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.     

Resonant and Off-resonance ionization of laser-excited sodium vapor

Electrons produced in a sodium effusive beam irradiated by pulsed laser light have been energy-analyzed. For resonant excitation of the atoms to the 3p state, we have studied associative ionization of excited Na(3p) (AI), Penning ionization (PI) and photoionization of highly-excited Na(n l),n l=3d, 4p, 5s, 4d/4f, by measurements of electron energy spectra. Our interpretation of the spectra is supported by a numerical analysis of the data which leads to estimates of the cross sections compatible with values previously measured in other experiments. Off-resonance ionization is considered at a particular wavelength. It is presumed to involve laser-excited dimers Na ₂ ^** . Spectra show that highly-excited atoms are produced by photodissociation of Na ₂ ^** or from Na ₂ ^** -Na collisional energy transfer, and that these atoms support the dominant off-resonance ionization channel in our laser excitation conditions.     

Alignment and orientation effects in resonant charge exchange from laser excited Na*(3p)

A collisional alignment and orientation study with planar symmetry is described, determining the complete density matrix for resonant charge transfer from laser excited atoms. Results are reported for the Na⁺+Na*(3p) system over the collision energy rangeE _c.m.=50?100 eV. We communicate the optimal alignment angle γ and linear polarisationP _l ⁺ of the charge cloud as well as its relative height ρ₀₀ and the angular momentumL _⊥ ⁺ transferred in the collision as a function of the scattering angle. For preparation of the sodium 3p orbital in the scattering plane (positive reflection symmetry) we observe that at small reduced scattering angles (<20 eV°) the preparation of apσ at large internuclear distances contributes most to the scattering intensity whereas at larger reduced scattering angles (>60 eV°) apπ⁺ preparation is more important. In contrast, preparation of thepπ^? orbital (perpendicular to the scattering plane) is large at small and vanishes at larger scattering angles. We conclude that orbital following cannot be assumed in this resonant charge transfer process. The angular momentum transfer is observed to be small, indicating only little coherence in the process, but shows nevertheless an interesting behaviour as a function of scattering angle.     

The Jellium—Atom quasimolecular model for the investigation of charge transfer in alkali-cluster-ion/alkali-atom interactions: the Na 19 + /Na system

The potential energy curves of the Na ₁₉ ⁺ /Na quasimolecular (Jellium—Atom)⁺ system determined by Guissani and Sidis [3] are used to calculate the vibrational energy levels of a sodium atom stuck to a Na ₁₉ ⁺ Jellium-like cluster and to determine excitation and charge transfer cross sections in Na ₁₉ ⁺ + Na collisions in the 0.2 10⁷ cm/s < v < 1.5 10⁷ cm/s velocity range.     

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.     

Observations and spectral simulations of the7Li2 21 Σ u + →X 1 Σ g + transition

The⁷Li₂ 2¹ Σ _u ⁺ →X ¹ Σ _g ⁺ electronic transition has a bound-bound and a bound-free part due to the double minimum nature of the upper 2¹ Σ _u ⁺ state. We have studied this transition both experimentally and by performing spectral simulations. When inner well was excited the bound-free part at 4525 Å was observed due to the collisions between Li ₂ ^* and argon. We found that when levels above the barrier are excited the bound-free emission is strongly affected by collisional relaxation of Li ₂ ^* by Li atoms. Conditions for the observation of the bound-free part are discussed.     

Reaction dynamics of Na n + in collision with molecular oxygen

Reaction dynamics of sodium cluster ions, Na _n ⁺ (n = 2–9), in collision with molecular oxygen, O₂ was investigated by measuring the absolute dissociation cross sections and the branching fractions by using a tandem mass spectrometer equipped with several octapole ion guides. The mass spectrum of the product ions show that the dominant reaction channels are production of oxide ions, Na_kO_i (i =1, 2), and intact ions, Na _p ⁺ (p < n). With increase in the collision energy, the cross section for the production of the oxide ions decreased, while that for the production of the intact ions increased. The collision-energy dependences of the cross section for the oxide formation reveals that electron harpooning from the molecule to Na _n ⁺ preludes the oxideion formation. On the other hand, the collision-energy dependences of the cross sections for the intact ion formation is explained by a hard-sphere-collision model similar to the collisional dissociation of Na _n ⁺ by rare-gas impact.     

