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).

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.

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.

Machine learning (ML) is increasingly becoming a helpful tool in the search for novel functional compounds. Here we use classification via random forests to predict the stability of half-Heusler (HH) compounds, using only experimentally reported compounds as a training set. Cross-validation yields an excellent agreement between the fraction of compounds classified as stable and the actual fraction of truly stable compounds in the ICSD. The ML model is then employed to screen 71,178 different 1:1:1 compositions, yielding 481 likely stable candidates. The predicted stability of HH compounds from three previous high throughput ab initio studies is critically analyzed from the perspective of the alternative ML approach. The incomplete consistency among the three separate ab initio studies and between them and the ML predictions suggests that additional factors beyond those considered by ab initio phase stability calculations might be determinant to the stability of the compounds. Such factors can include configurational entropies and quasihar-monic contributions.

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.