Theoretical Insights into the Electron Capture Behavior of H2SO4···N2O Complex: A DFT and Molecular Dynamics Study

Both sulfuric acid (H2SO4) and nitrous oxide (N2O) play a central role in the atmospheric chemistry in regulating the global environment and climate changes. In this study, the interaction behavior between H2SO4 and N2O before and after electron capture has been explored using the density functional theory (DFT) method as well as molecular dynamics simulation. The intermolecular interactions have been characterized by atoms in molecules (AIM), natural bond orbital (NBO), and reduced density gradient (RDG) analyses, respectively. It was found that H2SO4 and N2O can form two transient molecular complexes via intermolecular H-bonds within a certain timescale. However, two molecular complexes can be transformed into OH radical, N2, and HSO4− species upon electron capture, providing an alternative formation source of OH radical in the atmosphere. Expectedly, the present findings not only can provide new insights into the transformation behavior of H2SO4 and N2O, but also can enable us to better understand the potential role of the free electron in driving the proceeding of the relevant reactions in the atmosphere.


Introduction
As the primary component in the production of secondary aerosols, sulfuric acid (H 2 SO 4 ) plays a central role in atmospheric aerosol nucleation [1][2][3][4]. It is mainly produced from sulfur dioxide via oxidation by hydroxyl radical. Generally, when H 2 SO 4 collides with other molecules, it can form small clusters of molecules that can grow into new stable aerosols [1]. As a result, many interaction models of H 2 SO 4 with water, ammonia, and organic molecules have been constructed to elucidate new atmospheric particle formation and nucleation mechanisms [5][6][7][8][9][10]. Meanwhile, H 2 SO 4 also plays an important role in perturbing atmospheric hydroperoxyl radical levels via the formation of strong H-bonding complexes [11,12]. In addition, H 2 SO 4 has been involved in the formation of the polar stratospheric clouds (PSCs) associated with the stratospheric ozone depletion [13]. Therefore, it is necessary to acquire the detailed interactions of H 2 SO 4 with other atmospheric species so as to better understand the potential role of H 2 SO 4 in the atmosphere.
As one of the important nitrogen-containing species in the atmosphere and a main greenhouse gas, nitrous oxide (N 2 O) has a long atmospheric lifetime and radiative forcing of about 200 times higher than that of CO 2 [14,15]. It has been demonstrated that the emission of N 2 O is mainly from both natural (about 60%) and anthropogenic sources (about 40%) [16]. In 2016, the globally averaged N 2 O concentration reached 328.9 ± 0.1 ppb, which is 122% of the pre-industrial level (270 ppb) [16]. In addition, N 2 O has also been implicated in the ozone depletion. Ravishankara's [17] studies suggested that N 2 O emission is the single most important ozone-depleting emission and is expected to remain the largest throughout the 21st century. Therefore, it is also necessary to investigate the transformation of N 2 O to reduce its negative effects on environments.
Given the fact that H 2 SO 4 and N 2 O coexist in the atmosphere, it is expected that both of them could interact with each other in some way. Can they form stable complexes? If so, what are the interaction modes adopted between them? Especially, what happens to these complexes if an additional electron is introduced since a large number of electrons can be generated by cosmic ray radiation in the atmosphere? Here, it is well known that the excess electrons can be captured by the stratospheric molecules [18][19][20] and the cosmic-ray-driven electron-induced reactions have been involved in the ozone depletion and global climate change [21][22][23]. Unfortunately, despite the atmospheric importance of H 2 SO 4 and N 2 O, the interaction behavior between them in the absence and presence of an additional electron remains unclear. No relevant studies have been reported so far to the best of our knowledge. In this case, theoretical studies are highly desirable to carry out to provide useful information for the relevant experiments.
Therefore, to address those questions mentioned above, the interaction behavior between H 2 SO 4 and N 2 O before and after the electron capture has been systematically explored by using the density functional theory (DFT) method and ab initio molecular dynamics simulation. Hopefully, the present study can provide new insights into the potential role of H 2 SO 4 and the excess electrons in the atmosphere as well as the transformation of N 2 O.

