Size limits and fission channels of doubly charged noble gas clusters

Small, highly charged liquid droplets are unstable with respect to spontaneous charge separation when their size drops below the Rayleigh limit or, in other words, their fissility parameter X exceeds the value 1. The absence of small doubly charged atomic cluster ions in mass spectra below an element-specific appearance size na has sometimes been attributed to the onset of barrierless fission at X = 1. However, more realistic models suggest that na marks the size below which the rate of fission surpasses that of competing dissociative channels, and the Rayleigh limit of doubly charged van der Waals clusters has remained unchartered. Here we explore a novel approach to form small dicationic clusters, namely by Penning ionization of singly charged noble gas (Ng) clusters that are embedded in helium nanodroplets; the dications are then gently extracted from the nanodroplets by low-energy collisions with helium gas. We observe Ngn2+ ions that are about 40% smaller than previously reported for xenon and krypton and about 20% for argon. These findings suggest that fission barriers have been underestimated in previous theoretical work. Furthermore, we measure the size distributions of fragment ions that are produced by collisional excitation of mass-selected dications. At lowest collision gas pressure, dicationic Kr and Xe clusters that are smaller than previously observed are found to evaporate an atom before they undergo highly symmetric fission. The distribution of fragments resulting from fission of small dicationic Ar clusters is bimodal.

The minimum distance between charge carriers in multiply charged HNDs.Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics.This journal is © the Owner Societies 2024 Cluster ions with n/z = 49 would show up in the right-most section in panel b.The expected pattern of isotopes expected for this region is displayed below in panel c for 98 ++ , and further below in panel d for 49 + .Their isotope patterns are markedly different.The expected isotope pattern of 98 ++ matches the experimental data while that of 49 + does not.This proves the assertion that the main contribution to the peak at n/z = 49 comes from dications rather than monocations.
The two minor mass peaks in the mass region due to n/z = 45 ions are about equally high; monocationic and dicationic clusters contribute about equally.In the spectrum at n/z = 44.5 the mass peaks at 2 and 4 units below the main peak are more intense than expected for 89 ++ , and additional mass peaks appear.Ions other than pure Ar n 2+ contribute in this section.The mass spectrum at n/z = 35 is well accounted for by the expected isotope pattern of 35 + , but for n/z = 34.5 the isotope pattern of Ar clusters does not account for the measurement which is swamped by ions that contain impurities, such as H 2 OAr n z+ , or by He p Ar n z+ .
Fig. S1 Schematic of the experimental apparatus.Fig. S2 Sections of mass spectra of HNDs doped with Kr.Fig. S3 Mass spectrum of Ar clusters, and comparison with expected isotope patterns.Fig. S4 CID mass spectra of Ar 115 2+ .Fig. S5 CID mass spectra of Xe 55 2+ Fig. S6 Abundance of Kr n + and Kr n 2+ versus size n.Table Fig. S2 Sections of a mass spectrum of HNDs doped with Kr.Red lines indicate the expected distributions of isotopologues of Kr n 2+ .Kr 43 2+ is the smallest doubly charged cluster that can be identified.
Fig. S1 Extraction of dopant ions emerging from a collision cell filled with He and collisioninduced dissociation of mass selected ions occur in the Q-TOF which is a modified commercial Quadrupole mass spectrometer (Q-TOF Ultima) from Micromass, Waters).
Fig. S3 Panel a: A mass spectrum of HNDs doped with Ar.The prominent series of mass peaks are due to Ar n 2+ (n odd) and Ar n + combined with Ar 2n 2+ ; they are marked by asterisks and triangles, respectively.Panel b zooms into sections of the spectrum where Ar n 2+ with n = 69, 70, 89, 90, 97, and 98 would show up; singly charged cluster ions with n = 35, 45, and 49 would contribute to three of these sections.Mass peaks that arise from isotopically pure 40 Ar n z+ are marked by triangles and asterisks for integer and half-integer values of n/z, respectively.The size n and charge state z are indicated by n z+ .Cluster ions with n/z = 49 would show up in the right-most section in panel b.The expected pattern of isotopes expected for this region is displayed below in panel c for 98 ++ , and further below in panel d for 49 + .Their isotope patterns are markedly different.The expected isotope pattern of 98 ++ matches the experimental data while that of 49 + does not.This proves the assertion that the main contribution to the peak at n/z = 49 comes from dications rather than monocations.The two minor mass peaks in the mass region due to n/z = 45 ions are about equally high; monocationic and dicationic clusters contribute about equally.In the spectrum at n/z = 44.5 the mass peaks at 2 and 4 units below the main peak are more intense than expected for 89 ++ , and additional mass peaks appear.Ions other than pure Ar n 2+ contribute in this section.The mass spectrum at n/z = 35 is well accounted for by the expected isotope pattern of 35 + , but for n/z = 34.5 the isotope pattern of Ar clusters does not account for the measurement which is swamped by ions that contain impurities, such as H 2 OAr n z+ , or by He p Ar n z+ .
Fig. S4 Panels a through c: Fragment ions produced from Ar 115 2+ precursor ions by collisions with argon gas.The collision gas pressure is increasing from top to bottom; values are indicated.The charge state of the dominant fragment ions is indicated above the horizontal arrows.Panel d zooms into a section of the spectrum displayed in panel c.
Fig. S5 Fragment ions produced from precursor ions Xe 55 2+ by collisions with argon gas.The collision gas pressure is increasing from top to bottom; values are indicated.The charge state of the dominant fragment ions is indicated above the horizontal arrows.
Fig. S6 Abundance of singly and doubly charged Kr clusters.The abundance of dications with integer values of n/z has been deduced from the mass spectrum with the fitting routine IsotopeFit.

Table S1
The minimum distance between charge carriers in multiply charged HNDs Based on the assumption that the charges in a spherical multiply charged HND arrange according to the Thomson problem (https://doi.org/10.1080/14786440409463107),we calculate the minimum distance between two charge carriers by multiplying the shortest distance taken from Wales and Ulker (https://www-wales.ch.cam.ac.uk/~wales/CCD/Thomson/table.html) with the radius of the HND.With the critical sizes published by Laimer et al. (https://doi.org/10.1103/PhysRevLett.123.165301)we obtain the following values of d min for z=2 up to 55.