Analytical photoion spectroscopy applied to dissociative single and double photoionization of diatomic molecules (H2, N2, O2, CO,and NO)

This work reports the principle, advantage, and limitations of analytical photoion spectroscopy which has been applied to dissociative photoionization processes for diatomic molecules such as H₂, N₂, CO, and NO. Characteristic features observed in the differential photoion spectra are summarized with a focus on (pre)dissociation of(i) multielectron excitation states commonly observed in the inner valence regions,(ii) shape resonances, and(iii) doubly charged parent ions. Possible origins for negative peaks in the differential spectra are discussed. This spectroscopy is applied to the reported photoion branching ratios for D₂ (and H₂ at high energies). The main findings are as follows: (1) The direct dissociation of theX ²Σ _g ⁺ (1sσ _g ) state of D ₂ ⁺ , the two-electron excited state¹Σ _u ⁺ (2pσ _u 2sσ _g ) of D₂, and the²Σ _u ⁺ (2pσ _u ) state of D ₂ ⁺ appear clearly in the differential spectrum, as previously observed for H₂. (2) Decay of H ₂ ⁺ (D ₂ ⁺ ) to H⁺ (D⁺) above 38 eV is due to the direct dissociation of highly excited states of H ₂ ⁺ (D ₂ ⁺ ) such as the²Σ _g ⁺ (2sσ _g ) and high-lying Rydberg states converging on H ₂ ²⁺ (D ₂ ²⁺ ). (3) In the ionization continuum of H ₂ ²⁺ (D ₂ ²⁺ ) peculiar dissociation pathways are observed. The differential photoion spectra for O₂ derived from the reported photoion branching ratios are also presented. The (pre)dissociation of theb ⁴Σ _g ^? ,B ²Σ _g ^? , III²Π _u ,²Σ _u ^? , and^2,4Σ _g ^? states of O ₂ ⁺ appears as the corresponding positive values in the spectra in accord with previous observations. Some other dissociation pathways possibly contributing to the spectra are discussed including dissociative double ionization.     

Octacoordination of the nitrogen atom in M4NO 4 + systems (M = Li, Na, K)

The electronic and geometric structures of M₄NO ₄ ⁺ compounds (M = Li, Na, K) in classical and nonclassical isomeric forms were studied by the ab initio (MP2(full)/6-311+G**) and density functional theory (B3LYP/6-311+G**) methods. For all M atoms, structurally stable nonclassical isomers were found with octacoordinated nitrogen atoms and tetracoordinated oxygen atoms. For Li₄NO ₄ ⁺ , the classical structure with the tetracoordinated nitrogen atom is energetically more stable, whereas nonclassical structures with the octacoordinated nitrogen center are more stable for Na₄NO ₄ ⁺ and K₄NO ₄ ⁺ .     

The lifetime of the (μHe) 2S + metastable state in helium gas

The ion-clustering mechanism of the quenching of the metastable 2S-state of the muonic helium ion (μHe) _2S ⁺ in gaseous helium is studied on the basis of quantum-chemical calculations of clusters He _n (μHe)⁺. It is shown that the quenching rates do not depend on the cluster ordern atn ≥ 2. In the helium gas at the pressure 0.1 ?p(atm) ? 10 the quenching of (μHe) _2S ⁺ proceeds, mainly, at the vibrationally excited levels of He(μHe) _2S ⁺ cluster, while atp ? 10 atm, at the ground vibrational state of the cluster He₂(μHe) _2S ⁺ . Atp ≥0.1 atm the calculated quenching rates agree with the recent experimental data.     

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.     

On the stability of Pb n m+ -clusters

The stability of multiply charged Pb _n ^m+ -clusters (n ≤ 3;m=0, 1, 2) was studied by solving exactly for the valencep-electrons a many body Hubbard-like Hamiltonian with intra- and interatomic Coulomb interactions. Particularly we obtain that Pb ₃ ²⁺ has a metastable ground state, in which Pb ₃ ²⁺ has isosceles shape (bond lengthR=3.2 Å, bond angle θ=124°) and a positive binding energyE _B =3.4 eV. The activation barrier against dissociation into Pb ₂ ⁺ + Pb⁺ is 0.13 eV, yielding a very long lifetime. This is in agreement with recent experiments [1] in which the lifetime of Pb ₃ ²⁺ was determined to be at least 10^?6 s. Comparison with self consistent Hartree-Fock calculations shows that the metastability of Pb ₃ ²⁺ is due to electronic correlations within the paramagnetic ground state.     