Computational Details
In this study, full geometric optimizations were performed employing the B3LYP and M06-2X methods as well as the 6-311++G(3df,3pd) basis set, where the reliability of the DFT method has been confirmed by many systems [24][25][26][27][28][29]. As a result, it was found that both methods can give consistent results for the geometry and energy parameters overall. Given the compromise between computational accuracy and cost, and to keep the consistency of the results for the optimization and molecular dynamics at the same level of theory, the results at the B3LYP/6-311++G(3df,3pd) level of theory have been mainly discussed below unless otherwise noted. To explore the nature of the optimized structure, we performed vibration frequency analysis at the same level of theory. Moreover, intrinsic reaction coordinate (IRC) calculations have been performed to further confirm the connectivity between the given transition state and the corresponding reactant and product. In addition, to further improve the energy parameters in the formation process of the neutral complexes, single-point energy calculations have also been carried out at the CCSD(T)/AUG-cc-pVTZ level of theory based on the optimized geometries mentioned above.
To explore the implicit solvent effects on the title reaction, the solvent model density (SMD) solvation model has been employed in aqueous solution at the B3LYP/6-311++G(3df,3pd) level of theory. As a result, similar results have been obtained as those of the results in the gas phase.
To characterize the intermolecular H-bonds between H 2 SO 4 and N 2 O before and after electron capture, atoms in molecules (AIM) [30], natural bond orbital (NBO) [31], and the reduced density gradient (RDG) analyses have been performed based on the optimized geometries [32,33]. In the AIM theory, the presence and nature of the intermolecular H-bonds can be characterized by the bond critical point (BCP). As for the formation mechanism of the intermolecular H-bonds, it can be elucidated from the orbital interactions between the lone pairs of the proton acceptor and the anti-bonding σ orbital (σ*) of the proton donor within the NBO method, accompanying with the electron transfer from the former to the latter. Moreover, the orbital interaction strength can be assessed from the second-order stabilization energy E (2) . In addition, the intermolecular H-bonds can also be indicated by the presence of the spikes within the RDG analyses.
To obtain the interaction strength between H 2 SO 4 and N 2 O, interaction energy between them has been calculated as the energy differences between the formed complexes and the reactants. Meanwhile, zero-point vibrational energy (ZPVE) corrections and basis set superposition errors (BSSEs) have also been considered [34].
To investigate the dynamic stability of the formed complexes and the microscopic details of the electron capture process for those complexes, we performed ab initio molecular dynamics simulation employing the Atom Centered Density Matrix Propagation (ADMP) method at the B3LYP/6-311++G(3df,3pd) level of theory on the basis of their optimized geometries [35][36][37]. The whole simulation was performed at 298 K for the neutral complexes and the electron captured products with a canonical ensemble. For the electron capture processes of the neutral complexes, a microcanonical ensemble has been employed. The total simulation time is 1 ps with a time step of 0.5 fs.
To evaluate the ability to accept an electron for those neutral complexes, the adiabatic electron affinity (AEA), vertical electron affinity (VEA), and vertical electron detachment energy (VEDE) have been calculated. Here, AEA is calculated as the enthalpy difference between the optimized neutral and anionic complexes and VEA is calculated as the electronic energy difference between the optimized neutral and anionic states on the basis of the optimized neutral complexes. As for the VEDE, it is calculated as the electronic energy difference between the neutral and anionic states at the same geometry of the anionic state.

Structural Features
As displayed in Figure 1, two complexes named as A and B have been formed between H 2 SO 4 and N 2 O through intermolecular H-bonds. Namely, one of the protons in H 2 SO 4 interacts with the terminal N and O atoms of N 2 O in complexes A and B, respectively. This point can be confirmed by the location of the corresponding BCPs between H 2 SO 4 and N 2 O as shown in Figure 1. The intermolecular H-bond distances of 2.030 (2.171) and 1.935 (1.895) A suggest that the H-bonding interactions should be weak, where the data in parentheses refer to the results at the M06-2X/6-311++G(3df,3pd) level of theory. Actually, as shown in Table 1, the positive Laplacians and energy densities at the BCPs of the H-bonds indicate that the above H-bonds are predominated by electrostatic interaction.
employing the Atom Centered Density Matrix Propagation (ADMP) method at the B3LYP/6-311++G(3df,3pd) level of theory on the basis of their optimized geometries [35][36][37]. The whole simulation was performed at 298 K for the neutral complexes and the electron captured products with a canonical ensemble. For the electron capture processes of the neutral complexes, a microcanonical ensemble has been employed. The total simulation time is 1 ps with a time step of 0.5 fs.
To evaluate the ability to accept an electron for those neutral complexes, the adiabatic electron affinity (AEA), vertical electron affinity (VEA), and vertical electron detachment energy (VEDE) have been calculated. Here, AEA is calculated as the enthalpy difference between the optimized neutral and anionic complexes and VEA is calculated as the electronic energy difference between the optimized neutral and anionic states on the basis of the optimized neutral complexes. As for the VEDE, it is calculated as the electronic energy difference between the neutral and anionic states at the same geometry of the anionic state.

