Superfluid effects in rotating helium clusters

We study the response of Bose⁴He clusters to an external field corresponding to a rotation with frequency ω. An explicit form for the normal (nonsuperfluid) fraction of the system as a function of the temperatureT and of the mass numberN of the cluster is obtained under the assumption that only surface modes are thermally excited. The critical behaviour of⁴He clusters at high rotational frequencies is also investigated.     

Molecular impurities in helium clusters

We review recently developed theories of molecular interactions with helium clusters. Ground state energies and structures are obtained from Monte Carlo and density functional calculations for a variety of impurities and a range of cluster sizes. Of particular interest are chemical potentials, location of the impurity, and shape of the helium density surrounding it. Included in the work summarized here are results for light molecules (H₂ and D₂) which interact weakly with He and results for heavier molecules (Cl₂ and SF₆) which interact more strongly with He. Finally, theoretical and experimental results are compared for SF₆ in helium clusters.     

Small helium clusters formation

We investigated small helium clusters formation in nonequilibrium conditions using the non-Hermitian formalism. Helium is a simple enough system for analytical study while complicated enough to have a rich variety of quantum properties. In this article, we used a new formalism based on non-Hermitian quantum mechanics for describing the electronic excited states in clusters. This formalism enabled to estimate the decay time of excited states within a single scheme. Its implementation to helium shows the existence of new long-lived excited states in small helium clusters at the distance of 5.6 Bohr radii between atoms. Moreover, several helium excimers and exciplexes at the distances between helium atoms of 35.5, 22.8, 14.0, and 8.5 Bohr radii with the scaling factor of about 1.6 were found. It is related to the restructuring of the electronic structure caused by powerful external excitations. These results give a new insight on clustering processes providing more profound and complete understanding.     

Quantum statistical mechanics with Gaussians: equilibrium properties of van der Waals clusters

The variational Gaussian wave-packet method for computation of equilibrium density matrices of quantum many-body systems is further developed. The density matrix is expressed in terms of Gaussian resolution, in which each Gaussian is propagated independently in imaginary time beta=(k(B)T)(-1) starting at the classical limit beta=0. For an N-particle system a Gaussian exp[(r-q)(T)G(r-q)+gamma] is represented by its center qinR(3N), the width matrix GinR(3Nx3N), and the scale gammainR, all treated as dynamical variables. Evaluation of observables is done by Monte Carlo sampling of the initial Gaussian positions. As demonstrated previously at not-very-low temperatures the method is surprisingly accurate for a range of model systems including the case of double-well potential. Ideally, a single Gaussian propagation requires numerical effort comparable to the propagation of a single classical trajectory for a system with 9(N(2)+N)/2 degrees of freedom. Furthermore, an approximation based on a direct product of single-particle Gaussians, rather than a fully coupled Gaussian, reduces the number of dynamical variables to 9N. The success of the methodology depends on whether various Gaussian integrals needed for calculation of, e.g., the potential matrix elements or pair correlation functions could be evaluated efficiently. We present techniques to accomplish these goals and apply the method to compute the heat capacity and radial pair correlation function of Ne(13) Lennard-Jones cluster. Our results agree very well with the available path-integral Monte Carlo calculations.     

Quantum cascade laser spectroscopy and photoinduced chemistry of Al-(CO)n clusters in helium nanodroplets

Helium nanodroplet isolation and a tunable quantum cascade laser are used to probe the fundamental CO stretch bands of aluminum carbonyl complexes, Al-(CO)(n) (n ≤ 5). The droplets are doped with single aluminum atoms via the resistive heating of an aluminum wetted tantalum wire. The downstream sequential pick-up of CO molecules leads to the rapid formation and cooling of Al-(CO)(n) clusters within the droplets. Near 1900 cm(-1), rotational fine structure is resolved in bands that are assigned to the CO stretch of a linear (2)Π(1/2) Al-CO species and the asymmetric and symmetric CO stretch vibrations of a planar C(2v) Al-(CO)(2) complex in a (2)B(1) electronic state. Bands corresponding to clusters with n ≥ 3 lack resolved rotational fine structure; nevertheless, the small frequency shifts from the n = 2 bands indicate that these clusters consist of an Al-(CO)(2) core with additional CO molecules attached via van der Waals interactions. A second n = 2 band is observed near the CO stretch of Al-CO, indicating a local minimum on the n = 2 potential consisting of an "unreacted" (Al-CO)-CO cluster. The line width of this band is ～0.3 cm(-1), which is about 30 times broader than the transitions within the Al-CO band. The additional broadening is consistent with a homogeneous mechanism corresponding to a rapid vibrational excitation induced reaction within the (Al-CO)-CO cluster to form the covalently bonded Al-(CO)(2) complex. Ab initio CCSD(T) calculations and natural bond orbital (NBO) analyses are carried out to investigate the nature of the bonding in the n = 1, 2 complexes. The NBO calculations show that both π-donation (from the occupied aluminum p orbital into a π* antibonding CO orbital) and σ-donation (from CO into the empty aluminum p orbitals) play a significant role in the bonding, analogous to transition-metal carbonyl complexes. The large red shift observed for the CO stretch vibrations is consistent with this bonding analysis.     

