Electron bubbles in helium clusters. I. Structure and energetics

In this paper we present a theoretical study of the structure, energetics, potential energy surfaces, and energetic stability of excess electron bubbles in ((4)He)(N) (N=6500-10(6)) clusters. The subsystem of the helium atoms was treated by the density functional method. The density profile was specified by a void (i.e., an empty bubble) at the cluster center, a rising profile towards a constant interior value (described by a power exponential), and a decreasing profile near the cluster surface (described in terms of a Gudermannian function). The cluster surface density profile width (approximately 6 A) weakly depends on the bubble radius R(b), while the interior surface profile widths (approximately 4-8 A) increase with increasing R(b). The cluster deformation energy E(d) accompanying the bubble formation originates from the bubble surface energy, the exterior cluster surface energy change, and the energy increase due to intracluster density changes, with the latter term providing the dominant contribution for N=6500-2 x 10(5). The excess electron energy E(e) was calculated at a fixed nuclear configuration using a pseudopotential method, with an effective (nonlocal) potential, which incorporates repulsion and polarization effects. Concurrently, the energy V(0) of the quasi-free-electron within the deformed cluster was calculated. The total electron bubble energies E(t)=E(e)+E(d), which represent the energetic configurational diagrams of E(t) vs R(b) (at fixed N), provide the equilibrium bubble radii R(b) (c) and the corresponding total equilibrium energies E(t) (e), with E(t) (e)(R(e)) decreasing (increasing) with increasing N (i.e., at N=6500, R(e)=13.5 A and E(t) (e)=0.86 eV, while at N=1.8 x 10(5), R(e)=16.6 A and E(t) (e)=0.39 eV). The cluster size dependence of the energy gap (V(0)-E(t) (e)) allows for the estimate of the minimal ((4)He)(N) cluster size of N approximately 5200 for which the electron bubble is energetically stable.     

Recurrences in rotational dynamics and experimental measurement of superfluidity in doped helium clusters

We present the first experimental evidence of recurrences in the rotational dynamics of doped helium clusters. Using the dopant molecule as an experimental microscopic probe of superfluidity, we show that in small He(N)-N2O complexes, superfluidity builds up in stages correlated with the filling and completion of a solvation shell.     

Rotational fluctuation of molecules in quantum clusters. II. Molecular rotation and superfluidity in OCS-doped helium-4 clusters

In this paper, quantum fluctuations of a carbonyl sulfide molecule in helium-4 clusters are studied as a function of cluster size N in a small-to-large size regime (2or=20, which is larger than the experimental nanodroplet value. Superfluid response of the doped cluster is found to show remarkable anisotropy especially for N相似文献   

OCS in para-hydrogen clusters: rotational dynamics and superfluidity

We present a detailed analysis of the rotational excitations of the linear OCS molecule solvated by a variable number of para-hydrogen molecules (9 < or = N < or = 17). The effective rotational constant extracted from the fit of the rotational energy levels decreases up to N = 13, indicating near-rigid coupling between OCS rotations and para-hydrogen motion. Departure from rigidity is instead seen for larger clusters with 14 < or = N < or = 17. Path-integral Monte Carlo calculations show that the N dependence of the effective rotational constant can be explained in terms of a partial superfluid response of para-hydrogen to rotations about an axis perpendicular to the OCS axis. Complete para-hydrogen superfluid response to rotations about the OCS axis is found for N > or = 10.     

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.     

Spectroscopy of nonspherical atomic bubbles in solid helium

We analyze the effect of the host crystal symmetry on the optical spectra of the 6P(1/2)-6S(1/2) and 6P(3/2)-6S(1/2) transitions of atomic Cs in solid (4)He matrices. In particular, we address the deformation of the bubble structures formed by Cs in such quantum crystals. We show that the anisotropy of the stiffness tensor leads to static quadrupolar bubble shape deformations in hexagonally close-packed (hcp) crystals, while the corresponding deformations in the body-centered cubic (bcc) phase of the matrix have a hexadecupolar symmetry. A comparison of the measured excitation spectra with our model calculations allow us to infer quantitative values of the deformation parameters.     

