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.     

Photoexcitation of mass/charge selected hemin(+), caught in helium nanodroplets

We report on a method by which mass/charge selected ions are picked up from a linear ion trap by liquid helium droplets. The size distributions of the doped droplets are measured via acceleration experiments. Depending on the source temperature, droplet sizes ranging from tens of thousands to several million helium atoms are obtained. Droplets doped with hemin, an iron containing porphyrin molecule, in the charge state +1 are then investigated using laser spectroscopy. It is observed that excitation with UV/VIS light can lead to ejection of the ion from the droplet. For doped droplets with a median size of ～150?000 helium atoms, the absorption of two photons at 380 nm is needed for ejection to become efficient. When droplets become smaller, the ejection efficiency is observed to strongly increase. Monitoring the ejection yield as a function of excitation wavelength can be used to obtain the optical spectrum of hemin(+). Compared to the spectrum of free gas-phase hemin(+) at room temperature, the here obtained spectrum is slightly narrower and shifted to the blue.     

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.     

Bias in the temperature of helium nanodroplets measured by an embedded rotor

The rovibrational spectra of molecules dissolved in liquid 4He nanodroplets display rotational structure. Where resolved, this structure has been used to determine a temperature that has been assumed to equal that of the intrinsic excitations of the helium droplets containing the molecules. Consideration of the density of states as a function of energy and total angular momentum demonstrates that there is a small but significant bias of the rotor populations that make the temperature extracted from a fit to its rotational level populations slightly higher than the temperature of the ripplons of the droplet. This bias grows with both the total angular momentum of the droplet and with the moment of inertia of the solute molecule.     

The shell structure of3He droplets

Liquid³He droplets and their shell structure are investigated in the framework of mean-field calculations using a recently developed effective energy functional which employs realistic finite range interactions throughout. The samples range fromN=20 up toN=1360. The shell closures found agree with the harmonic oscillator scheme up toN=168. Above that, magic droplets appear atN=198, 274, 300, 368, 398, 482, 516... The first and second differences of the free energy are computed as signals for the shell structure in future experiments. Shell closures are found to be still visible in these signals at comparatively high temperatures. The finite range character of the effective interaction generates oscillations in the density profile which are suppressed in comparable calculations with zero range interactions.     

Photodissociation of alkyl iodides in helium nanodroplets. II. Solvation dynamics

The solvation dynamics of nonthermal species in liquid helium has been investigated by photolyzing alkyl iodide molecules, CH3I, C2H5I, and CF3I, embedded in helium nanodroplets. Iodine and CH3 fragments are found to leave the droplets solvated by a finite number of helium atoms, this in contrast to C2H5 and CF3 fragments. The speed distributions of the IHeN and CH3HeN complexes show a prominent correlation with the degree of solvation N. It is argued that this correlation is caused by a dynamical adjustment of the solvation structure size to the relative speed of the traveling fragments as they pass through the helium bath. The absence of C2H5HeN and CF3HeN complexes is attributed to the large internal energy of these alkyl fragments which leads to a rapid destruction of any possibly formed complexes.     

Helium Droplets: An Apparatus to Study Ultra Cold Chemistry

A new pulsed helium nano droplets machine has been constructed. The droplets were gener-ated by expansion of the pure helium through the cryogenic valve attached to a closed-cycle cryostat. The mean size of helium droplets can be controlled between 103 and 105 helium atoms by tuning the backing pressure (10-40 bar) and temperature (10-30 K). Compared with the continuous-flow beam source, the density of droplet is at least one order of magni-tude higher, which offers the opportunity to combine the system with the commercial pulsed laser to study chemical reactions inside of the superfluid helium at ultra-low temperature. The performance for the system has been checked by studying the photodissociation of CH₃I doped droplets at 252 nm with the velocity map imaging technique. The photofragments, CH₃, were detected by (2+1) resonance enhanced multiphoton ionization. The speed and angular distributions derived from resulting images show clear evidence of the relaxation effect by the surrounding helium atoms. The pulsed helium droplets depletion spectroscopy was also demonstrated. The depletion spectrum of benzene doped helium droplets indicatesthat less than 3% depletion can be observed with the newly constructed apparatus.     