Structural Features
As displayed in Figure 1, two complexes named as A and B have been formed between H2SO4 and N2O through intermolecular H-bonds. Namely, one of the protons in H2SO4 interacts with the terminal N and O atoms of N2O in complexes A and B, respectively. This point can be confirmed by the location of the corresponding BCPs between H2SO4 and N2O as shown in Figure 1. The intermolecular H-bond distances of 2.030 (2.171) and 1.935 (1.895) A suggest that the H-bonding interactions should be weak, where the data in parentheses refer to the results at the M06-2X/6-311++G(3df,3pd) level of theory. Actually, as shown in Table 1, the positive Laplacians and energy densities at the BCPs of the H-bonds indicate that the above H-bonds are predominated by electrostatic interaction.   To further verify the formation of intermolecular H-bonds mentioned above, we have performed RDG analyses for the complexes A and B. As shown in Figure 2, the intermolecular H-bonds can be verified by the presence of the corresponding spikes between H 2 SO 4 and N 2 O.  To further verify the formation of intermolecular H-bonds mentioned above, we have performed RDG analyses for the complexes A and B. As shown in Figure 2, the intermolecular H-bonds can be verified by the presence of the corresponding spikes between H2SO4 and N2O. To explore the formation mechanisms for the above intermolecular H-bonds, NBO analyses have been carried out based on the optimized complexes. As shown in Figure 3, the formation of the intermolecular H-bonds in complexes A and B is mainly attributed to the electron transfer from the lone pairs of the terminal N and O atoms of N2O to the anti-bonding σ orbital (σ*) of the O4-H5 bond of H2SO4, respectively. Moreover, as given in Table 2, the larger total second-order stabilization energies of the orbital interactions in complex B imply that the H-bond in complex B is stronger than that of complex A, which can be further confirmed by the interaction energy mentioned below. To explore the formation mechanisms for the above intermolecular H-bonds, NBO analyses have been carried out based on the optimized complexes. As shown in Figure 3, the formation of the intermolecular H-bonds in complexes A and B is mainly attributed to the electron transfer from the lone pairs of the terminal N and O atoms of N 2 O to the anti-bonding σ orbital (σ*) of the O4-H5 bond of H 2 SO 4 , respectively. Moreover, as given in Table 2, the larger total second-order stabilization energies of the orbital interactions in complex B imply that the H-bond in complex B is stronger than that of complex A, which can be further confirmed by the interaction energy mentioned below.

Complexes
Donor NBO Acceptor NBO According to the NBO analyses, the O4-H5 bond of H2SO4 participating in the H-bonds should be elongated due to the electron transfer from the lone pairs of the proton acceptor to the σ* orbital of the proton donor. As a result, compared with the isolated state, the O4-H5 bond of H2SO4 has been elongated by about 0.006 and 0.008 A, respectively. Correspondingly, as shown in Figure 4, red-shifts of 115 and 152 cm −1 occur for the vibrational frequencies of the O4-H5 bond in complexes A and B, respectively. Moreover, the characteristic absorption peaks at 3650.0 and 3612.8 cm −1 are originated from the stretching vibration of the O4-H5 bond of H2SO4 fragment in complexes A and B, providing the direct spectra proof for the existence of intermolecular H-bonds. For the sake of reference, the detailed IR results including peak positions and intensities have been given in Table S1 of the Supplementary Material (SM).

