Ca+ Ions Solvated in Helium Clusters

Abstract

We present a combined experimental and theoretical investigation on Ca+ ions in helium droplets, HeNCa+. The clusters have been formed in the laboratory by means of electron-impact ionization of Ca-doped helium nanodroplets. Energies and structures of such complexes have been computed using various approaches such as path integral Monte Carlo, diffusion Monte Carlo and basin-hopping methods. The potential energy functions employed in these calculations consist of analytical expressions following an improved Lennard-Jones formula whose parameters are fine-tuned by exploiting ab initio estimations. Ion yields of HeNCa+ -obtained via high-resolution mass spectrometry- generally decrease with N with a more pronounced drop between N=17 and N=25, the computed quantum HeNCa+ evaporation energies resembling this behavior. The analysis of the energies and structures reveals that covering Ca+ with 17 He atoms leads to a cluster with one of the smallest energies per atom. As new atoms are added, they continue to fill the first shell at the expense of reducing its stability, until N=25, which corresponds to the maximum number of atoms in that shell. Behavior of the evaporation energies and radial densities suggests liquid-like cluster structures.

Keywords: classical/quantum monte carlo calculations; helium nanodroplets; helium-alkaline earth ion interactions; mass spectrometry; molecular clusters; solvation.

Figure 1

Schematic illustration of the experimental setup. Calcium vapor is picked up by neutral helium nanodroplets that are formed by expansion of precooled and pressurized helium into vacuum. The doped helium nanodroplets are ionized via electron impact and all product ions ejected from the heavy droplets are analyzed by a reflectron time-of-flight mass spectrometer.

Figure 2

Well resolved mass spectra (arb. units) around the mass-to-charge ratio $m/z=48$ showing the contribution of cations that have to be considered for fitting the measured signal.

Figure 3

Potential energy curves for the He-Ca${}^{+}$ interaction. Open black circles are CCSD(T) results and the red line depicts the analytical expression given by the ILJ potential of Equation (1). Inset: Comparison of the well regions of He-Ca${}^{+}$ (red) and He-He [40] (black) interaction potentials.

Figure 4

Experimental ion yield for He${}_N$Ca${}^{+}$. Lines red, green and blue are a guide to the eye of three regions of cluster sizes with distinct behavior.

Figure 5

Upper panel: Evaporation energies ($\Delta E_N=E_{N-1}-E_N$) for He${}_N$Ca${}^{+}$ obtained with PIMC (black squares) and DMC (blue open diamonds) calculations are compared with experimental ion yields (red circles, except for N multiples of 10 which are shown in green, see text). Left and right y axes show the scales of the theoretical and experimental results, respectively. Lower panel: Energy per He atom ($E_N/N$) obtained by the PIMC (black squares) and DMC (open blue diamonds) approaches.

Figure 6

Cluster radial densities (in Å${}^{-3}$) as functions of the He${}_N$Ca${}^{+}$ distance (in Å) obtained by means of the PIMC method for different sizes of He${}_N$Ca${}^{+}$ clusters: $N=8$ (red), $N=15$ (blue), $N=20$ (black), $N=25$ (green) and $N=30$ (pink).