Theoretical investigation of the relative stability of Na+Hen (n = 2–24) clusters: Many-body versus delocalization effects

Abstract

The solvation of the Na(+) ion in helium clusters has been studied theoretically using optimization methods. A many-body empirical potential was developed to account for Na(+)-He and polarization interactions, and the most stable structures of Na(+)He(n) clusters were determined using the basin-hopping method. Vibrational delocalization was accounted for using zero-point energy corrections at the harmonic or anharmonic levels, the latter being evaluated from quantum Monte Carlo simulations for spinless particles. From the static perspective, many-body effects are found to play a minor role, and the structures obtained reflect homogeneous covering up to n = 10, followed by polyicosahedral packing above this size, the cluster obtained at n = 12 appearing particularly stable. The cationic impurity binds the closest helium atoms sufficiently to negate vibrational delocalization at small sizes. However, this snowball effect is obliterated earlier than shell completion, the nuclear wavefunctions of (4)He(n)Na(+) with n = 5-7, and n > 10 already exhibiting multiple inherent structures. The decrease in the snowball size due to many-body effects is consistent with recent mass spectrometry measurements.

The quantum structure of anionic hydrogen clusters

“…In other cryogenic media such as helium droplets, the stronger interaction experienced by the charged impurity and the solvent is responsible for the formation of the so-called snowballs in which the immediately surrounding layer freezes and localizes, superfluidity being also suppressed. Such effects have been evidenced experimentally by mass spectrometry 22 but also computationally and for both cationic [23][24][25][26] and anionic 27 dopants.…”

Density functional theory of doped superfluid liquid helium and nanodroplets

“…197,198 was carried out on Na + . 201 These studies have highlighted the importance of the manybody interactions that arise from charge-induced dipole interaction between the ion and the surrounding helium atoms. Note that this interaction cannot be accounted for by including just the −αe 2 /(2r 4 ) polarization term in the cation-helium pair interaction.…”

Snowball formation for Cs+ solvation in molecular hydrogen and deuterium

“…In contrast to the solvation of ions in helium, [14][15][16][17][18][19][20][21][22][23] studies on (H 2 ) n M + clusters are scarce and limited to small cluster sizes. 5,[24][25][26][27][28][29] Clampitt and Jefferies 24 carried out mass spectrometry measurements of (H 2 ) n Li + clusters up to n = 7 and found indications that Li + is solvated by six H 2 molecules, a conjecture that was later confirmed theoretically.…”