Complexes
Donor NBO Acceptor NBO According to the NBO analyses, the O4-H5 bond of H 2 SO 4 participating in the H-bonds should be elongated due to the electron transfer from the lone pairs of the proton acceptor to the σ* orbital of the proton donor. As a result, compared with the isolated state, the O4-H5 bond of H 2 SO 4 has been elongated by about 0.006 and 0.008 A, respectively. Correspondingly, as shown in Figure 4, red-shifts of 115 and 152 cm −1 occur for the vibrational frequencies of the O4-H5 bond in complexes A and B, respectively. Moreover, the characteristic absorption peaks at 3650.0 and 3612.8 cm −1 are originated from the stretching vibration of the O4-H5 bond of H 2 SO 4 fragment in complexes A and B, providing the direct spectra proof for the existence of intermolecular H-bonds. For the sake of reference, the detailed IR results including peak positions and intensities have been given in Table S1 of the Supplementary Material (SM).

Complexes
Donor NBO Acceptor NBO According to the NBO analyses, the O4-H5 bond of H2SO4 participating in the H-bonds should be elongated due to the electron transfer from the lone pairs of the proton acceptor to the σ* orbital of the proton donor. As a result, compared with the isolated state, the O4-H5 bond of H2SO4 has been elongated by about 0.006 and 0.008 A, respectively. Correspondingly, as shown in Figure 4, red-shifts of 115 and 152 cm −1 occur for the vibrational frequencies of the O4-H5 bond in complexes A and B, respectively. Moreover, the characteristic absorption peaks at 3650.0 and 3612.8 cm −1 are originated from the stretching vibration of the O4-H5 bond of H2SO4 fragment in complexes A and B, providing the direct spectra proof for the existence of intermolecular H-bonds. For the sake of reference, the detailed IR results including peak positions and intensities have been given in Table S1 of the Supplementary Material (SM).  To investigate the electron redistribution details for H 2 SO 4 and N 2 O upon complexation, the electron density difference maps of them have been constructed based on the optimized complexes A and B. As shown in Figure 5, electron redistribution mainly occurs along the intermolecular H-bond axis in the complexes, which is consistent with the features of the H-bonding complexes [39][40][41]. In more details, in complex A, the loss of the electron is mainly concentrated on the positions of the proton involved in the intermolecular H-bond in H 2 SO 4 and the other two atoms of N 2 O not participating in the H-bonds. As for the gain of the electron, it is mainly concentrated on the terminal N atom of N 2 O and the O atom of H 2 SO 4 involving in the H-bonds. Similarly, the same is also true for complex B. As a result, it was found that N 2 O and H 2 SO 4 act as an electron donor and electron acceptor in both complexes, where the net electron transfer is 0.014 and 0.017 in complexes A and B based on the NBO analyses, respectively. To investigate the electron redistribution details for H2SO4 and N2O upon complexation, the electron density difference maps of them have been constructed based on the optimized complexes A and B. As shown in Figure 5, electron redistribution mainly occurs along the intermolecular Hbond axis in the complexes, which is consistent with the features of the H-bonding complexes [39][40][41]. In more details, in complex A, the loss of the electron is mainly concentrated on the positions of the proton involved in the intermolecular H-bond in H2SO4 and the other two atoms of N2O not participating in the H-bonds. As for the gain of the electron, it is mainly concentrated on the terminal N atom of N2O and the O atom of H2SO4 involving in the H-bonds. Similarly, the same is also true for complex B. As a result, it was found that N2O and H2SO4 act as an electron donor and electron acceptor in both complexes, where the net electron transfer is 0.014 and 0.017 in complexes A and B based on the NBO analyses, respectively.

Energy Analyses
As displayed in Table 3, the calculated interaction energies between H2SO4 and N2O are −2.14(−2.72) and −2.77(−4.22) kcal/mol in complexes A and B, respectively, where the data in parentheses refer to the results at the CCSD(T)/AUG-cc-pVTZ level of theory. As a result, complex B is more stable than complex A by 0.76 (1.72) kcal/mol, which is in agreement with the larger H-bond in complex B. Thermodynamically, the calculated enthalpy changes (ΔH) for complexes A and B are all negative, indicating that the formation processes of them are exothermic reactions. On the other hand, the small positive values for the Gibbs free energy changes (ΔG) suggest that the formation processes of them are non-spontaneous at 298 K. As shown in Figure 6, the ΔG values become more negative with the decreasing of the temperature. Therefore, low temperature should be favorable for the formation of complexes thermodynamically.

