# Photoluminescence of _Cis_-Polyacetylene Semiconductor Material
## 3 Results and Discussion
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. 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\({}^{\prime}\)/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 4a describes several examples of \(M_{ijkl}(\tau)\). Using Equations (14)-(17), we can explain the average nonadiabatic interaction using the autocorrelation function of the electron-lattice interaction. This autocorrelation function shows several amplitudes, which provides information about the intensity of dissipative electronic transitions for the given indices \(i,j,k\) and \(l\). Interestingly, for any tested combination of indices, the autocorrelation function decayed abruptly within less than 5 fs, and from 0 fs to 350 fs, it showed a fluctuation in the autocorrelation function of the electron-to-lattice nonadiabatic interaction (as explained in what follows), and after 350 fs, there was no fluctuation in the autocorrelation function, as indicated by the straight line which goes up to \(\infty\) fs. This result justifies the Markovian approximation and time-independent form of the relaxation kernel in Equations (18) and (13) [18]. Figure 4: (**a**) Examples of autocorrelation functions for nonadiabatic coupling matrix elements, according to Equations (15) and (19). The figure shows the autocorrelation functions \(M_{ijkl}(\tau)\) 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 \(\left|R_{iij}\right|\) used to simulate the photoexcited dynamics. 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.  
At first, we extracted the Redfield tensor \(R_{iijj}\) from the nonadiabatic calculations of a single oligomer of the undoped _cis_-polyacetylene then simulated the photoexcitation dynamics (time evolution of electron\(-\)hole pairs of orbitals) of the model. Figure 4b shows the absolute values of selected elements of \(R_{iijj}\), where the blue diagonal lines refer to the valence band (VB) and the yellow diagonal lines indicate the conduction band. There are several diagonal lines from the left bottom corner to the right top corner.