Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

The Journal of Chemical Physics

Rotational excitations of quantum liquid clusters: He7 and (H2)7

Michele A. McMahon, R. N. Barnett, K. Birgitta Whaley

Published Dec 1, 1993• 35 citations
Publisher

Abstract

We have studied the quantum clusters, He7 and (H2)7, in their ground (L=0) and rotationally excited states (L=2–8 for He and L=2–12 for H2) by variational Monte Carlo, and selectively by diffusion Monte Carlo. The optimized trial wave functions are eigenfunctions of L2, and, as such, are orthogonal and yield upper bounds to the energy of each state. We report energies and structural results, including density profiles and moments-of-inertia distributions. Overall, the He7 cluster is more delocalized than the (H2)7 cluster, but the computed structures show that both He7 and (H2)7 are highly nonclassical and nonrigid, evolving from spherical to toroidal structures as the angular momentum increases. We find that by L=2 for He7 and by L=6 for (H2)7, the clusters become metastable with respect to dissociation, as determined by comparison of excited-state energies of the N=7 clusters with the ground-state energies for N=6. The root-mean-square bond length fluctuations indicate that both N=7 clusters are liquidlike in the L=0 ground state, according to the Lindemann criterion. These fluctuations increase with L, implying a further decrease in rigidity for the rotationally excited states.

DOI
10.1063/1.465550

Related papers

Current and condensate distributions in rotational excited states of quantum liquid clusters

E. Cheng, Michele A. McMahon, K. Birgitta Whaley

Recent quantum Monte Carlo calculations of small quantum clusters have shown that it is feasible to study their rotationally excited states directly. [M. A. McMahon, R. N. Barnett, and K. B. Whaley, J. Chem. Phys. 99, 8816 (1993).] We extend this work by sampling, from optimized variational wave functions, the current and Bose condensate distributions in (4He)7, (H2)7, and (4He)40 clusters. We demonstrate that these distributions are useful tools in identifying the location and nature of rotational excitations. With different constructions of rotational wave functions, the excitations can be either localized (as surface modes), or delocalized throughout the cluster analogous to the bulk superfluid vortex states. Condensate depletions in the excited states are observed, except for the delocalized excitation, where we find a higher condensate fraction than in the ground state.

The Journal of Chemical Physics•Feb 15, 1996•24 citations

Structure and energetics of small helium clusters: Quantum simulations using a recent perturbational pair potential

Marius Lewerenz

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.

The Journal of Chemical Physics•Mar 15, 1997•134 citations

Dynamics of He4 droplets

E. Krotscheck, Robert E. Zillich

Optimized variational calculations have been carried out for clusters of He4 between N=20 and N=1000 atoms. For small cluster sizes with less or equal to 112 particles, where comparisons with existing diffusion Monte Carlo results are possible, we find good agreement for the ground state energies and densities. Using a somewhat simpler approximation, we also calculate the bound state energies of He3 atoms attached to these clusters. We then calculate excitations and the dynamic structure function. The complex and nonlocal self-energy introduced for that purpose gives access to the calculation of both elastic and inelastic scattering processes for He4 and He3 atoms impinging on the clusters.

The Journal of Chemical Physics•Dec 8, 2001•52 citations

Quantum Monte Carlo investigation of small He4 clusters with a He3 impurity

Dario Bressanini, Matteo Zavaglia, Massimo Mella +1 more

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.

The Journal of Chemical Physics•Jan 8, 2000•50 citations

Excited states of 4He droplets

R. Guardiola, Jesús Navarro, M. Portesi

We study low-lying excited states of ${}^{4}\mathrm{He}$ clusters up to a cluster size of 40 atoms in a variational framework. The ansatz wave function combines two- and three-body correlations, coming from a translationally invariant configuration interaction description, and Jastrow-type short-range correlation. We have previously used this scheme to determine the ground-state energies of ${}^{4}\mathrm{He}$ and ${}^{3}\mathrm{He}$ clusters. Here we present an extension of this ansatz wave function having a good quantum angular momentum L. The variational procedure is applied independently to the cases with $L=0,2,4,$ and upper bounds for the corresponding energies are thus obtained. Moreover, centroid energies for L excitations are calculated through the use of sum rules. A comparison with previous calculations is also made.

