Triplet State Radical Chemistry: Significance of the Reaction of 3SO2 with HCOOH and HNO3

The triplet excited states of sulfur dioxide can be accessed in the UV region and have a lifetime large enough that they can react with atmospheric trace gases. In this work, we report high level ab initio calculations for the reaction of the a3B1 and b3A2 excited states of SO2 with weak and strong acidic species such as HCOOH and HNO3, aimed to extend the chemistry reported in previous studies with nonacidic H atoms (water and alkanes). The reactions investigated in this work are very versatile and follow different kinds of mechanisms, namely, proton-coupled electron transfer (pcet) and conventional hydrogen atom transfer (hat) mechanisms. The study provides new insights into a general and very important class of excited-state-promoted reactions, opening up interesting chemical perspectives for technological applications of photoinduced H-transfer reactions. It also reveals that atmospheric triplet chemistry is more significant than previously thought.

The reaction of the 3 SO 2 excited states with HCOOH.
Figure S1 shows how the different stationary points (reactants, pre-reactive complexes, transition states, post-reactive complexes, and products) are connected.The schematic potential energy surface is displayed in Figure 1 of the main text.As pointed out in the main text, we have employed the B3LYP/aug-cc-pvtz approach to optimize and characterize all stationary points, although some stationary points of interest were further optimized using the BH&HLYP/aug-cc-pVTZ, M06-2X/aug-cc-pVTZ, and CCSD(T)/6-311+G(2df,2p) theoretical approaches.Thus, ACR1, ACR2, ACR3, ACR3, ATS1, ATS2, ATS3, and ATS4 were optimized with all mentioned theoretical approaches, although we failed to find ACR4 and ATS4 at B3LYP level of theory.The corresponding Cartesian coordinates are listed below in Tables S6 to S9. Figure S2 shows the most relevant geometrical parameters of all stationary points.The geometrical parameters optimized with the different theoretical approaches differ in less than 0.03 Angstroms, except for some hydrogen bond distances in the case of pre-reactive complexes, that differ in up to 0.25 Angstroms.

TS-ACR1ACR4
3][4][5][6] The results displayed in Table S1 show that the relative energies computed at CCSD(T)/CBS differ in less than 1.5 kcal•mol -1 .It has been pointed out previously, that quite large differences are found in the computed geometrical parameters of some pre-reactive complexes.Despite these differences, the relative energies computed at CCSD(T)/CBS over the pre-reactive complexes obtained with different theoretical approaches remain very small, indicating that the potential energy surface in these regions is very flat.Regarding the relative energies of the transition states, it is also worth mentioning that the entropic effect favors the acyclic (hat) structures with respect to the cyclic (pcet) transition states as expected.
Thus, for instance, Table S1 shows that the energy gap between ATS1 and ATS4 is 4.96 kcal/mol and the Gibbs free energy gap is 3.51 kcal/mol, and a similar effect is shown in Table S3 for the reaction between triplet SO 2 and HNO 3 (see below).
Table S1.Relative energies, energies with zero-point corrections, enthalpies and free energies at 298 K and 1 atm for the reaction of 3  Finally, for the ATS1, ATS2, and ATS3 electronic states we have calculated the topological properties of the bond critical points as displayed in Table S2 Table S2.Electron density ((r b ) in e•bohr -3 ), Laplacian of the electron density ( (r b ) ∇ 2 in e•bohr -5 ), the ellipticity () and local energy density (E(r b ) in hartree•bohr -3 ) for all bond critical points (r b ) at ATS1, ATS2, and ATS3.a  The reaction of the 3 SO 2 excited state with HNO 3 .
The computed relative energies for the reaction between 3 B 1 and 3 A 2 electronic states of SO 2 with HNO 3 are collected in Table S3. Figure S3 shows how are connected the different stationary points (reactants, pre-reactive complexes, transition states, postreactive complexes, and product) .
Table S3.Relative energies, energies with zero-point corrections, enthalpies and free energies at 298 K and 1 atm for the reaction of 3