Energy Analyses
As displayed in Table 3, the calculated interaction energies between H 2 SO 4 and N 2 O are −2.14(−2.72) and −2.77(−4.22) kcal/mol in complexes A and B, respectively, where the data in parentheses refer to the results at the CCSD(T)/AUG-cc-pVTZ level of theory. As a result, complex B is more stable than complex A by 0.76 (1.72) kcal/mol, which is in agreement with the larger H-bond in complex B. Thermodynamically, the calculated enthalpy changes (∆H) for complexes A and B are all negative, indicating that the formation processes of them are exothermic reactions. On the other hand, the small positive values for the Gibbs free energy changes (∆G) suggest that the formation processes of them are non-spontaneous at 298 K. As shown in Figure 6, the ∆G values become more negative with the decreasing of the temperature. Therefore, low temperature should be favorable for the formation of complexes thermodynamically.

Molecular Dynamics Analyses
To further explore the dynamic stability of the complexes A and B, molecular dynamics simulations have been performed on the basis of their optimized geometries. The time evolution of the potential energy and the H-bond in both complexes have been given in Figure 7. On the one hand, both intermolecular H-bonds in complexes can still be observed during the initial stage of the dynamics simulation, indicating that the complexes can exist in a short period of time. On the other hand, the intermolecular H-bonds disappear with the evolution of the simulation time, implying the instability of the complexes. Therefore, complexes A and B can exist transiently within a certain period of time.

Molecular Dynamics Analyses
To further explore the dynamic stability of the complexes A and B, molecular dynamics simulations have been performed on the basis of their optimized geometries. The time evolution of the potential energy and the H-bond in both complexes have been given in Figure 7. On the one hand, both intermolecular H-bonds in complexes can still be observed during the initial stage of the dynamics simulation, indicating that the complexes can exist in a short period of time. On the other hand, the intermolecular H-bonds disappear with the evolution of the simulation time, implying the instability of the complexes. Therefore, complexes A and B can exist transiently within a certain period of time.

Molecular Dynamics Analyses
To further explore the dynamic stability of the complexes A and B, molecular dynamics simulations have been performed on the basis of their optimized geometries. The time evolution of the potential energy and the H-bond in both complexes have been given in Figure 7. On the one hand, both intermolecular H-bonds in complexes can still be observed during the initial stage of the dynamics simulation, indicating that the complexes can exist in a short period of time. On the other hand, the intermolecular H-bonds disappear with the evolution of the simulation time, implying the instability of the complexes. Therefore, complexes A and B can exist transiently within a certain period of time.

Electron Capture Process
On the basis of the neutral complexes A and B mentioned above, the electron capture properties of them have been investigated.

Structural Features for the Electron Capture Products
As shown in Figure 8, complex A has been located for the complex A upon electron capture. Obviously, the original H5 atom of H 2 SO 4 fragment has been transferred to the terminal N10 atom of N 2 O, resulting in the formation of two fragments HSO 4 − and HNNO as well as a new intermolecular H-bond N10-H5···O4. At the same time, an additional intermolecular H-bond O6-H7···O8 has also formed between the other proton of H 2 SO 4 and the terminal O8 atom of N 2 O. As shown in Figure 9, complex A is characterized by the double intermolecular H-bonds from the presence of the BCPs and the spikes between two fragments in RDG maps as displayed in Figure S1 of Supplementary Materials. Especially, for the intermolecular H-bond N10-H5···O4, its larger strength should be highlighted from its short H-bonding distance of 1.491 A. Actually, as presented in Table 1 Figure 9 and Figure S1 of Supplementary Materials, complex A is also characterized by the double intermolecular H-bonds. Moreover, analyses of the energy parameters suggest that the forward and reverse barrier heights are 0.31(−1.44) and 9.05(7.62) kcal/mol, where the data in parentheses are the results including the ZPVE corrections. Clearly, the disappearance of the forward barrier height suggests that the reaction can take place readily. Meanwhile, the calculated ∆H and ∆G for the conversion process from complex A to A are −8.74 and −9.39 kcal/mol, implying that the conversion process is also favorable thermodynamically. Therefore, complex A should be converted to complex A upon electron capture, where the dynamic stability of the complex A will be explored below. In addition, as displayed in Figure 10, the excess electron has been mainly distributed on the HNNO and NNOH fragments, exhibiting the nature of them as a radical.

Electron Capture Process
On the basis of the neutral complexes A and B mentioned above, the electron capture properties of them have been investigated.

