Mechanism of the Photochemical Isomerization and Oxidation of 2-Butenedial: A Theoretical Study

Under tropospheric conditions, 2-butenedial is photochemically removed to produce secondary organic aerosol. Upon solar irradiation in the lower troposphere, the main photochemical products are ketene-enol (a key intermediate product), furanones, and maleic anhydride. The oxidative reaction mechanism was studied using the multireference method CASSCF to explore the hypersurface of the two most accessible singlet excited states, and by DFT for the ground state. Photoisomerization of 2-butenedial in the first excited state directly produces ground state ketene-enol upon nonradiative relaxation. From this intermediate, furan-2-ol and successively 3H-furan-2-one and 5H-furan-2-one are formed. The cooperative effect of two water molecules is essential to catalyze the cyclization of ketene-enol to furan-2-ol, followed by hydrogen transfers to furanones. Two water molecules are also necessary to form maleic anhydride from furan-2-ol. For this last reaction, in which one extra oxygen must be acquired, we hypothesize a mechanism with singlet oxygen as the oxidant.


Introduction
Unsaturated 1,4-dicarbonyl compounds are produced by an OH reaction with aromatic hydrocarbons, such as toluene, xylenes, trimethylbenzenes, ethylbenzene [1], and o-ethyltoluene, benzene [2], or by biomass combustion [3]. The oxidation mechanisms of some of these reactions have been theoretically investigated and have been shown to form carbonyl compounds (see for instance Ref. [4]). In particular, under atmospheric conditions, dicarbonyl compounds are rapidly photochemically degraded [5].
The photolysis and the reaction with OH of Z-and E,E-2,4-hexadienedial were investigated by Barnes et al. [6]. They concluded that the reaction with OH radicals was normally a secondary channel and only during the summertime could OH radical concentrations compete with photolysis. The identified products of the photolysis were 2-formyl-2H-pyran, 3,4-diformyl-cyclobutene, and 2-butenal-4-yl-ketene.
In a recent experimental study [7], Newland and co-workers investigated the photochemistry of 2-butenedial and 4-oxo-2-pentenal in an outdoor photoreactor (Euphore), in the presence and absence of OH radicals. The major products of the degradation of 2butenedial, detected in situ by FTIR spectroscopy, were 3H-furan-2-one, maleic anhydride, CO, and an unidentified carbonyl compound. Maleic anhydride was supposed to form after tautomerization of the ketene-enol (which appears to be an important intermediate) to ketene-carbonyl. Formaldehyde, glyoxal, 5H-furan-2-one, and acrolein were also detected in minor quantity. The amount of HCO and CH 3 CO radicals were negligible under these experimental conditions. On the other hand, the formation of CO, CO 2 , and C 2 H 2 products upon photolysis of butenedial was also reported by Marshall et al. and by Back and Parsons [8,9]. Maleic anhydride can in turn produce maleic acid. Röhrl et al. observed that its hydrolysis, promoted by water molecules, could be a possible source of the acid being detected in the atmosphere [10].
Despite all these studies, the formation mechanism of 3H-furan-2-one and maleic anhydride under photolysis of butenedial remain still uncertain and open to further investigations.
In this study, we theoretically investigate the singlet reaction mechanisms of 2-butenedial photooxidation, focusing on the formation of the experimentally detected furanones (isomerization) and maleic anhydride (oxidation). The postulated formation mechanisms of these products proposed in the experimental papers will be flanked by our computations, by which we will explore the lowest energy singlet surfaces to see if some viable pathways to these products are present; if these pathways are fully defined on the excited surfaces or only in part; in this case, we will determine under which circumstances the ground state surface is involved.
Because we found a low-barrier mechanism leading to the ketene-enol in the S 1 surface, followed by an S 1 /S 0 conical intersection, we focused on the singlet multiplicity, but we cannot exclude the contribution of low-energy triplet states.
The more promising reactant isomer to initiate some chemical transformation is the (Z)-2-butenedial with the two carbonyls in s-cis and s-trans conformations with respect to the central double bond (for short: Zze, in Figure 1).
Molecules 2023, 28, x FOR PEER REVIEW 3 of 12 conditions, the photolysis reaction is considered the major atmospheric sink for E-butenedial [25]. Despite all these studies, the formation mechanism of 3H-furan-2-one and maleic anhydride under photolysis of butenedial remain still uncertain and open to further investigations.
In this study, we theoretically investigate the singlet reaction mechanisms of 2-butenedial photooxidation, focusing on the formation of the experimentally detected furanones (isomerization) and maleic anhydride (oxidation). The postulated formation mechanisms of these products proposed in the experimental papers will be flanked by our computations, by which we will explore the lowest energy singlet surfaces to see if some viable pathways to these products are present; if these pathways are fully defined on the excited surfaces or only in part; in this case, we will determine under which circumstances the ground state surface is involved.
Because we found a low-barrier mechanism leading to the ketene-enol in the S1 surface, followed by an S1/S0 conical intersection, we focused on the singlet multiplicity, but we cannot exclude the contribution of low-energy triplet states.
The more promising reactant isomer to initiate some chemical transformation is the (Z)-2-butenedial with the two carbonyls in s-cis and s-trans conformations with respect to the central double bond (for short: Zze, in Figure 1).

