Small Alkali Clusters Research Articles

Communication: Dopant-induced solvation of alkalis in liquid helium nanodroplets.

Alkali metal atoms and small alkali clusters are classic heliophobes and when in contact with liquid helium they reside in a dimple on the surface. Here we show that alkalis can be induced to submerge into liquid helium when a highly polarizable co-solute, C60, is added to a helium nanodroplet. Evidence is presented that shows that all sodium clusters, and probably single Na atoms, enter the helium droplet in the presence of C60. Even clusters of cesium, an extreme heliophobe, dissolve in liquid helium when C60 is added. The sole exception is atomic Cs, which remains at the surface.

Submersion of potassium clusters in helium nanodroplets

Small alkali clusters do not submerge in liquid helium nanodroplets but instead survive predominantly in high spin states that reside on the surface of the nanodroplet. However, a recent theoretical prediction by Stark and Kresin [Phys. Rev. B 81, 085401 (2010)], based on a classical description of the energetics of bubble formation for a fully submerged alkali cluster, suggests that the alkali clusters can submerge on energetic grounds when they exceed a critical size. Following recent work on sodium clusters, where ion yield data from electron impact mass spectrometry was used to obtain the first experimental evidence for alkali cluster submersion, we report here on similar experiments for potassium clusters. Evidence is presented for full cluster submersion at $n>80$ for K${}_{n}$ clusters, which is in good agreement with the recent theoretical prediction. In an additional observation, we report ``magic number'' sizes for both K${}_{n}$${}^{+}$ and K${}_{n}$${}^{2+}$ ions derived from helium droplets, which are found to be consistent with the jellium model.

Alkali-helium snowball complexes formed on helium nanodroplets

We systematically investigate the formation and stability of snowballs formed by femtosecond photoionization of small alkali clusters bound to helium nanodroplets. For all studied alkali species Ak = (Na,K,Rb,Cs) we observe the formation of snowballs Ak(+)He(N) when multiply doping the droplets. Fragmentation of clusters Ak(N) upon ionization appears to enhance snowball formation. In the case of Na and Cs we also detect snowballs Ak(2) (+)He(N) formed around Ak dimer ions. While the snowball progression for Na and K is limited to less than 11 helium atoms, the heavier atoms Rb and Cs feature wide distributions at least up to Ak(+)He(41). Characteristic steps in the mass spectra of Cs-doped helium droplets are found at positions consistent with predictions on the closure of the first shell of helium atoms around the Ak(+) ion based on variational Monte Carlo simulations.

Finite lifetime effects on the polarizability within time-dependent density-functional theory

We present an implementation for considering finite lifetime of the electronic excited states into linear-response theory within time-dependent density-functional theory. The lifetime of the excited states is introduced by a common phenomenological damping factor. The real and imaginary frequency-dependent polarizabilities can thus be calculated over a broad range of frequencies. This allows for the study of linear-response properties both in the resonance and nonresonance cases. The method is complementary to the standard approach of calculating the excitation energies from the poles of the polarizability. The real and imaginary polarizabilities can then be calculated in any specific energy range of interest, in contrast to the excitation energies which are usually solved only for the lowest electronic states. We have verified the method by investigating the photoabsorption properties of small alkali clusters. For these systems, we have calculated the real and imaginary polarizabilities in the energy range of 1-4 eV and compared these with excitation energy calculations. The results showed good agreement with both previous theoretical and experimental results.

