We first briefly report on the status and recent achievements of the ELPA-AEO (Eigen value Solvers for Petaflop Applications—Algorithmic Extensions and Optimizations) and ESSEX II (Equipping Sparse Solvers for Exascale) projects. In both collaboratory efforts, scientists from the application areas, mathematicians, and computer scientists work together to develop and make available efficient highly parallel methods for the solution of eigenvalue problems. Then we focus on a topic addressed in both projects, the use of mixed precision computations to enhance efficiency. We give a more detailed description of our approaches for benefiting from either lower or higher precision in three selected contexts and of the results thus obtained.

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Efficient structure search is a major challenge in computational materials science. We present a modification of the basin hopping global geometry optimization approach that uses a curvilinear coordinate system to describe global trial moves. This approach has recently been shown to be efficient in structure determination of clusters [C. Panosetti et al., Nano Lett. 15, 8044-8048 (2015)] and is here extended for its application to covalent, complex molecules and large adsorbates on surfaces. The employed automatically constructed delocalized internal coordinates are similar to molecular vibrations, which enhances the generation of chemically meaningful trial structures. By introducing flexible constraints and local translation and rotation of independent geometrical subunits, we enable the use of this method for molecules adsorbed on surfaces and interfaces. For two test systems, trans-β-ionylideneacetic acid adsorbed on a Au(111) surface and methane adsorbed on a Ag(111) surface, we obtain superior performance of the method compared to standard optimization moves based on Cartesian coordinates.

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Identification of relevant reaction pathways in ever more complex composite materials and nanostructures poses a central challenge to computational materials discovery. Efficient global structure search, tailored to identify chemically relevant intermediates, could provide the necessary first-principles atomistic insight to enable a rational process design. In this work we modify a common feature of global geometry optimization schemes by employing automatically generated collective curvilinear coordinates. The similarity of these coordinates to molecular vibrations enhances the generation of chemically meaningful trial structures for covalently bound systems. In the application to hydrogenated Si clusters, we concomitantly observe a significantly increased efficiency in identifying low-energy structures and exploit it for an extensive sampling of potential products of silicon-cluster soft landing on Si(001) surfaces.

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Vibrational spectra of Xe-tagged cationic silicon oxide clusters Si_nO_m⁺ with n = 3-5 and m = n, n ± 1 in the gas phase are obtained by resonant infrared multiple photon dissociation (IRMPD) spectroscopy and density functional theory calculations. The Si_nO_m⁺ clusters are produced in a laser vaporization ion source and Xe complexes are formed after thermalization to 100 K. The clusters are subsequently irradiated with tunable light from an IR free electron laser and changes in the mass distribution yield size-specific IR spectra. The measured IRMPD spectra are compared to calculated linear IR absorption spectra leading to structural assignments. For several clusters, Xe complexation alters the energetic order of the Si_nO_m⁺ isomers. Common structural motifs include the Si₂O₂ rhombus, the Si₃O₂ pentagon, and the Si₃O₃ hexagon.

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Density-functional theory based global geometry optimization is used to scrutinize the possibility of using endohedrally doped hydrogenated Si clusters as building blocks for constructing highly magnetic materials. In contrast to the known clathrate-type facet-sharing, the clusters exhibit a predisposition to aggregation through double Si-Si bridge bonds. For the prototypical CrSi 20H20 cluster we show that reducing the degree of hydrogenation may be used to control the number of reactive sites to which other cages can be attached, while still preserving the structural integrity of the building block itself. This leads to a toolbox of CrSi20H 20-2n monomers with different number of double "docking sites", that allows building network architectures of any morphology. For (CrSi20H18)2 dimer and [CrSi20H 16](CrSi20H18)2 trimer structures we illustrate that such aggregates conserve the high spin moments of the dopant atoms and are therefore most attractive candidates for cluster-assembled materials with unique magnetic properties. The study suggests that the structural completion of the individual endohedral cages within the doubly bridge bonded structures and the high thermodynamic stability of the obtained aggregates are crucial for potential synthetic polimerization routes via controlled dehydrogenation.@en

Density-functional theory based global geometry optimization is employed to systematically scrutinize the possibility of multidoping of hydrogenated Si clusters to achieve high spin states beyond the septet limit of a single-atom dopant. While our unbiased configurational search reveals that the previously suggested Si18H12 double hexagonal prism structure is generally too small to accommodate two dopants in magnetized state, the larger Si24H24 cage turns out to be suitable for such applications. For dimer dopants M2+ = Cr2 +, Mn2+, and CrMn+, the structural integrity of the host cage is conserved in the ground-state structure of corresponding M2+@Si24H24 aggregates, as is the unusually high spin state of the guest dopant, which in the case of Cr2+ already exceeds the single-atom dopant septet limit by almost a factor of 2. Moreover, the possibility of further increasing the cluster spin moment by encapsulating an even larger number of dopants into a suitably sized hydrogenated Si cage is illustrated for the example of a (CrMn+)2@Si28H28 aggregate with a total number of 18 unpaired electrons. These results strongly suggest multidoping of Si clusters as a viable route to novel cluster-based materials for magneto-optic applications.@en

Density-functional theory based global geometry optimization is used to scrutinize the possibility of endohedral doping of hydrogenated Si fullerenes as a route to Si nanostructures with high magnetic moments. In contrast to previous suggestions, our unbiased sampling finds the smallest Si 16H 16 endohedral cage generally too small to encapsulate 3d metal dopant atoms. For the next larger fullerene-like cage, however, we identify perfectly symmetric M@Si 20H 20 (M=Co, Ti, V, and Cr) cage structures as ground states. These structures conserve the high spin moment of the dopant atom and therewith underscore the potential of this Si nanoform for novel cluster-based materials with unique magnetic properties.@en

Density-functional theory is used to study the geometric and electronic structure of cationic Si16+ clusters with a Ti, V, or Cr dopant atom. Through unbiased global geometry optimization based on the basin-hopping approach, we confirm that a Frank-Kasper polyhedron, with the metal atom at the center, represents the ground-state isomer for all three systems. The endohedral cage geometry is thus stabilized even though only VSi16+ achieves electronic shell closure within the prevalent spherical potential model. Our analysis of the electronic structure traces this diminished role of shell closure for the stabilization back to the adaptive capability of the metal-Si bonding, which is more the result of a complex hybridization than the originally proposed mere formal charge transfer. The resulting flexibility of the metal-Si bond can also help to stabilize non-magic cage-dopant combinations, which suggests that a wider range of materials may eventually be cast into this useful geometry for cluster-assembled materials.@en