Figure S3
: Scheme of the connection of the stationary points for the reaction between the electronic states 3 B 1 and 3 A 2 of SO 2 with HNO 3 .All cartesian coordinates obtained with the different methods employed are reported below in Table S8.
In Figure S4 we have drawn electronic features of the most relevant natural orbitals of the transition states BTS1, BTS2, BTS3, and BTS4.As pointed out in the main text, the processes take place by interaction of three electrons in two orbitals, (orbitals 31a and 32a with bonding and antibonding character, respectively) whereas orbital 33a (that corresponds to the 3b 1 of 3 SO 2 ) does not participate in the reaction and acts as spectator.Figure S4 shows that in BTS1 the electron is transferred from the oxygen atom of the acid to one oxygen atom of 3 SO 2 while the acidic proton jumps to the other oxygen atom of sulfur dioxide in a seven-member ring structure.

BTS2 pcet
In BTS2 the electron transferred goes to the sulfur atom and the proton moves to one of the oxygen atoms of 3 SO 2 in a six-member ring structure.BTS3 has a five-member ring structure where the electron is transferred to one of the oxygen atoms of 3 SO 2 and the acidic proton jumps to the same oxygen atom.Finally, BTS4 has a hat mechanism and    The reaction of SO 2 ( 3 B 1 ) with H 2 O has been reported in a previous work, 1 and we address the reader to that article for a deep discussion.In this work, we have updated the previous work by re-optimizing the stationary points with the B3LYP/aug-cc-pVTZ level of theory, studying two additional reaction paths (CTS3 and CTS4) and performing a full kinetic study, with the aim of comparing the rate constants with those of the reactions of 3 SO 2 with HCOOH and HNO 3 .Table S4 contains the relative energies, whereas Figure S6 shows a scheme of the potential energy surface and Figure S7 the connection of the stationary points.Just mention that the lowest reaction path (via CTS1) has a pcet mechanism while the reaction paths via CTS2, CTS3, and CTS4 follow a hat mechanism, CTS2 lying lower than CTS3 and CTS4 because it is stabilized by a hydrogen bond.No stationary points were found for the reaction of 3 A 2 of SO 2 with H 2 O.   S9.

Kinetic study.
Along this work we have shown that the reaction of 3  and 336 for SO 2 , 7 4.04 and 183.9 for HCOOH, 8 3.98 and 189 for HNO 3 , 9 and 2.71 and 506 for H 2 O. 10 The numerical integration has been performed by an ad-hoc made program written in python. 11

Figure S1 :
Figure S1: Scheme for the connection of the stationary points for the reaction between the electronic states 3 B 1 and 3 A 2 of SO 2 with HCOOH.

Figure S4 .
Figure S4.Picture of the natural orbitals involving the pcet and hat mechanisms for the SO 2 (a 3 B 1 ) + HNO 3 reaction.The processes are described by the double occupied orbital

Figure
Figure S4 shows the features of the homolytic breaking and forming of the (O 2 NO)-H-(OSO) bonds.In Figure S5 we have shown the most relevant geometrical parameters of the stationary points investigated.

Figure S5 .
Figure S5.Main geometrical parameters of the stationary points for the reaction of 3 B 1 and 3 A 2 of SO 2 with HNO 3 , optimized at B3LYP/aug-cc-pVTZ level of theory.Distances in Angstroms and angles in degrees.

Figure S6 .Figure S7 :
Figure S6.Schematic potential energy surface for the reaction of 3 SO 2 with H 2 O. Energies in Hartree including zero-point corrections.

