# Photoluminescence of Cis-Polyacetylene Semiconductor Material

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Ground-State DFT

#### 2.2. Nonadiabatic Calculations

^{e(h)}shows the average relaxation time of the system and refers to the dynamics of the electronic relaxation for the electron (hole). In Equation (19), for ${P}_{e\left(h\right)}\left(t\right)$, we use the index $e$ to denote that the equation is the same for electrons and holes as well.

#### 2.3. Computational Details

## 3. Results and Discussion

_{gap(HSE06)}/E

_{gap(PBE)}. Figure 3b shows a comparison of the experimental spectra with the PBE simulated and HSE06 simulated absorption spectra, where the results obtained by the different functions (the PBE and HSE06 functions) qualitatively agreed with each other but there was a slight redshift in the B and C absorption peaks. Peak A shows the lowest transition energy but the highest intensity of absorption, and this occurred because of the bright transition. After we compared the simulated results with the experimental spectra, it can be concluded that the transition energies seem to agree, but the intensities and positions of peaks do not, probably because here, we looked at a single oligomer but, in the experiment, there was an ensemble.

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Geometry-optimized structure (ground state) of the polymer model aligned in the y−z plane. Cyan and grey colors represent C and H atoms, respectively.

**Figure 2.**Energies of the KS orbitals for single oligomer of undoped cis-polyacetylene and DOS represented by envelope functions, which follow the pattern of a particle in a box for both the occupied and unoccupied orbitals. (

**a**) Energy of the HO, HO + 1, HO + 2, LU, LU-1 and LU-2 orbitals. Occupied/unoccupied orbitals are counted by the quantum number n’/n. A pair of such indices labels a transition. (

**b**) The charge density of the orbitals: HO, HO + 1 and HO + 2, and LU, LU-1 and LU-2. Blue dashed lines indicate that the transition energy between the pair of orbitals in the cis-polyacetylene increased with an increase in the index of the unoccupied orbital and decreased with a decrease in the index of the occupied orbital.

**Figure 3.**Experimental and calculated ground-state absorption spectra of the polyacetylene. (

**a**) The absorption spectra were calculated using the PBE GGA function and the calculated absorption spectra using HSE06 hybrid functions [27]. (

**b**) Energy-shifted absorption calculated using the PBE function and the experimental absorption of cis- and trans-poly(1-ethynyl-pyrene) molecules [28]. The labeling of the transitions is the same as in Figure 2.

**Figure 4.**(

**a**) Examples of autocorrelation functions for nonadiabatic coupling matrix elements, according to Equations (15) and (19). The figure shows the autocorrelation functions ${M}_{ijkl}\left(\tau \right)$ for $i=k$ and $j=l$ for the following pairs of orbitals: $i=\mathrm{HO}-2,j=\mathrm{HO}-1$ (green), $i=\mathrm{HO},j=\mathrm{LU}$ (blue) and $j=\mathrm{LU}+1$ (red). Interestingly, all of them decay abruptly within 5 fs. (

**b**) Examples of the absolute values of Redfield tensor elements $\left|{R}_{iijj}\right|$ used to simulate the photoexcited dynamics.

**Figure 5.**(

**a**) Iso-contours of the distribution $\mathsf{\Delta}n\left(a,b\right)\left(\epsilon ,t\right)$ computed by Equation (23) providing the dynamics of electrons (yellow) and a hole (blue) after HO-1→LU + 1 photoexcitation in the cis-PA single oligomer; turquoise corresponds to the ground state distribution. (

**b**) Dynamics of the spatial distribution of charge distribution $\mathsf{\Delta}n\left(a,b\right)(z,t$ ) computed by Equation (31). (

**c**) Atomistic model of a single oligomer of cis-PA $=\mathrm{CH}-{\mathrm{CH}}_{3}$, where turquoise spheres represent carbon $\left(\mathrm{C}\right)$ and white spheres represent hydrogen $\left(\mathrm{H}\right)$. Vertical lines labeled as ${\tau}_{e}$ and ${\tau}_{h}$ indicate the time of the population transfer between the electron and hole orbitals.

**Figure 6.**Simulated photoexcited dynamics after excitation at 2.0 eV of the single undoped cis-polyacetylene oligomer. (

**a**) Dynamics of the exciton’s (electron−hole pair) energy dissipation with time. Colors correspond to the population scale according to a continuous change in the color: yellow stands for the maximum population and navy blue for zero population. (

**b**) Calculated time-resolved emission spectrum. Colors correspond to the intensity (oscillator strength) of the transition scaled from yellow (maximum intensity) to navy blue (zero). (

**c**) Integrated emission spectrum, where the features A, B and C correspond to the inter-band transitions and the feature M corresponds to the intra-band transition.

**Figure 7.**The transition energies and excitation energies (absorption (red) and emission/PL (blue) spectra) of the undoped single cis-polyacetylene oligomer. Note that inter-band transitions (A/A’, B/B’ and C/C’) are observed in both spectra, while the intra-band transition (M) is observed only in the PL spectrum.

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**MDPI and ACS Style**

Keya, K.N.; Jabed, M.A.; Xia, W.; Kilin, D. Photoluminescence of *Cis*-Polyacetylene Semiconductor Material. *Appl. Sci.* **2022**, *12*, 2830.
https://doi.org/10.3390/app12062830

**AMA Style**

Keya KN, Jabed MA, Xia W, Kilin D. Photoluminescence of *Cis*-Polyacetylene Semiconductor Material. *Applied Sciences*. 2022; 12(6):2830.
https://doi.org/10.3390/app12062830

**Chicago/Turabian Style**

Keya, Kamrun N., Mohammed A. Jabed, Wenjie Xia, and Dmitri Kilin. 2022. "Photoluminescence of *Cis*-Polyacetylene Semiconductor Material" *Applied Sciences* 12, no. 6: 2830.
https://doi.org/10.3390/app12062830