Wave functions of helium clusters

Abstract

The ground and several l=0 breathing mode vibrational excited state wave functions of HeN clusters are determined for N=3–5, 20, 70, and 240, using the variational Monte Carlo method. These wave functions incorporate one-, two-, and three-particle correlation effects and give binding energies, density profiles, and vibrational excitation energies accurately. The larger clusters have liquid-like structure, characterized by a pair distribution function showing approximately two coordination shells. The smallest clusters (N=3, 4) have extensively delocalized structures, which on average are equilateral triangular and tetrahedral, respectively. The N=5 cluster has a totally symmetric average structure, which can only be described in terms of a quantum liquid. No molecular structure, whether rigid or floppy can be assigned in this case. The relative importance of various correlation effects in clusters of different sizes is analyzed and discussed. These wave functions are completely analytical and are convenient as importance functions in diffusion and Green’s function Monte Carlo calculations.

Imaging the structure of the trimer systems 4He3 and 3He4He2

“…For the case of the helium trimer this is different. In 4 He 3 there is apart from the ground state only one other predicted 18 Barletta and Kievsky 19 Gonzalez-Lezana et al 22 Paola et al 33 Blume et al 34 Figure 1 | Internuclear two-body distances. (a) Experimental distribution of the 4 He- 4 He distance of 4 He 3 and the 4 He- 3 He distances of 3 4 He- 4 He comparison with theoretical predictions.…”

“…Although there is theoretical consensus concerning the floppy nature of both the 4 He 3 and 3 He 4 He 2 molecules, the geometrical shape is a matter of extensive current debates. In the particular case of the 4 He 3 trimer some calculations suggest an equilateral triangular structure [18][19][20] , while others indicate a significant contribution of linear configurations 21,22 . It has also been recently suggested that this controversy is often mislead by drawing false conclusions from correctly calculated distributions 3 .…”

Energetics and structural properties of three-dimensional bosonic clusters near threshold

“…(5) and (6) does not give a good variational energy and we additionally include a variational Fermi function which depends on the distance R j of the jth atom to the center of mass of the cluster [38],…”

High-quality variational wave functions for small4Heclusters

“…The experimental research has faced the difficulties of size detecting the clusters. Recently, molecular beam diffraction from a transmission gratting [5] has proven to be successful to detect even the 4 He dimer [6], giving further impetus to the study of helium clusters.As the atom-atom interaction is well-known and relatively simple, the solution of the Schrödinger equation has been obtained using several microscopic methods, mainly based on Monte Carlo techniques [7,8,9,10,11]. Variational Monte Carlo (VMC) calculations, using a Jastrow-like ansatz for the many-body wave function, are currently used for systems dominated by strong shortrange interactions.…”

“…As the atom-atom interaction is well-known and relatively simple, the solution of the Schrödinger equation has been obtained using several microscopic methods, mainly based on Monte Carlo techniques [7,8,9,10,11]. Variational Monte Carlo (VMC) calculations, using a Jastrow-like ansatz for the many-body wave function, are currently used for systems dominated by strong shortrange interactions.…”