The chemical reactions in electrosprays of water do not always correspond to those at the pristine air–water interface

The recent application of electrosprays to characterize the air–water interface, along with the reports on dramatically accelerated chemical reactions in aqueous electrosprays, have sparked a broad interest. Herein, we report on complementary laboratory and in silico experiments tracking the oligomerization of isoprene, an important biogenic gas, in electrosprays and isoprene–water emulsions to differentiate the contributions of interfacial effects from those of high voltages leading to charge-separation and concentration of reactants in the electrosprays. To this end, we employed electrospray ionization mass spectrometry, proton nuclear magnetic resonance, ab initio calculations and molecular dynamics simulations. We found that the oligomerization of isoprene in aqueous electrosprays involved minimally hydrated and highly reactive hydronium ions. Those conditions, however, are non-existent at pristine air–water interfaces and oil–water emulsions under normal temperature and pressure. Thus, electrosprays should be complemented with surface-specific platforms and theoretical methods to reliably investigate chemistries at the pristine air–water interface.

The chemical reactions in electrosprays of water do not always correspond to those at the pristine airwater interface † Adair Gallo, Jr, abc Andreia S. F. Farinha, abc Miguel Dinis, ad Abdul-Hamid Emwas, ae Adriano Santana, abc Robert J. Nielsen, f William A. Goddard, III f and Himanshu Mishra * abc The recent application of electrosprays to characterize the air-water interface, along with the reports on dramatically accelerated chemical reactions in aqueous electrosprays, have sparked a broad interest. Herein, we report on complementary laboratory and in silico experiments tracking the oligomerization of isoprene, an important biogenic gas, in electrosprays and isoprene-water emulsions to differentiate the contributions of interfacial effects from those of high voltages leading to charge-separation and concentration of reactants in the electrosprays. To this end, we employed electrospray ionization mass spectrometry, proton nuclear magnetic resonance, ab initio calculations and molecular dynamics simulations. We found that the oligomerization of isoprene in aqueous electrosprays involved minimally hydrated and highly reactive hydronium ions. Those conditions, however, are non-existent at pristine air-water interfaces and oil-water emulsions under normal temperature and pressure. Thus, electrosprays should be complemented with surface-specific platforms and theoretical methods to reliably investigate chemistries at the pristine air-water interface.
The air-water interface plays a critical role in numerous natural and applied contexts, such as atmospheric chemistries, 1-3 precipitation, 4 spray coatings, 5 and materials synthesis. 6,7 Indeed, it has been hypothesized that microdroplets generated during the splashing of waves in oceans could have been the chemical reactors leading to the origin of life. [8][9][10] Despite its ubiquity and importance, a variety of fundamental phenomena at the air-water interface remain incompletely understood, such as the specic adsorption of ions [11][12][13] and chemistries therein. 10,[14][15][16][17][18][19][20] The interfacial region, with a typical thickness d o z 0.5 nm, separates the gas-phase (vapor) from the condensed phase (water), two drastically different regions in terms of hydrationreactions spontaneous in one phase are forbidden in the other. 21 In fact, the chemical activities of species at the air-water interface can depart signicantly from those in the bulk, as has been demonstrated by surface-specic techniques, including vibrational second harmonic generation and sum frequency generation, 20,22,23 and polarization-modulated infrared absorption reection spectroscopy, 10,13 and indirect approaches, including NMR 24 and confocal uorescence microscopy. 25 Even though vibrational spectroscopy-based techniques report directly on thermodynamic properties of the air-water interface, they suffer from interpretational ambiguities and limitations due to low signal-to-noise ratios. [26][27][28][29][30][31][32] Thus, new techniques with higher sensitivity and unambiguous response are needed to help resolve the poorly understood features of the air-water interface while providing benchmarks to judge previous interpretations. 33 In this work, we assess the application of electrospray ionization mass spectrometry (ESIMS) to unravel the thermodynamic properties of pristine air-water interface (Henceforth, we will use the qualier 'pristine' to refer to the air-water interface that is not under the inuence of any external sources/agents, such as electrical voltage or a drying gas).