Ionization of methane clusters in helium nanodroplets

The electron ionization of helium droplets doped with methane clusters is investigated for the first time using high-resolution mass spectrometry. The dominant ion products ejected into the gas phase are the unprotonated (CH(4))(n)(+) cluster ions along with the protonated ions, CH(5)(+)(CH(4))(n-1). The mass spectra show clear evidence for magic numbers, which are broadly consistent with icosahedral shell closings. However, unusual features were observed, including different magic numbers for CH(5)(+)(CH(4))(n-1) (n=55, 148) when compared to (CH(4))(n)(+) (n=54, 147). Possible interpretations for some of these differences are proposed. Products of the type [C(2)H(x)(CH(4))(n)](+), which result from ion-molecule chemistry, are also observed and these too show clear magic number features. Finally, we report the first observation of (CH(4))(n)(2+) dications from methane clusters. The threshold for dication survival occurs at n≥70 and is in good agreement with a liquid droplet model for fission of multiply charged ions. Furthermore, we present evidence showing that these dications are formed by an unusual two-step mechanism which is initiated by charge transfer to generate a monocation and is then followed by Penning ionization to generate a dication.     

Quantum Monte Carlo study of helium clusters doped with nitrous oxide: quantum solvation and rotational dynamics

Dynamical and structural properties of small (4)He(N)-N(2)O complexes have been analyzed using ground-state and finite-temperature Monte Carlo simulations. The effective rotational constants resulting from the ground-state calculations are in excellent agreement with the results of a recent spectroscopic study [Y. Xu et al., Phys. Rev. Lett. 91, 163401 (2003)]. After an initial decrease for cluster sizes up to N=8, the rotational constant increases, signaling a transition from a molecular complex to a quantum-solvated system. Such a turnaround is not present in the rotational constants extracted from the finite-temperature Monte Carlo calculations, performed for Boltzmann statistics, thus highlighting the importance of exchange effects to explain the decoupling between a solvated dopant and the helium motion.     

Unraveling excited states of doped helium clusters

We discuss the use of generalized, symmetry-adapted, imaginary-time correlation functions to study the rotational spectrum of doped helium clusters within the frame of the reptation quantum Monte Carlo method. Analysis of these correlation functions allows one to enhance the computational efficiency in the calculation of weak spectral features, as well as to get a qualitative insight into the nature of the different lines. The usefulness of this approach is demonstrated by a study of the He-CO binary complex, used as a benchmark case, as well as by preliminary results for the satellite band recently observed in the IR spectrum of the CO2 molecule solvated in He nanodroplets.     

Quantum phenomena in magnetic nano clusters

One of the fascinating fields of study in magnetism in recent years has been the study of quantum phenomena in nanosystems. While semiconductor structures have provided paradigms of nanosystems from the stand point of electronic phenomena, the synthesis of high nuclearity transition metal complexes have provided examples of nano magnets. The range and diversity of the properties exhibited by these systems rivals its electronic counterparts. Qualitative understanding of these phenomena requires only a knowledge of basic physics, but quantitative study throws up many challenges that are similar to those encountered in the study of correlated electronic systems. In this article, a brief overview of the current trends in this area are highlighted and some of the efforts of our group in developing a quantitative understanding of this field are outlined.     

Computational spectroscopy of carbon monoxide isotopomers in helium clusters

The rotational excitation spectrum, including the vibrational shift of the rotational band, of several CO isotopomers solvated in He clusters has been calculated. Reptation quantum Monte Carlo simulations are used in conjunction with an accurate He-CO potential energy surface, which quantitatively describes the rovibrational spectrum of the binary complex. Our simulations, when compared with number-selective infrared spectra taken for different isotopomers, help discriminate among the alternative assignments proposed for cluster sizes around 15 He atoms. The origin of the vibrational band has a red shift that is nearly linear with the cluster size within the first solvation shell and is almost constant up to the largest cluster studied, well beyond completion of the second solvation shell. A blue upturn at even larger sizes would be needed to attain the nanodroplet limit, as recently estimated from the isotopic dependence of the measured R(0) transitions.     

