A theoretical study of He2ICl van der Waals cluster

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.

Modelling interactions of cationic dimers in He droplets: microsolvation trends in HenK2+ clusters

We report the results of a detailed theoretical investigation of small K₂⁺-doped He clusters. The structural characteristics and stabilities of such cations are determined from ab initio electronic structure calculations at the MRCI+Q level of theory. The underlying interactions show a multireference character and such effects are analyzed. The interaction potentials are constructed employing an interpolation technique within the inverse problem theory method, while the nuclear quantum effects are computed for the trimers, their spatial arrangements are discussed, and information was extracted on the orientational anisotropy of the forces. We found that energetically the most stable conformer corresponds to linear arrangements that are taking place under large amplitude vibrations, with high zero-point energy. We have further looked into the behavior of higher-order species with various He atoms surrounding the cationic dopant. By using a sum of potentials approach and an evolutionary programming method, we analyzed the structural stability of clusters with up to six He atoms in comparison with interactions energies obtained from MRCI+Q quantum chemistry computations. Structures containing He_n motifs that characterize pure rare gas clusters, appear for the larger K₂⁺-doped He clusters, showing selective growth during the microsolvation process of the alkali-dimer cation surrounded by He atoms. Such results indicate the existence of local solvation microstructures in these aggregates, where the cationic impurity could get trapped for a short time, contributing to the slow ionic mobility observed experimentally in ultra-cold He-droplets.

Vibrational Calculations of Higher-Order Weakly Bound Complexes: The He3,4I2 Cases

The structure and relative stability of higher-order He3,4I2 clusters are investigated by carrying out full-dimensional quantum calculations within the multiconfiguration time-dependent Hartree framework. The full interaction between the I2 molecule and the He atoms is based on analytical three-body ab initio He-I2 potentials obtained from high level ab initio calculations plus the He-He interaction. The low-lying minima on the potential surfaces are found to be very close in energy with the He atoms in a ring encircling the dopant for the global minimum structure, while for the local minima one or two of the He atoms prefer the linear arrangements along the I2-axis. Such classical description on the basis of the potential energy landscape is corrected by including anharmonic quantum effects, present in highly floppy systems, by carrying out full dimensional quantum calculations. The potential energy operator was constructed by natural potential fits, while a mode combination scheme was employed to optimize the computational cost of the improved relaxation calculations. The obtained results predict the relative stability of the He3,4I2 isomers at zero temperature and provide benchmark data on binding energies and structural properties of these van der Waals systems. The (2,1) and (2,2), involving two He atoms in the T-shape and one or two He atoms in the linear configurations, respectively, are found to be the most stable isomers, although extremely close in energy with the (3,0) and (4,0) ones as predicted by classical optimizations. Comparison with experimental data on similar systems at low temperatures is also discussed. This analysis indicates once more the importance of quantum delocalization and the need of accurate quantum-mechanical treatments to characterize such doped helium nanosystems.

Ab initio potential energy curves of the valence, Rydberg, and ion-pair states of iodine monochloride, ICl

We present for the first time a coherent ab initio study of 39 states of valence, Rydberg, and ion-pair character of the diatomic interhalogen ICl species through large scale multireference variational methods including spin-orbit effects coupled with quantitative basis sets. Various avoided crossings are responsible for a non-adiabatic behaviour creating a wonderful vista for its theoretical description. Our molecular constants are compared with all available experimental data with the aim to assist experimentalists especially in the high energy regime of up to ~95,000 cm(-1).

Energetics and solvation structure of a dihalogen dopant (I2) in (4)He clusters

The energetics and structure of small HeNI2 clusters are analyzed as the size of the system changes, with N up to 38. The full interaction between the I2 molecule and the He atoms is based on analytical ab initio He-I2 potentials plus the He-He interaction, obtained from first-principle calculations. The most stable structures, as a function of the number of solvent He atoms, are obtained by employing an evolutionary algorithm and compared with CCSD(T) and MP2 ab initio computations. Further, the classical description is completed by explicitly including thermal corrections and quantum features, such as zero-point-energy values and spatial delocalization. From quantum PIMC calculations, the binding energies and radial/angular probability density distributions of the thermal equilibrium state for selected-size clusters are computed at a low temperature. The sequential formation of regular shell structures is analyzed and discussed for both classical and quantum treatments.

