The influence of shells,electron thermodynamics,and evaporation on the abundance spectra of large sodium metal clusters

Measurements of the mass abundance spectra of sodium clusters containing up to 600 atoms are presented. The clusters are produced in a seeded supersonic expansion of Ar or Kr gas, and the spectra are obtained by a time-of-flight technique. The sawtooth features in the spectra are interpreted as evidence of a regular spherical shell structure with magic numbers,N ₀, scaling approximately with the cube root of the number of sodium atoms. Altogether twelve shell closings are observed,N ₀=2, 8, 20, 40, 58, 92, 138, 196, 260, 344, 440 and 558. There is also a pronounced odd-even staggering all the way up toN=70. The experimentally observed intensity changes for the clusters around the magic numbers are discussed in terms of the electronic free energy,F(N), calculated at finite temperature, and the second differences of the free energy Δ₂ F(N)=F(N?1)?2F(N)+F(N+1). The processes behind the non-uniform abundance distributions, and the thermodynamics of finite electron systems with non-uniform level spacings are discussed on this basis.     

Modified Nilsson model for large sodium clusters

We propose a modified Nilsson model for spheroidal sodium clusters and investigate the modification of shell structure by deformation for sizes up toN=850. For spherical clusters, our potential is fitted to the single-particle spectra obtained from microscopically selfconsistent Kohn-Sham calculations using the jellium model and the local density approximation. Employing Strutinsky's shell-correction method, the surface energy of the jellium model is renormalized to its experimental value. We find good agreement between our theoretically predicted deformed magic numbers and the experimentally observed ones extracted from recent sodium mass abundance spectra.     

Semiclassical variational calculation of liquid-drop model coefficients for metal clusters

We report on semiclassical density variational calculations for spherical alkali metal clusters in the jellium model. We derive liquid-drop model expansions for total energy, ionisation potential and electron affinity and test the coefficients numerically for clusters with up toN=10⁵ atoms. From the limitN→∞, we obtain excellent agreement with surface tensions and work functions evaluated for an infinite plane metal surface.     

Stability and structure of singly-charged xenon-argon clusters [Xe1Arn−1]+,n=3–27

Monte-Carlo calculations have been performed for positively charged xenon-argon clusters in the temperature range between 10K and 40K for cluster sizes up ton=27. The argon-argon interaction potential stems from empirical data, the Xe⁺-Ar potential is determined by ab initio MRD-CI calculations and a semi-empirical treatment of spin-orbit effects. Special stability is found for cluster sizesn=10, 13, 19 and less pronounced forn=23 and 25 fairly independent of the temperature. The geometrical structure of the clusters are given and the construction principle is discussed in light of the interactions among neutral argon atoms and the xenon ion — argon interaction. Comparison with measured mass spectra for mixed rare-gas clusters and [Xe_n]⁺ clusters is made and shows a consistent picture for the building principle.     

Resonances in helium atoms associated with theN=4 andN=5 He+ thresholds

Some doubly excited autoionising states of helium atoms converging on theN=4 andN=5 He⁺ thresholds are calculated by use of a method of complex-coordinates. States withL≧2 and with parities of (?1) ^L and (?1) ^L+1 are calculated by using products of Slater-orbital type wave functions with expansion lengths up to 319 terms. Resonance parameters (both resonance energy and autoinoisation width) are calculated for states with angular momentum up toL=7 forN=4 resonances, andL=8 forN=5 resonances.     

Molecules of jellium dimers

A simple tight-binding-like model of the electronic structure of simple metal clusters is presented which relies on the special stability of the first shell closures atN _el=2 andN _el=8. The wavefunctions, energy levels, and ground state deformations of the “ultimate jellium model”, which is based on a full Kohn-Sham treatment of the electrons, can be explained relying on a simple geometrical growth pattern complemented by an extremely simplified Hamiltonian matrix. The bulk and surface limits of the model also yield reasonable results.     

Triaxial shapes of sodium clusters

A modified Nilsson-Clemenger model is combined with Strutinsky's shell correction method. For spherical clusters, the model potential is fitted to the single-particle spectra obtained from selfconsistent Kohn-Sham calculations. The deformation energy surfaces of sodium clusters with sizes of up toN=270 atoms are calculated for a combination of triaxial, quadrupole and hexadecapole deformations. The ground state shapes and energies are determined by simultaneous minimization with respect to the three shape parameters. A significant fraction of the clusters is predicted to be triaxial. The deviations from the axial shape do not generate any systematic odd-even staggering of the binding energies.     