Structural Features for the Electron Capture Products
As shown in Figure 8, complex A′ has been located for the complex A upon electron capture. Obviously, the original H5 atom of H2SO4 fragment has been transferred to the terminal N10 atom of N2O, resulting in the formation of two fragments HSO4 − and HNNO as well as a new intermolecular H-bond N10-H5···O4. At the same time, an additional intermolecular H-bond O6-H7···O8 has also formed between the other proton of H2SO4 and the terminal O8 atom of N2O. As shown in Figure 9, complex A′ is characterized by the double intermolecular H-bonds from the presence of the BCPs and the spikes between two fragments in RDG maps as displayed in Figure S1 of Supplementary Materials. Especially, for the intermolecular H-bond N10-H5···O4, its larger strength should be highlighted from its short H-bonding distance of 1.491 A. Actually, as presented in Table 1, the positive and negative values of the Laplacian and energy density at the BCP of H-bond suggest that it has partial covalent properties. In this case, can H atom transfer occur for the H-bond N10-H5···O4? To clarify this point, the H atom transfer behavior has been studied for complex A′. As a result, it was found that another complex A′′ can be obtained via the double H atom transfer, i.e., the H5 atom has been transferred from N10 of N2O to O4 of H2SO4 accompanying with the transfer of H7 from O6 of H2SO4 to O8 of N2O, where the corresponding transition state A′-TS has been confirmed by the IRC calculations. Similar to complex A′, as shown in Figures 9 and S1 of Supplementary Materials, complex A′′ is also characterized by the double intermolecular H-bonds. Moreover, analyses of the energy parameters suggest that the forward and reverse barrier heights are 0.31(−1.44) and 9.05(7.62) kcal/mol, where the data in parentheses are the results including the ZPVE corrections. Clearly, the disappearance of the forward barrier height suggests that the reaction can take place readily. Meanwhile, the calculated ∆H and ∆G for the conversion process from complex A′ to A′′ are −8.74 and −9.39 kcal/mol, implying that the conversion process is also favorable thermodynamically. Therefore, complex A should be converted to complex A′′ upon electron capture, where the dynamic stability of the complex A′′ will be explored below. In addition, as displayed in Figure 10, the excess electron has been mainly distributed on the HNNO and NNOH fragments, exhibiting the nature of them as a radical.   For complex B, as displayed in Figure 8, its original intermolecular H-bond has disappeared upon electron capture and the whole complex has been collapsed into three fragments including OH radical, N2, and HSO4 − . As displayed in Figure 10, the excess electron is mainly localized on the OH fragment. As a result, OH radical can be produced in the electron capture process of complex B. Therefore, besides the main source of the OH production (e.g., solar radiation), the present study can also provide an alternative source of the OH radical in the atmosphere although its contribution to the total OH concentration is unknown at present.
In addition, to verify the fact that the above electron capture products are free from the overestimated stabilization of the delocalized state for B3LYP method, relevant calculations have also been carried out employing the long range corrected functional CAM-B3LYP method and the 6-311++G(3df,3pd) basis set. As a result, the calculated results are well consistent with the B3LYP results.

Electron Affinity
To explore the ability of the neutral complexes A and B to accept an electron thermodynamically, the electron affinities of them have been calculated. As shown in Table 4, the AEAs are 1.80 and 3.18 eV for complexes A and B, respectively. Here, the small AEA of complex A relative to complex B should be attributed to the instability of the electron capture product A′ mentioned above. The positive values of AEA suggest that the electron capture products are more stable than those of the neutral complexes. At the same time, the large difference between AEA and VEA suggests the significant geometrical changes for complexes A and B before and after electron capture. Obviously, this point is consistent with the optimized geometries for complexes A′ and B′ mentioned above. In addition, the calculated VEDEs of the complexes A′ and B′ are 5.22 and 7.44 eV, respectively. Therefore, the electron capture products are stable relative to the detachment of an electron.  For complex B, as displayed in Figure 8, its original intermolecular H-bond has disappeared upon electron capture and the whole complex has been collapsed into three fragments including OH radical, N2, and HSO4 − . As displayed in Figure 10, the excess electron is mainly localized on the OH fragment. As a result, OH radical can be produced in the electron capture process of complex B. Therefore, besides the main source of the OH production (e.g., solar radiation), the present study can also provide an alternative source of the OH radical in the atmosphere although its contribution to the total OH concentration is unknown at present.
In addition, to verify the fact that the above electron capture products are free from the overestimated stabilization of the delocalized state for B3LYP method, relevant calculations have also been carried out employing the long range corrected functional CAM-B3LYP method and the 6-311++G(3df,3pd) basis set. As a result, the calculated results are well consistent with the B3LYP results.

