^{1,a)}, Kyung-Ryang Wee

^{1}, Jeong Won Kim

^{2}, Chyongjin Pac

^{1}and Sang Ook Kang

^{1,a)}

### Abstract

Effects of intermolecular interactions on the occupied electronic structure of amorphous solid of a carbazole-based material were investigated under an assumption that the organic solid consists of randomly oriented assemblies of dimers. The electronic energy states were calculated on the ensemble of large number of random dimers, of which geometries are relaxed using semiempirical van der Waals density functional theory.Intermolecular interactions result in splitting of energy level, and further disorders occur by aggregation of randomly orientated molecules. As a result, frontier occupied energy states can be represented by a superposition of Gaussian distributions, including (i) a main distribution with full width at half maximum of 80–110 meV, depending on the methods of relaxation and (ii) shoulders separated from the center of the main distribution with a value as large as 150 meV. A possible origin for the appearance of these shoulders was ascribed to the presence of molecular assemblies consisting of more tightly bound dimers compared with the others.

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (MEST) of Korea (2011-0018595) and by the Center for Next Generation Dye-Sensitized Solar Cells (Grant No. 2011-0001055). We also acknowledge the Industrial strategic technology development program (10030814, Development of Organic materials for OLED) funded by the Ministry of Knowledge Economy (MKE, Korea).

I. INTRODUCTION

II. EXPERIMENTAL AND COMPUTATIONAL DETAILS

III. RESULTS AND DISCUSSION

A. Calculation of valence electronic states in single crystal geometry

B. Relaxation methods of ensemble of randomly oriented dimers

C. Dependence of distribution of energy states on the sampling condition from initial random dimers.

IV. CONCLUSION

### Key Topics

- Amorphous solids
- 21.0
- Intermolecular forces
- 19.0
- Density functional theory
- 16.0
- Photoemission
- 11.0
- Single crystals
- 10.0

## Figures

Comparison of the calculation results, (a) binding energy and (b) **H** and **H-1** energy levels as a function of distance between two molecules of 3PCBP.

Comparison of the calculation results, (a) binding energy and (b) **H** and **H-1** energy levels as a function of distance between two molecules of 3PCBP.

(a) Energy level diagrams for single crystal geometries with 1UC, 5UCs along a-axis, disordered UCs, and single molecule, in which single crystal structure is monoclinic, with lattice parameters of a = 12.62 Å, b = 7.27 Å, c = 16.01 Å, α = 90.00°, β = 110.75°, γ = 90.00°. (b) Comparison of UPS spectrum with simulated curves. The UPS was obtained for 10 nm thick film of 3PCBP. M1 denotes a single molecule of 3PCBP with optimized geometry and M2 denote a single molecule of 3PCBP of which geometry was obtained from X-ray diffraction. (c) Detailed illustration of **H** and **H-1** energy states.

(a) Energy level diagrams for single crystal geometries with 1UC, 5UCs along a-axis, disordered UCs, and single molecule, in which single crystal structure is monoclinic, with lattice parameters of a = 12.62 Å, b = 7.27 Å, c = 16.01 Å, α = 90.00°, β = 110.75°, γ = 90.00°. (b) Comparison of UPS spectrum with simulated curves. The UPS was obtained for 10 nm thick film of 3PCBP. M1 denotes a single molecule of 3PCBP with optimized geometry and M2 denote a single molecule of 3PCBP of which geometry was obtained from X-ray diffraction. (c) Detailed illustration of **H** and **H-1** energy states.

Distribution of **H** and **H-1** energy states of (a) random 500 dimers with fixed separation of 9.5 Å and (b) separation relaxed 500 dimers, where each circle represents the number of states in a 0.01 eV range. The distributions appearing in the range of less than –3.5 eV originated from **H-2** and **H-3** energy levels. (Left insets) Definition of separation, polar, and azimuthal angles. (Right insets) Radial distribution of 500 dimers.

Distribution of **H** and **H-1** energy states of (a) random 500 dimers with fixed separation of 9.5 Å and (b) separation relaxed 500 dimers, where each circle represents the number of states in a 0.01 eV range. The distributions appearing in the range of less than –3.5 eV originated from **H-2** and **H-3** energy levels. (Left insets) Definition of separation, polar, and azimuthal angles. (Right insets) Radial distribution of 500 dimers.

(a) Binding energy curve as a function of beta angle and (b) corresponding optimized z coordinate

(a) Binding energy curve as a function of beta angle and (b) corresponding optimized z coordinate

(a) Average separation, average binding energy, and (b) average energy level splittings of 500 dimers as a function of optimization cycles. Optimization cycle indexes of –1 and 0 represent random and R only optimization, respectively. (c) Distribution of **H** and **H-1** energy levels of finally optimized dimers. The distributions appearing in the range of less than −3.5 eV originated from **H-2** and **H-3** energy levels. (Inset) Radial distribution of 500 dimers.

(a) Average separation, average binding energy, and (b) average energy level splittings of 500 dimers as a function of optimization cycles. Optimization cycle indexes of –1 and 0 represent random and R only optimization, respectively. (c) Distribution of **H** and **H-1** energy levels of finally optimized dimers. The distributions appearing in the range of less than −3.5 eV originated from **H-2** and **H-3** energy levels. (Inset) Radial distribution of 500 dimers.

Distribution of **H** and **H-1** energy levels of 500 dimers of which geometries were obtained from (a) optimization of Euler angles and separations from the 500 dimers in Fig. 3(a) using analytic potential, and (b) optimization of separations from 500 dimers in Fig. 6(a) using B97D. The distributions appearing in the range of less than –3.5 eV originated from **H-2** and **H-3** energy levels.

Distribution of **H** and **H-1** energy levels of 500 dimers of which geometries were obtained from (a) optimization of Euler angles and separations from the 500 dimers in Fig. 3(a) using analytic potential, and (b) optimization of separations from 500 dimers in Fig. 6(a) using B97D. The distributions appearing in the range of less than –3.5 eV originated from **H-2** and **H-3** energy levels.

Distribution of energy states of optimized 500 dimers, of which initial geometries were randomly sampled from the regions with binding energy smaller than –0.35, –0.2, –0.1, and +0.3 eV, respectively. (Note that the values of binding energy were obtained using Eq (2), and these are different from those of Fig. 5(a), which were obtained using B97D) The monomer energy states are also shown for comparison. The distributions appearing in the range of less than –3.5 eV originated from **H-2** and **H-3** energy levels. (Inset) Distribution of binding energies of the initial 1 355 260 random dimers, in which the binding energies were calculated using Eq. (2).

Distribution of energy states of optimized 500 dimers, of which initial geometries were randomly sampled from the regions with binding energy smaller than –0.35, –0.2, –0.1, and +0.3 eV, respectively. (Note that the values of binding energy were obtained using Eq (2), and these are different from those of Fig. 5(a), which were obtained using B97D) The monomer energy states are also shown for comparison. The distributions appearing in the range of less than –3.5 eV originated from **H-2** and **H-3** energy levels. (Inset) Distribution of binding energies of the initial 1 355 260 random dimers, in which the binding energies were calculated using Eq. (2).

## Tables

Energy scale adjustment to fit the experimental UPS spectrum and comparison of the optimum distances and binding energies for 3PCBP obtained using different methods.

Energy scale adjustment to fit the experimental UPS spectrum and comparison of the optimum distances and binding energies for 3PCBP obtained using different methods.

Comparison of the physical properties among several ensembles of dimers obtained using different relaxation methods.

Comparison of the physical properties among several ensembles of dimers obtained using different relaxation methods.

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