98
D. Dell’Angelo
10.6 a 0 . The angular density distribution ρ(θ) shows three peaks at 60
◦ , 120
◦ , and
180
◦ . The structure is more pronounced than with n = 7, consistent with the closing
of a first solvation shell. If we add one helium atom, all density distributions change,
showing that the 7th helium floats around the first shell. With n ≥ 7 a third broadened
peak appears at ∼17 a 0 in the He-He density distribution whereas the K-He density
distribution shows that one helium is far 5 a 0 from the first shell. These findings are
in agreement with the solvation structures obtained by Takayanagi and Shiga [50]
who investigated helium solvation structures of K
He n exciplexes by path integral
molecular dynamics simulations. Considering the radial density distributions of the
clusters shown in Fig. 9, one can conclude that the second solvation shells around
the np-orbital are likely completed with n = 11, because the first and the second
peak do not increase after this value. However, if we look at the symmetry of the
cluster which can be evaluated looking at the relative position of its center of mass,
light alkali helium clusters present such a symmetry for n = 9 (Li) and n = 10 (Na).
Since these values of n correspond also to the closure of the second shell as argued by
examining the chemical potentials, we can estimate that the shells are able to host one
(Na) or two (Li) additional atoms. With Fig. 8 I want to discuss the case of Na more
in details. Beyond the first shell, inspection via Ak-He density distributions becomes
more difficult as peaks broaden. Anyway, if we examine the density distribution of
the distance between He atoms and the He-He center of mass, we can notice two
more pronounced peaks in the He-Na
He 10 density profiles with respect to those
of the other cluster sizes. Moreover, the density between peaks decreases and this
indicates that a symmetric structure with Na as dopant is obtained for n = 10. Also
the density distribution of the distance between Na and NaHe 10 center of mass is
consistent with a second shell of 5 helium atoms. The right panel of Fig. 5 shows
the profiles of Ak-He radial distributions when n = 12, that is one atom after the
second shell. Each minimum corresponds to the separation between two peaks in the
Ak-He density distribution. These minima become less and less pronounced from
Li to Rb. This could mean that the possibility of exchange between He atoms of
different shells should increase moving down the alkali periodic group. However, an
alternative QMC approach by path integral simulations could measure the exchange
of He atoms. By examining the least squares plane of all the n + 1 atoms [51],
alkali clusters remained almost flat up to the second shell, after which tridimensional
structures become more relevant, as shown on the top panel of Fig. 8. In agreement
with Takayanagi and Shiga [50], these clusters have nearly planar structures due to
the repulsive interaction of He and the electron in the p-orbital of the Ak atom. Table
4 summarizes some structural informations concerning the external shell. Its radius,
found by considering the maximum of the second peak of He-He n center of mass
distribution, is roughly twice that of the inner shell. Obviously, the rigidity of the
cluster decreases from the second to the first shell. In fact, the height of the peaks
of radial density distributions decreases as a function of n. Although the density
profile suggests an interpretation in terms of shells, the ongoing density increase in
the nearest neighbor density maximum shows that the concept of shells, irrespective
of the dopant considered, becomes inappropriate for n 11. In the fact that the
density between peaks remains very high and particles exchange positions between
D. Dell’Angelo
10.6 a 0 . The angular density distribution ρ(θ) shows three peaks at 60
◦ , 120
◦ , and
180
◦ . The structure is more pronounced than with n = 7, consistent with the closing
of a first solvation shell. If we add one helium atom, all density distributions change,
showing that the 7th helium floats around the first shell. With n ≥ 7 a third broadened
peak appears at ∼17 a 0 in the He-He density distribution whereas the K-He density
distribution shows that one helium is far 5 a 0 from the first shell. These findings are
in agreement with the solvation structures obtained by Takayanagi and Shiga [50]
who investigated helium solvation structures of K
He n exciplexes by path integral
molecular dynamics simulations. Considering the radial density distributions of the
clusters shown in Fig. 9, one can conclude that the second solvation shells around
the np-orbital are likely completed with n = 11, because the first and the second
peak do not increase after this value. However, if we look at the symmetry of the
cluster which can be evaluated looking at the relative position of its center of mass,
light alkali helium clusters present such a symmetry for n = 9 (Li) and n = 10 (Na).
Since these values of n correspond also to the closure of the second shell as argued by
examining the chemical potentials, we can estimate that the shells are able to host one
(Na) or two (Li) additional atoms. With Fig. 8 I want to discuss the case of Na more
in details. Beyond the first shell, inspection via Ak-He density distributions becomes
more difficult as peaks broaden. Anyway, if we examine the density distribution of
the distance between He atoms and the He-He center of mass, we can notice two
more pronounced peaks in the He-Na
He 10 density profiles with respect to those
of the other cluster sizes. Moreover, the density between peaks decreases and this
indicates that a symmetric structure with Na as dopant is obtained for n = 10. Also
the density distribution of the distance between Na and NaHe 10 center of mass is
consistent with a second shell of 5 helium atoms. The right panel of Fig. 5 shows
the profiles of Ak-He radial distributions when n = 12, that is one atom after the
second shell. Each minimum corresponds to the separation between two peaks in the
Ak-He density distribution. These minima become less and less pronounced from
Li to Rb. This could mean that the possibility of exchange between He atoms of
different shells should increase moving down the alkali periodic group. However, an
alternative QMC approach by path integral simulations could measure the exchange
of He atoms. By examining the least squares plane of all the n + 1 atoms [51],
alkali clusters remained almost flat up to the second shell, after which tridimensional
structures become more relevant, as shown on the top panel of Fig. 8. In agreement
with Takayanagi and Shiga [50], these clusters have nearly planar structures due to
the repulsive interaction of He and the electron in the p-orbital of the Ak atom. Table
4 summarizes some structural informations concerning the external shell. Its radius,
found by considering the maximum of the second peak of He-He n center of mass
distribution, is roughly twice that of the inner shell. Obviously, the rigidity of the
cluster decreases from the second to the first shell. In fact, the height of the peaks
of radial density distributions decreases as a function of n. Although the density
profile suggests an interpretation in terms of shells, the ongoing density increase in
the nearest neighbor density maximum shows that the concept of shells, irrespective
of the dopant considered, becomes inappropriate for n 11. In the fact that the
density between peaks remains very high and particles exchange positions between