Finite element investigation of the ground states of the helium trimers 4He3 and 4He2–3He

A three‐dimensional finite element method is applied to the ground states of the symmetric and asymmetric atomic helium trimers ⁴He₃ and ⁴He₂–³He. Three different He–He interaction potentials of hard‐core nature were studied. Two extrapolation procedures based on the convergence properties of the finite element method are investigated. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Collisional quenching of rotations in lithium dimers by ultracold helium: the Li2(a3Sigma u+) and Li2+(X2Sigma g+) targets

Quantum coupled-channel scattering calculations have been carried out at ultralow energies (down to 10(-5) K) for rotational quenching of ionic and spin-stretched states of the lithium dimer in collision with He atoms. Marked cross section differences, to be related to changes in their interactions with He, have been observed with respect to the singlet case while little changes in the collisional behavior are seen to occur upon ionization when the spin-stretched target is considered. Both effects originate from an interplay of structural and dynamical features of the colliding partners which are analyzed in detail.     

Ab initio potential-energy surfaces of O2(X3Sigmag -, a1Deltag, b1Sigmag +) +O2 (X3Sigmag -, a1Deltag, b1Sigmag +): mechanism of quenching of O2 (a 1Deltag)

Ab initio computational studies were carried out in order to explore the possible mechanisms of quenching of O(2)(a (1)Delta(g)) by O(2)(X (3)Sigma(g) (-)): the self-quenching of O(2)(a (1)Delta(g)) and other energy-transfer processes involving two O(2) molecules. All eighteen states arising from two O(2) molecules in the X (3)Sigma(g) (-), a (1)Delta(g), and b (1)Sigma(g) (+) states are considered. After scans at the state-averaged complete active space self-consistent field method to identify possible regions of crossing between states belonging to different asymptotes, complete active state second-order perturbation theory high-symmetry optimization and low-symmetry scans established that four different minima on the seams of crossing (MSXs), arising between the a+a manifold and the X+b manifold and responsible for self-quenching: O(2)(a (1)Delta(g))+O(2)(a (1)Delta(g))-->O(2)(X (3)Sigma(g) (-))+O(2)(b (1)Sigma(g) (+)), have coplanar C(2h) or C(2v) symmetries and are only 0.45 eV barrier relative to the a+a asymptote and energetically easily accessible. The rate constant for this process was estimated based on the Landau-Zener formalism. The MSXs for quenching of O(2)(a (1)Delta(g)) by the ground state O(2)(X (3)Sigma(g) (-)):O(2)(a (1)Delta(g))+O(2)(X (3)Sigma(g) (-))-->O(2)(X (3)Sigma(g) (-))+O(2)(X (3)Sigma(g) (-)) require higher energies and the process is not likely to be important.     

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.     

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.     

Fully quantum rovibrational calculation of the He(H2) bound and resonance states

In a recent paper [J. Chem. Phys. 2005, 122, 124318], a full-dimensional quantum method, designed to efficiently compute the rovibrational states of triatomic systems with long-range interactions, was applied to the benchmark Li-(H2) ion-molecule system. The method incorporates several key features in order to accurately represent the rovibrational Hamiltonian using only modestly sized basis sets: (1) exact analytical treatment of Coriolis coupling; (2) a single bend-angle basis for all rotational states; (3) phase space optimization of the vibrational basis; (4) G(4) symmetry adaptation of the rovibrational basis. In this paper, the same methodology is applied for the first time to a van der Waals complex system, He(H2). As in the Li-(H2) study, all of the rovibrational bound states, and a number of resonance states, are computed to very high accuracy (1/10,000 of a wavenumber or better). Three different isotopologues are considered, all of which are found to have a single bound state with a very low binding energy. Several extremely long-lived Feshbach resonances are also reported.     

The binding of 4He and 3He to a hydrogen molecule: a computational study for pH2 and oH2

One bound state for the very weakly interacting complex of H(2) with one He atom is computed using a recently obtained, very accurate potential energy surface [A. I. Boothroyd and P. G. Martin, J. Chem. Phys. 119, 3187 (2003)] and employing a discrete variable representation expansion. The spatial features of this very diffused, "halo" state are analyzed and discussed for various isotopic variants of the title system.     

Energies and radial couplings for the Σ and Σ states of the NaHe quasimolecule

We present the energies and radial couplings for the five ¹Σ and four ³Σ states of lowest energy of the NaHe⁺ quasimolecule, with a precision which is sufficient to treat Na/He⁺ collisions. The characteristics of energies and couplings are studied in detail with the aid of qualitative orbital and state-correlation diagrams.     