In the recent years, ESIMS, which has been widely used to characterize ionic/molecular species in polar/apolar solvents, 34 has been adapted to investigate the pristine air-water interface. In the standard conguration, ESIMS experiments entail the formation of electrosprays by the application of electrical potential and/or pneumatic pressure leading microscale droplets with excess electrical charge; those microdroplets pass through a glass/metallic capillary maintained at elevated temperature ($473 K) to evaporate the solvent and facilitate the mass spectrometric detection of analytes downstream. [34][35][36][37][38] In the experiments designed to investigate chemistries at the airwater interface, electrosprays containing one or more reactant(s) are intersected with gases or other electrosprays containing other reactant(s) followed by mass spectrometric detection. For instance, using this platform, thermodynamic properties of the pristine air-water interface have been explored under ambient conditions, including the relative concentrations of interfacial hydronium and hydroxide ions and their activities [39][40][41][42][43] leading to interpretations that have elicited scientic debate. 11,12,[17][18][19]44,45 Further, by intersecting electrosprays of pH-adjusted water with gaseous organic acids, 40 isoprene, 41 and terpenes, 40,41,46,47 researchers observed instantaneous protonation (<1 ms), and in some cases oligomerization of organics, which led them to conclude that as the bulk acidity of water approaches pH # 3.6, the pristine air-water interface behaves as a superacid. While a clear understanding of the emergence of the putative superacidity at the air-water interface is unavailable, we note that in the condensed phase proton-catalyzed oligomerization of isoprene (or olens in general) requires 60-80% concentrated H 2 SO 4 solutions (pH < À0.5). 48 Similar rate enhancements in aqueous electrosprays have also been observed for the syntheses of abiotic sugar phosphates, 15,49 the Pomeranz-Fritsch synthesis of isoquinoline, 50 the reaction between o-phthalaldehyde and alanine, 51 and the ozonation of oleic acid, 52 among others. 16,53 Herein, we assess the relationships between the chemistries observed in aqueous electrosprays to those at pristine air-water interfaces; we also seek to decouple the factors that contribute to the mechanisms underlying reported dramatic rate enhancements by addressing the following questions: (i) Do aqueous electrospray-based platforms report on thermodynamic properties of the pristine air-water interface?
(ii) Do accelerated reactions in aqueous electrosprays arise only from the signicant enhancement of the hydrophobewater (air-water) interfacial area? If yes, the mechanisms underlying the dramatic rate enhancements therein should be insightful in explaining the accelerated organic reactions in oilwater emulsions also referred to as 'on-water' catalysis. [54][55][56][57] (iii) Are the rate accelerations in aqueous electrosprays driven solely by the non-equilibrium conditions therein, especially the enhanced concentration of reactants in the micro-/ nano-droplets due to the evaporation of water? [58][59][60][61] (iv) Are gas-phase reactions implicated in the acceleration of chemical reactions in aqueous electrosprays? 36,44,50,[62][63][64] To address those questions, we investigated the oligomerization of isoprene by proton nuclear magnetic resonance ( 1 H-NMR), a non-invasive technique, as a complementary platform to the ESIMS. Questions (i and ii) were addressed by comparing the effects of enhancing the water-hydrophobe interfacial area in both liquid-vapor and liquid-liquid systems; questions (iii and iv) were addressed by varying the capillary voltages, ionic strengths of the aqueous solutions electrosprayed and intersected with gas-phase isoprene, and 1 H-NMR analysis of condensed vapor from the electrosprays. To highlight the role of hydration in electrosprays, we performed quantum mechanical calculations employing density functional theory (M06 avor).