Multiply Charged Helium Droplet Anions

The detection of multiply charged helium droplet anions is reported for the first time. By ionizing droplets of superfluid helium with low energy electrons (up to 25 eV), it was possible to produce droplets containing up to five negative charges, which remain intact on the timescale of the experiment. The appearance sizes for different charge states are determined and are found to be orders of magnitude larger than for the equivalent cationic droplets, starting at 4 million He atoms for dianions. Droplets with He*⁻ as charge carriers show signs of being metastable, but this effect is quenched by the pickup of water molecules.     

Mid-infrared spectroscopy of molecular ions in helium nanodroplets

High resolution IR spectra of aniline, styrene, and 1,1-diphenylethylene cations embedded in superfluid helium nanodroplets have been recorded in the 300-1700 cm(-1) range using a free-electron laser as radiation source. Comparison of the spectra with available gas phase data reveals that the helium environment induces no significant matrix shift nor leads to an observable line broadening of the resonances. In addition, the IR spectra have provided new and improved vibrational transition frequencies for the cations investigated, as well as for neutral aniline and styrene. Indications have been found that the ions desolvate from the droplets after excitation by a non-evaporative process in which they are ejected from the helium droplets. The kinetic energy of the ejected ions is found to be ion specific and to depend only weakly on the excitation energy.     

Formulation ofN- and υ-representable density functional theory. III: Excited states

The local-scaling transformation version of density functional theory is extended to the treatment of excited states. This is accomplished in the context of the super-particle formulation of Katriel [Int. J. Quant. Chem. 23(19$3)1767]. It is shown that for a given superparticle generating wave function, the energy density functional corresponding to the excited-state super-system may be explicitly constructed. The derivation of an Euler-Lagrange equation for the composite excited-state density is discussed. A preliminary calculation for the 21S state of helium is reported.     

Piris natural orbital functional study of the dissociation of the radical helium dimer

We have investigated the dissociation behavior of the radical helium dimer He(2) (+) using the Piris natural orbital functional (PNOF). This system is particularly challenging to be described by standard density functionals. The restricted open formulation of the PNOF-2, as well as the PNOF-2 energy plus the extended Koopmans' vertical ionization potential calculations of the neutral helium dimer, have been tested for calculating the ground-state energies of He(2) (+) as a function of the internuclear distance. For comparison, we present the dissociation curve obtained with the diffusion Monte Carlo method. The dissociation energies, equilibrium bond lengths, and rovibrational levels are reported. The obtained potential energy curves indicate that PNOF-2 yields a correct and accurate dissociation behavior for the helium radical dimer.     

Adiabatic approximation of time-dependent density matrix functional response theory

Time-dependent density matrix functional theory can be formulated in terms of coupled-perturbed response equations, in which a coupling matrix K(omega) features, analogous to the well-known time-dependent density functional theory (TDDFT) case. An adiabatic approximation is needed to solve these equations, but the adiabatic approximation is much more critical since there is not a good "zero order" as in TDDFT, in which the virtual-occupied Kohn-Sham orbital energy differences serve this purpose. We discuss a simple approximation proposed earlier which uses only results from static calculations, called the static approximation (SA), and show that it is deficient, since it leads to zero response of the natural orbital occupation numbers. This leads to wrong behavior in the omega-->0 limit. An improved adiabatic approximation (AA) is formulated. The two-electron system affords a derivation of exact coupled-perturbed equations for the density matrix response, permitting analytical comparison of the adiabatic approximation with the exact equations. For the two-electron system also, the exact density matrix functional (2-matrix in terms of 1-matrix) is known, enabling testing of the static and adiabatic approximations unobscured by approximations in the functional. The two-electron HeH(+) molecule shows that at the equilibrium distance, SA consistently underestimates the frequency-dependent polarizability alpha(omega), the adiabatic TDDFT overestimates alpha(omega), while AA improves upon SA and, indeed, AA produces the correct alpha(0). For stretched HeH(+), adiabatic density matrix functional theory corrects the too low first excitation energy and overpolarization of adiabatic TDDFT methods and exhibits excellent agreement with high-quality CCSD ("exact") results over a large omega range.     