Formation of Ketene-Enol
In 2-butenedial, the first two excited states S1 and S2 are close in energy: with respect to the ground state, 82.2 and 88.9 kcal mol −1 (corresponding to ≈350 nm, S1 and ≈320 nm, S2, respectively) for vertical transitions, or 65.7 (S1) and 75.5 (S2) kcal mol −1 for adiabatic transitions, as presented in Scheme 1. Ketene-enol is formed by the photochemical process. When irradiated, aldehydes with chains longer than four carbon atoms undergo a Norrish type II reaction step, which involves intramolecular H atom abstraction in the first excited state. The two closest excited states are both characterized by excitation from the in-plane pO − pO and pO + pO combinations to the empty  4 orbital (see Section 3).

Formation of Ketene-Enol
In 2-butenedial, the first two excited states S 1 and S 2 are close in energy: with respect to the ground state, 82.2 and 88.9 kcal mol −1 (corresponding to ≈350 nm, S 1 and ≈320 nm, S 2 , respectively) for vertical transitions, or 65.7 (S 1 ) and 75.5 (S 2 ) kcal mol −1 for adiabatic transitions, as presented in Scheme 1. Ketene-enol is formed by the photochemical process. When irradiated, aldehydes with chains longer than four carbon atoms undergo a Norrish type II reaction step, which involves intramolecular H atom abstraction in the first excited state. The two closest excited states are both characterized by excitation from the in-plane p O − p O and p O + p O combinations to the empty π 4 orbital (see Section 3).
In the S 2 state, the barrier for hydrogen transfer from C to O to obtain ketene-enol is very large (∆E ‡ = 28.7 kcal mol −1 ). Ring closure (∆E ‡ = 14.6 kcal mol −1 ) has a lower barrier, but internal conversion through a conical intersection S 2 /S 1 is the fastest step (∆E ‡ = 8.9 kcal mol −1 ). In any case, the oscillator strength (Table A1 in the Appendix A) indicates that the S 2 state is scarcely populated.
In the S 1 state, the H transfer has a barrier of 6.4 kcal mol −1 only, much lower than ring closure (∆E ‡ = 29.1 kcal mol −1 ). However, the ketene-enol in the first excited state does not exist as a minimum, since a ketene-enol-like structure corresponds to a conical intersection S 1 /S 0 . A second conical intersection with geometry closer to the TS for Htransfer is present but its energy is less favorable. The energies of the most relevant pathway (thick arrows in Scheme 1) were refined by calculations with a better basis set (see Section 3). With the larger basis set, the Norrish type II barrier is only ∆E ‡ = 2.1 kcal mol −1 . The atomic displacements for the imaginary frequency of the TS H-transfer (1292 i cm −1 ) correspond to a [1,5] hydrogen shift. This barrier was also estimated by EOM-CCSD/6-31G(d) computations [26][27][28], which gave an even lower value ∆E ‡ = 0.1 kcal mol −1 .
The non-existence of ketene-enol as a minimum in the S 1 hypersurface and the conical intersection S 1 /S 0 was also found by Blancafort for o-phthalaldehyde photochemistry [17]. In the S2 state, the barrier for hydrogen transfer from C to O to obtain ketene-enol is very large (E ‡ = 28.7 kcal mol −1 ). Ring closure (E ‡ = 14.6 kcal mol −1 ) has a lower barrier, but internal conversion through a conical intersection S2/S1 is the fastest step (E ‡ = 8.9 kcal mol −1 ). In any case, the oscillator strength (Table A1 in the Appendix A) indicates that the S2 state is scarcely populated.
In the S1 state, the H transfer has a barrier of 6.4 kcal mol −1 only, much lower than ring closure (E ‡ = 29.1 kcal mol −1 ). However, the ketene-enol in the first excited state does not exist as a minimum, since a ketene-enol-like structure corresponds to a conical intersection S1/S0. A second conical intersection with geometry closer to the TS for H-transfer is present but its energy is less favorable. The energies of the most relevant pathway (thick arrows in Scheme 1) were refined by calculations with a better basis set (see Section 3). With the larger basis set, the Norrish type II barrier is only E ‡ = 2.1 kcal mol −1 . The atomic displacements for the imaginary frequency of the TS H-transfer (1292 i cm −1 ) correspond to a [1,5] hydrogen shift. This barrier was also estimated by EOM-CCSD/6-31G(d) computations [26][27][28], which gave an even lower value E ‡ = 0.1 kcal mol −1 .
The non-existence of ketene-enol as a minimum in the S1 hypersurface and the conical intersection S1/S0 was also found by Blancafort for o-phthalaldehyde photochemistry [17].