ESIMS
All experiments were conducted in a commercial Thermo Scientic -LCQ Fleet electrospray ionization mass spectrometer in the positive ion mode, where a DC potential of 6-8 kV was applied to the needle, the tube lens voltage was 75 V, the sheath gas ow rate was 10 arb, the pressure was 1.2 torr at the convection gauge and 0.8 Â 10 À5 torr at the ion-gauge, the ow rates of analytes were controlled by a calibrated syringe pump and ranged between 1-10 mL min À1 , the distances from the ion source and the inlet to the mass spectrometer were $2 cm, and the distance between the electrospray and the tube ejecting isoprene was 1 cm.

H-NMR
All NMR spectra were acquired using a Bruker 700 AVANAC III spectrometer equipped with a Bruker CP TCI multinuclear CryoProbe (BrukerBioSpin, Rheinstetten, Germany); Bruker Topspin 2.1 soware was used to collect and analyze the data. We transferred 100 mL of the (A1) samples into 5 mm NMR tubes, followed by 600 mL of deuterated chloroform (CDCl 3 ). The 1 H-NMR spectra were recorded at 298 K by collecting 32 scans with a recycle delay of 5 s, using a standard 1D 90 pulse sequence and standard (zg) program from the Bruker pulse library. The chemical shis were adjusted using tetramethylsilane (TMS) as an internal chemical shi reference. The (A) samples and a sample of as-purchased isoprene (B) were prepared by transferring 100 mL of each to 5 mm NMR tubes, and then adding 550 mL of deuterated water D 2 O to the NMR tubes. The 1 H-NMR spectra were recorded by collecting 512 scans with a recycle delay time of 5 s, using an excitation sculpting pulse sequence (zgesgp) program from the Bruker pulse library. The chemical shis were adjusted using 3-trimethylsilylpropane sulfonic acid (DSS) as an internal chemical shi reference. The free induction decay (FID) data were collected at a spectral width of 16 ppm into 64 k data points. The FID signals were amplied by an exponential line-broadening factor of 1 Hz before Fourier transformation.

Computational methods
To gain molecular-level insights into the protonation and oligomerization of the isoprene in our experiments, we performed (and benchmarked) DFT calculations at the following levels: (A) geometry and transition state optimization with M06/6-311G* followed by single point calculations with a larger basis set (6-311++G**); 65 (B) geometry and transition state optimization with M06/6-311++G**; (C) geometry and transition state optimization with M06/6-311++G**, followed by single point calculations with CCSD(T). 66 We calculated the internal reaction coordinate (IRC) along the potential energy surface connecting adduct (A), transition state (TS), and product (P). Frequency calculations of the optimized geometries yielded Hessians with zero and one imaginary frequency, respectively, for the minima and the transition state structures. The force constants from the frequency calculations on the TS structures were subsequently used to calculate the IRC path along the forward and backward direction of the transition vector, connecting transition state to the minima. 67,68 The vibrational frequencies from the Hessians were also used to provide the zero-point energies and vibrational contributions to the enthalpies and entropies. The free energies of isoprene at 1 atm were calculated using statistical mechanics for ideal gases.

Molecular simulations
Born-Oppenheimer molecular dynamics (BOMD) 66 simulations were carried out with the M06 functional and 6-311G(d,p) basis set in the NVT ensemble coupled with a Nose-Hoover thermostat 69 at 298 K. The total simulation times were 5 ps with 1 fs timesteps.
We used the Gaussian 09 soware package 70 to perform these calculations and simulations.

