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The Journal of Chemical Physics

A complete configurational study for the bound states of Ne trimers

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

Published Feb 16, 2005• 22 citations
Publisher

Abstract

The structural properties and the energetics of the ground and the excited bound states of Ne(3) for zero total angular momentum are examined using different modelings for the two-body interactions. We employ a method consisting of a variational approach with a distributed Gaussian functions (DGF) basis set expansion. We discuss at length the advantages and possible limitations of such an approach, comparing it to other methods which have been applied in the literature to the same system. The DGF method turns out to be very accurate in giving us the bound states energetics and also provides in a natural way a convincing pictorial description of all the states, including those with dominant linear configurations. Additional bound states are found for the Ne(3) system with respect to those indicated in previous works and we suggest a "stabilization" procedure that can be used to assess the truly bound nature of a state. Some considerations on the relative reliability of the examined two-body interactions are also reported.

DOI
10.1063/1.1850096

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The structural properties and the energetics of the ground and the excited bound states of Ne(3) for zero total angular momentum are examined using different modelings for the two-body interactions. We employ a method consisting of a variational approach with a distributed Gaussian functions (DGF) basis set expansion. We discuss at length the advantages and possible limitations of such an approach, comparing it to other methods which have been applied in the literature to the same system. The DGF method turns out to be very accurate in giving us the bound states energetics and also provides in a natural way a convincing pictorial description of all the states, including those with dominant linear configurations. Additional bound states are found for the Ne(3) system with respect to those indicated in previous works and we suggest a "stabilization" procedure that can be used to assess the truly bound nature of a state. Some considerations on the relative reliability of the examined two-body interactions are also reported.
Helium trimer bound states are calculated by means of a variational method described in terms of atom pair coordinates and distributed Gaussian basis functions for zero total angular momentum. To show the feasibility of this method, we also apply it to the calculation of the first vibrational levels of the Ar3 and Ne3 clusters. Special emphasis is made on the study of the possible Efimov behavior of the first excited state found in the He34 trimer. Geometrical configurations of the ground and first excited states of these rare gas trimers have been exhaustively studied owing to the proper symmetry of the coordinates chosen.
Helium trimer bound states are calculated with a variational method described in terms of pair atom coordinates and distributed Gaussian functions by assuming zero total angular momentum. With the two-body interaction potential used, a weakly bound state for the dimer and only two bound states for the trimer are found. Although strictly speaking the first excited trimer state is not an Efimov state, we show that this state presents several characteristics of the Efimov behavior which are extensively discussed in the present work. Special emphasis is placed on the main geometrical configurations contributing to the two bound trimer states, and suggestions are made on the possible ways of experimentally detecting the Efimov-type state.
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.
We study theoretically the ground and excited bound states of the bosonic rare gas van der Waals trimer Ne(3). A slow variable discretization approach is adopted to solve the nuclear Schrödinger equation, in which the Schrödinger equation in hyperangular coordinates is solved using basis splines at a series of fixed finite-element methods discrete variable representation hyper-radii. We consider not only zero total nuclear orbital angular momentum, J = 0, states but also J > 0 states. By using the best empirical neon dimer interaction potentials, all the bound state energy levels of Ne(3) will be calculated for total angular momenta up to J = 6, as well as their average root-mean-square radii. We also analyze the wave functions in hyperspherical coordinates for several selected bound states.
The rotationless, vibrational states of two weakly bound triatomic species are calculated using a variational expansion over multicentred Gaussian functions (the DGF method described in the main text) and corrections are introduced by using the three-body potentials vis à vis the sum-of-potentials approximation. The effects are seen to be very small and isotopic substitution is further introduced to evaluate changes on the vibrational structures of both systems, aiming at possibly detecting Efimov behaviour in such special trimers: no Efimov states are found with the available potentials and when the two-body potential strengths are varied. An additional study on the effects of isotopic substitutions for H atoms is also presented.
Despite their apparent simplicity, the properties of the two helium trimers, (4)He3 and (3)He(4)He2, are still not completely understood. In particular, the existence of a bound state of the asymmetric trimer (3)He(4)He2 was established many years ago, using different theoretical approaches, and later it was experimentally detected. However its structural properties have not been thoroughly investigated so far, probably because an accurate theoretical description of this very weakly bound system is computationally quite demanding. In this work we give for the first time an accurate and complete theoretical description of the geometrical structure of this fragile system using quantum Monte Carlo techniques employing the TTY potential and compare its properties with those of (4)He2 and (4)He3. We compute average values of distances and angles, along with the angle-angle distribution function: a two-dimensional probability distribution well suited to discuss the shape of a trimer. Our analysis shows that the lighter isotope is very diffuse and can be found at large distances from the other two atoms, but also close to the center of mass of the system in nearly linear configurations. For this system the concept of "equilibrium structure" is meaningless and all kinds of three-atom configurations must be taken into account in its description.