Bridging Gaussian Density Fluctuations from Microscopic to Macroscopic Volumes: Applications to Non-Polar Solute Hydration Thermodynamics

Abstract

The hydration of hydrophobic solutes is intimately related to the spontaneous formation of cavities in water through ambient density fluctuations. Information theory-based modeling and simulations have shown that water density fluctuations in small volumes are approximately Gaussian. For limiting cases of microscopic and macroscopic volumes, water density fluctuations are known exactly and are rigorously related to the density and isothermal compressibility of water. Here, we develop a theory—interpolated gaussian fluctuation theory (IGFT)—that builds an analytical bridge to describe water density fluctuations from microscopic to molecular scales. This theory requires no detailed information about the water structure beyond the effective size of a water molecule and quantities that are readily obtained from water’s equation-of-state—namely, the density and compressibility. Using simulations, we show that IGFT provides a good description of density fluctuations near the mean, that is, it characterizes the variance of occupancy fluctuations over all solute sizes. Moreover, when combined with the information theory, IGFT reproduces the well-known signatures of hydrophobic hydration, such as entropy convergence and solubility minima, for atomic-scale solutes smaller than the crossover length scale beyond which the Gaussian assumption breaks down. We further show that near hydrophobic and hydrophilic self-assembled monolayer surfaces in contact with water, the normalized solvent density fluctuations within observation volumes depend similarly on size as observed in the bulk, suggesting the feasibility of a modified version of IGFT for interfacial systems. Our work highlights the utility of a density fluctuation-based approach toward understanding and quantifying the solvation of non-polar solutes in water and the forces that drive them toward surfaces with different hydrophobicities.

Connecting Non-Gaussian Water Density Fluctuations to the Lengthscale Dependent Crossover in Hydrophobic Hydration

“…21 Recently, Ashbaugh, Vats, and Garde demonstrated that Gaussian fluctuations away from the critical point can be accurately captured simply from knowledge of water's density and compressibility, eliminating the need to invoke the water structure for describing molecular-scale hydrophobic hydration. 25 Quantifying and understanding the nature of p v (N) is an important focus of the work presented here.…”

Reversal of the Temperature Dependence of Hydrophobic Hydration in Supercooled Water

“… 20 Assuming that the discrete Gaussian can be approximated using a continuous function, the excess chemical potential of an HS solute in water is where ⟨ n ⟩ = ρ(4 πR 3 /3) is the average number of waters residing within an observation sphere determined by the product of the solvent number density and volume, while χ = (⟨ n 2 ⟩ – ⟨ n ⟩ 2 /⟨ n ⟩ is the normalized solvent fluctuation in the observation sphere. While χ is determined by an integral over water’s radial distribution function performed over the observation volume, Ashbaugh, Vats, and Garde 21 recently developed an analytical expression for χ in spherical volumes that smoothly interpolates between the known microscopic and macroscopic limits to provide an excellent quantitative approximation away from the liquid–vapor critical point over all observation volume radii In this expression, κ T is the macroscopic solvent isothermal compressibility and η = πρd ww 3 /6 is the solvent packing fraction. The effective solvent diameter fitted to our simulation results is d ww = 2.663 Å, closely corresponding to the separation between water oxygens at which the radial distribution function first crosses one.…”

“…The effective solvent diameter fitted to our simulation results is d ww = 2.663 Å, closely corresponding to the separation between water oxygens at which the radial distribution function first crosses one. 21 This expression enables eq 3 to predict the hydration free energies of HS solutes. While eq 4 interpolates the normalized cavity occupation fluctuations over all radii, the range of solute sizes for which eq 3 is applicable is limited due to its divergence below d ww /2, where the continuous distribution approximation breaks down and the necessity of considering higher-order moments of the distribution for larger solutes where interfacial contributions become important.…”

“…While χ is determined by an integral over water’s radial distribution function performed over the observation volume, Ashbaugh, Vats, and Garde recently developed an analytical expression for χ in spherical volumes that smoothly interpolates between the known microscopic and macroscopic limits to provide an excellent quantitative approximation away from the liquid–vapor critical point over all observation volume radii In this expression, κ T is the macroscopic solvent isothermal compressibility and η = πρd ww 3 /6 is the solvent packing fraction. The effective solvent diameter fitted to our simulation results is d ww = 2.663 Å, closely corresponding to the separation between water oxygens at which the radial distribution function first crosses one . This expression enables eq to predict the hydration free energies of HS solutes.…”

Crustwater: Modeling Hydrophobic Solvation

“…And, the model gives interpretations of the observables on the basis of water structure and energies and solute size. Our work can be compared with a recent information theory-based model developed by Ashbaugh, Vats, and Garde, 54 which shows that the temperature dependence of hydrophobic hydration for hard-sphere solutes with varying sizes such as water’s density and compressibility, can be captured with only a few parameters. And Patel 55 also includes a solute–water attractive interaction in an information-theory-based model.…”