First-principles calculation of H vibrational excitations at a dislocation core of Pd

Palladium is an ideal system for understanding the behavior of hydrogen in metals. In Pd, H is located both in octahedral sites and in dislocation cores, which act as nanoscale H traps and form Cottrell atmospheres. Adjacent to a dislocation core, H experiences the largest possible distortion in alpha-Pd. Ab initio density-functional theory computes the potential energy for a hydrogen in an octahedral site in alpha-Pd and in a trap site at the core of a partial of an edge dislocation. The Pd partial dislocation core changes the environment for H, distorting the H-Pd bonding which changes the local potential, vibrational spectra, and inelastic form factor for an isolated H atom. The decrease in excitation energy is consistent with experiments, and the calculations predict distortions to the H wavefunction.Comment: 12 pages, 3 figure

Accurate and efficient algorithm for Bader charge integration

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 non-uniform 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.Comment: 19 pages, 8 figure

Energy density in density functional theory: Application to crystalline defects and surfaces

We propose a method to decompose the total energy of a supercell containing defects into contributions of individual atoms, using the energy density formalism within density functional theory. The spatial energy density is unique up to a gauge transformation, and we show that unique atomic energies can be calculated by integrating over Bader and charge-neutral volumes for each atom. Numerically, we implement the energy density method in the framework of the Vienna ab initio simulation package (VASP) for both norm-conserving and ultrasoft pseudopotentials and the projector augmented wave method, and use a weighted integration algorithm to integrate the volumes. The surface energies and point defect energies can be calculated by integrating the energy density over the surface region and the defect region, respectively. We compute energies for several surfaces and defects: the (110) surface energy of GaAs, the mono-vacancy formation energies of Si, the (100) surface energy of Au, and the interstitial formation energy of O in the hexagonal close-packed Ti crystal. The surface and defect energies calculated using our method agree with size-converged calculations of the difference between the total energies of the system with and without the defect. Moreover, the convergence of the defect energies with size can be found from a single calculation.Comment: 25 pages, 6 figure