Ab initio study of small He cluster ions He n + ,n=2, 3, 4, 5, and low-lying Rydberg states of He4

SCF and CEPA calculations are applied to study the structure of small He cluster ions, He _n ⁺ ,n=2, 3, 4, 5 and some low-lying Rydberg states of He₄. The effect of electron correlation upon the equilibrium structures and binding energies is discussed. He ₃ ⁺ has a linear symmetric equilibrium geometry with a bond length of 2.35a ₀ and a binding energyD _e =0.165 eV with respect to He ₂ ⁺ +He (experimentally:D ₀=0.17 eV which corresponds toD _e ≈0.20 eV). He ₄ ⁺ is a very floppy molecular ion with several energetically very similar geometrical configurations. Our CEPA calculations yield a T-shaped form with a He ₃ ⁺ centre (R _e = 2.35a ₀) and one inductively bound He atom (4.39a ₀ from the central He atom of He ₃ ⁺ ) as equilibrium structure. Its binding energy with respect to He ₃ ⁺ +He is 0.031 eV. A linear symmetric configuration consisting of a He ₂ ⁺ centre with a bond length of 2.10a ₀ and two inductively bound He atoms (4.20a ₀ from the centre of He ₂ ⁺ ) is only 0.02–0.03 eV higher in energy. We expect that in larger He cluster ions structures with He ₂ ⁺ and He ₃ ⁺ centres andn?2 orn?3 inductively bound He atoms have nearly the same energies. In He₄ a low-lying metastable Rydberg state (³ Π symmetry for linear He ₄ ^* ,³ B ₁ for the T-shaped form) exists which is slightly stronger bound with respect to He ₃ ^* +He than the corresponding ion.     

Fragmentation of clusters induced by collision with a solid surface: comparison of antimony and bismuth cluster ions

Mass-selected antimony cluster ions Sb _n ⁺ (n = 3-12) and bismuth cluster ions Bi _{ntn} ⁺ (n = 3-8) are allowed to collide with the surface of highly oriented pyrolytic graphite at energies up to 350 eV. The resulting fragment ions are analysed in a time-of-flight mass spectrometer. Two main fragmentation channels can be identified. At low impact energies both Sb _n ⁺ and Bi _n ⁺ cluster ions lose neutral tetramer and dimer units upon collision. Above about 150 eV impact energy Sb ₃ ⁺ becomes the predominant fragment ion of all investigated antimony clusters. The enhanced stability of these fragment clusters can be explained in the framework of the polyhedral skeletal electron pair theory. In contrast, Bi _n ⁺ cluster scattering leads to the formation of Bi ₃ ⁺ , Bi ₂ ⁺ and Bi+ with nearly equal abundances, if the collision energy exceeds 75 eV. The integral scattering yield is substantially higher in this case as compared to Sb _n ⁺ clusters.     

Ab initio calculation of the vertical excitation energies of small helium cluster ions

Quantum chemical ab initio calculations have been performed for the vertical excitation energies and oscillator strengths of all low-lying electronically excited states of small helium cluster ions, He _n ⁺ ,n=2, ..., 7. The geometrical structures of the ions were fixed at the equilibrium geometries of the respective ground states, for He ₄ ⁺ and He ₅ ⁺ also one alternative structure was considered. The low-lying excited states can be classified into two categories: the electronic transition can occur either within the central He ₂ ⁺ or He ₃ ⁺ unit or from the peripheral weakly bound He atoms to this unit. The latter transitions are very weak (f≈0.001), closely spaced, with vertical excitation energies of about 5.7 eV. The He ₂ ⁺ and He ₃ ⁺ units have strong transitions at 9.93 and 5.55 eV, respectively; these transitions are only slightly blue-shifted if He ₂ ⁺ or He ₃ ⁺ are placed as “chromophores” into the centre of a larger He _n ⁺ cluster. The large difference in the vertical excitation energy of the strong transition should enable an experimental decision of the question whether the cluster ions have He ₂ ⁺ or He ₃ ⁺ cores.     

