## 2 Methods  
The photodegradation mechanism of ATZ in methanol has been suggested [18] taking into account the observed photoproduct pyrimidine (P). The mechanism, shown in Figure 1, involves the formation of a triplet biradical intermediary (M1), after the photoextrusion of molecular nitrogen. Pyrimidinone is formed after this intermediate undergoes a conformational rearrangement (M2) through the allyl group and an intramolecular proton transfer. Note that in the postulated mechanism, the pyrimidinone (P) is in the singlet state, after an intersystem crossing from the triplet state, although not shown in Figure 1 and in Ref [18].  
To validate the postulated mechanism, DFT and TDDFT electronic structure methods, as implemented in GAMESS [35], have been used to characterise energetically the relevant molecular intermediates and transition states. Methanol effects have been simulated by PCM [33; 34] for all structures, in which it is described as a polarised dielectric medium and characterised by the macroscopic dielectric constant \(\varepsilon=32.63\) obtained at \(T=298\,\mathrm{K}\). A cavity of molecular shape hosts the solute, and is usually built as a series of interlocking spheres centred on the solute nuclei. The solvent polarisation is represented by an apparent surface charge spread on the cavity surface. In the computational implementation, the surface charge is discretised in finite elements and the PCM integral operators are replaced by their matrix representation [36].  
Inherently to the (TD)DFT formulation is the issue related to the choice of the functional. Previously [19], B3 LYP has been used to rationalise the vibrational spectroscopy of the ATZ in gas phase. Several studies [37; 38] have shown detailed benchmarks for a more reliable functional selection. It has been shown [37; 38] that M06-HF and PBE0 show better performance than B3 LYP in a large set of systems, particularly in describing the barrier height of transition states and systems containing \(\pi\) electrons. For the current work, the B3 LYP functional was also employed, which provides a comparison with previous studies. Other possibilities could be also employed according to a process being studied as CAM-B3 LYP [39] for vertical excitations, or B3 LYP-D3 [40], LC-wPBE [41], wB97 XD [42], and M06-2X [30] to account for long-rage forces. However, the selection of the functionals employed has been based on the benchmarks [37; 38] and as an accuracy compromise that may describe the complete photochemical reaction process here studied. To improve previous results, keeping a balance between accuracy and computational effort, the [PERSON]'s cc-pVDZ basis-set [32] has been chosen for all calculations.  
The molecular structures for the singlet ground-state, \(S_{0}\), of ATZ and pyrimidine have been optimised using DFT, and the RHF self-consistent field wavefunction. The triplet state of ATZ, pyrimidine, and intermediates have been optimised using DFT with the ROHF self-consistent field wavefunction. Please note that the reaction mechanism occurs on the triplet state, except in the UV photoexcitation of ATZ and the final product. For the latter, both the singlet ground-state and the first triplet excited state has been characterised. The minimum localisation for all stable species has been carried out in a step-descent method using the quadratic approximation, with the gradient convergence criteria of \(1\times 10^{-4}\) E\({}_{0}\)a\({}_{0}^{-1}\) for the largest component of the gradient and 1/3 of that value for the root mean square gradient. After the stationary point geometry has been obtained, the harmonic vibrational calculation has been performed to confirm the minimum. For the transition states, the same criteria has been used but in a step-ascent approach, being confirmed by the presence of one imaginary frequency in the vibrational analysis.