The structure of a weakly bound ionic trimer: Calculations for the 4He2H− complex

Computational Modeling: Up-to-Date Approaches and Cutting-Edge Applications from Clusters, Nanostructures to Bulk Systems

The contributions in this special theme collection, in honor to Prof. P. Villarreal, cover a broad variety of computational methodologies and experimental techniques, containing studies on gas phase, clusters and condensed phase systems.

A nuclear configuration interaction approach to study nuclear spin effects: an application to ortho- and para-3 He2 @C60

We introduce a non-orthogonal configuration interaction approach to investigate nuclear quantum effects on energies and densities of confined fermionic nuclei. The Hamiltonian employed draws parallels between confined systems and many-electron atoms, where effective non-Coulombic potentials represent the interactions of the trapped particles. One advantage of this method is its generality, as it offers the potential to study the nuclear quantum effects of various confined species affected by effective isotropic or anisotropic potentials. As a first application, we analyze the quantum states of two 3 He atoms encapsulated in C60 . At the Hartree-Fock level, we observe the breaking of spin and spatial symmetries. To ensure wavefunctions with the correct symmetries, we mix the broken-symmetry Hartree-Fock states within the non-orthogonal configuration interaction expansion. Our proposed approach predicts singly and triply degenerate ground states for the singlet (para-3 He2 @C60 ) and triplet (ortho-3 He2 @C60 ) nuclear spin configurations, respectively. The ortho-3 He2 @C60 ground state is 5.69 cm-1 higher in energy than the para-3 He2 @C60 ground state. The nuclear densities obtained for these states exhibit the icosahedral symmetry of the C60 embedding potential. Importantly, our calculated energies for the lowest 85 states are in close agreement with perturbation theory results based on a harmonic oscillator plus rigid rotor model of 3 He2 @C60 .

Cold atom-atom-ion three-body recombination of 4He-4He-X- (X = H or D)

The atom-atom-ion three-body recombination (TBR) of mixed ⁴He and X^- (X = H or D) systems is investigated by solving the Schrödinger equation using the adiabatic hyperspherical representation method. It is shown that the dominant products after a TBR in the ultracold limit (E ≤ 0.1 mK × k_B) are different for the two systems. For the ⁴He⁴HeH^- system, the rate of TBR into the ⁴HeH^- ion is nearly two orders of magnitude larger than that of TBR into the neutral ⁴He₂ molecule. In contrast, the yield of ⁴He₂ is a little higher than that of ⁴HeD^- for the ⁴He⁴HeD^- system. Furthermore, since the adiabatic potentials become more attractive and the nonadiabatic couplings become much stronger by substituting D for H in the ⁴He⁴HeH^- system, the total TBR rate for the ⁴He⁴HeD^- system is nearly two orders of magnitude larger than that for the ⁴He⁴HeH^- system.

Ground state of small mixed helium and spin-polarized tritium clusters: a quantum Monte Carlo study

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.

Adiabatic hyperspherical study of weakly bound He(2)H(-), He(2)H, and HeH(2) systems

The He(2)H(-), He(2)H, and HeH(2) triatomic systems are studied using the adiabatic hyperspherical representation. By adopting the best empirical interaction potentials, we search for weakly bound states of (4)He(2) H(-), (4)He(2) H, and (4)HeH(2). We consider not only zero total nuclear orbital angular momentum, J=0, states but also J>0 states. We find no bound state for the (4)He(2) H systems, while the (4)He(2) H(-) and (4)HeH(2) systems are shown to possess three and one bound states, respectively, for J(Pi)=0(+). Interestingly, one bound state has been found each for the J(Pi)=1(-) and 2(+) symmetries of the (4)He(2) H(-) anion. We shall calculate the bound state energies and analyze the molecular structure of these species in detail.

New method for calculating bound states: the A(1) states of Li(3) on the spin-aligned Li(3)(1 (4)A(')) potential energy surface

In this paper, we present a calculation for the bound states of A(1) symmetry on the spin-aligned Li(3)(1 (4)A(')) potential energy surface. We apply a mixture of discrete variable representation and distributed approximating functional methods to discretize the Hamiltonian. We also introduce a new method that significantly reduces the computational effort needed to determine the lowest eigenvalues and eigenvectors (bound state energies and wave functions of the full Hamiltonian). In our study, we have found the lowest 150 energy bound states converged to less than 0.005% error, and most of the excited energy bound states converged to less than 2.0% error. Furthermore, we have estimated the total number of the A(1) bound states of Li(3) on the spin-aligned Li(3)(1 (4)A(')) potential surface to be 601.

A complete configurational study for the bound states of Ne trimers

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.

First principles determination of the bound levels of HeLi-

An analytical potential energy curve is developed from high quality ab initio calculations for the He+Li- interaction. The HeLi- electrostatic complex is found to have an Re of 18.5 bohrs and a De of 0.974 cm(-1). Numerical solution of the rovibrational Schrödinger equation with this potential indicates two bound levels, (v,J)=(0,0) and (0,1), for all naturally occurring isotopologs (i.e., 4He7Li-, 4He6Li-, 3He7Li-, and 3He6Li-). For the common isotopolog, 4He7Li-, a D0 of 0.207 cm(-1) and an R0 of 26.5 bohrs is determined.

Energy levels and wave functions of weakly-bound 4Hex 20NeyH (x+y=2) systems using Pekeris coordinates and a symmetry-adapted Lanczos approach

Energy levels and wave functions of floppy triatomic rare gas hydrides are calculated using a Pekeris coordinate system and the importance of various triangular configurations is assessed through the calculation of reduced distribution functions and relative weights. The calculations are performed using a symmetry-adapted Lanczos recursion within the discrete variable representation. For the 4He2H- anion, the present results are compared with those obtained from calculations based on other methods, and the accuracy of the present method is discussed. Calculations are also performed for the case of 4He2H and 20Ne2H, as well as for the mixed 4He 20NeH neutrals. Our results show that no bound states are found for 4He2H while only one bound state is found for both the 20Ne2H and 4He 20NeH complexes. Interestingly, a very important and common property of these systems is that there is a significant contribution from linear configurations to their bound states.