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 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)].
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.
Besides the use as cold matrix for spectroscopic studies, superfluid helium droplets have served as a cold environment for the synthesis of molecules and clusters. Since vibrational frequencies of molecules in helium droplets exhibit almost no shift compared to the free molecule values, one could assume the solvated particles move frictionless and undergo a reaction as soon as their paths cross. There have been a few unexplained observations that seemed to indicate cases of two species on one droplet not forming bonds but remaining isolated. In this work, we performed a systematic study of helium droplets doped with one rubidium and one strontium atom showing that besides a reaction to RbSr, there is a probability of finding separated Rb and Sr atoms on one droplet that only react after electronic excitation. Our results further indicate that ground-state Sr atoms can reside at the surface as well as inside the droplet.
Abstract Alkali atoms and small clusters are known to reside on the surface of a helium droplet rather than its inside as most other dopant species. A theoretical investigation suggested that alkali clusters (Li–Rb) exceeding a certain critical size can become submerged in the droplet, which was experimentally confirmed for sodium and potassium. Here, we report an analogous experimental study of rubidium cluster submersion by means of electron impact mass spectrometry. We recorded size distributions of Rb cluster ions at various electron energies between 8 and 160 eV. Our data suggest that Rb clusters attached to helium droplets undergo a gradual submersion transition similar to potassium, ultimately leading to the full submersion of clusters larger than ∼100Rb ∼ 100 Rb atoms. Our findings are consistent with previous theoretical and experimental studies. Graphic abstract
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.
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.
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.