Formation of Furanones
Considering the work of Newland et al. [7], it can be seen in Figure S10 that during irradiation, the formation rates of 2-butenedial and ketene-enol showed specular behavior: as butenedial was photolyzed and its concentration declined, that of ketene-enol increased. In the dark, a similar specular behavior was observed for ketene-enol and 3H-furan-2-one. It can be noticed that 3H-furan-2-one is formed both during irradiation and in the dark. When irradiated, its concentration increased almost linearly; in the dark, its formation went on, but slowing down and tending to a plateau. This behavior can be attributed to the conversion of the declining amount of ketene-enol to 3H-furan-2-one. Our proposed mechanism is consistent with this picture.
Ring closure on the ground state surface to form the furanone ring directly from the ketene-enol (A) is not possible (see Scheme 2). When the enolic oxygen approaches C1, a purely repulsive energy profile is obtained. The hypothetically zwitterionic intermediate, the precursor of the furanones does not even exist as a minimum on the potential energy surface (compare Figure 6 in Ref. [12] and Figure 9 in Ref. [7]).
tributed to the conversion of the declining amount of ketene-enol to 3H-furan-2-one. Our proposed mechanism is consistent with this picture.
Ring closure on the ground state surface to form the furanone ring directly from the ketene-enol (A) is not possible ( see Scheme 2). When the enolic oxygen approaches C1, a purely repulsive energy profile is obtained. The hypothetically zwitterionic intermediate, the precursor of the furanones does not even exist as a minimum on the potential energy surface (compare Figure 6 in Ref. [12] and Figure 9 in Ref. [7]).
Despite our efforts to identify a viable pathway connecting ketene-enol A to 3H-furan-2-one and 5H-furan-2-one, all attempts failed. Further details are provided in the Scheme S1 in the Supplementary Materials.
Weingart et al. studied the formation of 3-methylphthalide from a ketene intermediate [29]. In their work, the ketene was formed by photoexcitation of o-acetylbenzaldehyde by a Norrish type II reaction, similar to that shown in Scheme 1. Their computed barrier connecting the ketene-enol to a cyclic enol, the precursor of the lactone, was 40 kcal mol −1 . The authors demonstrated that water molecules catalyze ring closures. Although a single water molecule was not sufficient to significantly change the energy barrier, the addition of a second water molecule lowered the above-mentioned barrier to 2.5 kcal mol −1 . In effect, a cooperative action of water has been invoked under many disparate circumstances (see for instance Refs [30,31]).
In our case, the formation of the main products requires the presence of water molecules too, and a cooperative effect seems to be needed to promote both cyclization and hydrogen migration to form furan-2-ol and the two furanones. An intermediate similar to furan-2-ol was also previously hypothesized by Scaiano et al. [16] and Fröbel et al. [18], who both studied the photochemistry of o-phthalaldehyde.
Under typical tropospheric conditions, with a relative humidity of 50%, the water concentration in the gas phase is about 10 17 molec cm −3 , but in the Euphore photoreactor, Newland et al. carried out their experiments under dry conditions [7]. The water vapor concentration was estimated to be below 1% [32] but above 1·10 15 molec cm −3 . Under such conditions, the ratio of water to 2-butenedial molecules is still above 100:1, and the assumption of water intervention in the reaction mechanism seems to be reasonable.
