A quantum chemistry approach to energies, structures, and spectroscopy of doped helium clusters
Ricardo Pérez de Tudela, David López‐Durán, María Pilar de Lara‐Castells, Rita Prosmiti, Octavio Roncero, Gerardo Delgado-Barrio, Francesco Antonio Gianturco, Julius Jellinek, Pablo Villarreal
Diffusion and path integral Monte Carlo methods are currently, and successfully, used to describe structures and binding energies of helium clusters doped with some impurity. For diatomic dopants, by considering the He atoms as "electrons" and the dopant as "nuclei" within a Hartree/Hartree-Fock framework, our group has developed a complementary tool which, in addition to the above mentioned properties, provides us with wave-functions. It allows to perform spectral simulations that can be compared with the experiment. This paper reviews the fundamental aspects of such quantumchemistry-like methodology in which, together with masses, Coulomb interactions are replaced by proper molecular ones. Extensions towards more accurate ab initio methodologies are outlined. Finally, the challenging scenario arising when the impurity is not immersed but attached to the nanodroplet, giving rise to an unusual "solar" system in which the planets no longer move around the dopant as a "sun", is addressed.
Diffusion and path integral Monte Carlo methods are currently, and successfully, used to describe structures and binding energies of helium clusters doped with some impurity. For diatomic dopants, by considering the He atoms as "electrons" and the dopant as "nuclei" within a Hartree/Hartree-Fock framework, our group has developed a complementary tool which, in addition to the above mentioned properties, provides us with wave-functions. It allows to perform spectral simulations that can be compared with the experiment. This paper reviews the fundamental aspects of such quantumchemistry-like methodology in which, together with masses, Coulomb interactions are replaced by proper molecular ones. Extensions towards more accurate ab initio methodologies are outlined. Finally, the challenging scenario arising when the impurity is not immersed but attached to the nanodroplet, giving rise to an unusual "solar" system in which the planets no longer move around the dopant as a "sun", is addressed.
Many experiments on pure and doped helium clusters result in the production of a broad distribution of charged fragment ions after electron impact or laser ionisation. These ion yield distributions occasionally exhibit distinct stability patterns. We use the diffusion quantum Monte Carlo technique to study these stability patterns and structural features of helium clusters with open shell atomic and molecular dopants. These simulations require reliable many-body potentials which we construct from high level ab initio CCSD(T) calculations for several electronic states mixed by spin-orbit coupling and including non-additive interactions arising from induction. For small clusters numerically exact calculations of rovibrational properties are used to establish the quality of our potential surfaces. The approach is illustrated with applications to Iq@Hen, q=-1,0,+1,+2 clusters which appear in ionisation and photodissociation experiments. Spin-orbit coupling due to the iodine atom is found to have a profound effect on the structure of the mixed clusters. Radial and angular helium density profiles are computed and show that even in the presence of pronounced radial structuring exchange between 'shells' remains possible and angular disorder remains significant. The identification of a well defined ionic snowball core appears incorrect. We present first results for CO+ ions in helium clusters. He-CO+ is an interesting astrophysical collision system but its interest for helium cluster studies is the similarity of the CO+ rotational constant with the one of neutral CO. Our present understanding of rotation inside helium clusters relies on studies of molecules where changing the molecule implies changing dynamical parameters and the interaction potential. The CO/CO+ case allows to study the specific effect of changing only the interaction energy. CO+@Hen should be relatively easy to make by cluster ionisation or aggregation in ion drift tubes and its strong dipole and vibrational transition moment make it an easy target for high resolution spectroscopy. We have computed accurate ab initio surfaces for the two lowest electronic states of He-CO+ to predict rovibrational spectroscopic and collisional properties. A many-body model using these surfaces is used to study larger CO+Hen clusters.
