We propose an efficient, accurate method to integrate the basins of attraction of a smooth function defined on a general discrete grid and apply it to the Bader charge partitioning for the electron charge density. Starting with the evolution of trajectories in space following the gradient of charge density, we derive an expression for the fraction of space neighboring each grid point that flows to its neighbors. This serves as the basis to compute the fraction of each grid volume that belongs to a basin (Bader volume) and as a weight for the discrete integration of functions over the Bader volume. Compared with other grid-based algorithms, our approach is robust, more computationally efficient with linear computational effort, accurate, and has quadratic convergence. Moreover, it is straightforward to extend to nonuniform grids, such as from a mesh-refinement approach, and can be used to both identify basins of attraction of fixed points and integrate functions over the basins.

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Impurities control phase stability and phase transformations in natural and man-made materials, from shape-memory alloys to steel to planetary cores. Experiments and empirical databases are still central to tuning the impurity effects. What is missing is a broad theoretical underpinning. Consider, for example, the titanium martensitic transformations: diffusionless structural transformations proceeding near the speed of sound. Pure titanium transforms from ductile alpha to brittle omega at 9 GPa, creating serious technological problems for beta-stabilized titanium alloys. Impurities in the titanium alloys A-70 and Ti-6Al-4V (wt%) suppress the transformation up to at least 35 GPa, increasing their technological utility as lightweight materials in aerospace applications. These and other empirical discoveries in technological materials call for broad theoretical understanding. Impurities pose two theoretical challenges: the effect on the relative phase stability, and the energy barrier of the transformation. Ab initio methods calculate both changes due to impurities. We show that interstitial oxygen, nitrogen and carbon retard the transformation whereas substitutional aluminium and vanadium influence the transformation by changing the d-electron concentration. The resulting microscopic picture explains the suppression of the transformation in commercial A-70 and Ti-6Al-4V alloys. In general, the effect of impurities on relative energies and energy barriers is central to understanding structural phase transformations.

A description of the martensitic transformations between the α, β and ω phases of titanium that includes nucleation and growth requires an accurate classical potential. Optimization of the parameters of a modified embedded atom potential to a database of density-functional calculations yields an accurate and transferable potential as verified by comparison to experimental and density functional data for phonons, surface and stacking fault energies and energy barriers for homogeneous martensitic transformations. Molecular dynamics simulations map out the pressure-temperature phase diagram of titanium. For this potential the martensitic phase transformation between α and β appears at ambient pressure and 1200 K, between α and ω at ambient conditions, between β and ω at 1200 K and pressures above 8 GPa, and the triple point occurs at 8GPa and 1200 K. Molecular dynamics explorations of the dynamics of the martensitic α − ω transformation show a fast-moving interface with a low interfacial energy of 30 meV/ Å2 . The potential is applicable to the study of defects and phase transformations of Ti.