The chemistry and physics of molecular surfaces

Configuration interaction calculations are carried out to study the potential energy surface for the system Ar-Ar ₂ ⁺ . An all-electron as well as a pseudopotential treatment is employed. It is found that in the perpendicular Ar approach the Ar ₂ ⁺ partner remains essentially unchanged and the potential can be characterized by an electrostatic ion-induced dipole interaction. In the collinear mode of Ar approach the Ar ₂ ⁺ bond separation increases considerably, the charge is redistributed and the interaction can be characterized as chemical bonding. The minimum on the surface is found to be the linear symmetric molecule with bond lengths of 2.62 Å. The optimum structure in the perpendicular approach lies 0.13 eV above the minimum and is the T-shaped molecule in which the Ar is 3.65 Å away from the midpoint of the Ar ₂ ⁺ (r=2.46 Å) system; the best equilateral triangle structure has a bond length of 2.99 Å but is found to lie 0.64 eV above the Ar ₃ ⁺ minimum. The dissociation energy into Ar ₂ ⁺ + Ar is calculated to be 0.16 eV in reasonable agreement with experimental values of 0.21 eV. The potential curves for the four lowest states of Ar ₂ ⁺ are also treated.     

Photoemission from tin and lead cluster anions

Photoelectrons from mass-identified jet-cooled tin and lead cluster anions (Sn _n ^? , Pb _n ^? ) are detached by ultraviolet laser light (hν=3.68 eV). The photoelectron energy spectra give the detachment energies of ground state cluster anions (electron affinities) as well as excitation energies of neutral clusters in the geometry of the anions. The energy spectra for Sn _n ^? are dominated by flat thresholds with ann-dependence similar to that of other group IV clusters. In contrast, for Pb _n ^? we find pronounced narrow lines close to threshold, generally followed by a 0.3–1.4 eV gap which indicates closed-shell behaviour of Pb _n ^? for nearly alln.     

Shell correction study of fission of doubly charged silver clusters

Fission of doubly charged silver clusters is investigated by the method of shell corrections. The following fission events are considered: Ag ₂₂ ²⁺ → Ag _n ⁺ + Ag _{22 ?n} ⁺ , (n=11, 10, 9, 8); Ag ₂₁ ²⁺ → Ag _n ⁺ + Ag _{21 ?n} ⁺ , (n=10, 9, 8, 7); Ag ₁₈ ²⁺ → Ag _n ⁺ + Ag _{18 ?n} ⁺ , (n=9, 8, 7, 6). It is found that the shell correction energy is comparable to or larger than the deformation energy of the liquid drop. Threshold energies for the fission events are calculated and compared with the experimental abundance spectra obtained by Katakuse et al. (1990). Correspondence between the calculated threshold energies with the shell corrections and the experimental abundance is very good, showing products from lower threshold fission channels yield more abundance. The threshold energies without the shell corrections are almost constant irrespective of the fission channels and cannot explain the experimental abundance. Abundance of some products are too small to be accounted for only by the threshold energies. The low abundance of those products may be explained by the presence of competing fission channels that have similar minimal energy paths. It is found in fission of Ag ₁₈ ²⁺ that the shell correction overwhelms the Coulomb energy and the fission channel to Ag₈ + Ag ₁₀ ²⁺ is preferred over the fission channel to Ag ₈ ⁺ + Ag ₁₀ ⁺ .     

The smoke ion source: a device for the generation of cluster ions via inert gas condensation

We report the development of an ion source for generating intense, continuous beams of both positive and negative cluster ions. This device is the result of the marriage of the inert gas condensation method with techniques for injecting electrons directly into expanding jets. In the preliminary studies described here, we have observed cluster ion size distributions ranging fromn=1?400 for Pb _n ⁺ and Pb _n ^? , and fromn=12?5700 for Li _n ^? .     

Cluster cations ejected from liquid metal ion source: alkali metals (Li,Na) and group IV elements (Si,Ge, Sn,Pb)

Cluster abundance of Li _n ⁺ (n≤19), Na _n ⁺ (n≤25), Si _n ^z+ (n≤8 forz=1, 3≤n≤7 forz=2), Ge _n ^z+ (n≤11 forz=1, 3≤n≤9 forz=2,n=4 forz=3), Sn _n ^z+ (n≤7 forz=1, 3≤n≤9 forz=2,n=4 forz=3) and Pb _n ^z+ (n≤6 forz=1, 5≤n≤7 forz=2) ejected from a liquid metal ion source has been investigated by mass spectrometry. The abundance spectra of alkali metal clusters showed distinct maxima and steps atn=3, 7, 9, 13 and 19 for Li, and atn=3, 5, 11, 13 and 19 for Na. Mass spectra of Si, Ge and Sn clusters were very similar each other, showing intensity drops aftern=4 and 6 (and alson=10 for Ge) for singly charged clusters. The magic numbers observed are discussed in terms of stability of charged clusters.     