Results
We investigated chemical reactions between pH-adjusted water and isoprene (C 5 H 8 , 2-methyl-l,3-butadiene, MW ¼ 68 amu, and solubility in water, S ¼ 0.7 g L À1 at normal temperature and pressure (NTP): 293 K and 1 atm). We chose to examine reactions of isoprene because (i) we wanted to reproduce previous experimental results to ensure a clear comparison, (ii) isoprene is an important biogenic gas whose fate in the atmosphere is not completely understood, 1,41,71,72 and (iii) we could investigate chemistries in electrosprays and emulsions by taking advantage of the low boiling point of isoprene (T b ¼ 307 K) and the high vapor pressure at NTP (p ¼ 61 kPa). 73 As delineated in Fig. 1 and summarized in Table 1, we report on the following sets of ESIMS (detection limit ¼ $1 nM) and 1 H-NMR (detection limit ¼ $10 mM) experiments: At NTP, we combined liquid isoprene with pH-adjusted H 2 O or D 2 O, 1 # pH # 13, in a volumetric ratio 1 : 6 : 3 (isoprene : water : air), agitated the emulsions at 1200 rpm in a vortexer for 6, 60, or 360 minutes, and analyzed the organic phases aer phase-separation by ESIMS and 1 H-NMR. Since the air in the reaction vessels was saturated with isoprene, those experiments also ensured the presence of the products of reactions between the gas-phase isoprene and pH-adjusted water in the organic phase.
(A1) Condensed vapors from electrosprays of organic phase from (A). Aer the liquid-liquid collision reactions (A) were over and the organic phases were electrosprayed in ESIMS for characterization, we condensed the sprays and analyzed them by 1 H-NMR. The 1 H-NMR-based investigation of the reaction products from experiments (A) before and aer electrospraying was carried out to pinpoint the effects, if any, of electrospraying on the formation of the products.

(B) Pure components
We analyzed as-purchased isoprene, acetone, and ethanol by ESIMS and 1 H-NMR.

(C) Gas-liquid collisions
We created electrosprays of aqueous solutions with varying ionic strengths and pH, and intersected them with a stream of gas-phase isoprene (0.48 g min À1 carried by N 2 gas owing at 600 mL min À1 , i.e. isoprene gas concentration was 800 mg L À1 ) followed by mass spectrometric detection (Methods).
Hereaer, throughout the paper, we will refer to our experiments on the liquid-liquid collisions as (A), condensed vapors from the electrosprays (A1), pure isoprene as (B), and gas-liquid collisions in the ESIMS as (C) (Fig. 1, Table 1).
Intriguingly, the ESIMS spectra from the above-mentioned experiments (A) at pH ¼ 1, (B), and (C) at pH ¼ 1 were nearly identical aer normalizing with the maximum intensity ( Fig. 2A-C and Section S a †). The positions of the main peaks in the mass spectra tted the general formula, [(Isop) n $H] + , which corresponded to covalently bonded oligomers of isoprene with one excess proton. In Section S b and Fig. S1 † we present the evidence proving that the peaks did not correspond to physisorbed clusters. In experiments (A), the mass spectra remained the same as the duration of mixing varied from 6 min to 6 h (Fig. S2 †). We also observed numerous secondary peaks between the primary [(Isop) n $H] + peaks. While a detailed characterization of those peaks falls beyond the scope of this work, we speculate that they are composed of C1-C4 fragments covalently bonded with the [(Isop) n $H] + oligomers, for example m/z ¼ 233 ( Fig. 2C and S3 †).
Next, we investigated the role of water pH on the oligomerization of isoprene in experiments (A) and (C). When the products were characterized by ESIMS, we noticed that the oligomers [(Isop) n $H] + appeared when the aqueous phase had pH # 3.6 (Fig. 3). Those observations have been reported previously 18,40,41,46,47 and ascribed to the superacidity of the airwater interface at pH # 3.6. However, we also found that the ESIMS spectra from both experiments, (A) and (C), yielded oligomers [(Isop) n $H] + for the acidic, basic, and pH-neutral salty solutions ( Fig. 3; compare Fig. 2A and C with Fig. S3 † panels C1, C2, and C3). We note that for electrosprays produced from pH > 7 water and salty water, counterions, such as Na + , could inuence the fate of reactions, but we have not investigated those factors.
