Modelling Metal Foam Formation
in Helium Nanodroplets
David McDonagh, The Centre for Interdisciplinary Science
Project Supervisor: Professor Andrew Ellis, Department of Chemistry
ABSTRACT:
Conflicting experimental evidence for metal foam formation in aluminium-doped helium
nanodroplets highlights the need for a deeper understanding of the favourable conditions for
metastable complexes to form. Potential energy surface calculations of dimers were
superimposed to simulate the environment of both magnesium and aluminium-doped
nanodroplets. UV-Vis calculations were then carried out at predicted local minima and
compared to experimental values. In the magnesium system, UV-Vis calculations indicate a
preferred metastable state partially stabilised by favourable helium-helium interactions. The
same methods applied to the aluminium system found no local minima, and UV-Vis
calculations at the suspected distance of one bubble diameter produced a red-shift
significantly beyond that found by experiment. These results indicate metastable complexes
are unlikely to form in aluminium-doped droplets, and double-peaked UV-Vis spectra for this
system is likely a result of a distortion of the bubble cavity.
Introduction
From a lack of Aln+ clusters in mass spectrometric analyses of
aluminium-doped droplets, and a comparable UV-Vis spectrum to the
magnesium system, it has been suggested that the same behaviour may
be true for aluminium[5]. However, more recent experimental work
appears to contradict these findings[6].
Methods
To assess the differences in these two systems, a more detailed
analysis of the potential energy surface of magnesium-doped
nanodroplets was carried out, and UV-Vis calculations were run to
assess the likelihood of each metastable state from experimental values.
This was then repeated for aluminium-doped nanodroplets. Mg2, MgHe
and He2 potential energy surfaces were calculated at the Coupled
Cluster level of theory up to double excitations, with triple excitations
treated using perturbation theory (CCSD(T)). The augmented correlation
consistent polarised valence quadrupole zeta basis set (aug-cc-pVQZ)
was used in each case, with the addition of bond functions developed by
F. Tao & Pan (1992) for weakly bound systems found to be more
consistent with literature values for MgHe. Superimposing dimer
potentials was done assuming a spherical bubble cavity, shown in figure
1. UV-Vis spectra for the 3  3p transition were calculated at the
Configuration Interaction level of theory up to double excitations, with
results shown in table 1.
To accurately model the aluminium open-shelled systems, Density
Functional Theory (DFT) was used, where the three parameter hybrid
functional developed by Becke (1993) with the 6-311+G* Pople basis set
was found to be most consistent with literature values. In light of this,
UV-Vis spectra were calculated using the same functional and basis set,
using Time-Dependent Density Functional Theory (TD-DFT). All
calculations were carried out in the Gaussian 03 Software Package, with
orbitals rendered in Chemdraw.
0
5
Embedded Mg Dimer Potential
-10
-5
Figure 1: The embedded
potential
energy
curve
predicted for two magnesium
atoms solvated in a helium
nanodroplet. Local minima
are observed at 10.2 Å and
13.7 Å, with binding energies
of approximately 9 cm-1 and
5 cm-1, respectively.
-15
Energy (cm-1)
Embedded Mg dimer potential
Free Mg dimer potential
-20
A growing body of research now involves the study of molecular
complexes in helium nanodroplets, most notably due to the free rotation
and translation of molecules not available in other cooling techniques,
and the solvent providing a medium transparent to ultraviolet and
infrared radiation[1]. The degree of solvation has been found to differ
depending on the molecule used, where the level of interaction between
helium atoms can result in a surface or solvated state, in the latter case
resulting in clustering of the dopant species[2]. In magnesium-doped
nanodroplets, however, an interesting case is observed. Resonant-twoionisation (R2PI) spectra indicate magnesium atoms enter a solvated
state, but remain delocalised at a preferred distance, producing a
metastable complex or ‘foam’[3]. Further evidence for this is found in
potential energy surface and helium density calculations, indicating
helium atoms between dopants provide several potential energy
barriers, preventing cluster formation[4].
A helium density profile of
an embedded magnesium
dimer, Przystawik et al.
2008
6
8
10
12
14
16
Interatomic Distance (Å)
Mg gas
phase (nm)
Embedded
Mg (nm)
Two embedded Mg
atoms at 10.2 Å (nm)
Two embedded Mg
atoms at 13.7 Å (nm)
Experimental
285.212
279.0
282.5
282.5
CIS(D)
285.628
278.561
281.420
279.904
Table 1: UV-Vis spectra for the 3p  3s transition. The experimental gas phase value
is taken from NIST (2014), and the embedded magnesium data is taken from
Przystawik et al. (2008). The embedded environment was simulated using a number
explicit solvent molecules based on helium density calculations for this system[4].
Discussion
The potential energy curves calculated for magnesium-doped droplets
are in good agreement with literature values[3], and several local minima
are observed. Through extending this to three dopant atoms, the 10.2 Å
minimum was found to be the most favourable metastable state.
Calculated UV-Vis spectra for this system appear to confirm this, where
transitions with dopants placed at a distance of 10.2 Å show a red shift
most consistent with experimental values[3]. Interestingly, in using a
solvation shell density calculated from previous work[4], solvent atoms in
neighbouring shells are placed at the helium-helium equilibrium distance
when dopants are placed at 10.2 Å. This could therefore act in further
stabilising this metastable state.
The most accurate dimer potentials for aluminium-doped nanodroplets
show no evidence of local minima, and calculated UV-Vis values show a
redshift significantly beyond that observed experimentally. This work
hence finds evidence in agreement with recent mass spectrometric
analysis that aluminium atoms cluster in helium nanodroplets[6]. A more
detailed analysis of the spectra of aluminium-doped nanodroplets with
single dopant atoms is recommended to assess whether the doublepeaked spectrum for this system is due to delocalisation at distances
greater than the bubble diameter, or a distortion of the bubble cavity.
References:
[1] Toennies, J.P., & Vilesov, A. F. (2004). Angewandte Chemie, 43 (20), 2622-2648
[2] Ancilotto, F., & Barone, V. (1997). Chemical Physics Letters, 274 (1-3), 242-250
[3] Przystawik, A. et al. (2008). Physical Review A, 78(2)
[4] Hernando, A. et al. (2008). Physical Review B, 78(18)
[5] Krasnokutski, S. A., & Huisken, F. (2011). Journal of Physical Chemistry A, 115
[6] Spence, D. et al. (2014). International Journal of Mass Spectrometry, 365