## 3 Results and Discussion
### ATZ Singlet Electronic States
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{2}{c}{**B3 LYP**} & \multicolumn{2}{c}{**M06-HF**} & \multicolumn{2}{c}{**PBE0**} \\ \cline{2-7}
**Property** & \(\mathbf{S_{0}}\) & \(\mathbf{T  
Vibronic spectra features are more notorious for molecules in both gas and apolar media, but (although more smooth and broadened) can also be seen in polar media. The band around 250 nm is due to the aromatic ring and the typical progression in the symmetric ring-breathing vibration with a value of about 1500 cm\({}^{-1}\) observed, for example, see [PERSON] et al. [44]. As expected for a broadened spectra taken in polar media, the vibronic progression shoulders are more evident far from the main (high probability) absorption. The spectra that arises from the M06-HF shifts toward a lower wavelength centred at 200 nm although no experimental evidence corroborates such a behaviour. As expected from the oscillator strength and energy gap of the transitions, the B3 LYP and PBE0 are centred in a region near the experimental value \(\sim 250\) nm. It is also important to note that there are considerable difficulties associated with the comparison of the computed vertical excitation energies with the experimental band maximum value. The experimental bands for all these systems are quite diffuse, meaning there can be considerable uncertainty in the positions of the band maximum. In addition, in the calculation of the vertical excitation energies, several effects that can significantly change the positions of the band maxima in the experimental spectrum were ignored. In particular, these calculations neglect the effects of vibrations (e.g., vibronic coupling and Jahn-Teller distortions) [45], spin-orbit coupling [46], and the environment [47], in cases where the spectra have been measured in solution or in a condensed medium. Hence, without including these additional effects in our calculations, there may be considerable discrepancies between the computed excitation energies and experimental band maxima, even with higher levels of theory and large basis sets. In general it has been observed that the computed vertical excitation energies are larger than the experimental band [48]. No attempt has been made to include the adiabatic and the 0-0 transitions in the absorption spectra [49]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**State** & \(\Delta\)**E/eV** & \(\mu_{s}\)**/D** & \(\mu_{y}\)**/D** & \(\mu_{z}\)**/D** & \(f\) \\ \hline
**B3 LYP** & & & & & \\ \(S_{1}\) & 4.828 & 1.7950 & 0.0207 & \(-\)0.1817 & 0.3850 \\ \(S_{2}\) & 5.021 & \(-\)0.5511 & \(-\)0.0515 & 0.0439 & 0.0379 \\ \(S_{3}\) & 5.266 & 0.0730 & \(-\)0.0003 & 0.2090 & 0.0063 \\ \(S_{4}\) & 5.438 & \(-\)0.1353 & 0.0251 & \(-\)0.0600 & 0.0030 \\ \(S_{5}\) & 5.670 & 0.6462 & \(-\)0.2856 & 0.0912 & 0.0705 \\ \hline
**M06-HF** & & & & & \\ \(S_{1}\) & 5.677 & 0.2548 & 0.0990 & \(-\)0.0488 & 0.0107 \\ \(S_{2}\) & 6.003 & \(-\)0.0488 & 0.0136 & \(-\)0.3475 & 0.0181 \\ \(S_{3}\) & 6.085 & 2.0851 & 0.1603 & \(-\)0.2364 & 0.6603 \\ \(S_{4}\) & 6.544 & \(-\)0.2037 & \(-\)0.0297 & 0.1090 & 0.0087 \\ \(S_{5}\) & 7.082 & \(-\)1.0043 & \(-\)0.1280 & 0.0216 & 0.1779 \\ \hline
**PBE0** & & & & & \\ \(S_{1}\) & 5.042 & \(-\)1.7551 & \(-\)0.0594 & 0.1793 & 0.3849 \\ \(S_{2}\) & 5.203 & \(-\)0.8622 & \(-\)0.0361 & 0.0711 & 0.0956 \\ \(S_{3}\) & 5.499 & \(-\)0.1097 & \(-\)0.0062 & \(-\)0.2154 & 0.0079 \\ \(S_{4}\) & 5.749 & 0.1360 & \(-\)0.0439 & 0.0636 & 0.0034 \\ \(S_{5}\) & 5.962 & -0.5593 & 0.1908 & \(-\)0.1240 & 0.0533 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Vertical excitation energies, transition dipole and oscillator strength for the leading terms of the singlet electronic manifold.