temperature were set constant via Nose–Hoover chain and Martyna–Tobias–Klein method, respectively. There were no explicit constraints to geometry and/or positions to any of the molecules that were introduced in the simulation box. The simulations were performed over NVIDIA general-purpose GPU cards (K80).

### Rotation matrix method

Rotation matrix method was used for transformation of the TDM vector from the molecular coordinate to the laboratory coordinate. Rotation angles of α, β, and γ are defined as the clockwise rotations to laboratories axes of n x -, n y -, and n z -axes, respectively. Then, the rotation matrixes for α, β, and γ rotations are followings:

$${R_\alpha } = \left( {\begin{array}{*{20}{c}}\\ 1 & 0 & 0 \\ \\ 0 & {\cos \alpha } & {\sin \alpha } \\ \\ 0 & { - \sin \alpha } & {\cos \alpha } \\ \end{array}} \right),$$
(4)
$${R_\beta } = \left( {\begin{array}{*{20}{c}}\\ {\cos \beta } & 0 & { - \sin \beta } \\ \\ 0 & 1 & 0 \\ \\ {\sin \beta } & 0 & {\cos \beta } \\ \end{array}} \right),$$
(5)
$${R_\gamma } = \left( {\begin{array}{*{20}{c}}\\ {\cos \gamma } & {\sin \gamma } & 0 \\ \\ { - \sin \gamma } & {\cos \gamma } & 0 \\ \\ 0 & 0 & 1 \\ \end{array}} \right).$$
(6)

Sequential αβγ rotations of the dopant molecules were extracted in every configurations of the MD simulation. A product of the three rotation matrixes gives a matrix representing the orientation of the dopant molecule by

$${R_{{\rm{total}}}} = {R_\gamma }{R_\beta }{R_\alpha }.$$
(7)

Finally, the TDM vectors in the laboratory coordinate were obtained by

$${\rm{TD}}{{\rm{M}}_{{\rm{Lab}}}} = {R_{{\rm{total}}}}{\rm{TD}}{{\rm{M}}_{{\rm{Mol}}}}.$$
(8)

### Calculation of a probability density function of TDMH

Integration of a probability density function, f, indicates a probability of a variable X between X = a and b.

$$P(a < X < b) = {\int}_{\!\!\!\!\!a}^{b} {{f_X}(x){\rm{d}}x} ,$$
(9)

where

$${\int}_{\!\!\!\!\! - \infty }^{\infty} {{f_X}(x){\rm{d}}x} = 1.$$
(10)

To calculate the probability density function of $${\sin ^2}\varphi$$ from an arbitrary vector, we define an arcsine function of

$$y = \arcsin (\sqrt x ),\,0 \le x \le 1,$$
(11)

which is a reversed function of $$y = {\sin ^2}x$$. For a monotonic function, the variables are related by

$${f_X}(x) = {f_Y}(y)\frac{{{\rm{d}}y}}{{{\rm{d}}x}}.$$
(12)

If we put $${f_Y}(y) = \sin (y)$$ and $$\frac{{{\rm{d}}y}}{{{\rm{d}}x}} = \frac{1}{{2\sqrt {x - {x^2}} }}$$ into equation (A4), the probability density function (f X ) is obtained as

$${f_X}(x) = \frac{1}{{2\sqrt {1 - x} }}.$$
(13)

### Data availability

The authors declare that all data supporting the findings of this study are available in the article and in Supplementary Information file. Additional information is available from the corresponding author upon request.

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## Acknowledgements

This work was supported by the Midcareer Research Program through an NRF (National Research Foundation) grant funded by the MSIP (Ministry of Science, ICT, and Future Planning) (2014R1A2A1A01002030). We appreciate the helpful comments from Drs Mathew D. Halls and H. Shaun Kwak from Schrödinger Inc., Prof. Youn Joon Jung from Seoul National University, and Dr. Denis Andrienko from Max Planck Institute for Polymer Research (MPIP).

## Author information

Authors

### Contributions

C.-K.M. prepared samples, designed experiments, demonstrated calculations and simulations, prepared mathematical models, and prepared the manuscript; K.-H.K. prepared materials; J.-J.K. directed experiments, calculation, and the manuscript.

### Corresponding author

Correspondence to Jang-Joo Kim.

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### Competing interests

The authors declare no competing financial interests.

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Moon, CK., Kim, KH. & Kim, JJ. Unraveling the orientation of phosphors doped in organic semiconducting layers. Nat Commun 8, 791 (2017). https://doi.org/10.1038/s41467-017-00804-0

• Accepted:

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• DOI: https://doi.org/10.1038/s41467-017-00804-0

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