Quantum mechanical characterization of the He4ICl weakly bound complex

Vibrational calculations are performed for the 12-dimensional He4ICl van der Waals complex using the multiconfiguration time-dependent Hartree (MCTDH) method. The potential energy surface of the cluster is represented as a sum of the triatomic He-ICl ab initio parametrized terms plus the He-He interactions. The topology of the potential presents higher anisotropy compared to the one with a homonuclear dopant, and this is clearly reflected in the structure and energetics of the low-lying conformers of the system. In order to take advantage of the MCTDH method, natural potential fits are employed for the potential energy operator, and also, a mode combination scheme is introduced in order to speed up the computations. Zero-point energy, binding energies, and vibrationally averaged structures of different isomers of the He4ICl cluster are obtained. The present results predict that the (3,1,0) structure, involving three He atoms in the near T-shaped and one He atom in the linear configurations, to be the most stable one in accord with recent experimental findings. Comparisons with previous theoretical and experimental data are presented, and the stability of the high-order conformers is discussed in connection with the multiple minima (global and local) of the underlying potential surface.

Theoretical investigation of the He4Br2 conformers

Full dimensional quantum dynamics calculations of the three lowest isomers of the He(4)Br(2) van der Waals molecule in its ground electronic state are reported. The calculations are performed using the multiconfiguration time-dependent Hartree (MCTDH) method and a realistic potential form that includes the sum of three body ab initio coupled-cluster single double triple [CCSD(T)] He-Br(2) interactions plus the He-He and Br-Br interactions. This potential exhibits several multiple minima, with the three lowest ones lying very close in energy, just within 2 cm(-1). Such small differences are also found in the calculated binding energies of the three most stable conformers, indicating the floppiness of the system and, thus, the need of accurate potential forms and quantum full dynamics methods to treat this kind of complexes. The 12 dimensional results reported in this work present benchmark data and, thus, can serve to evaluate approximate methods aiming to describe higher order rare gas-dihalogen (N > 4) complexes. A comparison with previous studies using different potential forms and approaches to the energetics for the He(4)Br(2) cluster is also presented.

Weakly bound finite systems: (⁴He)N-Rb₂(³Σu), clustering structures from a quantum Monte Carlo approach

We report here ((4)He)(N)-Rb(2)((3)Σ(u)) complexes, 2 ≤ N ≤ 20, analysed through a quantum diffusion Monte Carlo stochastic approach. The calculations show that the spin stretched dimer molecule is bound outside the pure He sub-complex, due to the stronger He-He potential as compared with the He-Rb(2) interaction, while the rare gas atom moiety presents, in turn, a shell-like structure with ten He adatoms completing the first shell. Our results agree with previous findings on this and similarly weakly interacting systems.

Theoretical characterization of intermolecular vibrational states through the multi-configuration time dependent Hartree approach: the He2,3ICl clusters

Benchmark, full-dimensional calculations on the ground and excited vibrational states for the tetra-, and penta-atomic weakly bound He(2,3)ICl complexes are reported. The representation of the potential energy surfaces includes three-body HeICl potentials parameterized to coupled-cluster singles, doubles, and perturbative triples ab initio data. These terms are important in accurately describing the interactions of such highly floppy systems. The corresponding 6D/9D computations are performed with the multi-configuration time dependent Hartree method, using natural potential fits, and a mode combination scheme to optimize the computational effort in the improved relaxation calculations. For these complexes several low-lying vibrational states are computed, and their binding energies and radial/angular probability density distributions are obtained. We found various isomers which are assigned to different structural models related with combinations of the triatomic isomers, like linear, T-shaped, and antilinear ones. Comparison of these results with recent experimental data is presented, and the quantitative deviations found with respect to the experiment are discussed.

Full-dimensional multi configuration time dependent Hartree calculations of the ground and vibrationally excited states of He2,3Br2 clusters

Quantum dynamics calculations are reported for the tetra-, and penta-atomic van der Waals He(N)Br(2) complexes using the multiconfiguration time-dependent Hartree (MCTDH) method. The computations are carried out in satellite coordinates, and the kinetic energy operator in this set of coordinates is given. A scheme for the representation of the potential energy surface based on the sum of the three-body HeBr(2) interactions at CSSD(T) level plus the He-He interaction is employed. The potential surfaces show multiple close lying minima, and a quantum description of such highly floppy multiminima systems is presented. Benchmark, full-dimensional converged results on ground vibrational/zero-point energies are reported and compared with recent experimental data available for all these complexes, as well as with previous variational quantum calculations for the smaller HeBr(2) and He(2)Br(2) complexes on the same surface. Some low-lying vibrationally excited eigenstates are also computed by block improved relaxation calculations. The binding energies and the corresponding vibrationally averaged structures are determined for different conformers of these complexes. Their relative stability is discussed, and contributes to evaluate the importance of the multiple-minima topology of the underlying potential surface.

