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Time-resolved solvation dynamics of Li$^+$, Na$^+$ and K$^+$ ions in liquid helium nanodroplets

Jeppe K. Christensen, Simon H. Albrechtsen, Christian E. Petersen, Constant A. Schouder, Iker Sánchez-Pérez, Pedro Javier Carchi-Villalta, Massimiliano Bartolomei, Fernando Pirani, Tomás González-Lezana, Henrik Stapelfeldt

Abstract

In 2023, ultrafast pump-probe spectrocopy was used to record the solvation dynamics of a single Na$^+$ ion in a liquid helium droplet, atom-by-atom and with femtosecond time resolution [Albrechtsen \textit{et al., Nature}, 2023, \textbf{623}, 319]. Subsequently, theoretical studies showed that other alkali ions solvate in a similar manner but no experimental results were reported so far. Here, we extend the previous measurement on Na$^+$ to Li$^+$ and K$^+$ ions. A pump pulse selectively ionizes an alkali atom, initially residing at the droplet surface, and the ensuing solvation dynamics of the formed alkali cation, Ak$^+$, is followed by ionizing a Xe atom, located in the droplet interior, and recording the yields of Ak$^+$He$_n$ ions expelled from the droplet as a function of the pump-probe pulse delay. We find that Li$^+$, Na$^+$ and K$^+$ ions solvate with a binding rate of 1.8 $\pm$ 0.1, 1.8 $\pm$ 0.1 and 1.7 $\pm$ 0.1 He per ps, respectively. Furthermore, by comparing the number distribution of the Ak$^+$He$_n$ ion yields to the evaporation energies of these ion--He complexes, obtained by Path Integral Monte Carlo calculations, we identify signatures of the first solvation shells of Li$^+$, Na$^+$ and K$^+$. Lastly, we determine the time-dependent dissipation of the solvation energy from the vicinity of the three alkali ion species and find that the rate is highest (lowest) for Li$^+$ (K$^+$)

Time-resolved solvation dynamics of Li$^+$, Na$^+$ and K$^+$ ions in liquid helium nanodroplets

Abstract

In 2023, ultrafast pump-probe spectrocopy was used to record the solvation dynamics of a single Na ion in a liquid helium droplet, atom-by-atom and with femtosecond time resolution [Albrechtsen \textit{et al., Nature}, 2023, \textbf{623}, 319]. Subsequently, theoretical studies showed that other alkali ions solvate in a similar manner but no experimental results were reported so far. Here, we extend the previous measurement on Na to Li and K ions. A pump pulse selectively ionizes an alkali atom, initially residing at the droplet surface, and the ensuing solvation dynamics of the formed alkali cation, Ak, is followed by ionizing a Xe atom, located in the droplet interior, and recording the yields of AkHe ions expelled from the droplet as a function of the pump-probe pulse delay. We find that Li, Na and K ions solvate with a binding rate of 1.8 0.1, 1.8 0.1 and 1.7 0.1 He per ps, respectively. Furthermore, by comparing the number distribution of the AkHe ion yields to the evaporation energies of these ion--He complexes, obtained by Path Integral Monte Carlo calculations, we identify signatures of the first solvation shells of Li, Na and K. Lastly, we determine the time-dependent dissipation of the solvation energy from the vicinity of the three alkali ion species and find that the rate is highest (lowest) for Li (K)
Paper Structure (16 sections, 8 equations, 5 figures, 4 tables)

This paper contains 16 sections, 8 equations, 5 figures, 4 tables.

Table of Contents

  1. Section
  2. Introduction
  3. Methods
  4. Results and discussion
  5. Conclusion
  6. Author contributions
  7. Conflicts of interest
  8. Data availability
  9. Acknowledgements

Figures (5)

  • Figure 1: The evaporation energy, $E_{\text{evap}}(N)$, of the Ak$^+$He$_N$ complexes calculated by PIMC. Results for Li$^+$ (red), Na$^+$ (blue) and K$^+$ (green). Values for Li$^+$ are from Ref.rastogi_lithium_2018, values for Na$^+$ are from Ref.albrechtsen_femtosecond-and-atom-resolved_2025 and K$^+$ results are from this paper.
  • Figure 2: Structures of relevant solvation complexes with evaporation energies shown in Figure \ref{['fgr:evaporation_energies']} and obtained by considering either an average (Li$^+$) or a limited value (Na$^+$ and K$^+$) of quantum beads for a better ilustration. (a) and (b) are PIMC results adapted from Ref. rastogi_lithium_2018 for Li$^+$He$_6$ and Li$^+$He$_8$, respectively; (c), (d) and (e) have been estimated from the calculation reported Ref. albrechtsen_femtosecond-and-atom-resolved_2025 for Na$^+$He$_6$ and Na$^+$He$_{12}$, respectively and finally (f) is the structure from the present PIMC calculation for K$^+$He$_{12}$.
  • Figure 3: Time-dependent ion yields, $Y_n(t)$. Left column of panels (red): Li$^+$He$_n$. Second left column of panels (blue): Na$^+$He$_n$. Two rightmost columns of panels (green): K$^+$He$_n$. Black dots are experimental data, full lines are the results from a fit to Eq. \ref{['eq:poiss']} and dashed lines are extrapolated values of the fit beyond the fitted range.
  • Figure 4: Number distributions, $P_{\text{exp}}(n;t)$, Left panels (red): Li$^+$He$_n$. Central panels (blue): Na$^+$He$_n$. Right panels (green): K$^+$He$_n$. Filled bars: experimental data included in the fit, greyed-out bars: data excluded in the fit, filled black lines: result of the fit, dashed lines: result of the fit extrapolated beyond the fitted range.
  • Figure 5: Mean dissipated energy as a function of time for Li$^+$ (red), Na$^+$ (blue) and K$^+$ (green). The dark-colored regions indicate values included in the fit of Eq. (\ref{['eqn:newt']}). The fit is shown as the full colored lines, while the dashed colored lines represent the fit extrapolated beyond the fitted time ranges