Rovibrational spectra for the HCCCN*HCN and HCN*HCCCN binary complexes in 4He droplets

Rovibrational spectra are measured for the HCCCN*HCN and HCN*HCCCN binary complexes in helium droplets at low temperature. Though no Q-branch is observed in the infrared spectrum of the linear HCN*HCCCN dimer, which is consistent with previous experimental results obtained for other linear molecules, a prominent Q-branch is found in the corresponding infrared spectrum of the HCCCN*HCN complex. This Q-branch, which is reminiscent of the spectrum of a parallel band of a prolate symmetric top, implies that some component of the total angular momentum is parallel to the molecular axis. The appearance of this particular spectroscopic feature is analyzed here in terms of a nonsuperfluid helium density induced by the molecular interactions. Finite temperature path integral Monte Carlo simulations are performed using potential energy surfaces calculated with second-order M?ller-Plesset perturbation theory, to investigate the structural and superfluid properties of both HCCCN*HCN(4He)N and HCN*HCCCN(4He)N clusters with N < or = 200. Explicit calculation of local and global nonsuperfluid densities demonstrates that this difference in the rovibrational spectra of the HCCCN*HCN and HCN*HCCCN binary complexes in helium can be accounted for by local differences in the superfluid response to rotations about the molecular axis, i.e., different parallel nonsuperfluid densities. The parallel and perpendicular nonsuperfluid densities are found to be correlated with the locations and strengths of extrema in the dimer interaction potentials with helium, differences between which derive from the variable extent of polarization of the CN bond in cyanoacetylene and the hydrogen-bonded CH unit in the two isomers. Calculation of the corresponding helium moments of inertia and effective rotational constants of the binary complexes yields overall good agreement with the experimental values.     

Superfluid helium droplets: a uniquely cold nanomatrix for molecules and molecular complexes

Herein, recent experiments on the spectroscopy and chemical reactions of molecules and complexes embedded in helium droplets are reviewed. In the droplets, a high spectroscopic resolution, which is comparable to the gas phase is achieved, while an isothermal low-temperature environment is maintained by evaporative cooling at T =0.37 K (4He droplets) or 0.15 K (3He droplets), lower than possible in most solid matrices. Thus the helium-droplet technique combines the benefits of both the gas phase and the classical matrix-isolation techniques. Most important, the superfluid helium facilitates binary encounters, and absorbs the released binding energy upon recombination. Thus the droplet can be viewed as an isothermal nanoscopic reactor, which isolates single molecules, clusters, or even a single reactive encounter at ultralow temperatures.     

A semiclassical density functional evaluation of the smoothly varying part of the Hartree–Fock binding energy in atoms

A semiclassical density functional approach is used to evaluate the smooth part of the variation of the Hartree–Fock (HF ) binding energy in atoms, from helium through xenon. The energy density functional is chosen with an improved form for the kinetic energy functional (KEF ). The variation of the HF binding energy is split into smooth and oscillating (shell-structure) parts, in accordance with Strutinskyøs self-consistent averaging procedure, which is equivalent to a semiclassical ?-expansion of the KEF . This enables a well-grounded evaluation of the oscillating part of the HF binding energy, which displays a quasi-periodic behavior expressing clearly the shell structure of atoms. © 1994 John Wiley & Sons, Inc.     

