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Physica Scripta

Diffusion Monte Carlo description of Cs2(3Σu)–(4He)Nclusters: an example of weak dopant–helium interaction

David López‐Durán, Ricardo Pérez de Tudela, R. Rodríguez-Cantano, Tomás González‐Lezana, María Pilar de Lara‐Castells, Gerardo Delgado-Barrio, Pablo Villarreal

Published Jul 6, 2011• 7 citations
Publisher

Abstract

In this paper, we study the energy and geometric properties of Cs 2 ( 3 Σ u )–( 4 He) N clusters, 2⩽ N ⩽20, N even, through a diffusion Monte Carlo methodology. Considering the results for doped clusters in which the He–impurity interaction dominates over the He–He one, our aim is to investigate the case when this assumption is not fulfilled anymore and the helium–helium potential becomes dominant. We find a scenario where a pure helium subcomplex is formed, leaving out the alkaline dimer, with the largest species gathering the helium atoms in a two-shell-like structure, the first of which is filled with ten particles. Our results are in agreement with previous theoretical and experimental findings.

DOI
10.1088/0031-8949/84/02/028107

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AIP conference proceedings•Jan 1, 2012•2 citations
In this paper, we study the energy and geometric properties of Cs 2 ( 3 Σ u )–( 4 He) N clusters, 2⩽ N ⩽20, N even, through a diffusion Monte Carlo methodology. Considering the results for doped clusters in which the He–impurity interaction dominates over the He–He one, our aim is to investigate the case when this assumption is not fulfilled anymore and the helium–helium potential becomes dominant. We find a scenario where a pure helium subcomplex is formed, leaving out the alkaline dimer, with the largest species gathering the helium atoms in a two-shell-like structure, the first of which is filled with ten particles. Our results are in agreement with previous theoretical and experimental findings.
We report here ((4)He)(N)-Rb(2)((3)Σ(u)) complexes, 2 ≤ N ≤ 20, analysed through a quantum diffusion Monte Carlo stochastic approach. The calculations show that the spin stretched dimer molecule is bound outside the pure He sub-complex, due to the stronger He-He potential as compared with the He-Rb(2) interaction, while the rare gas atom moiety presents, in turn, a shell-like structure with ten He adatoms completing the first shell. Our results agree with previous findings on this and similarly weakly interacting systems.
We present in this work the study of small (4)He(N)-Cs(2)((3)Σ(u)) aggregates (2 ≤ N ≤ 30) through combined variational, diffusion Monte Carlo (DMC), and path integral Monte Carlo (PIMC) calculations. The full surface is modeled as an addition of He-Cs(2) interactions and He-He potentials. Given the negligible strength and large range of the He-Cs(2) interaction as compared with the one for He-He, a propensity of the helium atoms to pack themselves together, leaving outside the molecular dopant is to be expected. DMC calculations determine the onset of helium gathering at N = 3. To analyze energetic and structural properties as a function of N, PIMC calculations with no bosonic exchange, i.e., Boltzmann statistics, at low temperatures are carried out. At T = 0.1 K, although acceptable one-particle He-Cs(2) distributions are obtained, two-particle He-He distributions are not well described, indicating that the proper symmetry should be taken into account. PIMC distributions at T = 1 K already compare well with DMC ones and show minor exchange effects, although binding energies are still far from having converged in terms of the number of quantum beads. As N increases, the He-He PIMC pair correlation function shows a clear tendency to coincide with the experimental boson-liquid helium one at that temperature. It supports the picture of a helium droplet which carries the molecular impurity on its surface, as found earlier for other triplet dimers.
A new full-dimension potential energy surface of the three-body He-Rb₂(³Σ(u)(+)) complex and a quantum study of small (⁴He)(N)-Rb₂(³Σ(u)(+)) clusters, 1 ≤ N ≤ 4, are presented. We have accurately fitted the ab initio points of the interaction to an analytical form and addressed the dopant's vibration, which is found to be negligible. A Variational approach and a Diffusion Monte Carlo technique have been applied to yield energy and geometric properties of the selected species. Our quantum structure calculations show a transition in the arrangements of the helium atoms from N = 2, where they tend to be separated across the diatomic bond, to N = 4, in which a closer packing of the rare gas particles is reached, guided by the dominance of the He-He potential over the weaker interaction of the latter adatoms with the doping dimer. The deepest well of the He-Rb₂ interaction is placed at the T-shape configuration, a feature which causes the dopant to be located as parallel to the helium "minidroplet". Our results are shown to agree with previous findings on this and on similar systems.
Small helium (4He) clusters containing the lighter isotope He3 are studied by means of quantum Monte Carlo methods. Accurate ground state energies and structural properties are obtained using accurate trial wave functions and the Tang–Tonnies–Yiu (TTY) helium–helium pair potential. The dimer He4–3He is not bound; as well as the trimer He4He23. The smallest cluster containing He3 is He24He3 with a nonrigid structure having a marked linear contribution. Interestingly, this weakly bound system, with an energy one order of magnitude less than the He34 trimer, is able to bind another He3 atom, forming the tetramer He24He23, which shows the odd feature of having five out of six unbound pairs. In general, the substitution of a single He4 atom in a pure cluster with a He3 atom leads to an energetic destabilization, as the pair He4–3He is not bound. The isotopic impurity is found to perturb only weakly the distributions of the remaining He4 atoms, which retain the high floppiness already found in the pure clusters. As the number of atoms increases the isotopic impurity has the marked tendency to stay on the surface of the cluster. This behavior is consistent with the formation of the so-called “Andreev states” of a single He3 in liquid He4 helium and droplets, where the impurity tends to form single-particle states on the surface of the pure He4.
We report accurate ground state energies and structural properties for small clusters of 4He computed with the diffusion quantum Monte Carlo (DMC) method combined with high quality trial wave functions and using the recent analytical pair potential of Tang, Toennies, and Yiu [Phys. Rev. Lett. 74, 1546 (1995)]. Calculations based on the older HFD-B(He) potential are reported for comparison. The clusters are found to be extremely floppy and to be characterized by very diffuse wave functions. The DMC results for 4He2 and 4He3 are in excellent agreement with other calculations using conventional methods. 4He3 is found to have a noticeable contribution from nearly linear geometries. The internal structure of the clusters is described by a three particle correlation function which reveals a significantly non-spherical internal cluster structure. The energies for all cluster sizes are found to be slightly higher than those obtained with the HFD-B(He) pair potential. Exploratory calculations on the helium trimer indicate that the effects of three body interactions do not exceed the uncertainty margin provided by different state of the art pair potentials.
Diffusion and path integral Monte Carlo methods are currently, and successfully, used to describe structures and binding energies of helium clusters doped with some impurity. For diatomic dopants, by considering the He atoms as "electrons" and the dopant as "nuclei" within a Hartree/Hartree-Fock framework, our group has developed a complementary tool which, in addition to the above mentioned properties, provides us with wave-functions. It allows to perform spectral simulations that can be compared with the experiment. This paper reviews the fundamental aspects of such quantumchemistry-like methodology in which, together with masses, Coulomb interactions are replaced by proper molecular ones. Extensions towards more accurate ab initio methodologies are outlined. Finally, the challenging scenario arising when the impurity is not immersed but attached to the nanodroplet, giving rise to an unusual "solar" system in which the planets no longer move around the dopant as a "sun", is addressed.