Can electric fields drive chemistry for an aqueous microdroplet?

This study addresses why many organic reactions exhibit accelerated kinetics in aqueous microdroplets relative to bulk solution. The central hypothesis is that strong, oriented electric fields localized at the air–water interface act as an electrostatic pre-organization that can lower activation barriers for bond breaking and formation, thereby enhancing surface reactivity. The authors aim to quantify the magnitude, orientation, heterogeneity, and molecular origins of interfacial electric fields in water microdroplets and assess their potential to drive chemistry. They consider longstanding discrepancies between experimental and theoretical determinations of surface potentials and fields and the role of the mean inner potential and interfacial structure in shaping reactivity.

Previous reports have documented 10^1–10^6-fold rate accelerations for reactions in microdroplets (e.g., Cooks and Zare and co-workers), as well as specific cases of spontaneous peroxide formation and abiotic synthesis in droplets. There is debate over the sign and magnitude of surface potentials and the distribution of ions at the air–water interface. Classical point-charge models generally yield negative surface potentials that reflect only external charge distributions, while AIMD/DFT includes contributions from the mean inner potential of water molecules, leading to positive surface potentials and larger interfacial fields, consistent with electron holography measurements. SREF experiments have inferred strong interfacial fields (~−10 MV/cm). Theoretical frameworks (Matyushov, Voth, Shaik and others) have emphasized the role of electric fields and their fluctuations in catalysis and bond activation, suggesting that oriented fields can significantly lower barriers. Infrared spectroscopy of charged nanodrops has also probed free OH bands as field-sensitive reporters. This work builds upon these insights by using a reactive force field with coarse-grained electrons to reconcile interfacial electronic structure with droplet-scale statistics of electric fields.

• System preparation and equilibration: Water droplets of radii 40, 60, and 80 Å (approximately 8,600 to 71,000 water molecules) with and without ions were constructed using PACKMOL. Initial minimization and equilibration were performed with the AMOEBA force field in Tinker–OpenMM. Systems were heated in the NVT ensemble from 50 to 300 K at 0.33 K/ps using a Bussi thermostat and a RESPA integrator with a 1 fs timestep. Ewald and van der Waals cutoffs were 9 Å and 12 Å, respectively. Cubic simulation boxes were (120 Å)^3, (160 Å)^3, and (200 Å)^3 for R40, R60, and R80 droplets.
• Reactive force field simulations: Equilibrated systems were transferred to LAMMPS using the ReaxFF/C-GeM reactive force field, which includes coarse-grained electrons to capture mean inner potential contributions. After 500 ps equilibration, production trajectories of 400 ps to 1 ns were run, saving snapshots every 1 ps for electric field analysis.
• Ion conditions: To model charged droplets near electrospray conditions, systems with excess H3O+ or OH− (24 ions, ~88% of the Rayleigh limit for the R40 droplet) were simulated. The Rayleigh limit QR = [8π(εγRR^3)]^1/2 with γ = 0.0523 N/m at 300 K was used to estimate ion concentrations.
• Charge density profiles: The instantaneous interface method defined surface layers L0 (outermost) and L1 (subsurface). For cumulative charge density, Gaussian electron densities were collapsed to point centers (+1 for cores, −1 for shells) and accumulated from −5 Å outside the interface inward at 0.2 Å resolution.
• Surface potential and electric fields: The electrostatic potential was computed on spatial grids via Vi = Σj qj/(4π ε0 rij), placing a unit test charge at Gaussian core/shell positions; electric fields were obtained as gradients of the potential on the same grids within LAMMPS. Potentials were averaged every 1 Å over 200 snapshots. Grid resolutions of 1.0 Å (and verified at 0.25 Å) were used.
• Field projections: The component normal to the interface was obtained by projecting the field onto vectors from the droplet center to grid points: E⊥ via Eq. (4). Electric field projections onto O–H bonds were computed with 1/r^2 weighting over grid points around the O–H midpoint, excluding points within 1 Å to minimize intramolecular contributions (Eq. (5)). Separate statistics were compiled for inner hydrogen-bonded waters and surface free O–H bonds.
• IRPD comparisons: Free OH stretch frequencies for clusters M(H2O)n (M = Ca2+, Na+, I−, Cl−) were compared against IRPD measurements as a function of n^−2/3, with theoretical values obtained using ReaxFF/C-GeM; initial cluster structures followed Paesani et al. for n up to 70, with subsets for n = 20–50.
• Validation: Electric fields inside water molecules were cross-checked against DFT (B97M-rV/TZV2P, CP2K), showing similar values and deviations no larger than variations across functionals. DFT slab calculations exhibited finite-size inconsistencies between direct grid field estimates and surface potential derivatives, underscoring the need for larger systems.