Sputtered metal cluster ions: Unimolecular decomposition and collision induced fragmentation

Cluster ions are produced by ion bombardment of thick metal targets and mass selected in a Wien filter. The unimolecular decomposition of Al _n ⁺ , Cu _n ⁺ , Mo _n ⁺ , W _n ⁺ , and Pb _n ⁺ is investigated under UHV conditions. The time evolution of the decay allows a glimpse into the cluster formation/fragmentation process. Highly excited metal cluster ions decompose mainly by evaporating single neutral atoms with rates reaching 100%. The collision induced fragmentation (CIF) of stable mass selected metal cluster ions in a low pressure Ar and O₂ gas target will be compared to the unimolecular decay.     

Low-energy decay pathways of doubly charged charged silver clusters Ag n 2+ n = 9–24)

The low-energy dissociation channels of mass selected silver cluster ions Ag _n ²⁺ (n = 9–24) are determined by collision induced dissociation (CID) in a Penning trap. While all clusters of the size n ≥ 17 evaporate neutral monomers, most smaller clusters undergo asymmetric fission of the form Ag _n ²⁺ → Ag _n?3 ⁺ + Ag _{3} ⁺ . However, Ag ₁₅ ²⁺ and Ag ₁₁ ²⁺ emit monomers which indicates shell or odd-even effects. The observed fragmentation pathways are different from previous reports of measurements with sputtered Ag _n ²⁺ .     

A theoretical study of internal rearrangements and open channels for fission and mass exchanges in Xe n + clusters

In a previous work the equilibrium geometrical and electronic structures of Xe _n ⁺ clusters had been established using a non-empirical model hamiltonian. The same model is used to determine the energetic barriers between the nearly degenerate isomers; the movement of the neutral atoms around the Xe ₃ ⁺ or Xe ₄ ⁺ ionized linear cores are quite easy (ΔE?0.9 kcal/mole), the changes from a Xe ₃ ⁺ to a Xe ₄ ⁺ core are more difficult (ΔE?2.0 kcal/mole). The energetically possible fissions from a vertical photoionization \(Xe_n \xrightarrow{{h v}}Xe_n^{v + } \to Xe_p^ + + Xe_{n - p} \) forn≦19,p=1–9 and 12–14 and mass exchanges Xe _p ⁺ +Xe _q →Xe _p+m ⁺ +Xe _q?m (m=1,2,3) from relaxed Xe _p ⁺ clusters are given forp+m≦9 and 12–14 andq≦19. Surprisingly the reverse reactions are shown to occur for some values ofp andq. Numerous processes lead to Xe ₁₃ ⁺ , which is especially stable.     

FTMS studies of sputtered metal cluster ions (IV): size-selective effects in the chemistry of Fe n + with NH3 and Pd n + with D2 or C2H4

Fe _n ⁺ and Pd _n ⁺ clusters up ton=19 andn=25, respectively, are produced in an external ion source by sputtering of the respective metal foils with Xe⁺ primary ions at 20 keV. They are transferred to the ICR cell of a home-built Fourier transform mass spectrometer, where they are thermalized to nearly room temperature and stored for several tens of seconds. During this time, their reactions with a gas leaked in at low level are studied. Thus in the presence of ammonia, most Fe _n ⁺ clusters react by simply adsorbing intact NH₃ molecules. Only Fe ₄ ⁺ ions show dehydrogenation/adsorption to Fe₄(NH) _m ⁺ intermediates (m=1, 2) that in a complex scheme go on adsorbing complete NH₃ units. To clarify the reaction scheme, one has to isolate each species in the ion cell, which often requires the ejection of ions very close in mass. This led to the development of a special isolation technique that avoids the use of isotopically pure metal samples. Pd _n ⁺ cluster ions (n=2...9) dehydrogenate C₂H₄ in general to yield Pd _n (C₂H₂)⁺, yet Pd ₆ ⁺ appear totally unreactive. Towards D₂, Pd ₇ ⁺ ions seem inert, whereas Pd ₈ ⁺ adsorb up to two molecules.     

A photoionization study of the ion-neutral complexes CH3CH +CH 3 · CH2CH3] and CH3CH2CH+CH 3 · CH3 in the gas phase: Formation,H-transfer and C—C bond formation between partners,and channeling of energy into dissociation