Electronically excited rubidium atom in helium clusters and films. II. Second excited state and absorption spectrum

Following our work on the study of helium droplets and film doped with one electronically excited rubidium atom Rb(?) ((2)P) [M. Leino, A. Viel, and R. E. Zillich, J. Chem. Phys. 129, 184308 (2008)], we focus in this paper on the second excited state. We present theoretical studies of such droplets and films using quantum Monte Carlo approaches. Diffusion and path integral Monte Carlo algorithms combined with a diatomics-in-molecule scheme to model the nonpair additive potential energy surface are used to investigate the energetics and the structure of Rb(?)He(n) clusters. Helium films as a model for the limit of large clusters are also considered. As in our work on the first electronic excited state, our present calculations find stable Rb(?)He(n) clusters. The structures obtained are however different with a He-Rb(?)-He exciplex core to which more helium atoms are weakly attached, preferentially on one end of the core exciplex. The electronic absorption spectrum is also presented for increasing cluster sizes as well as for the film.     

Quantum statistical effects in helium clusters

We discuss ground state and statistical properties of helium clusters with special emphasis to quantum statistical effects. We investigate the density of states of⁴He and³He clusters, their cooling due to evaporation as well as the role played by surface excitations in the superfluid motion.     

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.     

Electron and nuclear dynamics of molecular clusters in ultraintense laser fields. II. Electron dynamics and outer ionization of the nanoplasma

We explore electron dynamics in molecular (CD4)(1061) clusters and elemental Xen (n=249-2171) clusters, responding to ultraintense (intensity I=10(16)-10(19) W cm(-2)) laser fields. Molecular dynamics simulations (including magnetic field and relativistic effects) and analyses of high-energy electron dynamics and nuclear ion dynamics in a cluster interacting with a Gaussian shaped laser field (frequency 0.35 fs(-1), photon energy 1.44 eV, phase 0, temporal width 25 fs) elucidated the time dependence of inner ionization, the formation of a nanoplasma of unbound electrons within the cluster or its vicinity, and of outer ionization. We determined the cluster size and the laser intensity dependence of these three sequential-parallel electronic processes. The characteristic times for cluster inner ionization (tau(ii)) and for outer ionization (tau(oi)) fall in the femtosecond time domain, i.e., tau(ii)=2-9 fs and tau(oi)=4-15 fs for (CD4)(1061), tau(ii)=7-30 fs and tau(oi)=5-13 fs for Xe(n) (n=479,1061), with both tau(ii) and tau(oi) decreasing with increasing I, in accord with the barrier suppression ionization mechanism for inner ionization of the constituents and the cluster barrier suppression ionization mechanism for outer ionization. The positive delay times Deltatau(OI) between outer and inner ionization (e.g., Deltatau(OI)=6.5 fs for Xen at I=10(16) W cm(-2) and Deltatau(OI)=0.2 fs for (CD4)(1061) at I=10(19) W cm(-2)) demonstrate that the outer/inner ionization processes are sequential. For (CD4)(1061), tau(ii)tau(oi), reflecting on the energetic hierarchy in the ionization of the Xe atoms. Quasiresonance contributions to the outer ionization of the nanoplasma were established, as manifested in the temporal oscillations in the inner/outer ionization levels, and in the center of mass of the nanoplasma electrons. The formation characteristics, dynamics, and response of the nanoplasma in molecular or elemental clusters were addressed. The nanoplasma is positively charged, with a high-average electron density [rho(P)=(2-3)10(22) cm(-3)], being characterized by high-average electron energies epsilon(av) (e.g., in Xe(1061) clusters epsilon(av)=54 eV at I=10(16) W cm(-2) and epsilon(av)=0.56-0.37 keV at I=10(18) W cm(-2), with epsilon(av) proportional, variant I(1/2)). Beyond the cluster boundary the average electron energy markedly increases, reaching electron energies in the range of 1.2-40 keV for outer ionization of Xe(n) (n=249-2171) clusters. The nanoplasma exhibits spatial inhomogeneity and angular anisotropy induced by the laser field. Femtosecond time scales are predicted for the nanoplasma production (rise times 7-3 fs), for the decay (decay times approximately 5 fs), and for the persistence time (30-10 fs) of a transient nanoplasma at I=10(17)-10(18) W cm(-2). At lower intensities of I=10(16) W cm(-2) a persistent nanoplasma with a "long" lifetime of > 50 fs will prevail.     

