Nedko Drebov

Structures of Aln, its anions and cations up to n=34: A theoretical investigation

A systematic density functional study has been performed for neutral and singly charged clusters of aluminum with up to 34 atoms. A thorough search for global minimum structures has been carried out for Al(n) employing genetic algorithm and basin-hopping procedures. For Al(n) this confirms results of previous investigations up to n=22; new global minima have been located for n=23-31, 33. Structures for singly charged cations and anions have been obtained by reoptimization of the pool of 40 low-energy structures of the neutral clusters. The global minima of charged and neutral clusters are always low-spin states with the possible exception of a triplet state of Al(28), which is isoenergetic with a singlet. The cluster structures are mostly quite irregular and do not resemble fractions of the fcc bulk phase. High symmetries are found only for the global minimum of Al(23) and the triplet state of Al(28).

Structures and properties of neutral gallium clusters: A theoretical investigation

A systematic and unbiased structure search based on a genetic algorithm in combination with density functional theory (DFT) procedures has been carried out to locate low-energy isomers of Ga(n) up to n = 25. For the smaller clusters up to n = 8 results are checked by coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)) employing a quadruple zeta type basis set. The CCSD(T) calculations confirm a (3)Π(u) ground state for the dimer. Ga(3) has a doublet ground state 0.2 eV below two quartet states, whereas two isoenergetic triplet states are predicted for Ga(4) with D(4h) and a rhombus structure (D(2h)). Three low-lying isomers with doublet electronic states are found for Ga(5): a W-structure (C(2v)), a planar envelope (C(s)) at 0.015 eV, and a non-planar envelope (C(1)) 0.086 eV above the ground state. A triplet state for a trigonal prism (D(3h)) and a singlet for an open prism (C(2v)) are computed with virtually identical energy for Ga(6). The global minimum for Ga(7) is a capped trigonal prism (C(s)) and that for Ga(8) a distorted cube in D(2h). DFT provides a fair agreement with CCSD(T), deviations in dissociation energies are up to 0.2 eV for n ≤ 8. The structures for Ga(n) are mostly irregular for n ≥ 9, those for Ga(12) to Ga(17) can be derived from the truncated decahedron with D(5h) symmetry though highly distorted by Jahn-Teller effects, for example. For Ga(18) to Ga(23) we find stacks of five- and six-membered rings as global minima, e.g., 5-1-5-1-6 for Ga(18). Ga(24) and Ga(25) consist of layers with packing sequence ABCBA similar to those found for clusters of aluminum. The most important feature of computed cohesive energies is a rapid increase with n: for Ga(25) it reaches 2.46 eV, the experimental bulk value is 2.84 eV. Particularly stable clusters for Ga(n) are seen for n = 7, 14, and 20.

Structures and energetics of small lead cluster ions.

By a combination of gas phase ion mobility measurements and relativistic density functional theory calculations with inclusion of spin-orbit coupling, we assign structures of lead cluster cations and anions in the range between 4 and 15 atoms. We find a planar rhombus for the tetramer, a trigonal bipyramid for the pentamer, and a pentagonal bipyramid for the heptamer, independent of charge state. For the hexamer, the cation and anion structures differ: we find an octahedron for the anion while the cation consists of fused tetrahedra. For the octamer, we find in both cases structures based on the pentagonal bipyramid motif plus adatom. For the larger clusters investigated we always find different structures for cations and anions. For example, Pb(12)(-) is confirmed to be a hollow icosahedron while Pb(12)(+) is a truncated filled icosahedron. Pb(13)(+) is a filled icosahedron but Pb(13)(-) is a hollow icosahedron with the additional atom capping a face. In order to get experimental information on the relative stabilities, we investigated the collision induced dissociation mass spectra for the different cluster sizes and charge states, and observe a strong correlation with the calculated fragmentation energies. Up to n = 13 the main fragmentation channel is atom loss; for the larger cluster sizes we observe fission into two large fragments. This channel is dominant for larger anions, less pronounced but clearly present for the cations.

Communications: Tin cluster anions (Snn−, n=18, 20, 23, and 25) comprise dimers of stable subunits

The gas phase structures of tin cluster anions Sn(n)(-) have been studied by a combination of trapped ion electron diffraction and density functional theory calculations. In the size range of n=18-25 these clusters comprise dimers of stable subunits. In particular Sn(18)(-) and Sn(20)(-) are homodimers of Sn(9) and Sn(10) subunits, respectively. In Sn(23)(-) two Sn(10) units are linked by three additional bridging atoms and Sn(25)(-) is a heterodimer of Sn(10) and Sn(15) subunits. This rather unexpected growth mode is rationalized by the extraordinary stability of the building blocks Sn(9), Sn(10), and Sn(15).

Small clusters of aluminum and tin: Highly correlated calculations and validation of density functional procedures

We present results of molecular electronic structure treatments of multireference configuration interaction (MRCI) type for clusters Al(n) and Sn(n) in the range up to n = 4, and of coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)) type in the range up to n = 10. Basis sets of quadruple zeta size are employed, computed energy differences, such as cohesive energies, E(coh), or dissociation energies for the removal of a single atom, D(e), differ from the complete basis set limit by only a few 0.01 eV. MRCI and CCSD(T) results are then compared to those obtained from density functional theory (DFT) treatments, which show that all computational procedures agree with the general features of D(e) and E(coh). The best agreement of DFT with CCSD(T) is found for the meta-GGA (generalized gradient approximation) TPSS (Tao, Perdew, Staroverov, Scuseria) for which D(e) differs from CCSD(T) by at most 0.15 eV for Al(n) and 0.21 eV for Sn(n). The GGA PBE (Perdew, Burke, Ernzerhof) is slightly poorer with maximum deviations of 0.23 and 0.24 eV, whereas hybrid functionals are not competitive with GGA and meta-GGA functionals. A general conclusion is that errors of D(e) and/or energy differences of isomers computed with DFT procedures may easily reach 0.2 eV and errors for cohesive energies E(coh) 0.1 eV.

Structures of tin cluster cations Sn 3+ to Sn 15+

We employ a combination of ion mobility measurements and an unbiased systematic structure search with density functional theory methods to study structure and energetics of gas phase tin cluster cations, Sn(n)(+), in the range of n = 3-15. For Sn(13)(+) we also carry out trapped ion electron diffraction measurements to ascertain the results obtained by the other procedures. The structures for the smaller systems are most easily described by idealized point group symmetries, although they are all Jahn-Teller distorted: D(3h) (trigonal bipyramid), D(4h) (octahedron), D(5h) (pentagonal bipyramid) for n = 5, 6, and 7. For the larger systems we find capped D(5h) for Sn(8)(+) and Sn(9)(+), D(3h) (tricapped trigonal prism) and D(4d) (bicapped squared antiprism) plus adatoms for n = 10, 11, 14, and 15. A centered icosahedron with a peripheral atom removed is the dominant motif in Sn(12)(+). For Sn(13)(+) the calculations predict a family of virtually isoenergetic isomers, an icosahedron and slightly distorted icosahedra, which are about 0.25 eV below two C(1) structures. The experiments indicate the presence of two structures, one from the I(h) family and a prolate C(1) isomer based on fused deltahedral moieties.