In experiments (A), aer the emulsions comprising liquid isoprene, liquid water at pH ¼ 1.5, and air (containing saturated gaseous isoprene) were vigorously mixed (for 6 min, 60 min, and  360 min) we compared the organic layers aer phase separation by 1 H-NMR. We also recorded the 1 H-NMR spectra of pure, aspurchased isoprene (B). To our surprise, the 1 H-NMR spectra from all of the set (A) samples were identical to those of set (B), indicating that the effect of the duration of shaking (6-360 min), the pH (1-13), the isotope (H 2 O versus D 2 O) and the presence of gaseous isoprene colliding with pH-adjusted water did not lead to any oligomers within the detection limit of 10 mM ( Fig. 4A and B). To investigate further, we condensed the vapors from the ESIMS exhaust (A1) aer injecting the set (A) samples (1 # pH # 13), and obtained their 1 H-NMR spectra. All of (A1) samples showed spectra similar to each other (Fig. 4A1). The 1 H-NMR spectra of (A) and (B) showed no sign of oligomers in the products: they contained a singlet at 1.87 ppm due to the resonance of the 3 protons in CH 3 ; three dublets at 5.02 ppm due to the resonance of the two protons H5b and H5b (coupling constant, J ¼ 13.

Discussion
Our investigation of experiments (A) with 1 H-NMR revealed that a signicant enhancement in the hydrophobe-water surface area was not sufficient for observable rate accelerations in emulsions of isoprene (gas and liquid) with pH-adjusted water at NTP conditions. On the other hand, analysis of experiments (A), (B), and (C) by ESIMS and experiments (A1) with 1 H-NMR unambiguously demonstrated that the chemical reactions took place exclusively in aqueous electrospraysthe acidity, basicity, and saltiness of water all promoted the reactions. Further, as the capillary voltage was increased from 6 kV to 8 kV, the inection points in experiments (A) and (C) shied such that the oligomers [(Isop) n $H] + were detected at lower ionic strengths (Fig. 3C). Collectively, these ndings contradict previous claims of 'superacidity' of pristine air-water interfaces at pH # 3.6. Next, we sought to identify the mechanisms underlying the protonation and oligomerization of isoprene in electrosprays of mildly acidic water (experiments C). As discussed above, a variety of parameters could inuence reactions therein, including electrical voltage, salts, pH, electrochemical reactions, concentration of reactants in rapidly evaporating drops, and gas-phase reactions. [34][35][36]44,50,63,64,[75][76][77][78][79] Interestingly, by monitoring the changes in the surface tension of pendant water drops exposed to isoprene gas, we found that gas-phase isoprene molecules could adsorb at the air-water interface under NTP conditions (Fig. S4 †). While the adsorption of nonpolar molecules at the air-water interface might appear unexpected, similar phenomenon at the macroscale, entailing the adsorption of hydrophobic particles onto water drops of size 10 À3 m in air forming 'liquid marbles' is well known. 80 Thus, gas-phase isoprene molecules (partial pressure in our chamber: 0.28 atm) may adsorb onto the positively charged aqueous electrosprays comprising excess protons. 62 From this stance, three potential mechanisms for the oligomerization of isoprene emerge, which we discuss and evaluate based on our experimental results and quantum mechanical predictions: mechanism M 1the adsorption of isoprene molecules onto the electrosprays increases their concentration at the interface, leading to reactions under the inuence of high electric elds, similarly to the oligomerization of pure liquid isoprene on injection into ESIMS (Fig. 2B); mechanism M 2continuous evaporation of positively charged electrosprays renders them increasingly acidic, akin to 50% H 2 SO 4 solutions, 48 which drives the liquid-phase oligomerization of the adsorbed isoprene molecules (Section S c and Fig. S5 †); mechanism M 3high capillary voltages electrolyze mildly acidic water and the positive charge ensures that the electrosprayed drops contain excess protons that, during Coulomb explosions, eject highly reactive water clusters that protonate and oligomerize isoprene molecules in the gas phase. In the gas phase, strictly, protonation takes place if the proton affinity of the donor, e.g., H 2 O (165 kcal mol À1 at NTP), is lower than that of the acceptor, e.g., Isop (197 kcal mol À1 at NTP). 81 This observation has been extensively discussed by Enke and co-workers in the context of water-alcohol mixtures, 82 among others; 64,77 these protontransfer reactions also underlie the basis of the Proton Transfer Reaction Mass Spectrometry (PTRMS) that has been used to detect trace gases in the atmosphere. 