Synthesis and structure of cluster compounds containing a novel cluster core {Re4STe3}

Three novel cluster compounds K₄[Re₄STe₃(CN)₁₂]·₄H₂O (I), [{Cu(en)₂}₂Re₄STe₃(CN)₁₂]·₅H₂O (II) and [{Cu(trien)}₂Re₄STe₃(CN)₁₂]·2H₂O (III) (en is ethylenediamine, trien is triethylenetetraamine) containing a new cluster core {Re₄STe₃} have been prepared and structurally characterized. According to single crystal X-ray diffraction data, compound I is ionic and represents the arrangement of ions K⁺ and [Re₄STe₃(CN)₁₂]^4?; compounds II and III are molecular and formed by two cationic moieties {Cu(en)₂}²⁺ and {Cu(trien)}²⁺, respectively, coordinated to one cluster anion. In the solid state, S atom positions in the tetrahedron Q₄ (Q = S, Te) are disordered for all three compounds: in I and III sulfur atoms are split over all four Q positions, while in II over two positions.     

Relativistic corrections to the non-Born-Oppenheimer energies of the lowest singlet Rydberg states of 3He and 4He

In this work the authors present an approach to calculate the leading-order relativistic corrections for ground and excited states of helium isotopomers. In the calculations they used variational wave functions expanded in terms of explicitly correlated Gaussians obtained without assuming the Born-Oppenheimer approximation.     

Dissociative recombination of H+(H2O)3 and D+(D2O)3 water cluster ions with electrons: cross sections and branching ratios

Dissociative recombination (DR) of the water cluster ions H(+)(H(2)O)(3) and D(+)(D(2)O)(3) with electrons has been studied at the heavy-ion storage ring CRYRING (Manne Siegbahn Laboratory, Stockholm University). For the first time, absolute DR cross sections have been measured for H(+)(H(2)O)(3) in the energy range of 0.001-0.8 eV, and relative cross sections have been measured for D(+)(D(2)O)(3) in the energy range of 0.001-1.0 eV. The DR cross sections for H(+)(H(2)O)(3) are larger than previously observed for H(+)(H(2)O)(n) (n=1,2), which is in agreement with the previously observed trend indicating that the DR rate coefficient increases with size of the water cluster ion. Branching ratios have been determined for the dominating product channels. Dissociative recombination of H(+)(H(2)O)(3) mainly results in the formation of 3H(2)O+H (probability of 0.95+/-0.05) and with a possible minor channel resulting in 2H(2)O+OH+H(2) (0.05+/-0.05). The dominating channels for DR of D(+)(D(2)O)(3) are 3D(2)O+D (0.88+/-0.03) and 2D(2)O+OD+D(2) (0.09+/-0.02). The branching ratios are comparable to earlier DR results for H(+)(H(2)O)(2) and D(+)(D(2)O)(2), which gave 2X(2)O+X (X=H,D) with a probability of over 0.9.     

The Pd(4)(dppm)(4)(H)(2)(2+) cluster: a precatalyst for the homogeneous hydrogenation of alkynes

The catalytic properties of the title cluster toward the homogeneous hydrogenation of phenylacetylene, diphenylethyne and phenyl-1-propyne have been investigated as a function of temperature, pressure, solvents, substrate and cluster concentrations, and counterions. The title cluster is a precatalyst that exhibits a good catalytic activity under mild conditions (1 atm of H(2) at 20 degrees C) for the hydrogenation of alkynes and alkenes. For the alkyne substrates, the turnover frequencies (tof's) range between 200 and 500 h(-)(1), and the product distribution varies as: cis-products, 75-90%; trans-products; 0-8% after 3 h of reaction. Based on the graphs -d[substrate]/dt vs [Pd(4)](1/2), the mechanism indicates a cluster dissociation into two dimers (presumably of the type Pd(2)(dppm)(2)(H)(solvent)(+)). The variations of tof (or -d[substrate]/dt) as a function of [substrate] and pressure of H(2) are linear. At 1600 psi of H(2), the tof can reach 2500-3000 h(-)(1) (in THF). The tof also increases with temperature reaching a maximum at approximately 35 degrees C (tof: 1000-1300 h(-)(1)), but at higher temperatures cluster decomposition begins to occur, leading to a rapid decrease in rates of catalysis. At 50 degrees C, no catalysis is observed. The hydrogenation reaction can be stopped at the corresponding cis-alkenes with approximately 95% yields, depending on the substrate and experimental conditions used. The tof's also vary with the solvent, where stronger coordinating solvent molecules give higher tof's. In addition, the tof's do not change with the nature of the counterion, which acts as "spectator" in the catalysis.     

Relativistic correction to the 1ssigma and 2psigma electronic states of the H2 + molecular ion and the moleculelike states of the antiprotonic helium He+ -p

Effective potentials of the relativistic Breit-Pauli corrections for the 1ssigma(g) and 2psigma(u) electron states of the H(2) (+) molecular ion and the 1ssigma, 2ssigma, and 3psigma states of the antiprotonic helium atom He(+)(-)p are calculated within the Born-Oppenheimer approximation. The variational expansion with randomly chosen exponents has been used for numerical studies. The results obtained for the Breit-Pauli effective potentials are accurate up to ten significant digits for the H(2) (+) molecular ion and eight digits for the He(+)(-)p atom.     