Electron Affinity
To explore the ability of the neutral complexes A and B to accept an electron thermodynamically, the electron affinities of them have been calculated. As shown in Table 4, the AEAs are 1.80 and 3.18 eV for complexes A and B, respectively. Here, the small AEA of complex A relative to complex B should be attributed to the instability of the electron capture product A′ mentioned above. The positive values of AEA suggest that the electron capture products are more stable than those of the neutral complexes. At the same time, the large difference between AEA and VEA suggests the significant geometrical changes for complexes A and B before and after electron capture. Obviously, this point is consistent with the optimized geometries for complexes A′ and B′ mentioned above. In addition, the calculated VEDEs of the complexes A′ and B′ are 5.22 and 7.44 eV, respectively. Therefore, the electron capture products are stable relative to the detachment of an electron. For complex B, as displayed in Figure 8, its original intermolecular H-bond has disappeared upon electron capture and the whole complex has been collapsed into three fragments including OH radical, N 2 , and HSO 4 − . As displayed in Figure 10, the excess electron is mainly localized on the OH fragment. As a result, OH radical can be produced in the electron capture process of complex B. Therefore, besides the main source of the OH production (e.g., solar radiation), the present study can also provide an alternative source of the OH radical in the atmosphere although its contribution to the total OH concentration is unknown at present. In addition, to verify the fact that the above electron capture products are free from the overestimated stabilization of the delocalized state for B3LYP method, relevant calculations have also been carried out employing the long range corrected functional CAM-B3LYP method and the 6-311++G(3df,3pd) basis set. As a result, the calculated results are well consistent with the B3LYP results.

Electron Affinity
To explore the ability of the neutral complexes A and B to accept an electron thermodynamically, the electron affinities of them have been calculated. As shown in Table 4, the AEAs are 1.80 and 3.18 eV for complexes A and B, respectively. Here, the small AEA of complex A relative to complex B should be attributed to the instability of the electron capture product A mentioned above. The positive values of AEA suggest that the electron capture products are more stable than those of the neutral complexes. At the same time, the large difference between AEA and VEA suggests the significant geometrical changes for complexes A and B before and after electron capture. Obviously, this point is consistent with the optimized geometries for complexes A and B mentioned above. In addition, the calculated VEDEs of the complexes A and B are 5.22 and 7.44 eV, respectively. Therefore, the electron capture products are stable relative to the detachment of an electron. In addition, the ∆G for the electron capture process of complexes A and B are −38.9 and −80.2 kcal/mol, respectively. Therefore, the electron capture processes for the neutral complexes are exothermic and spontaneous processes and can occur easily thermodynamically.

Electron Capture Dynamics
To further explore the microscopic details in the electron capture process, the molecular dynamics calculations have been carried out based on the optimized complexes A and B.
As shown in Figure 11 and Figure S2   In addition, the ∆G for the electron capture process of complexes A and B are −38.9 and −80.2 kcal/mol, respectively. Therefore, the electron capture processes for the neutral complexes are exothermic and spontaneous processes and can occur easily thermodynamically.