77,83 In all those mechanisms, the initial ionic strength of water (acidic, basic, or salty) and electrical voltage were crucial for the formation of a stable stream of charged microdropletsthe higher the ionic strength of solutions, the lower the requirement for the electrical voltage. 35,36,[84][85][86] In fact, due to the electrochemical reactions at the electrospray needle under the inuence of high electric elds, the electrosprayed droplets from a positively charged capillary should contain more positive ions than in the bulk 58,63,85,87,88 (Section S c , Fig. S5 †). Interestingly, for pH-adjusted water electrosprayed at 6 kV, we detected oligomers (Fig. 3C) when pH # 3.6 or pH > 12, whereas for the NaCl solutions, we observed oligomers at concentrations as low as 10 À9 M (pNa ¼ 9). Yet, the higher intensities of the [(Isop) n -$H] + at pH # 3.6 in comparison to the salty solutions (Fig. 3C) indicate that the proposed mechanism M 1 is unlikely to play a crucial role in the case of gaseous isoprene interacting with electrosprays of water.
Following our logical exclusion of mechanism M 1 , we are le with mechanisms M 2 and M 3 , i.e. did the reactions take place on the surface of electrosprayed water droplets or in the gas-phase? Whether or not the electrospray spectra represent the solvent-or gas-phase chemistries/characteristics is a much-debated matter and case-specic. 36,38,76,89,90 Obviously, the answer would have a bearing on the questions (ii-iv) outlined above, because the kinetics and thermodynamics of reactions in bulk and gas-phase differ dramatically. 21 Recently, Silveira and co-workers employed cryogenic ion mobility mass spectrometry to demonstrate the effects of rapid dehydration on the structures of undecapeptite substance during the nal stages of electrospray ionization. 90 To further clarify the role of hydration on the protonation and oligomerization of isoprene in our experiments with mildly acidic water (electrosprays and emulsions), we carried out quantum mechanics calculations.

Computational calculations
To gain qualitative molecular-scale insights into our experiments with mildly acidic water, we carried out density functional theory (DFT) calculations (Computational methods). M06, a hybrid meta-generalized gradient approximation (meta-GGA) functional, is known to provide an accurate description of the ground-state thermochemistry, thermochemical kinetics, and transition state structures and energies for a wide series of organic reactions. [91][92][93][94][95][96] We have previously conrmed that the binding energies of water clusters, (H 2 O) n (range n ¼ 2-8, 20), along with the hydration and neutralization energies of hydroxide and hydronium ions using DFT functionals (M06, M06-2X, M06-L, B3LYP, X3LYP) are in excellent agreement with the high-level theory (CCSD(T)/aug-cc-p VDZ level), both with and without the basis set superposition error correction. 91 For instance, our ab initio predictions of the proton transfer thermodynamics between H 3 O + (g) and Isop(g) was DG 0 ¼ À30.7 kcal mol À1 , in accordance with the difference in the experimental gas-phase basicity (GB) of H 2 O (GB H2O ¼ À157.7 kcal mol À1 ) and Isop (GB ISO ¼ À190.6 kcal mol À1 ), DGB ¼ À32.9 kcal mol À1 (Fig. S6 †). 97 Furthermore, the trans-or cis-Isop(g) spontaneously added onto (Isop$H + + H 2 O), leading to cyclic (DG 0 ¼ À40 kcal mol À1 ) or acyclic monoterpenes (DG 0 ¼ À9 kcal mol À1 ), (Fig. S7 and S8 †), as also noted by other researchers. 48,98 Next, we calculated the kinetic barriers for protonation and oligomerization of Isop on a small water cluster containing an extra proton, (H 2 O) 3 $H + , as representative of our electrospray experiments and a larger cluster, (H 2 O) 36 $H + , representing the pristine air-water interface. The sizes of the clusters were guided, in principle, by previous experimental and theoretical work on the hydration of protons, [99][100][101] showing the asymptotic stabilization of a proton with increasing cluster size, and limited by computational expense. The initial geometry of the smaller cluster was obtained from the Cambridge Cluster Database, 102 while the larger cluster geometry was obtained from an SPC/E bulk water box equilibrated at 298 K and at 1 atm pressure yielding the bulk density of 1 g cm À3 . We took a cluster of 36 water molecules from the equilibrated water box as a surrogate for the air-water interface. We added a proton to this cluster and applied Born-Oppenheimer Molecular Dynamics (BOMD) simulations (Computational methods) to obtain various low-energy conformers (Table S2, Section S d †). We chose a cluster with the proton on the surface that facilitated the subsequent study of the activation barriers through DFT calculations (Computational methods).