Photoionization mass spectrometry was used to investigate the dynamics of ion-neutral complex-mediated dissociations of the n-pentane ion (1). Reinterpretation of previous data demonstrates that a fraction of ions 1 isomerizes to the 2-methylbutane ion (2) through the complex CH₃CH⁺CH ₃ ^· CH₂CH₃ (3), but not through CH₃CH⁺CH₂CH ₃ ^· CH₃ (4). The appearance energy for C₃Hin ₇ ⁺ formation from 1 is 66 kJ mol^?1 below that expected for the formation of n-C₃H ₇ ⁺ and just above that expected for formation of i-C₃H ₇ ⁺ . This demonstrates that the H shift that isomerizes C₃H ₇ ⁺ is synchronized with bond cleavage at the threshold for dissociation to that product. It is suggested that ions that contain n-alkyl chains generally dissociate directly to more stable rearranged carbenium ions. Ethane elimination from 3 is estimated to be about seven times more frequent than is C-C bond formation between the partners in that complex to form 2, which demonstrates a substantial preference in 3 for H abstraction over C-C bond formation. In 1 → CH₃CH⁺CH₂CH₃ + CH₃ by direct cleavage of the C1–C2 bond, the fragments part rapidly enough to prevent any reaction between them. However, 1 → 2 → 4 → C4H ₈ ⁺ + CH₄ occurs in this same energy range. Thus some of the potential energy made available by the isomerization of n-C₄H₉ in 1 is specifically channeled into the coordinate for dissociation. In contrast, analogous formation of 3 by 1 → 3 is predominantly followed by reaction between the electrostatically bound partners.     

Multi-reference configuration interaction calculations on the systems Xe 2 + and Xe 3 +

Potential curves for the ground (²Σ _u ⁺ ) and the three lowest excited states of the Xe ₂ ⁺ dimer ion (²Π _g ,²Π _u ,²Σ _g ⁺ ) have been calculated using pseudopotentials in MRD-CI (multi-reference single anddouble excitationconfigurationinteraction) calculations. Spin-orbit interaction — leading to the six states 1.(1/2) _u , 1.(3/2) _g , 1.(3/2) _u , 1.(1/2) _g , 2.(1/2) _u , 2.(1/2) _g — has been taken into account using a semiempirical technique [1]. Subsequently, starting with a relaxed Xe ₂ ⁺ ion in its ground state, the potential energy surface for the system Xe-Xe ₂ ⁺ was studied. We found that the collinear approach of the Xe atom leads to the most stable geometry. This is a linear symmetric molecule with bond lengths of 6.38 bohr. In the bestT-shaped structure, the Xe atom is 7.83 bohr away from the midpoint of the Xe ₂ ⁺ (r=6.1 bohr) dimer. The calculated binding energy of 0.25 eV for the equilibrium structure of the Xe ₃ ⁺ molecule (i.e. the linear symmetric geometry), is in very good agreement with experimental results of 0.27 ± 0.02 eV [2].     

Multiple H 3 + fragment production in single collision of fast H n + clusters with He atoms

The production of H ₃ ⁺ ions resulting from single collisions of mass-selected ionic hydrogen clusters, H _n ⁺ (n=9, 25, 31), with helium at high velocity (1.55 times the Bohr velocity) has been studied. A strong double H ₃ ⁺ ion production resulting from one incident cluster is observed. Moreover, evidence for a triple H ₃ ⁺ fragment production is presented forn=25 and 31. Thus, in this energy range, the collision gives rise to multifragmentation processes. The formation of H ₃ ⁺ ions takes place in the fragmentation of the multicharged cluster resulting from the collision.     

Reactivity of positively charged cobalt cluster ions with CH4, N2, H2, C2H4, and C2H2

Reactivity of positively charged cobalt cluster ions (Co _n ⁺ ,n=2?22), produce by laser vaporization, with various gas samples (CH₄, N₂, H₂, C₂H₄, and C₂H₂) were systematically investigated by using a fast-flow reactor. The reactivity of Co _n ⁺ with the various gas samples is qualitatively consistent with the adsorption rate of the gas to cobalt metal surfaces. Co _n ⁺ highly reacts with C₂H₂ as characterized by the adsorption rate to metal surfaces, and it indicates no size dependence. In contrast, the reactions of Co _n ⁺ with the other gas samples indicate a similar cluster size dependence; atn=4, 5, and 10?15, Co _n ⁺ highly reacts. The difference can be explained by the amount of the activation energy for chemisorption reaction. Compared with neutral cobalt clusters, the size dependence is almost similar except for Co ₄ ⁺ and Co ₅ ⁺ . The reactivity enhancement of Co ₄ ⁺ and Co ₅ ⁺ indicates that the cobalt cluster ions are presumed to have an active site for chemisorption atn=4 and 5, induced by the influence of positive charge.     

