Gaussian and Non-Gaussian Solvent Density Fluctuations within Solute Cavities in a Water-like Solvent

We report a Monte Carlo simulation study of length-scale-dependent density fluctuations in cavities in the coarse-grained mW representation of water at ambient conditions. Specifically, we use a combination of test particle insertion and umbrella sampling techniques to examine the full range of water occupation states in spherical cavities up to 6.3 Å radius in water. As has previously been observed, water density fluctuations are found to be effectively Gaussian in nature for atomic-scale cavities, but as the cavities get larger, they exhibit a non-Gaussian “fat-tail” distribution for lower occupancy states. We introduce a new statistical thermodynamic approach to analyze non-Gaussian fluctuations based on the radial distribution of waters about cavities with varying numbers of waters within its boundaries. It is shown that the onset of these non-Gaussian fluctuations is a result of the formation of a bubble within the cavity as it is emptied, which is accompanied by the adsorption of waters onto its interior surface. We revisit a theoretical framework we previously introduced to describe Gaussian fluctuations within cavities to incorporate bubble formation by including surface tension contributions. This modified theory accurately describes density fluctuations within both atomic and meso-scale cavities. Moreover, the theory predicts the transition from Gaussian to non-Gaussian fluctuations at a specific cavity occupancy, in excellent agreement with simulation observations.


Figures
Figures S1a -S1d.Cavity-water radial distribution functions for the 6.3 Å cavity at 25°C  = and 1 atm for to The radial distribution functions are indicated by the thin solid line. 0 ()  3 () The inner and outer cavity boundary contact values are indicated by the red and blue circles, respectively.

Figures
Figures S1e -S1h.Cavity-water radial distribution functions for the 6.3 Å cavity at 25°C  = and 1 atm for to The radial distribution functions are indicated by the thin solid line. 4 ()  7 () The inner and outer cavity boundary contact values are indicated by the red and blue circles, respectively.

Figures
Figures S1m -S1p.Cavity-water radial distribution functions for the 6.3 Å cavity at 25°C  = and 1 atm for to The radial distribution functions are indicated by the thin solid line. 12 ()  15 () The inner and outer cavity boundary contact values are indicated by the red and blue circles, respectively.

Figures
Figures S1q -S1t.Cavity-water radial distribution functions for the 6.3 Å cavity at 25°C  = and 1 atm for to The radial distribution functions are indicated by the thin solid line. 16 ()  19 () The inner and outer cavity boundary contact values are indicated by the red and blue circles, respectively.

Figures
Figures S1u -S1x.Cavity-water radial distribution functions for the 6.3 Å cavity at 25°C  = and 1 atm for to The radial distribution functions are indicated by the thin solid line. 20 ()  23 () The inner and outer cavity boundary contact values are indicated by the red and blue circles, respectively.

Figures
Figures S1ac -S1af.Cavity-water radial distribution functions for the 6.3 Å cavity at 25°C  = and 1 atm for to The radial distribution functions are indicated by the thin solid line. 28 ()  31 () The inner and outer cavity boundary contact values are indicated by the red and blue circles, respectively.

Figures
Figures S1ag -S1aj.Cavity-water radial distribution functions for the 6.3 Å cavity at 25°C  = and 1 atm for to The radial distribution functions are indicated by the thin solid line. 32 ()  35 () The inner and outer cavity boundary contact values are indicated by the red and blue circles, respectively.

Figures
Figures S1ak -S1an.Cavity-water radial distribution functions for the 6.3 Å cavity at 25°C  = and 1 atm for to The radial distribution functions are indicated by the thin solid line. 36 ()  39 () The inner and outer cavity boundary contact values are indicated by the red and blue circles, respectively.

Figures
Figures S1ao -S1ar.Cavity-water radial distribution functions for the 6.3 Å cavity at 25°C  = and 1 atm for to The radial distribution functions are indicated by the thin solid line. 40 ()  43 () The inner and outer cavity boundary contact values are indicated by the red and blue circles, respectively.

Figure S2 .
Figure S2.Differential change in the water occupational probability, for the ln  = ln(  + 1 /  ) 3.3 Å (a), 4.3 Å (b), and 5.3 Å (c) radius cavities at 25°C and 1 atm.The lines indicate result determined using umbrella sampling, while the points indicate results determined from the cavity radial distribution functions fitted to eq. (20).