Watching the Solvation of Atoms in Liquids One Solvent Molecule at a Time

We use mixed quantum-classical molecular dynamics simulations and ultrafast transient hole-burning spectroscopy to build a molecular-level picture of the motions of solvent molecules around Na atoms in liquid tetrahydrofuran. We find that even at room temperature, the solvation of Na atoms occurs in discrete steps, with the number of solvent molecules nearest the atom changing one at a time. This explains why the rate of solvent relaxation differs for different initial nonequilibrium states, and reveals how the solvent helps determine the identity of atomic species in liquids.

Figure 1

(a) Absorption spectrum of the $({\mathrm{Na}}^{+},e^{-})$ TCP in room-temperature THF: experimentally measured, blue circles [4]; calculated from our MQC MD simulations, black solid curve. We note that our inhomogeneously broadened simulated spectrum appears narrower than that measured experimentally, suggesting that the simulation does not capture the relative population of coordination motifs precisely; see the supplementary material for details [7]. (b) A snapshot of the (${\mathrm{Na}}^{+}$, $e^{-}$) TCP in THF and its first solvent shell from our MQC MD simulations. THF molecules are represented by pentagons, ${\mathrm{Na}}^{+}$ with a blue (dark) sphere, and the electron as a white isosurface at 50% of the charge density maximum. The equilibrium TCP is dominated by configurations in which oxygen sites on four local THF molecules (red or dark vertices) coordinate to ${\mathrm{Na}}^{+}$. Although this motif contributes heavily to the simulated absorption spectrum [orange short-dashed curve in (a)], fivefold (red dashed curves) and threefold (green dot-dashed curves) motifs also contribute to the full inhomogeneously broadened line shape.

Figure 2

(a) Transient hole-burning dynamics of the $({\mathrm{Na}}^{+},e^{-})$ TCP following 800-nm excitation [7]. (b) Transient difference spectra for the dynamics that accompany the nonequilibrium relaxation of $({\mathrm{Na}}^{+},e^{-}{)}^{*}$ created via photodetachment of ${\mathrm{Na}}^{-}$ in liquid THF [$S_{-}(t)$ in Eq. (2)] [2, 10]. (c) Time dependence of the spectral features in (a) (symbols) and (b) (curves), determined by integrating over the shaded regions. The amplitudes of the transients obtained from the 570- and 700-nm features (representing twofold- and threefold-coordinated TCPs, respectively) are normalized at 4 ps—a time at which the initial recombination kinetics of the nonequilibrated ensemble is complete [7]; the recovery of the 1000-nm band (fourfold- and fivefold-coordinated TCPs) is similarly normalized. The orange dotted curve was derived from the 1130-nm spectral dynamics following photoexcitation of ${\mathrm{Na}}^{-}$ [2], corresponding to the appearance of higher-coordinated solvent-solute motifs after detachment. Both the THB and nonequilibrium solvation dynamics are dominated by a two-step kinetic process that increases the solvent coordination of the solute: $2\to 3\to 4$.

Figure 3

Schematic free-energy surface illustrating the solvation coordinate of the neutral sodium TCP in liquid THF. The solvation coordinate is characterized by the number of THF molecules coordinated to ${\mathrm{Na}}^{+}$ (red circle, +) via their oxygen sites. Dynamic solvation involves discrete steps between different coordination motifs and degrees of electron (blue oval, −) displacement from ${\mathrm{Na}}^{+}$. The free-energy surface is drawn to emphasize that these solvent-solute motifs are chemically distinct species (albeit transiently lived) and that the relaxation of this solvent-solute system progresses through a specific sequence of solvation structures to reach equilibrium.