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Physical Chemistry Chemical Physics

The weakly bound ground state of the LiHe2 triatomic system

I. Baccarelli, Gerardo Delgado-Barrio, Franco Antonio Gianturco, Tomás González‐Lezana, Salvador Miret-Artés, Pablo Villarreal

Published Jan 1, 2000• 43 citations
Publisher

Abstract

We confirm the existence of and study the location and spatial shape for the ground bound state of the triatomic system that contains one lithium (6Li or 7Li) atom and two boson helium partners. The computational method employed involves a variationally determined multi-center expansion over Gaussian functions of variable width, as discussed in our previous recent work. The overall behavior of this very diffuse, bound wave-function with zero angular momentum is analyzed in detail to extract specific indicators on its spatial features. The strength of the available three-particle interaction is arbitrarily scaled in order to investigate the possible appearance of either halo or Efimov states in the present system.

DOI
10.1039/b002415p

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We confirm the existence of and study the location and spatial shape for the ground bound state of the triatomic system that contains one lithium (6Li or 7Li) atom and two boson helium partners. The computational method employed involves a variationally determined multi-center expansion over Gaussian functions of variable width, as discussed in our previous recent work. The overall behavior of this very diffuse, bound wave-function with zero angular momentum is analyzed in detail to extract specific indicators on its spatial features. The strength of the available three-particle interaction is arbitrarily scaled in order to investigate the possible appearance of either halo or Efimov states in the present system.
Weakly bound triatomic molecules consisting of two helium atoms and one alkali metal atom are studied by means of the diffusion Monte Carlo method. We determined the stability of 4He2A, 4He3HeA, and 3He2A, where A is one of the alkali atoms Li, Na, K, Rb, or Cs. Some of the trimers with 3He are predicted to be self-bound for the first time, but this is observed to be dependent on the He–A interaction potential model. In addition to the ground-state energy of the trimers, we determined their density, radial, and angular distributions. Many of them are spatially very extended, which qualifies them as quantum halo states.
We study the existence of stable bound states of triatomic molecules containing two helium atoms and one alkali atom X (X = Li, Na) and examine the dependence of their binding energies on the mass of the constituent atoms. The three-body systems are solved within the adiabatic approximation in hyperspherical coordinates using the He - He and He - X pair van der Waals interactions that are available in the literature. The binding energies of these systems are shown to be of less than 1 K for some isotope combinations. For the lighter isotopes it is shown that no bound states exist. We found no evidence of the existence of halo states or Efimov states for these systems.
The possible presence of Efimov-type states in isotopic variants of triatomic molecules composed of one Li and two boson He atoms is investigated. Firstly, through the study of two-body interactions in the frame of the effective range theory, it is shown that, at least with the present choice of dimer potentials, the system containing 7 Li unlikely presents any Efimov state, while the 6 Li isotopic variant would be a better candidate in this regard. Then, triatomic bound states are searched through variational calculations in terms of pair inter-atomic distances and distributed Gaussian functions (DGF). The calculations were performed at several values of a parameter λ controlling the strength of the potential. Each system presents two bound levels at the “physical” situation λ = 1. By increasing lambda, the excited levels become “ghost” states as their energies are above the helium dimer energy and present, therefore, an Efimov character. Hence, we conclude that three-body (3B) predictions coming only from two-body (2B) calculations do not have, at least for the systems studied here, any great relevance. Such predictions are not in fact fulfilled for LiHe 2 , as shown by the greatly reduced relevance of isotopic effects in our actual 3B calculations.
The weakly bound diatomic systems He24 and HeH−4 have been found able to support only one bound state for J=0, although the latter also supports an additional bound state for J=1. In the present paper we, therefore, study the structure of the bound states which might exist for the weakly bound triatomic He24H−, in its J=0 state, by describing the full potential as a simple addition of two-body (2B) interactions. We carry out bound state calculations using both Jacobi coordinates within a discrete variable representation (DVR) and pair coordinates with a distributed Gaussian function (DGF) expansion. The system is shown to possess two bound states with respect to its lower dissociation threshold and two further “ghost” states before the complete break-up threshold. The spatial structures of such states and of the floppy complex are analyzed in detail, as is the possibility of detecting Efimov-type states in such a weakly bound aggregate. Finally, the inclusion of three-body (3B) forces in the description of the full interaction and its effect on the number of possible bound states is also discussed.
The interactions between alkali atoms and 4 He, as well as those between H - and 4 He, are known to be even weaker than those between two helium atoms. In this work we show that when the three-particle potential energy surface is obtained as a sum of two-body functions, the ensuing ground state configurations are indeed very weakly bound and acquire spatial shapes difficult to describe in simple configurational terms. We have employed the quantum diffusion Monte Carlo method to analyse the He 2 Li, He 2 Na and He 2 H - systems, for which possible molecular `shapes' are extracted from the final DMC distributions by defining within them conventional chemical structures with varying degree of `stiffness' attached to the nuclear positions.
We study the structure of triatomic molecules containing two helium atoms and one alkali-metal atom X (X = Li, Na). The three-body Schr\"odinger equation is solved in hyperspherical coordinates using the He-He and He-X pair van der Waals potentials available in the literature. We calculate the structural properties of the He2Li{\mathrm{He}}_{2}\mathrm{Li}He2​Li and He2Na{\mathrm{He}}_{2}\mathrm{Na}He2​Na bound states, and analyze one-dimensional pair and angle distribution functions as well as two-dimensional pair-pair and angle-angle distribution functions. These bound states are characterized by so peculiar weakly bound structures that classifying them into particular sizes and geometrical shapes appears to be elusive. Particularly, the ${J}^{\mathrm{\ensuremath{\Pi}}}={0}^{+}$ excited states of 4He26Li^{4}\mathrm{He}_{2}^{6}\mathrm{Li}4He26​Li and 4He27Li^{4}\mathrm{He}_{2}^{7}\mathrm{Li}4He27​Li are found to constitute giant triatomic molecules with their size amounting to several hundred bohrs.