In the case of (H 2 O) 3 $H + , representative of electrosprays, the proton was extremely reactive/acidic due to insufficient hydrationthe incipient isoprene molecule (Isop) fell into a shallow potential well forming an adduct (Fig. 5). The free energy barrier for proton transfer from (H 2 O) 3 $H + to Isop(g) was DG ‡ ¼ 6.9 kcal mol À1 , and the barrier to the oligomerization with another free Isop(g) was DG ‡ ¼ 2.1 kcal mol À1 (Fig. 5). On the other hand, the predictions for those barriers for protonation and oligomerization of isoprene with the larger water cluster, (H 2 O) 36 $H + , representative of the air-water interface, were DG ‡ ¼ 25.5 kcal mol À1 and DG ‡ ¼ 40.2 kcal mol À1 , respectively, which are insurmountable under ambient conditions within a 1 ms time-frame (Fig. 6). The stark differences in the free energy landscapes for the interactions of Isop(g) with minimally hydrated hydronium ions, available in electrosprays, and larger water clusters can simply be understood in terms of the enthalpies of hydration of gas-phase protons that decrease monotonically with the addition of water molecules; 99-101 the proton activity also decreases commensurately and, in fact, is expected to be even lower for the air-water interface than in the (H 2 O) 36 $H + cluster.
To test the effects of larger basis-sets on these predictions, we compared the results of our M06/6-311+G*/6-311++G** calculations with M06/6-311++G** for the smaller cluster, and found very similar results (Section S d , Table S1 †). Towards further benchmarking, we carried out single point energy Fig. 5 Quantum mechanics-based free energy and enthalpy landscapes for protonation and oligomerization of isoprene while interacting with a cluster comprising three water molecules and one excess proton, (H 2 O) 3 $H + . Due to its incomplete hydration (compared to bulk), the proton exhibited extreme acidity. The free energy barrier for the proton transfer from (H 2 O) 3 $H + to isoprene(g) was DG ‡ ¼ 6.9 kcal mol À1 and the barrier to subsequent oligomerization with another free isoprene(g) was DG ‡ ¼ 2.1 kcal mol À1 , which are easily surmountable under ambient NTP conditions within the timescale of our experiments ($1 ms). These model predictions support mechanism M 3 .
calculations on the structures optimized at the M06/6-311++G**-level with the CCSD(T)-level theory, 66 and found that the qualitative trends in the reaction kinetics remained unchanged (Table S1 †). We note that we could only perform the benchmarking for the smaller system due to the computational expense. Thus, we expect that the relative differences in the barrier heights for the reactions are unlikely to change signicantly between DFT/M06 and CC for our systems. Besides, our 1 H-NMR experiments present unambiguous evidence for these predictions. To summarize, our calculations demonstrate that the kinetic barriers for the protonation and oligomerization of isoprene are easily surmountable in the smaller acidic cluster (available in electrosprays only) and prohibited in larger acidic clusters at 298 K and 1 atm (a surrogate for the pristine airwater interface).