Without water molecules, the barriers for ketene-enol cyclization (TS A-B, G ‡ = 46 kcal mol −1 ) and tautomerization of furan-2-ol (G ‡ = 61.3 and 96.4 kcal mol −1 for TS B-C and TS B-D, respectively) are exceedingly large (Scheme 3, in blue). The second water molecule is particularly important for TS B-C. Through water intervention, cyclization through TS A-B becomes viable. In TS A-B, the imaginary frequency (164 i cm −1 ) corresponds to multiple H transfers, which ultimately results in an H shift from one oxygen (enole) to the other (ketene) (see Figure S2).
Despite our efforts to identify a viable pathway connecting ketene-enol A to 3H-furan-2-one and 5H-furan-2-one, all attempts failed. Further details are provided in the Scheme S1 in the Supplementary Materials.
Weingart et al. studied the formation of 3-methylphthalide from a ketene intermediate [29]. In their work, the ketene was formed by photoexcitation of o-acetylbenzaldehyde by a Norrish type II reaction, similar to that shown in Scheme 1. Their computed barrier connecting the ketene-enol to a cyclic enol, the precursor of the lactone, was 40 kcal mol −1 . The authors demonstrated that water molecules catalyze ring closures. Although a single water molecule was not sufficient to significantly change the energy barrier, the addition of a second water molecule lowered the above-mentioned barrier to 2.5 kcal mol −1 . In effect, a cooperative action of water has been invoked under many disparate circumstances (see for instance Refs [30,31]).
In our case, the formation of the main products requires the presence of water molecules too, and a cooperative effect seems to be needed to promote both cyclization and hydrogen migration to form furan-2-ol and the two furanones. An intermediate similar to furan-2-ol was also previously hypothesized by Scaiano et al. [16] and Fröbel et al. [18], who both studied the photochemistry of o-phthalaldehyde.
Under typical tropospheric conditions, with a relative humidity of 50%, the water concentration in the gas phase is about 10 17 molec cm −3 , but in the Euphore photoreactor, Newland et al. carried out their experiments under dry conditions [7]. The water vapor concentration was estimated to be below 1% [32] but above 1·10 15 molec cm −3 . Under such conditions, the ratio of water to 2-butenedial molecules is still above 100:1, and the assumption of water intervention in the reaction mechanism seems to be reasonable.
Without water molecules, the barriers for ketene-enol cyclization (TS A-B, ∆G ‡ = 46 kcal mol −1 ) and tautomerization of furan-2-ol (∆G ‡ = 61.3 and 96.4 kcal mol −1 for TS B-C and TS B-D, respectively) are exceedingly large (Scheme 3, in blue). The second water molecule is particularly important for TS B-C. Through water intervention, cyclization through TS A-B becomes viable. In TS A-B, the imaginary frequency (164 i cm −1 ) corresponds to multiple H transfers, which ultimately results in an H shift from one oxygen (enole) to the other (ketene) (see Figure S2). 5H-furan-2-one Scheme 3. Formation of furanones form ketene-enol, in the ground state. Blue: gas phase without explicit water molecules; black: gas phase with one explicit water molecule; red: gas phase with two explicit water molecules. For the sake of clarity, the two water molecules are not shown in this scheme, but the relevant transition structures are shown in Figure 2. G(298 K) in kcal mol −1 . Further attempts to form furanones without explicit water molecules are reported in the Supplementary Materials.