The two-centre shell model for the fission of metallic clusters

We calculate potential energies for charged and neutral jellium clusters which fragment in two pieces, in the framework of the liquid drop model plus Strutinsky shell corrections obtained from the two-centre harmonic oscillator. We consider the symmetric fragmentation of Na ₄ ⁺ ₂ ⁺ , Na ₁ ⁺ ₈ ⁺ , and Na₃₈. Good agreement is found with results obtained by self-consistent methods, which are much more involved.     

Primary processes in the thiacyanine dimer-photosensitized reduction of p-nitroacetophenone in water by

Primary processes in the reduction of p-nitroacetophenone (p-NAP) by ascorbic acid (AA) in water photosensitized by thiacyanine dimers M ₂ ^2? have been considered. For M ₂ ^2? , the quantum yields of fluorescence and intersystem crossing to the triplet state (M ₂ ^2? )_T increases in comparison to the monomers M^?. The dimers (M ₂ ^2? )_T enter into the reactions of both one-electron photoreduction by ascorbic acid to give AA^+· and M ₂ ^3? and one-electron photooxidation by p-nitroacetophenone to give p-NAP^?· and the dimeric radical anion M ₂ ^? which dissociates to M^? and M^· within 25–30 μs. The primary oxidative or reductive photosensitization in the ternary systems containing (M ₂ ^2? )_T, p-NAP, and AA affords p-NAP^?· and AA^+·.     

Dipole excitation of Na clusters with a non-local energy density functional

The elementary dipole excitations of the ionized clusters Na ₉ ⁺ , Na ₂₁ ⁺ and Na ₄₁ ⁺ are investigated by solving the equations of the Random-Phase Approximation. The ground and excited states are described using the jellium model for the ionic background and a non-local energy density functional for the valence electrons. Non-local effects are specifically analyzed. The excitation energies thus obtained approach better than those of the Local Density Approximation both the full Hartree-Fock and the experimental results.     

On ionisation induced unimolecular dissociation of sodium clusters

Fragmentation of sodium cluster ions (Na _x ⁺ ,x<42) was studied via photoionisation of neutral precursors. Expansions of metal vapor out of cylindrical and conical nozzles yielded supersonic beams with differing cluster compositions. Measurements of photoionisation efficiency curves in the 3–6 eV range for both types of expansion allow quantitative separation of direct ionisation and unimolecular dissociation contributions to specific ion signals. Data for Na ₈ ⁺ and Na ₇ ⁺ are analysed to yield lower limits on bond energies. Results obtained for larger clusters are also discussed.     

Formation of helium cluster ions HHe x + (x≦14) and H3He x + (x≦13) in a very low temperature drift tube

The formation of cluster ions when hydrogen molecular ions H ₂ ⁺ and H ₃ ⁺ are injected into a drift tube filled with helium gas at 4.4 K has been investigated. When H ₂ ⁺ ions are injected, cluster ions HHe _x ⁺ (x≦14) are produced. No production of H₂He _x ⁺ ions is observed. When H ₃ ⁺ ions are injected, cluster ions HHe _x ⁺ (x≦14) are produced as well as H₃He _x ⁺ (x≦13), and very small signals corresponding to H₂He _x ⁺ (3≦x≦10) are observed. Information on the stability of HHe _x ⁺ and H₃He _x ⁺ is derived from the drift field dependence of the cluster size distributions. The cluster sizex=13 is found to be a magic number for HHe _x ⁺ , and for H₃He _x ⁺ ,x=10 and 11.     

Analysis of optical absorption spectra of transition metal cluster ions by the spin-polarized DV-Xα method

Optical absorption spectra of cobalt cluster ions, Co _n ⁺ , and vanadium cluster ions, V _n ⁺ , were analyzed by a theoretical calculation based on the spin-polarized DV-Xα method, and their electronic and geometric structures were obtained. Relative absorption cross section associated with each electronic transition was calculated; the calculation enables a qualitative comparison of calculated spectrum with a measured one not only in its transition energy but also in its intensity profile. This analysis shows that Co ₄ ⁺ , Co ₃ ⁺ , and V ₄ ⁺ have, respectively, a tetrahedral structure with a bond distance of 2.00Å, an equilateral triangle with a bond distance of 2.30Å, and a distorted tetrahedral structure with five bonds having a distance of 2.34 Å and one of 2.89Å. The differences in the population between majority and minority spins (spin-difference) evaluated from the electronic structure thus obtained were 2.0, 1.7, and zero per atom in Co ₃ ⁺ , Co ₄ ⁺ , and V ₄ ⁺ , respectively. These spin differences indicate a ferromagnetic and an antiferromagnetic spin-coupling in the cobalt and vanadium cluster ions, respectively.     

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.