Phenylene ethynylenes comprise a prototypical class of synthetic antimicrobial compounds that mimic antimicrobial peptides produced by eukaryotes and have broad-spectrum antimicrobial activity. We show unambiguously that bacterial membrane permeation by these antimicrobials depends on the presence of negative intrinsic curvature lipids, such as phosphatidylethanolamine (PE) lipids, found in high concentrations within bacterial membranes. Plate-killing assays indicate that a PE-knockout mutant strain of Escherichia coli drastically out-survives the wild type against the membrane-active phenylene ethynylene antimicrobials, whereas the opposite is true when challenged with traditional metabolic antibiotics. That the PE deletion is a lethal mutation in normative environments suggests that resistant bacterial strains do not evolve because a lethal mutation is required to gain immunity. PE lipids allow efficient generation of negative curvature required for the circumferential barrel of an induced membrane pore; an inverted hexagonal H II phase, which consists of arrays of water channels, is induced by a small number of antimicrobial molecules. The estimated antimicrobial occupation in these water channels is nonlinear and jumps from Ϸ1 to 3 per 4 nm of induced water channel length as the global antimicrobial concentration is increased. By comparing to exactly solvable 1D spin models for magnetic systems, we quantify the cooperativity of these antimicrobials.antibiotic resistant bacteria ͉ host defense peptides ͉ innate immunity ͉ protein-membrane interactions T he recent emergence of antibiotic-resistant bacteria is a worldwide public health problem (1). Antimicrobial peptides (AMPs) from innate immunity are known to have broad spectrum and selective activity against pathogens (2-7). Despite their diversity in sequence, secondary structures, and source, most of the more than 800 different AMPs that have been identified are amphiphilic and cationic (2, 3). It is thought that electrostatic interactions facilitate association of the peptide with the anionic bacterial membrane (2,8). Moreover, such peptides are often implicated in pore formation in the bacterial membrane. Although the amphiphilicity is important in pore formation, the exact molecular mechanism by which membrane pores are formed is still not clear. Over the last decade, synthetic molecules that mimic these features have been designed and investigated, including stereoisomers of natural AMPs (9), ␣-peptides (10-12), ␤-peptides (13-16), peptoids (17), aromatic oligomers (18,19), and synthetic polymers (20-24), such as phenylene ethynylene. The precise molecular mechanism of activity for most of these compounds is also unknown, as is the reason why it is difficult for bacteria to evolve immunity to them.In this paper, we dissect the membrane activity of a prototypical synthetic antimicrobial (25, 26) from the bacterium level to the molecular self-assembly level. A number of biophysical differences exist between the membranes of bacteria and eukaryotes (2, 27...

The strain field of isolated screw and edge dislocation cores in aluminum are calculated using density-functional theory and a flexible boundary condition method. Nye tensor density contours and differential displacement fields are used to accurately bound Shockley partial separation distances. Our results of 5-7.5 A (screw) and 7.0-9.5 A (edge) eliminate uncertainties resulting from the wide range of previous results based on Peierls-Nabarro and atomistic methods. Favorable agreement of the predicted cores with limited experimental measurements demonstrates the need for quantum mechanical treatment of dislocation cores.

The core structures of screw and edge dislocations on the basal and prism planes in Mg, and the associated gamma surfaces, were studied using an ab initio method and the embedded-atom-method interatomic potentials developed by Sun et al and Liu et al. The ab initio calculations predict that the basal plane dislocations dissociate into partials split by 16.7 Å (edge) and 6.3 Å (screw), as compared with 14.3 Å and 12.7 Å (Sun and Liu edge), and 6.3 Å and 1.4 Å (Sun and Liu screw), with the Liu screw dislocation being metastable. In the prism plane, the screw and edge cores are compact and the edge core structures are all similar, while ab initio does not predict a stable prismatic screw in stress-free conditions. These results are qualitatively understood through an examination of the gamma surfaces for interplanar sliding on the basal and prism planes. The Peierls stresses at T = 0 K for basal slip are a few megapascals for the Sun potential, in agreement with experiments, but are ten times larger for the Liu potential. The Peierls stresses for prism slip are 10–40 MPa for both potentials. Overall, the dislocation core structures from ab initio are well represented by the Sun potential in all cases while the Liu potential shows some notable differences. These results suggest that the Sun potential is preferable for studying other dislocations in Mg, particularly the ⟨c + a⟩ dislocations, for which the core structures are much larger and not accessible by ab initio methods.

Solid-solution strengthening results from solutes impeding the glide of dislocations. Existing theories of strength rely on solutedislocation interactions, but do not consider dislocation core structures, which need an accurate treatment of chemical bonding. Here, we focus on strengthening of Mg, the lightest of all structural metals and a promising replacement for heavier steel and aluminum alloys. Elasticity theory, which is commonly used to predict the requisite solute-dislocation interaction energetics, is replaced with quantum-mechanical first-principles calculations to construct a predictive mesoscale model for solute strengthening of Mg. Results for 29 different solutes are displayed in a "strengthening design map" as a function of solute misfits that quantify volumetric strain and slip effects. Our strengthening model is validated with available experimental data for several solutes, including Al and Zn, the two most common solutes in Mg. These new results highlight the ability of quantum-mechanical first-principles calculations to predict complex material properties such as strength.