• Interfacial field orientation and magnitude: Electric fields at the air–water interface display a strong preference along the surface normal with mean values of approximately −8.9 to −9.2 MV/cm when sampled directly on grids, and −12.0 MV/cm when inferred from the slope of the surface potential—both consistent with SREF experimental estimates (~−10 MV/cm).
• Distribution shape and heterogeneity: Surface field distributions are strongly non-Gaussian (Lorentzian-like), with large variances (σ ~ 224–226 MV/cm) and tails extending to hundreds up to ~1000 MV/cm, indicating fields can be ~30× larger than the average due to non-linear coupling between intramolecular polarization and intermolecular solvent modes.
• Mean inner potential and consistency: ReaxFF/C-GeM includes mean inner potential contributions and yields consistent average surface fields by both direct and derivative methods. In contrast, DFT slab models give inconsistent values (~150 MV/cm from potential derivatives vs. ~50 MV/cm from direct fields), attributed to finite-size effects.
• Effect of ions: Excess hydronium (24 H3O+) is somewhat surface-enriched, while excess hydroxide (24 OH−) is more broadly distributed across surface and interior. Average interfacial field shifts due to ions are modest because of screening: slight decrease in magnitude with H3O+ (μ ≈ −8.66 MV/cm) and slight increase with OH− (μ ≈ −9.24 MV/cm), but local fields near ions can be large.
• Projections on O–H bonds: Surface free O–H bonds experience substantially larger projected fields than interior H-bonded waters—mean surface projections ~15.7–16.6 MV/cm versus interior ~0.3–0.6 MV/cm—indicating an average increase of ~16 MV/cm at the surface.
• Energetic implications: Using a bond dipole–field model with a transition-state bond dipole of ~2.75 D, the ~16 MV/cm field enhancement at the surface corresponds to a transition state free energy lowering of ~2.1 kcal/mol (~3 kT), implying potential increases in equilibrium constants or rates by ~1–2 orders of magnitude on average. Given the broad distribution, fluctuations may enable even higher accelerations for subsets of droplets or reactant orientations.
• Agreement with spectroscopy: The model reproduces trends in IRPD free OH frequencies for size- and ion-selected nanodrops and aligns with experimental determinations of strong interfacial fields from SREF.

The findings support a mechanistic picture in which strong, oriented, and highly heterogeneous electric fields localized at the air–water interface serve as an electrostatic pre-organization that lowers activation barriers for bond rearrangements of species residing at or near the surface. Inclusion of the mean inner potential is essential for obtaining field magnitudes and signs consistent with experiments sensing electronic density within water molecules, explaining discrepancies with classical point-charge models. The Lorentzian nature of the field distributions arises from non-linear coupling between intramolecular polarization and collective solvent modes, yielding rare but very large fields that may disproportionately contribute to observed reaction accelerations in microdroplets. Although average enhancements are modest compared with enzymatic catalysis, the combination of orientational alignment (notably along free O–H bonds) and field fluctuations across many droplets in electrospray conditions can produce substantial net rate increases. Small average shifts due to ions belie potentially large local fields in their vicinity, modulating specific bond weakening or breaking events depending on ion proximity and reactant orientation.

This work establishes, using a reactive force field with coarse-grained electrons (ReaxFF/C-GeM), that aqueous microdroplet air–water interfaces host strongly oriented electric fields of mean magnitude around −10 MV/cm with broad, Lorentzian-like distributions extending to much larger values. Projection onto surface free O–H bonds reveals an average ~16 MV/cm field enhancement relative to the interior, sufficient to lower transition state barriers by ~2.1 kcal/mol and plausibly account for 10- to 100-fold reaction accelerations on average, with higher accelerations possible due to fluctuations. The results reconcile experimental observations (SREF, IRPD) with theory by emphasizing the role of the mean inner potential and interfacial electronic structure. Future research should: (i) extend analyses to diverse organic reactions and bond types to quantify field–reactivity correlations; (ii) model realistic electrospray processes, including charge fragmentation and droplet evolution; (iii) explore ion-specific and concentration effects at varying droplet sizes; and (iv) refine multiscale models that bridge AIMD accuracy with droplet-scale statistics.

• Finite-size and methodology constraints: AIMD slab models showed inconsistencies between direct field estimates and surface potential derivatives due to limited system size; while ReaxFF/C-GeM mitigates this with larger droplets, it remains an approximate force field model.
• Electrospray realism: Ion concentrations modeled approach the Rayleigh limit for a fixed droplet size; actual electrospray involves evolving droplet sizes, charge fragmentation, and fission events not explicitly simulated.
• Screening and locality: Average field shifts in the presence of ions are small due to screening, though local fields near ions can be large; quantifying their impact on specific reactions requires reactant-explicit simulations.
• Probing scope: Field projections excluded grid points within 1 Å of bonds to minimize intramolecular contributions; while appropriate for external fields, it may underrepresent very short-range interactions for specific reactants.
• Code availability: Analysis scripts are not yet publicly archived (available on request), which may limit immediate reproducibility of post-processing pipelines.