Electronic structures and stabilities of GeC n and Ge2C n in Hückel theory

Some recent results about Ge _p C _n ⁺ ions (p=1, 2;n < 6) produced in laser microprobe mass analyser experiments (LAMMA) show very marked alternations in the emission intensities I(Ge _p C _n ⁺ ) as a function of then andp parities. I(Ge _p C _n ⁺ ) are maxima for evenn. Thus, intensity maxima occur when the total atom numberm of the aggregates is odd for GeC _n ⁺ (m=n+1) and even for Ge₂C _n ⁺ (m=n+2). As a result, GeC _n ⁺ ions seem to behave as C _m ⁺ ions, whereas the behaviour of Ge₂C _n ⁺ ions is quite similar to that of Ge _p ⁺ ions formed in SIMS or vaporization experiments on pure germanium. It is well known (correspondence rule) that the parity effect in the emissions corresponds to alternations in the ion stabilities. These results are analysed from a model built in Hückel approximation with hybridization. Forp=1, the clusters are assumed to be insp hybridization as for C _m ⁺ ions, hence with linear shapes, and forp=2, they would rather be insp ² orsp ³ hybridization as for Ge _p ⁺ ions. Relative stabilities and distributions of the energy levels of the aggregates are then calculated. The relative stabilities given for Ge _p C _n ⁺ by this model show maxima for evenn as in experiments, and we have thus a good agreement between our calculation results and the experimental data. Moreover, we found that Ge₂C _n ⁺ would rather be insp ³ hybridization, that is under three dimensional shapes.     

Stability of Au 2 2+ : metastability through an excited state?

We discuss the stability of doubly charged Auclusters. From a calculation using semi-empirical linear combination of atomic-orbitals (LCAO) method, we conclude that Au ₂ ²⁺ in an excited state (³Σ _u ⁺ or¹Σ _u ⁺ ) is metastable with an energy barrier of about 0.3 eV. In the ground state (¹Σ _g ⁺ ) Au ₂ ²⁺ is unstable, except for small values of Δ(=ε _s ?ε _d ) (difference between thes andd atomic energy levels of Au), when a very shallow minimum appears in the binding energy curve. These results are critically discussed and compared with those obtained by different calculations.     

Fragmentation by electron impact ionization and intracluster reactions of size selected (N2H4) n and (OCS) n clusters

The hydrogen-bonded (N₂H₄) _n clusters and the van der Waals (OCS) _n clusters are size selected in a scattering experiment with a He beam up to the cluster sizen=6. By measuring the angular distributions of the scattered clusters the complete fragmentation pattern of electron impact ionization is obtained. For Hydrazine the two main fragment masses are the protonated species (N₂H₄) _n?1H⁺ and with somewhat weaker intensities also the nominal ion mass (N₂H₄) _n ⁺ . The largest intensity is observed for the monomer ion N₂H ₄ ⁺ to which clusters up ton=5 fragment. For carbonylsulfide, completely different results are obtained. Aside from the fragments of the OCS monomer and the van der Waals cluster fragments (OCS) ₂ ⁺ and (OCS) ₃ ⁺ signals at mass S ₂ ⁺ , S ₃ ⁺ and S₂OCS⁺ are detected. This indicates a fast chemical reaction in the cluster according to: S + OCS → CO + S₂ which occurs for clusters of sizen ≥ 2. Peaks at S ₃ ⁺ and S₂OCS⁺ are seen for the first time forn ≥ 5 according to a further reaction of S₂ in the cluster.     

Fragmentation of doubly charged ammonia cations NH 3 ++ studied by the photoion-photoion coincidence (PIPICO) method

Doubly charged NH ₃ ⁺⁺ cations were produced by double photoionization of neutral ammonia molecules by using the synchrotron radiation from ACO as a photon source of variable energy in the 35–49 eV energy range. The fragmentation of NH ₃ ⁺⁺ was studied by the photoion-photoion coincidence (PIPICO) method. NH ₃ ⁺⁺ cations were produced in the \(\tilde X^1 \) A ₁ and \(\tilde B^1 \) electronic states of which the onset energies were measured at, respectively, 35.4±0.5 eV and 44.5±0.5 eV. It was shown that the NH ₃ ⁺⁺ ions, initially produced in their \(\tilde X^1 \) A ₁ state, rapidly dissociate (in less than 50 ns), into NH ₂ ⁺ + H⁺. Furthermore, the comparison with results obtained by other methods indicates that NH ₃ ⁺⁺ ions can either be long-lived (τ>10 µs) or slowly dissociating (1 µs<τ<10 µs) or rapidly dissociating (τ<50 ns), depending on their geometry and/or internal energy in their \(\tilde X^1 \) E A ₁ electronic state.