Electron Capture Dynamics
To further explore the microscopic details in the electron capture process, the molecular dynamics calculations have been carried out based on the optimized complexes A and B.
As shown in Figures 11 and S2 of Supplementary Materials, for complex A upon electron capture, H2SO4 and N2O begin to approach to each other, accompanying with the strengthening of the intermolecular H-bond. Meanwhile, the O4-H5 bond participating in the H-bond in H2SO4 fragment increases gradually. On the contrary, the distance between the terminal N10 atom of N2O and the H5 atom of H2SO4 fragment decreases simultaneously. As a result, the H5 atom of H2SO4 fragment has been transferred to the terminal N10 atom of N2O fragment. For example, at 88.5 fs, the distances N10···H5 and O4···H5 have been changed from the initial 2.030 and 0.974 A to 0.981 and 1.699 A, respectively. At 134.5 fs, the H5 atom of H2SO4 has been transferred to the N10 atom of N2O, producing the HNNO and HSO4 − fragments, which is consistent with the optimized complex A′. Moreover, as mentioned above, complex A′ can be transformed into complex A′′ easily. To further explore the dynamic stability of complex A′′, molecular dynamics calculations have been carried out based on its optimized geometry. As displayed in Figures 12 and S3 of Supplementary Materials, the N-O bond of HONN fragment has been elongated gradually with the evolution of simulation time. At 60 and 90 fs, the N-O bond has been elongated to 2.128 and 2.950 A, respectively. Therefore, complex A′′ is unstable and can be further transformed into OH radical, N2, and HSO4 − fragments. Moreover, as mentioned above, complex A can be transformed into complex A easily. To further explore the dynamic stability of complex A , molecular dynamics calculations have been carried out based on its optimized geometry. As displayed in Figure 12 and Figure S3 of Supplementary Materials, the N-O bond of HONN fragment has been elongated gradually with the evolution of simulation time. At 60 and 90 fs, the N-O bond has been elongated to 2.128 and 2.950 A, respectively. Therefore, complex A is unstable and can be further transformed into OH radical, N 2 , and HSO 4 − fragments. As for the complex B upon electron capture, as shown in Figures 13 and S4 of Supplementary Materials, the H5 atom involved in the intermolecular H-bond in H2SO4 fragment approaches the terminal O8 atom of N2O fragment gradually, accompanying with the elongation of the N9-O8 bond of N2O fragment simultaneously. At 50 fs, the O4-H5 bond of H2SO4 and N9-O8 bond of N2O have been changed from 0.976 and 1.191 to 1.473 and 2.047 A, respectively. With the evolution of the simulation time, complex B has been transformed into OH radical, N2, and HSO4 − fragments, which is consistent with the optimized geometry of complex B′. In addition, as shown in Figures 11 and 13, the energies of the neutral complexes have been decreased significantly upon electron capture, reflecting the easy proceeding of the electron capture process once again. As for the complex B upon electron capture, as shown in Figure 13 and Figure S4  As for the complex B upon electron capture, as shown in Figures 13 and S4 of Supplementary Materials, the H5 atom involved in the intermolecular H-bond in H2SO4 fragment approaches the terminal O8 atom of N2O fragment gradually, accompanying with the elongation of the N9-O8 bond of N2O fragment simultaneously. At 50 fs, the O4-H5 bond of H2SO4 and N9-O8 bond of N2O have been changed from 0.976 and 1.191 to 1.473 and 2.047 A, respectively. With the evolution of the simulation time, complex B has been transformed into OH radical, N2, and HSO4 − fragments, which is consistent with the optimized geometry of complex B′. In addition, as shown in Figures 11 and 13, the energies of the neutral complexes have been decreased significantly upon electron capture, reflecting the easy proceeding of the electron capture process once again. In addition, as shown in Figures 11 and 13, the energies of the neutral complexes have been decreased significantly upon electron capture, reflecting the easy proceeding of the electron capture process once again.
As a result, the neutral complexes A and B can be eventually transformed into OH radical, N 2 , and HSO 4 − fragments upon electron capture. Certainly, further experiments are needed to further confirm the present findings.

Conclusions
In the present study, the electron capture properties of the formed complex of H 2 SO 4 with N 2 O in the gas phase have been systematically explored theoretically. It was found that H 2 SO 4 and N 2 O can form two transient complexes via intermolecular H-bonds in the atmosphere, which has been characterized by using AIM, NBO, and RDG analyses. Upon electron capture, two neutral complexes have been eventually transformed into OH radical, N 2 , and HSO 4 − species. Therefore, the present study not only provides an alternative formation source of OH radical in the atmosphere as well as new insights into the degradation and transformation behavior of N 2 O, but also enables us to better understand the potential role of H 2 SO 4 and the excess electron in the atmosphere. Certainly, more extensive experiments are highly desirable to verify the present findings.
Supplementary Materials: RDG maps of the electron capture products, the time evolution of the selected bond distances for complexes A, A , and B in the molecular dynamics calculations, and the IR data for complexes A and B. The following are available online, Figure S1: RDG maps of the electron capture products, Figure S2: The evolution of the selected bond distances for complex A in the electron capture process as a function of time, Figure S3: The evolution of the selected bond distances for complex A as a function of time, Figure S4: The evolution of the selected bond distances for complex B in the electron capture process as a function of time,

Conflicts of Interest:
The authors declare no conflicts of interest.