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Fig. 22.1C, our simulations of 1 M TMAO solutions are in agreement with the experimental value of0.17 A2/ps (Gostling and Akely, 1952). Simulations of 1, 2, 3, and 4 M TMAO demonstrate a nearly linear decrease in water self-diffusion with respect to concentration (Fig. 22.1B).

Radial distribution functions of water oxygen atoms were calculated for each TMAO solution simulation. The positions of the first and second peaks in the RDFs of each simulation are equivalent to those of pure water (Fig. 22.2C). This indicates that the general tetrahedral structure of water remains intact. The height ofthe first peak in the TMAO simulations is larger («7%) than in pure water.

The reduction in water diffusion is a result of more persistent intermolecular interactions. Analyses show that average lifetimes of hydrogen bonds between water and TMAO are longer (7 ps) than water—water lifetimes

Figure 22.3 Water—water "hydrogen bond''distance and angle distributions for various cosolvent simulation systems. The D-H in the center of each plot represents the donor and proton; in this case the water oxygen and hydrogen. From the D in the inner center to the edge of the circle represents 3.6 A. As a representative subset of data, 2000 points are plotted in the center circle, showing the position and angle of an acceptor (note the upper/lower half symmetry). Angular distributions are represented by the histograms surrounding the circle. Each histogram bin is weighted by the sine of the solid angle to account for conical volume variation. (A) Data from a pure water simulation at 298 K; (B) and (C) show data from a 4 M TMAO simulation and an 8 Murea simulation, respectively.

Figure 22.3 Water—water "hydrogen bond''distance and angle distributions for various cosolvent simulation systems. The D-H in the center of each plot represents the donor and proton; in this case the water oxygen and hydrogen. From the D in the inner center to the edge of the circle represents 3.6 A. As a representative subset of data, 2000 points are plotted in the center circle, showing the position and angle of an acceptor (note the upper/lower half symmetry). Angular distributions are represented by the histograms surrounding the circle. Each histogram bin is weighted by the sine of the solid angle to account for conical volume variation. (A) Data from a pure water simulation at 298 K; (B) and (C) show data from a 4 M TMAO simulation and an 8 Murea simulation, respectively.

(1 ps) (Zou et al., 2002). Water orientation relaxation times increase with increasing concentrations of TMAO to a value of 19 ps at 4 M TMAO (Table 22.2).

8 M urea 4 M TMAO

Figure 22.4 Hydration site population and orientation from cosolvent simulations. (a) Urea and (b) TMAO. The population color scale increases from lowest (red) to highest (blue). Only the top 15% populated hydration sites are displayed; i.e., only sites with a GxoM above 1.8 pairs are shown.

8 M urea 4 M TMAO

Figure 22.4 Hydration site population and orientation from cosolvent simulations. (a) Urea and (b) TMAO. The population color scale increases from lowest (red) to highest (blue). Only the top 15% populated hydration sites are displayed; i.e., only sites with a GxoM above 1.8 pairs are shown.

Unlike urea, TMAO does not substantially disturb the hydrogen bonding of the hydration shell (Table 22.3; see Zou et al., 2002). There also is no effect on water—water residence times (Table 22.2). The three-dimensional structure of TMAO that is presented to hydration water, which has been discussed previously, nicely supports the tetrahedral arrangement of waters (Zou et al., 2002). Only minor evidence of a shift toward linear hydrogen bonds in the water—water hydrogen bonding structure of the first coordination shell is observed in donor—proton—donor angular distributions shown in Fig. 22.3B. However, Table 22.3 shows that as the concentration of TMAO is increased, 3 to 5% of single donor hydrogen bonds are "broken" or "melted" such that no hydrogen bond donors are present.

The time-averaged hydration site population and water orientation depiction shown in Fig. 22.4B reveals the expected hydration site off the oxygen. Because of the molecular symmetry of TMAO, what appears as three hydration sites is actually one with threefold radial symmetry.

This depiction is rather interesting, as the entire hydration shell can be seen (short red and white vectors). As seen in Fig. 22.4B, an upturned semisphere encapsulates the hydrophobic methyl groups, forcing water to optimize interactions with itself rather than with the molecule. Also visible is a "belt" that adjoins the highly populated hydration site to the lower "bowl." Finally, a "cap" forming the second hydration shell can be seen. The lack of persistent orientation or high population sites in this second shell is a result of the symmetry of the highly populated hydration site.

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