Electric potential variation, δϕ(z), across the vapor-liquid and the liquid-solute interfaces for the neutral LJ solute I0 immersed in liquid water (SPC/E), at z = 50 Å. The Gibbs dividing surface (GDS) of the macroscopic interface and the solute position are indicated by dashed vertical lines.
The dipole moment density, P z (z), for all studied liquids at the vapor-liquid interface. Dashed vertical lines represent the GDS of both interfaces for SPC/E.
(a) Total, (b) dipolar, and (c) quadrupolar potential profiles, δϕ(z) (in volts) for the studied liquids characterized by positive molecular quadrupolar moments.
Vapor-liquid interface potential drops for all studied models: standard (blue) and flipped (F)-charge (black) with respect to (molecular quadrupole moment).
The system parameters [γ is the H–O–H angle; μ0 and are the permanent molecular dipole and quadrupole moments; ρ l is the liquid density at the center of the slab (estimated error of ±0.005 g/cm3)], total interfacial potential ϕ lv , the corresponding quadru- ( ) and dipolar ( ) contributions, and the “isotropic” quadrupolar approximation ( , Eq. (19) ); estimated standard error of ±0.5 mV for the vapor-liquid interface potentials of the studied liquid models (obtained using the block averaging method).
Lennard-Jones parameters σ and ε and polarizability α for ions.
Solute-liquid interface potentials with multipolar contributions for neutral solutes solvated in SPC/E water (for which the vapor-liquid interface potential is ϕ lv = −600.3 mV with mV and mV). In principle . The less than 2% difference between the values obtained from the water slab and bulk simulations can be attributed to the differences in densities generated by the finite slab thickness and the barostat used in the NPT bulk simulations (cf. Eq. (19) ). To directly compare solute-liquid and vapor-liquid interface potentials, we correct for this small systematic liquid density difference by defining a solute-dependent rescaled vapor-liquid interface potential, , where (rescaled multipole vapor-liquid interface components are defined similarly). The estimated standard error for the interface potentials is ±0.15 mV and pol denotes polarizable.
Comparison of the different multipole contributions to the direct electrostatic solvation-free energies, , obtained using the rescaled vapor-liquid interface potentials (*), of various ions as obtained directly from the simulations (see Table II ) ( eV); estimated errors: 0.002 eV.
Comparison of electrostatic solvation-free energies for various ions as obtained directly from the simulations, , with the estimate obtained from the truncated direct contribution [ eV for monovalent anions (respectively, cations)] and the Born approximation, . R i is chosen as the distance from the ion center where the ion-water radial distribution functions first reach 1. 30 To correct for the small systematic differences in liquid density between water slab and bulk simulations, the rescaled vapor-liquid interface potentials, , are used in the evaluation of the direct contribution: (see Table III ). Estimated error of 0.025 Å for R i ; estimated standard errors: 0.002 eV for ΔG 0; 0.05 eV for the other solvation-free energies (1 eV = 23.06 kcal/mol ≃ 40k B T).
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