Coherent control of alkali cluster fragmentation dynamics

Metal clusters exhibit extraordinary chemical and catalytic properties, which sensitively depend upon their size. This behavior makes them interesting candidates for the real-time analysis of ultrafast photo-induced processes—ultimately leading to coherent control scenarii. We have performed transient multi-photon ionization experiments on small alkali clusters of different size in order to probe their wave packet dynamics, structural reorientations, charge transfers and dissociative events in different vibrationally excited electronic states including their ground state. The observed processes were highly dependent on the irradiated pulse parameters, like its phase, amplitude and duration; an emphasis to employ a feedback control system for generating the optimum pulse shapes. Their spectral and temporal behavior reflects interesting properties about the investigated system and the irradiated photochemical process. We present first the vibrational dynamics of bound, dissociated, and pre-dissociated electronically excited states of alkali dimers and trimers. The scheme for observing the wave packet dynamics in the electronic ground state using stimulated Raman-pumping is shown. Since the employed pulse parameters significantly influence the efficiency of the irradiated dynamic pathways photo-induced fragmentation experiments on bifurcating reaction channels were carried out. In these experiments different branching ionization and fragmentation pathways of electronically excited Na 2K were investigated. By employing an evolutionary algorithm for optimizing the phase and amplitude of the applied laser field, the yield of the resulting parent or fragment ions could significantly be influenced and interesting features could be concluded from the obtained optimum pulse shapes revealing the characteristic molecular oscillation period. Moreover, the influence on the optimal pulse shape due to fragmentation from larger clusters into NaK is obtained. The substructure of the optimal pulse shape thereby offers new insight into the fragmentation channel during the control process. Characteristic motions of the involved wave packets are proposed, in order to explain the optimized dynamic dissociation pathways.

Isomerisation and phase transitions in small sodium clusters

Using a distance-dependent tight-binding hamiltonian, we have studied the influence of the temperature on the geometries of small alkali clusters (Na4, Na8, and Na20). We have applied a Monte-Carlo thermodynamical method which consists in performing canonical samplings for various temperatures, these samplings being reexpressed in the microcanonical ensemble. This method provides thermodynamical values such as the entropy and the specific heat. Their behaviour shows one phase transition in the case of Na4 and Na8, and two phase transitions for Na20. As concerns Na4 and Na8, the transition occurs at ≈200 K, between a solid-like phase and a phase for which the geometry of these clusters oscillates between numerous shapes. In the case of Na20, the two observed phase transitions can be described as a melting of the surface atoms (at ≈200 K) preliminarily to the fluctuation of an inner icosahedron seed (at ≈300 K).

Collective electronic excitations and their damping in small alkali clusters

We calculate collective electronic excitations and their damping in small Na n and Li n clusters. The ground state properties of these systems are described using the local density approximation, and the electronic excitations by the random phase approximation. The collective excitations in the first two closed-shell clusters with n=2, 8 atoms are discussed in detail. We find that the coupling of electronic levels to vibrational degrees of freedom accounts quantitatively for the observed width of the collective electronic excitations in alkali dimers. The origin of the analogous line broadening in Na 8 is presently unresolved.

Magnetic properties of free alkali and transition metal clusters

The Stern-Gerlach deflections of small alkali clusters (N<6) and iron clusters (10<N<500) show that the paramagnetic alkali clusters always have a non-deflecting component, while the iron clusters always deflect in the high field direction. Both of these effects appear to be related to spin relaxation however in the case of alkali clusters it is shown that they are in fact caused by avoided level crossing in the Zeeman diagram. For alkali clusters the relatively weak couplings cause reduced magnetic moments where levels cross. For iron clusters however the total spin is strongly coupled to the molecular framework. Consequently this coupling is responsible for avoided level crossings which ultimately cause the total energy of the cluster to decrease with increasing magnetic field so that the iron clusters will deflect in one direction when introduced in an inhomogeneous magnetic field. Experiment and theory are discussed for both cases.

Electronic correlation and effective interactions in small alkali clusters

Electronic correlation and effective interactions in small alkali clusters

A b i n i t i o calculations of the electronic structure of small Nan, Na+n, Kn, and K+n clusters (n≤6) including core–valence interaction

The electronic structure of small Nan, Na+n, Kn, and K+n alkali clusters (n≤6) is investigated using nonempirical core pseudopotentials, configuration interaction within a 3s/1p/1d Gaussian basis set per atom and including the core–valence interaction through a perturbative treatment. Equilibrium geometries, stabilities, ionization potentials, and fragmentation channels are derived and the role of electronic correlation in small alkali clusters is examined.