Quantum solvation of phthalocyanine in superfluid helium droplets

We have measured quantum states of the solvent-solute system of phthalocyanine in superfluid helium droplets in a high resolution pump-probe experiment. This provides evidence for the attribution of a splitting effect in the emission spectra of phthalocyanine in helium droplets to the relaxation of the first helium layer upon electronic excitation, measured recently by us. Our experimental results are a strong indication for the first helium layer playing a key roll for the solvation of molecules in helium droplets and, thus, for their spectroscopic features.     

Microsolvation of LiH+ in helium clusters: many-body effects and additivity models for the interaction forces

The ab initio calculation of the interaction forces between the LiH+ molecular ion, at its equilibrium geometry, and several He atoms is carried out in order to isolate and assess the importance of many-body contributions in the search for realistic energy and geometry data. The full potential energy surface (PES) with a single helium partner is obtained first by using an aug-cc-pVQZ basis set for He and higher quality ones for Li and H. The calculations were performed at the CAS-SCF plus MRCI level for the lowest potential energy surface over a total of 480 grid points of the two intermolecular Jacobi coordinates, whereas the excited state surface has also been examined in order to exclude the presence of any significant nonadiabatic interaction between the two PESs. A numerical fit of the lower surface is presented and the general physical changes of the ionic interaction when going from the lower to the upper of the two potentials are described and discussed. The fairly limited importance of many-body effects for such systems is seen from further ab initio calculations including several He atoms: our results suggest that, at least in the present case, no strong charge migration occurs after He attachment, and therefore, one could realistically model larger clusters by implementing a sum-of-potentials approach via the presently computed PES.     

Interplay between charge and vibrational delocalization in cationic helium clusters

The stable structures and low temperature thermodynamics of cationic helium clusters are investigated theoretically using a diatomics-in-molecules model for the potential energy surfaces and a computational framework in which both electronic and nuclear degrees of freedom are treated on a quantum mechanical footing. While the charge is generally carried by two atoms, vibrational delocalization significantly spreads out the charge over multiple isomers for clusters containing five or more helium atoms. Our calculations indicate that large clusters are essentially fluid with a well-defined solvation shell around the charged core.     

Formation and properties of metal clusters isolated in helium droplets

The unique conditions forming atomic and molecular complexes and clusters using superfluid helium nanodroplets have opened up an innovative route for studying the physical and chemical properties of matter on the nanoscale. This review summarizes the specific characteristics of the formation of atomic clusters partly generated far from equilibrium in the helium environment. Special emphasis is on the optical response, electronic properties as well as dynamical processes which are mostly affected by the surrounding quantum matrix. Experiments include the optical induced response of isolated cluster systems in helium under quite different excitation conditions ranging from the linear regime up to the violent interaction with a strong laser field leading to Coulomb explosion and the generation of highly charged atomic fragments. The variety of results on the outstanding properties in the quantum size regime highlights the peculiar capabilities of helium nanodroplet isolation spectroscopy.     

Inelastic electron interaction with chloroform clusters embedded in helium droplets

The inelastic electron interaction (ionization/attachment) with chloroform embedded in helium droplets has been studied utilizing a two-sector field mass spectrometer. Positive mass spectra have been recorded at the electron energy of 70 eV and are compared with previous results in the gas phase and with other systems embedded in helium droplets. Moreover, the negative ion mass spectrum has been recorded at the electron energy of 1.5 eV. Both negative and positive mass spectra show that chloroform clusters are easily formed by embedding single molecules in the helium droplets. Moreover, for anions appearing in the mass spectrum, the ion yield has been determined as function of the electron energy. While no parent anion of chloroform can be observed in the gas phase, the present cluster environment allows the stabilization of the transient negative ion. The influence of the helium droplet upon the ionization or attachment process of the embedded chloroform is discussed.     

