We introduce a generic model of chain formation in break junctions by formulating criteria for the stability and producibility of suspended monatomic chains based on total energy arguments. Using ab initio calculations including spin-polarization and spin-orbit coupling, we apply our model to the formation of monatomic 4d and 5d transition metal (TM) chains. We explain the physical origin of the experimentally observed general trend of increasing probability for the creation of long chains for late 5d TMs and suppressed chain formation for 4d TMs. We also clarify why the probability of chain elongation can be greatly enhanced by the presence of adsorbates in experiments.

The electronic structure of nitrogen vacancies in gadolinium nitride are studied using the full-potential linearized muffin-tin orbital method in the local spin density approximation with Hubbard U corrections (LSDA+U). The vacancy is found to have two localized defect levels in the gap, one of each spin. The third electron of each vacancy in the neutral state dopes the conduction band. The single positive state is found to be the ground state for Fermi levels located anywhere within the band gap. The vacancy has a net magnetic moment of 1 μ B in the neutral charge state. The presence of the vacancy is found to increase the average exchange interactions between Gd atoms and hence the Curie temperature but only by about a factor 2 compared to GdN without vacancies.

Applications of existing precise electronic-structure methods based on density functional theory are typically limited to the treatment of about 1000 inequivalent atoms, which leaves unresolved many open questions in material science, e.g., on complex defects, interfaces, dislocations, and nanostructures. KKRnano is a new massively parallel linear scaling all-electron density functional algorithm in the framework of the KorringaKohn-Rostoker (KKR) Green's-function method. We conceptualized, developed, and optimized KKRnano for large-scale applications of many thousands of atoms without compromising on the precision of a full-potential all-electron method, i.e., it is a method without any shape approximation of the charge density or potential. A key element of the new method is the iterative solution of the sparse linear Dyson equation, which we parallelized atom by atom, across energy points in the complex plane and for each spin degree of freedom using the message passing interface standard, followed by a lower-level OpenMP parallelization. This hybrid four-level parallelization allows for an efficient use of up to 100 000 processors on the latest generation of supercomputers. The iterative solution of the Dyson equation is significantly accelerated, employing preconditioning techniques making use of coarse-graining principles expressed in a block-circulant preconditioner. In this paper, we will describe the important elements of this new algorithm, focusing on the parallelization and preconditioning and showing scaling results for NiPd alloys up to 8192 atoms and 65 536 processors. At the end, we present an order-N algorithm for large-scale simulations of metallic systems, making use of the nearsighted principle of the KKR Green's-function approach by introducing a truncation of the electron scattering to a local cluster of atoms, the size of which is determined by the requested accuracy. By exploiting this algorithm, we show linear scaling calculations of more than 16 000 NiPd atoms.