Communication: the formation of helium cluster cations following the ionization of helium nanodroplets: influence of droplet size and dopant

The He(n)(+)/He(2)(+) (n ≥ 3) signal ratios in the mass spectra derived from electron impact ionization of pure helium nanodroplets are shown to increase with droplet size, reaching an asymptotic limit at an average droplet size of approximately 50,000 helium atoms. This is explained in terms of a charge hopping model, where on average the positive charge is able to penetrate more deeply into the liquid helium as the droplet size increases. The deeper the point where the charge localizes to form He(2)(+), the greater the likelihood of collisions with the surrounding helium as the ion begins to leave the droplet, thus increasing the probability that helium will be ejected in the form of He(n)(+) (n ≥ 3) cluster ions rather than He(2)(+). The addition of a dopant alters the He(n)(+)/He(2)(+) ratio for small helium droplets, an observation attributed to the potential energy gradient created by the cation-dopant interaction and its effect in drawing the positive charge towards the dopant in the interior of the droplet.     

Application of Exact Analytic Total Energy Functional for Hooke’s Atom to He, Li+ and Be++: An Examination of the Universality of the Energy Functional in DFT

We employ the recently generated energy density functional for Hooke’s atom [Ludeña EV et al (2004) Intern J Quantum Chem 99:297], to which we introduce a simplification for the kinetic energy term, to evaluate the total energy of the helium atom and of the two-electron ions Li⁺ and Be⁺⁺. Using accurate representations for the one-particle densities of these systems we show that the energy density functional for Hooke’s atom leads, in these cases, to energy values that are below the exact ones. We discuss the implication of this finding with respect to the existence of a universal energy functional in DFT.     

Capillary bridges in electric fields

We analyzed the morphology of droplets of conductive liquids placed between two parallel plate electrodes as a function of the two control parameters electrode separation and applied voltage. Both electrodes were covered by thin insulating layers, as in conventional electrowetting experiments. Depending on the values of the control parameters, three different states of the system were found: stationary capillary bridges, stationary separated droplets, and periodic self-excited oscillations between both morphologies, which appear only above a certain threshold voltage. In the two stationary states, the morphology of the liquid is modified by the electric fields due to electrowetting and due to mutual electrostatic attraction, respectively. We determined a complete phase diagram within the two-dimensional phase space given by the control parameters. We discuss a model based on the interfacial and electrostatic contributions to the free energy. Numerical solutions of the model are in quantitative agreement with the phase boundaries found in the experiments. The dynamics in the oscillatory state are governed by electric charge relaxation and by contact angle hysteresis.     

Low-frequency dilational elasticity of the nematic 4'-pentyl-4-biphenylcarbonitrile (5CB)/water interface

Axisymmetric oscillating pendant drop shape analysis has been used to study the interfacial rheology of the liquid crystal 4'-pentyl-4-biphenylcarbonitrile (5CB) in water with homeotropic anchoring. Nearly spherical 5CB droplets were subjected to low frequency (1-5 mHz) volume oscillations, and the increase in tension with surface dilation was used to calculate the complex modulus. The droplet interface response is completely elastic, with no relaxations occurring on the experimental time scale. This surprising result is attributed to droplet storage of elastic energy in the form of distorted orientational distributions within the bulk (Frank elasticity) and on the surface (anchoring elasticity).     

Spectroscopy and dynamics of barium-doped helium nanodroplets

Excitation spectra up to the ionization threshold are reported for barium atoms located on the surface of helium nanodroplets. For states with low principal quantum number, the resonances are substantially broadened and shifted towards higher energy with respect to the gas phase. This has been attributed to the repulsive interaction of the excited atom with the helium at the Franck-Condon region. In contrast, for states with high principal quantum number the resonances are narrower and shifted towards lower energies. Photoelectron and ZEKE spectroscopy reveal that the redshift results from a lowering of the ionization threshold due to polarization of the helium by the barium ionic core. As a result of the repulsive interaction with the helium, excited barium atoms desorb from the surface of the droplets. Only when excited to the 6s6p (1)P(1) state, which reveals an attractive interaction with the helium, the atoms remain attached to the droplets.