An optimized full-configuration-interaction nuclear orbital approach to a “hard-core” interaction problem: Application to ([sup 3]He)[sub N]–Cl[sub 2](B) clusters (N≤4)

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 .

Mini Review: Quantum Confinement of Atomic and Molecular Clusters in Carbon Nanotubes

We overview our recent developments on a computational approach addressing quantum confinement of light atomic and molecular clusters (made of atomic helium and molecular hydrogen) in carbon nanotubes. We outline a multi-scale first-principles approach, based on density functional theory (DFT)-based symmetry-adapted perturbation theory, allowing an accurate characterization of the dispersion-dominated particle–nanotube interaction. Next, we describe a wave-function-based method, allowing rigorous fully coupled quantum calculations of the pseudo-nuclear bound states. The approach is illustrated by showing the transition from molecular aggregation to quasi-one-dimensional condensed matter systems of molecular deuterium and hydrogen as well as atomic ⁴He, as case studies. Finally, we present a perspective on future-oriented mixed approaches combining, e.g., orbital-free helium density functional theory (He-DFT), machine-learning parameterizations, with wave-function-based descriptions.

A nuclear spin and spatial symmetry-adapted full quantum method for light particles inside carbon nanotubes: clusters of 3He, 4He, and para-H2

A new nuclear spin and spatial symmetry-adapted full quantum method for light fermionic and bosonic particles under cylindrical carbon nanotube confinement.

From Molecular Aggregation to a One-Dimensional Quantum Crystal of Deuterium Inside a Carbon Nanotube of 1 nm Diameter

The quantum motion of clusters of up to four deuterium molecules under confinement in a single-wall (1 nm diameter) carbon nanotube is investigated by applying a highly accurate full quantum treatment of the most relevant nuclear degrees of freedom and an ab initio-derived potential model of the underlying dispersion-dominated intermolecular interactions. The wave functions and energies are calculated using an ad hoc-developed discrete variable representation (DVR) numerical approach in internal coordinates, with the space grid approaching a few billion grid points. We unambiguously demonstrate the formation of a solid-like pyramidal one-dimensional chain structure of molecules under the cylindrical nanotube confinement. The onset of solid-like packing is explained by analyzing the potential minima landscape. The stabilization of collective rotational motion through "rigid rotations" of four deuterium molecules provides conclusive evidence for the onset of a quantum solid-like behavior resembling that of quantum rings featuring persistent current (charged particles) or persistent flow (neutral particles).

Spectroscopy of a rotating hydrogen molecule in carbon nanotubes

Computing the energy levels of molecular hydrogen rotating in carbon nanotubes of increasing size.

Quantum confinement of molecular deuterium clusters in carbon nanotubes: ab initio evidence for hexagonal close packing

This study shows ab initio evidence for hexagonal close packing of D₂ molecules in carbon nanotubes, with a = 3.6 Å and .

Microscopic molecular superfluid response: theory and simulations

Since its discovery in 1938, superfluidity has been the subject of much investigation because it provides a unique example of a macroscopic manifestation of quantum mechanics. About 60 years later, scientists successfully observed this phenomenon in the microscopic world though the spectroscopic Andronikashvili experiment in helium nano-droplets. This reduction of scale suggests that not only helium but also para-H2 (pH2) can be a candidate for superfluidity. This expectation is based on the fact that the smaller number of neighbours and surface effects of a finite-size cluster may hinder solidification and promote a liquid-like phase. The first prediction of superfluidity in pH2 clusters was reported in 1991 based on quantum Monte Carlo simulations. The possible superfluidity of pH2 was later indirectly observed in a spectroscopic Andronikashvili experiment in 2000. Since then, a growing number of studies have appeared, and theoretical simulations have been playing a special role because they help guide and interpret experiments. In this review, we go over the theoretical studies of pH2 superfluid clusters since the experiment of 2000. We provide a historical perspective and introduce the basic theoretical formalism along with key experimental advances. We then present illustrative results of the theoretical studies and comment on the possible future developments in the field. We include sufficient theoretical details such that the review can serve as a guide for newcomers to the field.

Fully quantal calculation of H2 translation-rotation states in (H2)4@5(12)6(4) clathrate sII inclusion compounds

The quantal translation-rotation (TR) states of the (p-H2)4@5(12)6(4) and (o-D2)4@5(12)6(4) hydrate clathrate sII inclusion compounds have been computed by nuclear-orbital/configuration-interaction methods. The model of these compounds in a rigid, high-symmetry 5(12)6(4) cage is treated in detail. The low-energy TR level structures of both isotopomers within this model are found to consist of states that can be readily described in terms of a small number of single-H2 and double-H2 excitation modes. The use of the high-symmetry results to facilitate the calculation and interpretation of (p-H2)4 and (o-D2)4 TR states in low-symmetry physically realizable 5(12)6(4) cages is also reported.

Nuclear-orbital/configuration-interaction study of coupled translation-rotation states in (H2)2@C70

The quantal translation-rotation states of two endohedral H(2) moieties in C(70) are computed by means of a nuclear-orbital/configuration-interaction method. H(2) "nuclear orbitals" are calculated as the translation-rotation eigenfunctions of one H(2) molecule interacting with C(70) and the mean field of the second H(2) molecule. Configurations are constructed as symmetrized bilinear products of these orbitals. These configurations are employed as the basis in which the matrix of the translation-rotation Hamiltonian of the cluster is computed and diagonalized. We show that this scheme allows for an efficient means to calculate the Hamiltonian matrix elements. We show that the configuration basis states represent excellent first approximations to the eigenstates of the species. Finally, we present results pertaining to the (H(2))(2)@C(70) low-energy translation-rotation level structure that can be understood in terms of a small number of H(2) excitation types.

Quantum features of a barely bound molecular dopant: Cs2(3Σu) in bosonic helium droplets of variable size

We present in this work the study of small (4)He(N)-Cs(2)((3)Σ(u)) aggregates (2 ≤ N ≤ 30) through combined variational, diffusion Monte Carlo (DMC), and path integral Monte Carlo (PIMC) calculations. The full surface is modeled as an addition of He-Cs(2) interactions and He-He potentials. Given the negligible strength and large range of the He-Cs(2) interaction as compared with the one for He-He, a propensity of the helium atoms to pack themselves together, leaving outside the molecular dopant is to be expected. DMC calculations determine the onset of helium gathering at N = 3. To analyze energetic and structural properties as a function of N, PIMC calculations with no bosonic exchange, i.e., Boltzmann statistics, at low temperatures are carried out. At T = 0.1 K, although acceptable one-particle He-Cs(2) distributions are obtained, two-particle He-He distributions are not well described, indicating that the proper symmetry should be taken into account. PIMC distributions at T = 1 K already compare well with DMC ones and show minor exchange effects, although binding energies are still far from having converged in terms of the number of quantum beads. As N increases, the He-He PIMC pair correlation function shows a clear tendency to coincide with the experimental boson-liquid helium one at that temperature. It supports the picture of a helium droplet which carries the molecular impurity on its surface, as found earlier for other triplet dimers.