A DIM model for homogeneous noble gas ionic clusters

The method of diatomics-in-molecules (DIM) is applied to the calculation of the energy of the homogeneous noble-gas ionic clusters Ar _n ⁺ and Xe _n ⁺ forn=3, 4, ..., 22. The trimers are stable symmetric linear molecules exhibiting chemical binding, a result in agreement both with ab initio calculations and with previous DIM work. The clusters up ton=13 are best described as a trimer ion surrounded by neutrals, whereby the charge distribution changes slightly with increasingn. Both noble gases exhibit a special stability associated with the completion of the first shell of neutral atoms atn=13. Asn increases from 13 to 22, there is a greater delocalization of the positive charge, the central ion tending to become a linear tetramer, symmetric for Xe and unsymmetric for Ar. Energies of the excited electronic states are reported and the possibility of developing simpler DIM models for the clusters and for mixed noble gases is discussed.     

Multiple-electron processes in 1.4 MeV/u ion-atom collisions

Simultaneous multiple-electron capture and multiple ionization is studied for collisions of highly stripped ionsA ^q+ with rare gas atomsB=He, Ne, Ar, Kr and Xe. At a specific energy of 1.4 MeV/u coincidence measurements were conducted distinguishing between pure ionization, stripping and capture of up to four electrons by projectiles in charge states fromq=6 up toq=48. The coincident charge-state distributions of target recoil ionsB ⁱ⁺ range fromi=1 up toi=19 (in few cases). For highly charged projectiles the relative fractions of recoil ions for concomitant electron capture and ionization are found to be nearly independent of projectile charge or species. Average charge states 〈i〉 of the recoil ions produced by loss respectively capture ofk electrons (k=?2, ?1, 0, 1, 2, 3, 4) from/into the projectile ion were determined. Their systematic dependences onk, on the target atomic number and the projectile ion charge are discussed. A calculation of partial cross sections for multi-electron collision processes in the He target atoms using unitarized first order perturbation theory for impact parameter dependent probabilities and an independent-electron picture is presented and discussed on the basis of the experimental data.     

Hyperfine structure of N2 (B 3Π g andA 3Σ u + ) from LIF measurements on a beam of metastable N2 molecules

Crossing an intense beam of nitrogen molecules in the metastable N₂(A) state with the beam from a CW dye laser, laser-induced fluorescence was observed in the first positive system of N₂,B ³Π _g ?A ³Σ _u ⁺ . About 300 lines of the (10, 6) band were studied at sub-Doppler resolution (15 MHz FWHM). From the well-resolved hyperfine structure of the lines, the hyperfine splittings of both the upper and the lower state were derived for a range of rotational quantum numbers up toJ=12. Using multiple independent determinations of each splitting via lines belonging to different branches, the hfs could be measured with an accuracy of about 2 MHz. Fitting known theoretical expressions for the hyperfine energies to the data, the following nuclear coupling constants were obtained (in MHz): For theA state,v=6: α=12.86, β=?11.40,e ² q ₀ Q=?2.5. For theB state,v=10:K ₁₁=86.46,D ₁₁=12.67,D _1?1=?44.64,G ₁₁=69.18,Q ₁₁=0.64,Q _1?1=1.38. The hfs is mostly due to nuclear magnetic dipole interactions. For theA state the results are essentially in agreement with hfs constants derived from RF resonance experiments, but are superior as regards the data fit over the entireJ range covered. For theB state, the results are new and are interpreted in terms of a simple LCAO model. The Fermi contact coupling constant is in good agreement with unpublished SCF results by V. Staemmler. The striking dependences of the hfs splitting on the fine structure levels, Λ sublevels and onJ are explained both quantitatively and in terms of vector models.     

Spectroscopy of free sodium-ammonia clusters

Neutral sodium ammonia clusters are formed in apickup source by injecting a beam of sodium atoms into the expansion zone of a pulsed nozzle beam of neat ammonia gas. The clusters are studied by one-photon ionisation in the range of 266 nm to 500 nm with pulsed lasers and Time-of-Flight mass spectroscopy. Na(NH₃) _n cluster ion signals up ton=35 are observed. The ionisation potentials of complexes up ton=9 are reported.     

Crystal structure and conformation of N,N′-bis (3,5-dichlorosalicylidene)-2-hydroxy 1,3 diamino-2-propan

N,N′-bis(3,5-dichlorosalicylidene)-2-hydroxy-1,3-diamino-2-propan (C₁₇H₁₄Cl₄N₂O₃) was synthesized and its crystal structure determined. It crystallizes in the monoclinic space group, C2/c, with a=29.734(8), b=4.541(1), c=14.694(2) Å, β=115.85(2), R(F²)=0.048 for 1704 independent reflections. The title compound has a twofold axis passing through the central C9 atom. The intramolecular hydrogen bond occurs between the pairs of atoms N1 and O1 [2.648(5) Å] and the hydrogen atom is essentially being bonded to the nitrogen atom. There is no intermolecular proximity between molecules. Conformations of the title compound were investigated by semi-empirical quantum mechanical AM1 calculations. The optimized geometry of the molecular structure corresponding to the non-planar conformation is the most stable conformation in the theoretical calculations. The results strongly indicate that the minimum energy conformation is primarily determined by non-bonded steric interactions.     