Formation of Maleic Anhydride
Starting from the ketene-enol A, a widely accepted sequence of steps (triggered by OH and in the presence of a significant tropospheric NOx concentration) could lead to maleic anhydride. The reaction begins with hydrogen abstraction by OH and concerted cyclization. Subsequent O2 addition, NO intervention to transform a peroxyl radical into an oxyl radical, and finally H abstraction by O2 would produce maleic anhydride with low-computed energy barriers (see Scheme S2 in the Supplementary Materials).
However, Newland et al. [7] experimented the addition of propan-2-ol as an OH scavenger and noted that the measured yield of maleic anhydride did not change significantly. This indicates that the above OH-initiated sequence, cannot be the dominant pathway for the anhydride. Further attempts to form furanones without explicit water molecules are reported in the Supplementary Materials.

Formation of Maleic Anhydride
Starting from the ketene-enol A, a widely accepted sequence of steps (triggered by OH and in the presence of a significant tropospheric NO x concentration) could lead to maleic anhydride. The reaction begins with hydrogen abstraction by OH and concerted cyclization. Subsequent O 2 addition, NO intervention to transform a peroxyl radical into an oxyl radical, and finally H abstraction by O 2 would produce maleic anhydride with low-computed energy barriers (see Scheme S2 in the Supplementary Materials).
However, Newland et al. [7] experimented the addition of propan-2-ol as an OH scavenger and noted that the measured yield of maleic anhydride did not change significantly. This indicates that the above OH-initiated sequence, cannot be the dominant pathway for the anhydride.
Consequently, we put forward a different mechanism in which another oxidant could be responsible for the initial step toward the anhydride. Based on its concentration and reactivity, singlet oxygen ( 1 ∆ g O 2 , 1 O 2 for short) appears to be a reasonable candidate. 1 O 2 is detected in the troposphere at a concentration of ca. 10 8 molec cm −3 [33], which is two orders of magnitude higher than that of the OH radical. 1 O 2 could be the initiator by adding to furan-2-ol B, which can form as seen in the presence of two water molecules (see Scheme 4).
In our model, furan-2-ol B, formed after cyclization of the ketene-enol (see Scheme 1), undergoes a [π4 + π2] cycloaddition to form the endoperoxide E. The breaking of the O-O bond, accompanied by concerted H 2 O loss, leads to maleic anhydride F. The picture of this transition structure is shown in Figure 3. Although the O-O bond is weak, the free energy barrier for its homolytic dissociation is too large (25.7 kcal mol −1 ) compared to the experimental rate of the reaction. In this case, again, two explicit water molecules can catalyze the reaction, lowering the free energy barrier of TS E-F to 15.4 kcal mol −1 .
Consequently, we put forward a different mechanism in which another oxidant could be responsible for the initial step toward the anhydride. Based on its concentration and reactivity, singlet oxygen ( 1 Δg O2, 1 O2 for short) appears to be a reasonable candidate. 1 O2 is detected in the troposphere at a concentration of ca. 10 8 molec cm −3 [33], which is two orders of magnitude higher than that of the OH radical. 1 O2 could be the initiator by adding to furan-2-ol B, which can form as seen in the presence of two water molecules (see Scheme 4).   Figure 3. Although the O-O bond is weak, the free energy barrier for its homolytic dissociation is too large (25.7 kcal mol −1 ) compared to the experimental rate of the reaction. In this case, again, two explicit water molecules can catalyze the reaction, lowering the free energy barrier of TS E-F to 15.4 kcal mol −1 .
Other possible mechanisms of oxidation initiated by radical addition or hydrogen abstraction by OOH radical have been considered but they have been ruled out because of the high-energy barriers of some steps.

CASSCF Method
To explore the reaction hypersurface topology of the first and second excited states and formation of ground state ketene-enol, as described in Scheme 1, the multi-configuration self-consistent field approach (MCSCF), in its CASSCF (complete active space) version was used [34]. The third excited state lays about 100 kcal mol −1 (290 nm) above the ground state and its contribution should be negligible because of the scarce sunlight Scheme 4. Formation of maleic anhydride from 2-furanol B, initiated by 1 O 2 . Blue: gas phase without explicit water molecules; red: gas phase with two explicit water molecules. For the sake of clarity, the two water molecules are not shown in this scheme but a picture of TS E-F is shown in Figure 3. could be responsible for the initial step toward the anhydride. Based on its concentration and reactivity, singlet oxygen ( 1 Δg O2, 1 O2 for short) appears to be a reasonable candidate. 1 O2 is detected in the troposphere at a concentration of ca. 10 8 molec cm −3 [33], which is two orders of magnitude higher than that of the OH radical. 1 O2 could be the initiator by adding to furan-2-ol B, which can form as seen in the presence of two water molecules (see Scheme 4).   Figure 3. Although the O-O bond is weak, the free energy barrier for its homolytic dissociation is too large (25.7 kcal mol −1 ) compared to the experimental rate of the reaction. In this case, again, two explicit water molecules can catalyze the reaction, lowering the free energy barrier of TS E-F to 15.4 kcal mol −1 .
Other possible mechanisms of oxidation initiated by radical addition or hydrogen abstraction by OOH radical have been considered but they have been ruled out because of the high-energy barriers of some steps.