Conclusion and outlook
Based on our experimental investigation of oil-water and airwater interfaces of isoprene with pH-adjusted water, analyzed by ESIMS and 1 H-NMR along with quantum mechanical predictions, we address the questions outlined in the introduction as follows: (i) Aqueous electrosprays do not always report on the thermodynamic properties of pristine air-water interfaces.
(ii) The observed chemical reactions of isoprene in aqueous electrosprays were not driven by the enhancement in the hydrophobe-water interfacial area, as evidenced by the lack thereof in vigorously mixed emulsions of isoprene and pHadjusted water. Thus, the mechanisms underlying the 'onwater' catalysis 54-57 must be different from those leading to rate accelerations in the aqueous electrosprays. 103 Electrosprays of water must facilitate additional chemical pathways, such as reactions with partially hydrated (gas-phase) hydroniums, which are not accessible in vigorously mixed oil-water emulsions or pristine aqueous interfaces.
(iii) Reactions of isoprene in aqueous electrosprays were driven by non-equilibrium conditions thereinmost importantly, due to the rapid evaporation of water leading to highly concentrated droplets and partially hydrated hydronium ions (mechanism M 3 ). It is, thus, crucial to distinguish their contribution from purely 'interfacial effects' towards dramatic rate enhancements in aqueous electrosprays. 50,53,64,78,104,105 (iv) Gas-phase reactions could play a signicant role in the electrospraysin our experiments, reactions between partially hydrated protons and isoprene led to its protonation and Fig. 6 Quantum mechanics-based free energy and enthalpy landscapes for protonation and oligomerization of isoprene on a cluster consisting of 36 water molecules and an excess proton, (H 2 O) 36 $H + , representative of very small water droplets. The kinetic barriers preventing proton transfer to isoprene and its subsequent oligomerization were DG ‡ ¼ 25.5 kcal mol À1 and DG ‡ ¼ 40.2 kcal mol À1 respectively, which were insurmountable under ambient NTP conditions within the timescale of our experiments ($1 ms). The predictions of this model suggest that the reactions of isoprene in electrosprays cannot involve liquid-phase drops. These predictions also support the proposed mechanisms M 3 by ruling out the possible reactions through M 2 .
oligomerization, as recently suggested by Yan & co-workers 53 and demonstrated by Jacobs & co-workers. 106 Our experimental and theoretical results demonstrate that chemistries in aqueous electrosprays do not necessarily correspond to those at the pristine air-water interface and oil-water emulsions at NTP. These ndings also contradict the previous claims of the superacidity of the pristine air-water interface as the bulk acidity approaches pH # 3.6; 40 the proposal for the mildly acidic environmental surfaces to act as the primary sink for the atmospheric isoprene/terpenes should also be reevaluated. 41,46,47 While the potential of aqueous electrosprays to produce high-value products appears promising, those reactions are unlikely to be realized at pristine aqueous interfaces because of the seminal role of the non-equilibrium effects, such as the formation of water clusters with minimally hydrated hydronium ions. 49,78,106 We do note that air-water interfaces could, perhaps, be investigated semi-quantitatively through electrosprays, if the reactants do not participate in gas-phase, acid catalyzed, or redox reactions therein 51,107-109 and/or the gas-phase reactants do not dissolve in the droplets to re-emerge as interfacial species; a careful case-by-case assessment is needed. The mechanisms underlying the protonation and oligomerization of isoprene gas on electrosprays of pH > 7 water also warrant further investigation. We conclude by stressing on the importance of combining complementary experimental techniques, ab initio calculations and molecular dynamics simulations in the quest to unravel phenomena occurring at the pristine air-water interface.

Conflicts of interest
There are no conicts to declare.