Semiclassical description of multiple electron capture and ionization in fast bare nucleus-rare gas collisions

Multiple electron capture plus ionization processes inX ⁱ⁺-Ne collisions (i=6, 12, 20) in the energy regime from 50 keV/amu up to several MeV/amu are studied within a semiclassical quantum statistical (?=0) independent particle model. Good agreement is found with existing experimental data for the production of recoil ions with charges up toq=8.     

Emission cross sections for fully stripped carbon colliding with atomic hydrogen

In the impact velocity range of 0.2–0.6 a.u. we have measured line emission cross sections in the vuv and visible spectral region for collisions of C⁶⁺ with atomic hydrogen. The electron capture goes predominantly into then=4 shell and to a lesser extent into then=5 shell. For the dominant lines there is a good agreement with the molecular, the extended atomic and the unified atomic-molecular orbital calculations of respectively Green et al. [8], Fritsch and Lin [9], and Kimura and Lin [10]. However for transitions originating from then=5 level the measurements strongly support the molecular orbital calculations. Furthermore there are considerable differences between measured and calculated intensities for the lines of non-dominantly populated high-n states (n=7 and 8) and atomic orbital and UDWA calculations.     

Structural characterization of <Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>′-bis(2-methoxyethyl) -4,5-bis(2,4,6-trimethylphenyl)imidazolinium hexafluorophosphate

The crystal and molecular structure of the N,N′-bis(2-methoxyethyl)-4,5-bis(2,4,6-trimethylphenyl)- imidazolinium hexafluorophosphate, which is the first example of 1,3- and 4,5-disubstituted imidazolinium salts, have been determined and characterized by X-ray single crystal diffraction technique,¹H, ¹³C, ³¹P and ¹⁹F NMR spectroscopy. The compound, C₂₇H₃₉N₂O₂ ⁺·PF₆ ^?, crystallizes in the orthorhombic space group Pba2 with a = 15.8139(4) Å, b = 22.9346(7) Å, c = 8.069(3) Å. Two charge-assisted C–H\(\cdots\)F type crystal packing interactions between the imidazolinium C–H bonds and the F atoms of hexafluorophosphate counteranions build up zigzag chains along a-axis of the unit cell and indicate that the C–H bonds of the imidazolinium ring are also polarized. In addition, the title salt was modeled by DFT calculations in order to verify charge transfer mechanism observed in its imidazolinium ring.     

Isomers of Disulfur Dinitride,S2N2

UV photolysis (λ=248 or 255 nm) of cyclic S₂N₂ isolated in solid argon matrices yields two open‐shell S₂N₂ isomers, trans SNSN (³A′′) and cis SNSN (³A′′), as well as a closed‐shell C_2v dimer (SN)₂ (¹A₁). These novel isomers have been characterized by their IR spectra and mutual photo‐interconversion reactions. Quantum chemical calculations support the experimental results and also provide insight into the complex potential energy surface of S₂N₂.     

Experimental and theoretical study of the dissociation enthalpy of the N–O bond on 2-hydroxypyridine N-oxide: theoretical analysis of the energetics of the N–O bond for hydroxypyrydine N-oxide isomers

The standard (p^∘=0.1 MPa) molar enthalpy of formation of crystalline 2-hydroxypyridine N-oxide was measured, at T=298.15 K, by static bomb calorimetry and the standard molar enthalpy of sublimation, at T=298.15 K, was obtained using Calvet microcalorimetry. These values were used to derive the standard molar enthalpy of formation of 2-hydroxypyridine N-oxide in gaseous phase, and to evaluate the dissociation enthalpy of the N–O bond. Additionally, high-level density functional theory calculations using the B3LYP hybrid exchange-correlation energy functional have been performed for the three isomers of hydroxypyridine N-oxide in order to confirm the experimental trend for the dissociation enthalpy of the (N–O) bond.     

Theoretical study of the electronic spectrum of diimide by AB initio methods

A series of ab initio calculations is reported for the ground and low-lying valence and Rydberg states of diimide N₂H₂. Symmetric bending potential curves for both the cis and trans forms of this system have been obtained at the SCF level of treatment. In addition Cl calculations have been carried out for the trans-diimide ground state equilibrium nuclear conformation, using a configuration selection procedure described elsewhere; an associated energy extrapolation scheme is also employed which enables the effective solution of secular equations with orders of up to 40000. The ensuing Cl wavefunctions are interpreted in the discussion and the corresponding calculated energy differences between the various electronic states are compared with experimental transition energy results for both diimide and for related systems such as trans-azomethane. A more detailed analysis of the observed absorption bands in the ¹B_g-X¹A_g transition in N₂H₂ is also given, making use of calculated potential curve data as well as the pertinent Cl vertical energy difference. The dipole-forbiddenness of the excitation process is thereupon concluded to result in a distinct non-verticality for this electronic band system, causing its absorption maximum to occur at a position some 0.6 eV to the blue of the so-called vertical transition, i.e., that for which maximum vibrational overlap is obtained.