Physical review. B, Condensed matter•May 24, 2001•6 citations

The excited states of the Bosonicvan der Waals clusters: A Monte Carlo study

M. Meierovich

The computational physics methods of various processes have become very popular during the last several years. Our interest in his field is predominantly motivated by the expectation that it will be possible to perform a detailed comparison between experimental and theoretical results obtained in the study of clusters of a variety of sizes. Algebraic invariants are employed to deal efficiently with the many-body correlations. We study the applicability of the developed trial wave functions over some range of particle masses, from Ar to He and lighter. We compute the ground and excited states energies and various geometric sizes of small clusters as a function of a continuously varied mass parameter. For sufficiently small masses the cluster can no longer support a bound state, and we are interested in particular in the behavior of the clusters in the vicinity of the critical mass, i.e., the point at which the binding energy approaches zero. We show that the use of bosonic polynomials provides enough variational freedom to approximate ground and excited states of clusters of any mass. We discuss how the properties of clusters change with mass.

•Jan 1, 1997•0 citations
We have studied the quantum clusters, He7 and (H2)7, in their ground (L=0) and rotationally excited states (L=2–8 for He and L=2–12 for H2) by variational Monte Carlo, and selectively by diffusion Monte Carlo. The optimized trial wave functions are eigenfunctions of L2, and, as such, are orthogonal and yield upper bounds to the energy of each state. We report energies and structural results, including density profiles and moments-of-inertia distributions. Overall, the He7 cluster is more delocalized than the (H2)7 cluster, but the computed structures show that both He7 and (H2)7 are highly nonclassical and nonrigid, evolving from spherical to toroidal structures as the angular momentum increases. We find that by L=2 for He7 and by L=6 for (H2)7, the clusters become metastable with respect to dissociation, as determined by comparison of excited-state energies of the N=7 clusters with the ground-state energies for N=6. The root-mean-square bond length fluctuations indicate that both N=7 clusters are liquidlike in the L=0 ground state, according to the Lindemann criterion. These fluctuations increase with L, implying a further decrease in rigidity for the rotationally excited states.
Recent quantum Monte Carlo calculations of small quantum clusters have shown that it is feasible to study their rotationally excited states directly. [M. A. McMahon, R. N. Barnett, and K. B. Whaley, J. Chem. Phys. 99, 8816 (1993).] We extend this work by sampling, from optimized variational wave functions, the current and Bose condensate distributions in (4He)7, (H2)7, and (4He)40 clusters. We demonstrate that these distributions are useful tools in identifying the location and nature of rotational excitations. With different constructions of rotational wave functions, the excitations can be either localized (as surface modes), or delocalized throughout the cluster analogous to the bulk superfluid vortex states. Condensate depletions in the excited states are observed, except for the delocalized excitation, where we find a higher condensate fraction than in the ground state.
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.
Optimized variational calculations have been carried out for clusters of He4 between N=20 and N=1000 atoms. For small cluster sizes with less or equal to 112 particles, where comparisons with existing diffusion Monte Carlo results are possible, we find good agreement for the ground state energies and densities. Using a somewhat simpler approximation, we also calculate the bound state energies of He3 atoms attached to these clusters. We then calculate excitations and the dynamic structure function. The complex and nonlocal self-energy introduced for that purpose gives access to the calculation of both elastic and inelastic scattering processes for He4 and He3 atoms impinging on the clusters.
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 study low-lying excited states of 4He{}^{4}\mathrm{He}4He clusters up to a cluster size of 40 atoms in a variational framework. The ansatz wave function combines two- and three-body correlations, coming from a translationally invariant configuration interaction description, and Jastrow-type short-range correlation. We have previously used this scheme to determine the ground-state energies of 4He{}^{4}\mathrm{He}4He and 3He{}^{3}\mathrm{He}3He clusters. Here we present an extension of this ansatz wave function having a good quantum angular momentum L. The variational procedure is applied independently to the cases with L=0,2,4,L=0,2,4,L=0,2,4, and upper bounds for the corresponding energies are thus obtained. Moreover, centroid energies for L excitations are calculated through the use of sum rules. A comparison with previous calculations is also made.
The computational physics methods of various processes have become very popular during the last several years. Our interest in his field is predominantly motivated by the expectation that it will be possible to perform a detailed comparison between experimental and theoretical results obtained in the study of clusters of a variety of sizes. Algebraic invariants are employed to deal efficiently with the many-body correlations. We study the applicability of the developed trial wave functions over some range of particle masses, from Ar to He and lighter. We compute the ground and excited states energies and various geometric sizes of small clusters as a function of a continuously varied mass parameter. For sufficiently small masses the cluster can no longer support a bound state, and we are interested in particular in the behavior of the clusters in the vicinity of the critical mass, i.e., the point at which the binding energy approaches zero. We show that the use of bosonic polynomials provides enough variational freedom to approximate ground and excited states of clusters of any mass. We discuss how the properties of clusters change with mass.