The X1Sigmag+, B1Deltag, and B' 1Sigmag+ states of C2: a comparison of renormalized coupled-cluster and multireference methods with full configuration interaction benchmarks

Unusual bonding and electronic near degeneracies make the lowest-lying singlet states of the C2 molecule particularly challenging for electronic structure theory. Here we compare two alternative approaches to modeling bond-breaking reactions and excited states: sophisticated multireference configuration interaction and multireference perturbation theory methods, and a more "black box," single-reference approach, the completely renormalized coupled-cluster method. These approximate methods are assessed in light of their ability to reproduce the full configuration interaction potential energy curves for the X1Sigmag+, B1Deltag, and B' 1Sigmag+ states of C2, which are numerically exact solutions of the electronic Schrodinger equation within the space spanned by a 6-31G* basis set. Both the multireference methods and the completely renormalized coupled-cluster approach provide dramatic improvements over the standard single-reference methods. The multireference methods are nearly as reliable for this challenging test case as for simpler reactions which break only single bonds. The completely renormalized coupled-cluster approach has difficulty for large internuclear separations R in this case, but over the wide range of R=1.0-2.0 A, it compares favorably with the more complicated multireference methods.     

Stabilization of 3:1 site-differentiated cubane-type clusters in the [Fe(4)S(4)](1+) core oxidation state by tertiary phosphine ligation: synthesis, core structural diversity, and S = 1/2 ground states

An extensive series of 3:1 site-differentiated cubane-type clusters [Fe(4)S(4)(PPr(i)(3))(3)L] (L = Cl(-), Br(-), I(-), RO(-), RS(-), RSe(-)) has been prepared in 40-80% yield by two methods: ligand substitution of [Fe(4)S(4)(PPr(i)(3))(4)](1+) in tetrahydrofuran (THF)/acetonitrile by reaction with monoanions, and reductive cleavage of ligand substrates (RSSR, RSeSeR, I(2)) by the all-ferrous clusters [Fe(8)S(8)(PPr(i)(3))(6)]/[Fe(16)S(16)(PPr(i)(3))(8)] in THF. These neutral clusters are stable and do not undergo ligand redistribution reactions involving charged species in benzene and THF solutions. X-ray structural studies confirm the cubane stereochemistry but with substantial and variable distortions of the [Fe(4)S(4)](1+) core from idealized cubic core geometry. Based on Fe-S bond lengths, seven clusters were found to have compressed tetragonal distortions (4 short and 8 long bonds), and the remaining seven display other types of distortions with different combinations of long, short, and intermediate bond lengths. These results further emphasize the facile deformabililty of this core oxidation state previously observed in [Fe(4)S(4)(SR)(4)](3-) clusters. The Fe(2.25+) mean oxidation state was demonstrated from (57)Fe isomer shifts, and the appearance of two quadrupole doublets arises from the spin-coupled |9/2,4,1/2> state. The S = 1/2 ground state was further supported by electron paramagnetic resonance spectra and magnetic susceptibility data.     

Ab initio calculation of the mobility of C+(2P) and C+ (4P) in helium

The mobility of the ²P ground state and the ⁴P excited state of C⁺ in helium have been calculated using the two-temperature theory of ion transport and HeC⁺ interaction potentials calculated at the MP4SDQ/6311 + G(3df,3pd) level of theory. Agreement with experimental data is very good. The results confirm a recent experimental observation of the ⁴P state of C⁺.     

Ab initio quantum dynamics with very weak van der Waals interactions: Structure and stability of small Li2(1Sigmag+)-(He)n clusters

The potential energy surface (PES) for the interaction between Li2(1Sigmag+) and 4He has been computed using an accurate, post-Hartree-Fock quantum calculation for its ground electronic state. The orientational anisotropy of the forces and the interplay between repulsive and attractive effects within the PES are analyzed to extract information on the possible existence of bound states in the triatomic system. The structures of a few of the Li2(He)n small clusters are examined by comparing a classical approach with a full quantum one to generate bound configurations and to extract information on the possible spatial arrangements of the smaller clusters via à vis the location of the Li2 dopant. Some significant consequences on the Li2 behavior in larger clusters and droplets are drawn from the above findings.     

Syntheses, structure, and properties of a manganese-calcium cluster containing a Mn4Ca2 core

We describe here a novel, simple, efficient self-assembly method for the in situ generation of [Mn4Cl4(micro-OCH2CH2OMe)4(EtOH)4] and [Mn4(micro-Cl)Cl3(micro-OCH2CH2OMe)4(HOCH2CH2OMe)3]2 cubane-type compounds which react readily with calcium species to form cluster [Mn4Ca2Cl4(micro-OCH2CH2OMe)8], the calcium atoms attached to the Mn4 unit of flatten out the cubane inducing significant conformational changes.