88
D. Dell’Angelo
helium solvation structures up to the second shell of Ak
He n clusters using Importance Sampling Diffusion Monte Carlo (IS-DMC) technique. Though DMC simulations cannot recover the temporal evolution of the sytem, they provide many
important quantities that are hardly accessible experimentally, such as radial and
angular distribution functions, solvation energies, excitation spectra, as well as their
dependence on the size of the helium aggregate.
The inspection permitted to observe how the structures and the geometries of
these clusters change moving down the alkali periodic group. The model used for
the interaction potential of the full cluster is described in Sect. 2 together with the
technical details of the quantum Monte Carlo approach. Detailed analyses of Ak
He n
energetics and structural properties at the classical and quantum levels are presented
in Sect. 3. Finally, Sect. 4 concludes.
2 Classical Analysis
2.1 The Dimer Potential Energy Curves
The interaction potential of alkali atoms in their ground electronic state attached to
the surface of helium clusters [41] can be modeled quite accurately within the pair
potential approximation. By contrast, for p-electronically excited alkali atoms the
pair approximation is no longer valid due to the anisotropic character of the interaction. Like in previous works [51, 52], in which the description of the system has been
detailed, I rely on the Diatomics-In-Molecule (DIM) [53] approximation to account
for the anisotropy of Ak
interacting with multiple helium atoms. After including
the spin-orbit interaction assumed to be independent of the intermolecular distance,
three global Ak
He n potential energy surfaces have been obtained from the two first
excited adiabatic Ak-He one-dimensional potential energy curves by diagonalization
of a 6 × 6 complex matrix. Pascale’s curves [54, 55] have been used. The choice is
motivated by the classical analysis extended by IS-DMC computations of energetics
and structural properties of Li
He n≤5 and Na
He n≤5 clusters in the first electronic
excited state carried out in our previous work [56]. In particular, it was shown that
globally the results were independent of the diatomic curves used and the physical
conclusions obtained with Pascale’s curves were quite reasonable. Figure 1 shows
the
2
1/2 adiabatic curve for Ak
He dimers when Pascale’s interaction potential
together with the spin-orbit terms, listed in Table 1, are added. Most recently, curves
for Rb
He [57–59] and spin-orbit terms [60] have been calculated.
The shape of these curves results from the mixing of the attractive and repulsive
curves by the spin-orbit coupling term. All curves present two wells separated by
a barrier. A systematic reduction of the depth of the well occuring at short distance
is observed along the periodic table. This is due to the depth of the curves as well
as to the increased mixing with the repulsive state induced by growing the spinorbit value. The cesium represents an extreme case in which the first well is a local
D. Dell’Angelo
helium solvation structures up to the second shell of Ak
He n clusters using Importance Sampling Diffusion Monte Carlo (IS-DMC) technique. Though DMC simulations cannot recover the temporal evolution of the sytem, they provide many
important quantities that are hardly accessible experimentally, such as radial and
angular distribution functions, solvation energies, excitation spectra, as well as their
dependence on the size of the helium aggregate.
The inspection permitted to observe how the structures and the geometries of
these clusters change moving down the alkali periodic group. The model used for
the interaction potential of the full cluster is described in Sect. 2 together with the
technical details of the quantum Monte Carlo approach. Detailed analyses of Ak
He n
energetics and structural properties at the classical and quantum levels are presented
in Sect. 3. Finally, Sect. 4 concludes.
2 Classical Analysis
2.1 The Dimer Potential Energy Curves
The interaction potential of alkali atoms in their ground electronic state attached to
the surface of helium clusters [41] can be modeled quite accurately within the pair
potential approximation. By contrast, for p-electronically excited alkali atoms the
pair approximation is no longer valid due to the anisotropic character of the interaction. Like in previous works [51, 52], in which the description of the system has been
detailed, I rely on the Diatomics-In-Molecule (DIM) [53] approximation to account
for the anisotropy of Ak
interacting with multiple helium atoms. After including
the spin-orbit interaction assumed to be independent of the intermolecular distance,
three global Ak
He n potential energy surfaces have been obtained from the two first
excited adiabatic Ak-He one-dimensional potential energy curves by diagonalization
of a 6 × 6 complex matrix. Pascale’s curves [54, 55] have been used. The choice is
motivated by the classical analysis extended by IS-DMC computations of energetics
and structural properties of Li
He n≤5 and Na
He n≤5 clusters in the first electronic
excited state carried out in our previous work [56]. In particular, it was shown that
globally the results were independent of the diatomic curves used and the physical
conclusions obtained with Pascale’s curves were quite reasonable. Figure 1 shows
the
2
1/2 adiabatic curve for Ak
He dimers when Pascale’s interaction potential
together with the spin-orbit terms, listed in Table 1, are added. Most recently, curves
for Rb
He [57–59] and spin-orbit terms [60] have been calculated.
The shape of these curves results from the mixing of the attractive and repulsive
curves by the spin-orbit coupling term. All curves present two wells separated by
a barrier. A systematic reduction of the depth of the well occuring at short distance
is observed along the periodic table. This is due to the depth of the curves as well
as to the increased mixing with the repulsive state induced by growing the spinorbit value. The cesium represents an extreme case in which the first well is a local