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.

Spectroscopic identification of higher-order rare gas-dihalogen complexes with different geometries: He(2,3)...Br(2) and He(2,3)...ICl

Rovibronic transitions of multiple conformers of the He(2)...(79)Br(2)(X, v'' = 0), He(3)...(79)Br(2)(X, v'' = 0), He(2)...I(35)Cl(X, v'' = 0), and He(3)...I(35)Cl(X, v'' = 0) complexes stabilized in a pulsed, supersonic expansion are observed in action spectra recorded in the B-X region of the dihalogens. In addition to features associated with He(2)...(79)Br(2) and He(2)...I(35)Cl complexes with the rare gas atoms localized in the toroidal potential well lying in a plane perpendicular to the dihalogen bond, those associated with a ground-state conformer that has one He atom localized in the toroidal potential and the other He atom localized in the linear well at the end of the dihalogen moiety are also identified. Transitions of at least three conformers of the He(3)...Br(2) complex and two conformers of the He(3)...ICl complex are also observed. The relative populations of the different conformers are found to depend on where along the supersonic expansion the spectra are recorded, and thus on the local temperature regime sampled. The He(2)...(79)Br(2) and He(2)...I(35)Cl conformers with one He atom in each well are found to be the more stable conformers.

Exact, Born-Oppenheimer, and quantum-chemistry-like calculations in helium clusters doped with light molecules: The He2N2(X) system

Helium clusters doped with diatomic molecules, He(N)-BC, have been recently studied by means of a quantum-chemistry-like approach. The model treats He atoms as "electrons" and dopants as "nuclei" in standard electronic structure calculations. Due to the large mass difference between He atoms and electrons, and to the replacement of Coulomb interactions by intermolecular potentials, it is worth assessing up to what extent are the approximations involved in this model, i.e., decoupling of the BC rotation from the He-atom orbital angular momenta and Born-Oppenheimer separation of the BC stretch versus the He motions, accurate enough. These issues have been previously tackled elsewhere for the (4)He(2)-Br(2)(X) system, which contains a heavy dopant [Roncero et al., Int. J. Quantum Chem. 107, 2756 (2007)]. Here, we consider a similar cluster but with a much lighter dopant such as N(2)(X). Although the model does not provide the correct energy levels for the cluster, positions and intensities of the main detectable lines of the vibrotational Raman spectrum at low temperature are accurately reproduced.

A full-configuration interaction “nuclear orbital” method to study doped HeN3 clusters (N⩽4)

An efficient full configuration interaction (FCI) treatment, based on the Jacobi-Davidson algorithm, is developed in order to study small doped (3)He(N) clusters. The state of each He atom in a given cluster is described by a set of wave-functions which by extention of the quantum-chemistry notation are caller here "nuclear orbitals". The FCI treatment is applied to the calculation of binding energies and helium natural orbitals of (3)He(N)...Br(2)(X) complexes. In agreement with our previous calculations using a Hartree-Fock approach [Phys. Rev. Lett. 93, 053401 (2004)], in which the He-He interaction is modified at small distances to account for short-range correlation effects, the lowest-energy states of each multiplet are found to be very close in energy. The natural orbital analysis, in turn, indicates the adequacy of the "nuclear orbital" approach in these systems.

Solvent configuration-interaction calculations of intermolecular states in molecule-(atom)N clusters: application to Br2-4HeN

We describe variational calculations of J=0 intermolecular states in Br(2)-(4)He(N) clusters. The method employed is analogous to configuration-interaction calculations in electronic-structure work and relies on the ability to express the intermolecular Hamiltonian H(v) as a sum of one- and two-body terms. A basis set is built up from solutions to the Schrödinger equation in which only the one-body terms of H(v) are included. These configurations are products of N=1 eigenstates. The matrix of H(v) in a symmetry-adapted configuration basis is then computed, the two-body terms of H(v) serving to couple different configurations. This computation involves integrals of dimension five or less. Filter diagonalization is then used to obtain energies and eigenfunctions within a selected energy range. Results on clusters having N=2-5 are reported.