CASSCF Method
To explore the reaction hypersurface topology of the first and second excited states and formation of ground state ketene-enol, as described in Scheme 1, the multi-configuration self-consistent field approach (MCSCF), in its CASSCF (complete active space) version was used [34]. The third excited state lays about 100 kcal mol −1 (290 nm) above the ground state and its contribution should be negligible because of the scarce sunlight Other possible mechanisms of oxidation initiated by radical addition or hydrogen abstraction by OOH radical have been considered but they have been ruled out because of the high-energy barriers of some steps.

CASSCF Method
To explore the reaction hypersurface topology of the first and second excited states and formation of ground state ketene-enol, as described in Scheme 1, the multi-configuration self-consistent field approach (MCSCF), in its CASSCF (complete active space) version was used [34]. The third excited state lays about 100 kcal mol −1 (290 nm) above the ground state and its contribution should be negligible because of the scarce sunlight irradiation at ground level at that wavelength (see for instance Figure 3.32 ([35], p. 80)). The active space adopted in this study is labeled (12,10), indicating 12 electrons in 10 orbitals. It includes all six π system orbitals, two lone pairs of the oxygen atoms, and one σ C-H bonding MO of the aldehyde with its antibonding counterpart (the C-H involved in the initial tautomerization step). A plot of the molecular orbitals in the active space is shown in Figure 4.
The excited state structures of the minima, TS, and conical intersections were calculated as the state average (SA-CASSCF) of the first three states, considering equal weights. In the multireference calculations, the basis set used to optimize the geometries and to assess the nature of the critical points was Pople's polarized split valence shell 6-31G(d) [36,37]. For the S 1 state only, onto which the initial important step takes place, the energies were refined by single point calculations with Dunning's cc-pVTZ basis set [38].
The SA-CASSCF gradient optimizations with numerical Hessian computations were performed by the MOLPRO program [39]. Numerical harmonic vibrational frequencies were computed to test the nature of the critical points.
irradiation at ground level at that wavelength (see for instance Figure 3.32 ([35], p. 80)). The active space adopted in this study is labeled (12,10), indicating 12 electrons in 10 orbitals. It includes all six π system orbitals, two lone pairs of the oxygen atoms, and one C-H bonding MO of the aldehyde with its antibonding counterpart (the C-H involved in the initial tautomerization step). A plot of the molecular orbitals in the active space is shown in Figure 4. The excited state structures of the minima, TS, and conical intersections were calculated as the state average (SA-CASSCF) of the first three states, considering equal weights. In the multireference calculations, the basis set used to optimize the geometries and to assess the nature of the critical points was Pople's polarized split valence shell 6-31G(d) [36,37]. For the S1 state only, onto which the initial important step takes place, the energies were refined by single point calculations with Dunning's cc-pVTZ basis set [38].
The SA-CASSCF gradient optimizations with numerical Hessian computations were performed by the MOLPRO program [39]. Numerical harmonic vibrational frequencies were computed to test the nature of the critical points.

Density Functional Theory Study
To study the main products formation pathways, since explicit water molecules proved necessary, the occurrence of different chemical events and 1 O2 intervention had to be considered (see the Section 2). Consequently, the CASSCF active space would have grown too large. For this reason, the stationary points of chemical interest on the ground state energy hypersurface (minima and transition structures) were determined at DFT by gradient procedures and with the M06-2X functional [42] and the cc-pVTZ basis set [38]. The nature of the critical points was tested by vibrational analysis. Harmonic vibrational frequencies were computed by analytically determining the second derivatives of the Hessian matrix. The thermochemical corrections provided estimates of the relative Gibbs free energies (ΔG). Gibbs free energy and, in particular, the ΔS term were estimated by the total partition function, which includes translational, rotational, electronic, and vibrational contributions [43,44]. ΔG values at T = 298.15 K, are reported in this paper.
For singlet diradicaloid structures, originating from the reaction with 1 O2, the wavefunction stability was checked. Upon relaxation, by allowing orbital rotations, the resulting spin-mixed wavefunction gives a better description of the electron distribution, but alters the energy, so the energy values were corrected by Yamaguchi's formula [45,46].

