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Insight into the molecular mechanism of water evaporation via the finite temperature string method
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Image of FIG. 1.
FIG. 1.

Rendering of 1025 water molecules in the 31 × 31 × (4 × 31 Å) unit cell. The z-axis is in the horizontal direction.

Image of FIG. 2.
FIG. 2.

Time-averaged density profiles from four 2.0-ns simulations, with frames recorded every 5 ps.

Image of FIG. 3.
FIG. 3.

The dipole-dipole angle η and its distribution in bulk water. (a) The angle η between dipole vectors (blue cylinders) of two water molecules; for clarity, the dipole vectors are translated and reproduced. (b) Distribution of cosine of dipole-dipole angle η for water molecules with indicated O–O separation distances in a 1.0-ns bulk SPC/E water simulation.

Image of FIG. 4.
FIG. 4.

The two “absolute” orientation variables θ and ω, used to define q 4 = cos (θ) and q 5 = cos 2ω. The two angles are defined in relation to the interfacial normal vector and the evaporating molecule's dipole vector and the molecular normal, respectively. (a) Schematic illustration of the two “absolute orientation” angles. (b) Rendering of the dipole vector μ (blue cylinder), the molecular normal vector ν (yellow cylinder), and the interfacial normal (gray cylinder).

Image of FIG. 5.
FIG. 5.

Examples of restraint force and order parameter convergence from image 9 of string 4. (a) Restraint force for order parameter . (b) Value of order parameter

Image of FIG. 6.
FIG. 6.

Values of tetrahedrality order parameters in each Voronoi dynamics image. Bars indicate one semi-standard deviation over simulation trajectory.

Image of FIG. 7.
FIG. 7.

Frechét distance from initial string, and Frechét distance from each string's predecessor. See text for notes about methodological adjustments at string 18 and string 29.

Image of FIG. 8.
FIG. 8.

Minimum free energy path for evaporation, along with Voronoi cell boundaries between images, projected onto two order parameter dimensions at a time. The point labeled “GDS” is image 9, which contains the plane q 0 = z GDS , the Gibbs dividing surface. The free energy changed most dramatically over the images (numbers 9–14), highlighted with white centers. Note that Voronoi cell boundaries do not necessarily appear normal to the string because they respect the scaling of order parameters (see text), and because of the plots' axis scaling.

Image of FIG. 9.
FIG. 9.

Snapshots from the frames in images 8–13 in which the system was closest to its OP target values, as measured by minimal restraint energy. In these images, q 0 = z varied from 13 to 21 Å. (a) Water molecule's orientation during evaporation; the molecule's position and orientation (subject to translation) from images 9–13 is shown in a single figure. The other molecules' configuration is from image 9. The blue and yellow vectors are the dipole and molecular normal vectors, respectively. The transparent surface is the water surface. (b) Hydrogen bonds that an evaporating water molecule donates (yellow) and accepts (purple) in images 8–13. The blue arrow is the dipole vector of the evaporating molecule.

Image of FIG. 10.
FIG. 10.

Transition frequencies from home cell to other cells for four selected images during Voronoi dynamics simulations. Simulations for other images exhibited transitions to sequential cells, as in panels (a) and (b). (a) Image 2. (b) Image 10. (c) Image 14. (d) Image 17.

Image of FIG. 11.
FIG. 11.

Free energy measured through Voronoi milestoning, as a function of order parameter q 0 = relative z-position (left) and order parameter q 1 = local density (right). The local density achieves a minimum value in the vapor phase when only the evaporating molecule itself is contributing to the local density.

Image of FIG. 12.
FIG. 12.

Free energy as a function of order parameters 6 and 7.

Image of FIG. 13.
FIG. 13.

Free energy profile, along with average system energy values. Error bars are 1.5 standard errors.

Image of FIG. 14.
FIG. 14.

Mean first passage time to the final milestone as a function of order parameter q 0 = relative z-position (top) and as a function of q 6 and q 7, the number of hydrogen bonds accepted and donated (bottom).

Image of FIG. 15.
FIG. 15.

Schematic showing contributing trajectories in both reactant-to-product and product-to-reactant directions (solid curves) and non-contributing trajectories (dashed curves).

Image of FIG. 16.
FIG. 16.

Projection of contributing trajectory segments in the forward (evaporating) direction onto principle components. Image centers (Voronoi support points) are the black points, while the trajectories from images 10–13 are shown in alternating shades of gray. The rightmost point represents the final, vapor-phase image.

Image of FIG. 17.
FIG. 17.

Summary of PCA results. (a) Amount of variance explained by principal components. (b) Contributions of each order parameter to principal components 1 and 2.

Image of FIG. 18.
FIG. 18.

Coefficients of order parameters for the five models AE with best BIC values, and the linear model containing all order parameters. The coefficients are for the normalized order parameters, and the error bars are 95% confidence intervals.

Image of FIG. 19.
FIG. 19.

Observed and fitted values of the MFPT values at milestones, plotted against (a) local density and (b) number hydrogen bonds accepted. The fitted data were from model B of Table V and Figure 18 . (a) MFPT and z-position. (b) MFPT and number hydrogen bonds accepted.

Image of FIG. 20.
FIG. 20.

Smooth weighting functions used for calculating local density and local relative orientational order (top), and number of hydrogen bonds donated and accepted (bottom).


Generic image for table
Table I.

Description of order parameters used to describe state of water molecule near interface. Order parameters 8 and 9 have definitions that do not permit the imposition of forces, but listed force constants were used to calculate distances in order parameter-space.

Generic image for table
Table II.

Comparison of simulation measurements to experimental values for the evaporation or “desolvation” process at 298 K. All values are in kcal/mol.

Generic image for table
Table III.

Order parameter components of first and second principle components in analysis of contributing trajectories in Images 10–13. The three largest components in PC1 and the two largest in PC2 are highlighted with boldface type.

Generic image for table
Table IV.

Results of local direction analysis for forward-directed transitions in Images 8–14. The two largest components of the mean vector in each image are underlined.

Generic image for table
Table V.

Best models of τ = (1 − τ/τ bulk ) with different numbers of order parameters used. The combinations are sorted by BIC value.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Insight into the molecular mechanism of water evaporation via the finite temperature string method