2 (
Figures S1, S3, and S7 show the complexity of these reactions, where the interaction between the reactants leads to the formation of several pre-reactive complexes before the transition states and the formation of the products.Moreover, several pre-reactive complexes are interconnected and therefore may have an impact in the rection kinetics.Therefore, as pointed out above, we have considered all steps shown in FiguresS1, S3, and S7, and we have performed a numerical integration to calculate the corresponding rate constants.Regarding the unimolecular steps, we have employed conventional transition state theory (CTST) for the steps involving reorganization of the pre-reactive complexes, variational transition state theory (VTST) for the calculations at ground level, namely with pressure of 1 atm and different temperatures, and the RRKM approach for calculations at different temperatures and pressures.In all cases we have considered energies calculated at CCSD(T)/CBS level of theory and partition functions computed at B3LYP/aug-cc-pVTZ level of theory except for ATS4 where we have taken the partition functions at BH&HLYP/aug-cc-pVTZ level of theory.In the case of the VTST calculations we have calculated the hessian matrices and CCSD(T) energies of about 10 and 12 of each side of the potential energy surface and we have interpolated these values to the whole potential energy surface as described in Polyrate.In these calculations the tunneling parameter has been computed with the small curvature approach.In the case of the RRKM calculations we have considered that the reaction takes place in N 2 bath simulated with a Lennard-Jones potential with the following parameters σ = 4.07 Å and ε/ = 248.6 for the reaction of 3 SO 2 with HCOOH; σ = 4.05 Å and ε/ = 252.0for the Figure S2.Main geometrical parameters of the stationary points for the reaction of 3 B 1 and 3 A 2 of SO 2 with HCOOH.Distances in Angstroms and angles in degrees.Values in plain text correspond to B3LYP optimized geometries.Values in parenthesis correspond to BH&HLYP optimized geometries.Values in square brackets correspond to M06-2X optimized geometries, and values in braces correspond to CCSD(T) optimized geometries.
B 1 and 3 A 2 of SO 2 with HCOOH.

Table S4 .
Relative energies, energies with zero-point corrections, enthalpies at 298 K and free energies at 298 K for the reaction of 3 B 1 and 3 A 2 of SO 2 with H 2 O. a

Table 3
of the main text contains the rate constants calculated at different heights in the Earth's atmosphere, and in TableS5we have collected the rate constants at different temperatures at ground level.

Table S5 .
13te constants, in cm3•molecule -1 •s -1 , for the reactions of 3 SO 2 with HCOOH (k RS1 , k RS1 , and k RS1 + k RS2 ), with HNO 3 (k RS3 ), and with H 2 O (k RS4 ), at different temperatures T (in K) at ground level in the Earth's atmosphere.The branching ratios for RS1 (% RS1 ) and RS2 (% RS2 ) for the 3 SO 2 with HCOOH reaction are also given.Indeed, 3 SO 2 abstracts the acidic hydrogen instead of the formyl hydrogen, which is the opposite to what would be expected, since the bond dissociation energy (BDE) of the C-H bond (96.2  07 kcal•mol -1 ) is smaller than the BDE of the O-H bond (112.23.1 kcal•mol -1 ).12This behavior is consistent with previous findings for the reaction of formic acid with hydroxyl radical.13 2 + H 2 O), in line with the values discussed in the main text.Moreover, the reaction of 3 SO 2 with HCOOH produces almost exclusively HOSO• + HCOO• radicals (reaction RS1).

Table S6 .
Cartesian coordinates (in Angstroms) of the stationary points for the reaction of 3 B 1 and 3 A 2 of SO 2 with HCOOH, computed at B3LYP/aug-cc-pVTZ level of theory.

Table S7 .
Cartesian coordinates (in Angstroms) of the stationary points for the reaction of 3 B 1 of SO 2 with HCOOH, computed at BH&HLYP/aug-cc-pVTZ level of theory.

Table S8 .
Cartesian coordinates (in Angstroms) of the stationary points for the reaction of 3 B 1 of SO 2 with HCOOH, computed at M06-2X/aug-cc-pVTZ level of theory.

Table S9 .
Cartesian coordinates (in Angstroms) of the stationary points for the reaction of 3 B 1 of SO 2 with HCOOH, computed at CCSD(T)/6-311+G(2df,2p) level of theory.

Table S10 .
Cartesian coordinates (in Angstroms) of the stationary points for the reaction of 3 B 1 and 3 A 2 of SO 2 with HNO 3 , computed at B3LYP/aug-cc-pVTZ level of theory.

Table S11 .
Cartesian coordinates (in Angstroms) of the stationary points for the reaction of 3 B 1 of SO 2 with H 2 O, computed at B3LYP/aug-cc-pVTZ level of theory.