Electron bubbles in helium clusters. II. Probing superfluidity

In this paper we present calculations of electron tunneling times from the ground electronic state of excess electron bubbles in ((4)He)(N) clusters (N=6500-10(7), cluster radius R=41.5-478 A), where the equilibrium bubble radius varies in the range R(b)=13.5-17.0 A. For the bubble center located at a radial distance d from the cluster surface, the tunneling transition probability was expressed as A(0)phi(d,R)exp(-betad), where beta approximately 1 A(-1) is the exponential parameter, A(0) is the preexponential factor for the bubble located at the cluster center, and phi(d,R) is a correction factor which accounts for cluster curvature effects. Electron tunneling dynamics is grossly affected by the distinct mode of motion of the electron bubble in the image potential within the cluster, which is dissipative (i.e., tau(D)tau(0)) in superfluid ((4)He)(N) clusters, where tau(D) is the bubble motional damping time (tau(D) approximately 4 x 10(-12) s for normal fluid clusters and tau(D) approximately 10 s for superfluid clusters), while tau(0) approximately 10(-9)-10(-10) s is the bubble oscillatory time. Exceedingly long tunneling lifetimes, which cannot be experimentally observed, are manifested from bubbles damped to the center of the normal fluid cluster, while for superfluid clusters electron tunneling occurs from bubbles located in the vicinity of the initial distance d near the cluster boundary. Model calculations of the cluster size dependence of the electron tunneling time (for a fixed value of d=38-39 A), with lifetimes increasing in the range of 10(-3)-0.3 s for N=10(4)-10(7), account well for the experimental data [M. Farnik and J. P. Toennies, J. Chem. Phys. 118, 4176 (2003)], manifesting cluster curvature effects on electron tunneling dynamics. The minimal cluster size for the dynamic stability of the bubble was estimated to be N=3800, which represents the threshold cluster size for which the excess electron bubble in ((4)He)(N) (-) clusters is amenable to experimental observation.     

Size and isotope effects of helium clusters and droplets: identification of surface and bulk-volume excitations

We report a comprehensive investigation of the electronically excited states of helium clusters and droplets of sizes ranging from a few to several 10(7) atoms using time-resolved fluorescence excitation spectroscopy and quantum chemical ab initio calculations. We employ various approaches for our analysis considering the lifetime-dependence of the fluorescence intensity, spectral shifts, intensity scaling with cluster size, isotopic dependence, and density-dependence of the calculated electron wave function radii. A unique feature of helium clusters and droplets is their radially varying particle density. Our results show that short-lived fluorescence is sensitive to regions of increased density and probes excitations located in the bulk volume, whereas long-lived fluorescence is sensitive to regions of reduced density such as for small clusters or for the surface of large droplets. Spectra of (3)He droplets serve as a reference for low density, but are free from contributions of small clusters. This allows us to distinguish regions of reduced density as these can be due to both surface states or small clusters. Our analysis reveals a picture where spectral features are related to regions of different density due to isotopic composition, cluster size, and surface or bulk volume location of the excitations. The 2s and 2p related excitations appear as blue-shifted wings for small clusters or for excited atoms within the surface layer, whereas in the bulk-volume of large droplets, they appear as distinct bands with large intensities, dominating the entire spectrum. Excitations at energies higher than 23 eV are unambiguously assigned to regions of low and medium density location within the deeper parts of the surface layer but show no relation to the bulk volume. Our findings support the idea that in liquid helium high-lying states and, in particular, Rydberg states are quenched in favor of the 2s and 2p excitations.     

Density of states and evaporation rate of helium clusters

The density of states of⁴He clusters is calculated on the assumption that only surface vibrations are thermally excited. Results for mixed³He-⁴He and³He clusters are also given. The Weisskopf procedure is used to calculate the evaporation rates and the cooling laws of helium clusters at low temperatures.     

Ionization of doped helium nanodroplets: residual helium attached to diatomic cations and their clusters

Electron impact ionization of helium nanodroplets containing a dopant, M, can lead to the detection of both M(+) and helium-solvated cations of the type M(+)·He(n) in the gas phase. The observation of helium-doped ions, He(n)M(+), has the potential to provide information on the aftermath of the charge transfer process that leads to ion production from the helium droplet. Here we report on helium attachment to the ions from four common diatomic dopants, M = N(2), O(2), CO, and NO. For experiments carried out with droplets with an average size of 7500 helium atoms, the monomer cations show little tendency to attach and retain helium atoms on their journey out of the droplet. By way of contrast, the corresponding cluster cations, M(n)(+), where n ≥ 2, all show a clear affinity for helium and form He(m)M(n)(+) cluster ions. The stark difference between the monomer and cluster ions is attributed to more effective cooling of the latter in the aftermath of the ionization event.     

Excitation and decay processes in helium clusters studied by fluorescence spectroscopy

Excitation and decay processes of helium clusters are investigated with fluorescence methods. The results differ remarkably from that obtained for the heavier rare gas clusters. They are discussed in view of the unusual structural and electronic properties of helium.