Density Functional Theory Study
To study the main products formation pathways, since explicit water molecules proved necessary, the occurrence of different chemical events and 1 O 2 intervention had to be considered (see the Section 2). Consequently, the CASSCF active space would have grown too large. For this reason, the stationary points of chemical interest on the ground state energy hypersurface (minima and transition structures) were determined at DFT by gradient procedures and with the M06-2X functional [42] and the cc-pVTZ basis set [38]. The nature of the critical points was tested by vibrational analysis. Harmonic vibrational frequencies were computed by analytically determining the second derivatives of the Hessian matrix. The thermochemical corrections provided estimates of the relative Gibbs free energies (∆G). Gibbs free energy and, in particular, the ∆S term were estimated by the total partition function, which includes translational, rotational, electronic, and vibrational contributions [43,44]. ∆G values at T = 298.15 K, are reported in this paper.
For singlet diradicaloid structures, originating from the reaction with 1 O 2 , the wavefunction stability was checked. Upon relaxation, by allowing orbital rotations, the resulting spin-mixed wavefunction gives a better description of the electron distribution, but alters the energy, so the energy values were corrected by Yamaguchi's formula [45,46]. Some energies were refined using the CCSD(T) [47,48] method with the cc-pVTZ basis set [38].
Geometry optimizations and thermochemical calculations at DFT were carried out by using the GAUSSIAN16 system of programs [49].

Conclusions
From the experimental investigation by Newland et al. [7], we know that that the most important photochemical products obtained upon solar irradiation of butenedial are 3H-furan-2-one and maleic anhydride. Moreover, a key intermediate product is the keteneeno, generated by H transfer in the irradiated Zze reactant, H moving from one aldehydic carbon to the opposite oxygen. This theoretical study aimed to elucidate the mechanism by which the main products are obtained upon solar irradiation in the lower troposphere.
Two principal conclusions are drawn from the scrutiny of the three lowest electronic states in Zze butenedial.
(1) The second excited state has a role only in populating the first excited state because the system easily passes through a conical intersection S 2 /S 1 , in correspondence with geometry very close to that of the reactant Zze butenedial itself. In the first excited state, an even lower barrier is found in the correspondence of H transfer towards ketene-enol, and isomerization takes place. However, no ketene-enol minimum is present on this excited state surface, instead a conical intersection S 1 /S 0 is found just past the isomerization transition structure. Therefore, the reacting system is easily funneled to the ground state in correspondence of the ketene-enol minimum. Thus, although the reaction is triggered by light absorption, and the first isomerization step takes place involving the excited reactant, all the subsequent chemistry takes place in the ground state.
(2) The free energy barriers that the system should overcome to form the main products appear to be too high, even considering the energy gain consequent to the decay to the ground state. Therefore, the presence of two cooperating water molecules proved necessary, more than convenient: they operate by passing one hydrogen from one water to the other, thereby allowing a hydrogen shift from two positions of the same intermediate. Namely, they first catalyze the hydrogen transfer necessary for the cyclization of ketene-enol to furan-2-ol. Then, from furan-2-ol, further water-mediated H transfers produce the two final furanones. On the other hand, to obtain maleic anhydride, one extra oxygen is incorporated into the molecule. Because the findings of Newland et al. tend to exclude a significant role of the hydroxyl radical, we considered the possible role either of dioxygen, in its 1 ∆ g state, or of the hydroperoxyl radical, HOO. Both are present in appreciable concentrations under normal tropospheric conditions, 10 8 to 10 9 molec cm −3 . The latter was then discarded because the related computed free energy barriers were too high. In contrast, the former was found to open a viable pathway to maleic anhydride. In this case, intervention by two water molecules was found to be essential.

Supplementary Materials:
The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/molecules28134994/s1. Supplementary Materials for this article include the geometries and energetics of all optimized structures, and some schemes with other mechanisms that have been investigated but ruled out because they were not competitive. Figure S1: active orbitals; Figure S2: displacement vectors for the transition structures; Scheme S1: attempts to form furanones form ketene-enol; Scheme S2: formation of maleic anhydride form ketene-enol initiated by OH; Scheme S3: formation of maleic anhydride form ketene-enol initiated by 1

Conflicts of Interest:
The authors declare that they have no known competing financial interest or personal relationships that could have appeared to influence the work reported in this paper.
Sample Availability: Not available.

Appendix A
For the sake of comparison, we report here the characteristics of the first three electronic transitions obtained by TD-DFT [40,41] and EOM-CCSD [26][27][28].
Although the third excited state shows the highest oscillator strength (Table A1), it lays well above the ground state, and its contribution should be negligible because of the scarce sunlight irradiation at ground level at a wavelength below 290-300 nm (see, for instance, Figure 3.32, ( [35], p. 80)).