## 3 Results and Discussion  
### ATZ Singlet Electronic States  
ATZ shown in Figure 2 is known to have multiple conformers according to the spatial orientation of three main planes: Alyllic group, tetrazolic, and phenyl rings. For the current work, the relevant conformers arise from the torsion of the allylic group, defined by the  
Figure 1: Postulated mechanism for the photodegradation of 1-phenyl-4-allyl-tetrazol-5-one (ATZ) in methanol [18]. dihedral angle \(\phi_{1-7-8-9}\). Figure 3 shows the dihedral angle dependence for partially optimised structures of ATZ-\(S_{0}\) using PCM. For each point, an optimisation of all degrees of freedom, except the angle, is carried out to establish the torsion potential. The torsion behaviour of \(S_{0}\) is similar for PBE0 and M06-HF functionals, the \(\phi\sim 0\) deg being the most stable structure. For B3 LYP, the most stable conformer is the one with \(\phi=-124\) deg; a similar trend has been also observed in gas-phase studies [19]. The energetic difference between the most stable conformer and the other minimums is larger in the case of M06-HF (2.6 kJ mol\({}^{-1}\)). Note also that the M06-HF shows a more repulsive behaviour when departing from the global minimum, in particular for the \(\pm 180\) deg with a barrier height of 11.5 kJ mol\({}^{-1}\). The relevant geometry parameters calculated for the ground-state \(S_{0}\) with each functional are given on Table 1. For completeness, the full equilibrium geometry, energy, and spectroscopy properties are given in the Supplementary Materials. Figure 3: Partially optimised potential energy as a a function of the conformational angle \(\phi_{1-7-8-9}\). The lines are spline-type for a better analysis. Figure 2: Singlet ground-state optimised ATZ molecule with the adopted atom labelling. It is clear that the studied functionals give the same results for the most relevant structural parameters, within the accuracy of the methods. Three of the most relevant normal modes for the reaction pathway of ATZ were also compared: \(v_{a}\) correspond to the CO stretching, \(v_{b}\) to the phenyl carbons stretching, and \(v_{c}\) to the N(1)-C(10) stretching. In addition, within the accuracy and limitations of the harmonic approximation, the larger zero-point energy \(E_{0}\) can be found in the case of M06-HF and the lower value on the B3 LYP. Such behaviour may be associated to the shape of the potential within the normal mode coordinates as observed in the literature [43]. The excitation transitions on the singlet states of ATZ at equilibrium geometry of the more stable conformer have been calculated using the TDDFT with the Tamm-Dancoff approximation [27]. Table 2 shows the vertical excitation energies, the components of the transition momentum, and the oscillator strength for the leading terms of the singlet manifold. In two of the functionals here studied, B3 LYP and PBE0, the larger value of the oscillator strength is associated to the \(S_{0}\to S_{1}\) transition \(f\sim 0.385\), although the energy gap is 0.22 eV larger in the case of PBE0. The M06-HF results show that the most intense transition corresponds to the \(S_{0}\to S_{3}\) with a oscillator strength of 0.66 and an energy of 6.5 eV. From the TDDFT calculation, the absorption spectrum has been simulated, as shown in Figure 4, by using Gaussian functions centred at the calculated wavelengths and with bandwidths-at-half-height equal to 18 nm. The absorption spectrum in methanol has been measured with a Cary 5000 Series UV-Vis-NIR spectrophotometer (Agilent Technologies), with maximum absorption below 0.5. Contrary to the gas phase spectrum, the possible absorption bands with wavelengths lower than 250 nm are masked by solvent absorption and are hence not shown in Figure 4. The experimental spectrum has (at least) two well defined shoulders at wavelengths higher than the main band maximum. Those are most probably due to the simultaneous changes in electronic and vibrational energy levels of the molecule (vibronic spectra).