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.
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.
Abstract Small helium clusters Hen (n = 2, 3, ... , 10) in molecular beams produced by supersonic expansion of gaseous helium have been observed in several different experiments. Among these clusters the dimer, which has a single very slightly bound state, and the trimer, which could have many bound states, have especially unusual properties which QMC calculations can explain in detail. In this paper, diffusion QMC calculations were used to determine ground state properties for clusters (n = 2, ... , 10) using two accurate, but slightly different pairwise-additive potential energy expressions, a perturbation-based potential by Tang et al.a and an empirical potential (HFD-B) proposed by Aziz et al.b Trial functions for importance sampling were based on those determined earlier by Rick et alc. Expectation values and probability distributions were determined by the descendent-weighting technique to give results independent of the trial functions. As expected, a single bound state of the dimer was found, and its average internuclear distance was predicted to be 51.5 A. Energies for clusters with n = 2, 7 with the HFD-B potential were in good agreement with those of earlier calculations. Comparisons of the results for the two different potential energy expressions showed energies differing by a few percent. Tests of possible nonadditive interactions showed these to be far less important in their effects on predicted energies.
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.
A stability chart of mixed 4He and 3He clusters has been obtained by means of the diffusion Monte Carlo method, using both the Aziz HFD-B and the Tang-Toennies-Yiu atom-atom interaction. The investigated clusters contain up to eight 4He atoms and up to 20 3He atoms. One single 4He binds 20 3He atoms, and two 4He bind 1, 2, 8, and more than 14 3He atoms. All clusters with three or more 4He atoms are bound, although the combinations 4He33He9,10,11 and 4He43He9 are metastable. Clusters with 2, 8, and 20 3He atoms are particularly stable and define magic 3He numbers.
We report results for the ground-state energy and structural properties of small (4)He-T↓ clusters consisting of up to four T↓ and eight (4)He atoms. These results have been obtained using very well-known (4)He-(4)He and T↓- T↓ interaction potentials and several models for the (4)He- T↓ interatomic potential. All the calculations have been performed with variational and diffusion Monte Carlo methods. It takes at least three atoms to form a mixed bound state. In particular, for small clusters the binding energies are significantly affected by the precise form of the (4)He- T↓ interatomic potential but the stability limits remain unchanged. The only exception is the (4)He(2)T↓ trimer whose stability in the case of the weakest (4)He- T↓ interaction potential is uncertain while it seems stable for other potentials. The mixed trimer (4)He(T↓)(2), a candidate for the Borromean state, is not bound. All other studied clusters are stable. Some of the weakest bound clusters can be classified as quantum halo as a consequence of having high probability of being in a classically forbidden region.
Abstract This paper describes improved trial wavefunctions for helium clusters and their use in variational QMC calculations of their binding energies, structural properties, and breathing mode vibrational excited states, for clusters of 3 to 270 atoms. The wavefunctions developed were similar to those of earlier work but included convenient analytic functions for two- and three-body correlations. All terms were of the Jastrow exponential form, based on sums of one-, two-, and three-body terms t1(ri), t2(rij), and t3(rij, rjk,rki), expressed as functions of interparticle distances. Excited-state wavefunctions for the breathing vibrational mode were obtained with the aid of procedures adapted from treatment of the quantum mechanics of liquid drop models. The interactions of helium atoms were specified as pairwise-additive with an accurate semi-empirical pair potential. Optimizations of parameters in the trial wavefunctions were carried out for individual cluster sizes with an exhaustive search procedure in a series of trial variational calculations, in which the parameters were varied to minimize the energy. A partial correlation of results was obtained by use of identical initial coordinates and random number seeds in these optimization calculations. Once the wavefunctions were optimized, longer calculations were used to determine properties of the clusters. In addition, diffusion QMC calculations were used to obtain more accurate nonvariational energies for comparisons.
The 4He3 weakly interacting system is analysed by constructing the full interaction as a sum of two-body (2B) potentials chosen among the most recent proposals from the literature. The spatial density distributions of the three bound atoms are obtained using a diffusion Monte Carlo (DMC) algorithm and a stochastic analysis under specific geometric constraints is carried out with the resulting densities in order to recover a more conventional structural picture for such floppy system. The total binding energies were obtained with the chosen potentials analysed in the present work, using the DMC algorithm, and are compared with previous published results. The ensuing spatial distributions are analysed in some detail to select the dominant structures from a conventional triangular description of this very floppy molecule.