Spectroscopy of doped helium nanodroplets has become, in recent years, a popular tool for the study of bothfinite size samples of the helium quantum fluid and molecules isolated in this sub Kelvin environment. Whilemany dopants migrate to the center of the droplet, alkali (Ak) atoms in their ground electronic state, becauseof their so weak interaction with He, remain at the surface, the latter being in this way slightly distortedexhibiting a dimple. However, when in their first excited states, Ak atoms are forming exciplexes. These areanisotropic with the central atom surrounded by a ring of He atoms located in the nodal plane of the valenceelectron pz orbital. Structural properties, obtained by DMC and PIMC, are presented here for some Ak -Hen exciplexes.Ak2 dimers in helium environment have also gained interest in this last decade, in connexion with the generationof ultracold molecules. When attached to helium droplets, Ak atoms can float on the surface andform molecules in cold collisions. DMC and PIMC methods are used to compute energetics and structuralinformations for Rb2 in helium. In particular, the orientation of the dimer relative to the droplet surface isexamined.
A new full-dimension potential energy surface of the three-body He-Rb₂(³Σ(u)(+)) complex and a quantum study of small (⁴He)(N)-Rb₂(³Σ(u)(+)) clusters, 1 ≤ N ≤ 4, are presented. We have accurately fitted the ab initio points of the interaction to an analytical form and addressed the dopant's vibration, which is found to be negligible. A Variational approach and a Diffusion Monte Carlo technique have been applied to yield energy and geometric properties of the selected species. Our quantum structure calculations show a transition in the arrangements of the helium atoms from N = 2, where they tend to be separated across the diatomic bond, to N = 4, in which a closer packing of the rare gas particles is reached, guided by the dominance of the He-He potential over the weaker interaction of the latter adatoms with the doping dimer. The deepest well of the He-Rb₂ interaction is placed at the T-shape configuration, a feature which causes the dopant to be located as parallel to the helium "minidroplet". Our results are shown to agree with previous findings on this and on similar systems.
Below Tλ = 2.17 K, bulk 4He is a superfluid and has a non-zero Bose-Einstein condensate fraction. This work will focus primarily on how phenomena such as superfluidity, Bose condensation and superfluid vortices are manifested in microscopic, inhomogeneous helium systems. Path Integral Monte Carlo is a powerful method for calculating the equilibrium properties of quantum systems at finite temperature. We have achieved linear scaling of computer time with number of particles through the use of neighbor lists, allowing us to simulate systems of several thousand atoms. We have derived a local superfluid estimator and used it to examine the microscopic superfluid response around a molecule rotating in a helium nanodroplet. We found that the first solvation layer is well-described by a two dimensional superfluid, with thermal excitations occuring at a lower temperature than in bulk helium. The effective moment of inertia of a linear impurity in a helium droplet is calculated, and compared with experimental scattering results. In addition, we calculated the vortex formation energy for both pure droplets and droplets doped with linear impurities, and found that the linear impurities had a negligible impact on the formation energy. A possible spectroscopic signature of vortices in doped helium droplets was suggested. After deriving a local estimator, we calculated the condensate fraction throughout the free helium surface of a semi-infinite slab. These results, along with densitydensity correlation functions, were used to characterize the surface excitations and calculate the extent to which ripplons are present. In addition, the ripplon dispersion relation was calculated using imaginary-time correlation functions, and found to be lll in good agreement with experimental results. Finally, we have calculated the Dey be-Waller factor in solid helium for a range of temperatures and densities, and compared the scaling behavior with the predictions of harmonic theory. The first non-Gaussian contribution to the density distribution was calculated.
We present theoretical studies of helium droplets and films doped with one electronically excited rubidium atom Rb( *) ((2)P). Diffusion and path integral Monte Carlo approaches are used to investigate the energetics and the structure of clusters containing up to 14 helium atoms. The surface of large clusters is approximated by a helium film. The nonpair additive potential energy surface is modeled using a diatomic in molecule scheme. Calculations show that the stable structure of Rb( *)He(n) consists of a seven helium atom ring centered at the rubidium, surrounded by a tirelike second solvation shell. A very different structure is obtained when performing a "vertical Monte Carlo transition." In this approach, a path integral Monte Carlo equilibration starts from the stable configuration of a rubidium atom in the electronic ground state adsorbed to the helium surface after switching to the electronically excited surface. In this case, Rb( *)He(n) relaxes to a weakly bound metastable state in which Rb( *) sits in a shallow dimple. The interpretation of the results is consistent with the recent experimental observations [G. Aubock et al., Phys. Rev. Lett. 101, 035301 (2008)].
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.