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.     

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.     

Electron delocalization in trinuclear mixed-valence clusters

Possible trapped valence states in trimeric mixed-valence clusters are considered. The adiabatic potential in the space of a doubly-degenerate e vibration is calculated. Conditions under which minima with different electron distributions exist are determined. The coexistence of localized and delocalized distributions is possible.     

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.     

Electron impact ionization of haloalkanes in helium nanodroplets

Electron impact (EI) mass spectra of a selection of C1-C3 haloalkanes in helium nanodroplets have been recorded to determine if the helium solvent can significantly reduce molecular ion fragmentation. Haloalkanes were chosen for investigation because their EI mass spectra in the gas phase show extensive ion fragmentation. There is no evidence of any major softening effect in large helium droplets ( approximately 60 000 helium atoms), but some branching ratios are altered. In particular, channels requiring C-C bond fission or concerted processes leading to the ejection of hydrogen halide molecules are suppressed by helium solvation. Rapid cooling by the helium is not sufficient to account for all the differences between the helium droplet and gas phase mass spectra. It is also suggested that the formation of a solid "snowball" of helium around the molecular ion introduces a cage effect, which enhances those fragmentation channels that require minimal disruption to the helium cage for products to escape.     

Electron attachment to HCl clusters

Negatively charged cluster ions of hydrogen chloride are formed by electron attachment to HCl clusters, which are produced in a seeded supersonic beam traversing a sustained gas discharge. Cluster ions of (HCl) _n ^? , withn=2, and tentatively withn=3 and 4 are observed. Cluster ions like Cl _n ^? , Cl _n ^? (HCl) _m , and withAr attached to them are also seen. The relevance to radiation chemistry of HCl if briefly discussed. Atoms evaporating from the hot, thoriated tungsten filament of the glow discharge lead to clusters such as Th _n ^? and its oxides.     

Electron correlation effects in ionic hydrogen clusters

We employ density functional, post‐Hartree–Fock, and quantum Monte Carlo methods to study the electronic structure, geometries, and behavior of positively charged H_m⁺ clusters with m=3,5,…,17. Their structure consists of a tightly bound H₃⁺ core ion surrounded by successive solvation shells of H₂ molecules. For the largest clusters, we propose new geometries. We find that correlated methods yield the stepwise decrease of enthalpies for dissociation of H₂ from the clusters observed in experiments. Our best results are obtained by the diffusion Monte Carlo method, and by including finite temperature entropic effects, we are able to reproduce the experimental dissociation enthalpies with an unprecedented accuracy of less than 0.5 kcal/mol. These benchmark results contrast with erroneous predictions discovered in the density functional approaches. Finally, our analysis of the cluster energy surfaces indicates that under quantum and thermal fluctuations, the outer solvation shells will exhibit pronounced fluctional behavior. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 86–95, 2001     

Electron delocalization in asymmetric trimeric mixed-valence clusters

The statistical distribution of electron density in a C_2v one-electron trimeric mixed-valence cluster is considered in terms of the Piepho-Krausz-Schatz vibronic model using the adiabatic approximation. Conditions are revealed under which the lower branch of the adiabatic potential shows three minima, each corresponding to predominant localization of the electron on one of the three ionic centers. It is shown that when the symmetry of the system is disturbed, the potential has two minima, with the system localized on one of two equivalent centers at either minimum. Conditions are considered under which these minima merge into one minimum, which corresponds to delocalization of the electron over a pair of ions, i.e., partial delocalization. For a D_3h symmetric trimer, it is demonstrated that in the region of transfer parameters and vibronic couplings, where the localized and completely delocalized states coexist, even with insignificant distortions there are only three localization minima, and the central minimum, which corresponds to a completely delocalized state, vanishes. Valencia University, Spain. Institute of Chemistry, Academy of Sciences, Moldova Republic. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 4, pp. 654–666, July–August, 1995 Translated by I. Izvekova     

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.