Green's function multiple-scattering theory with a truncated basis set: An Augmented-KKR formalism

Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an efficient site-centered, electronic-structure technique for addressing an assembly of $N$ scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number $L_{max}=(l,m)_{max}$, while scattering matrices, which determine spectral properties, are truncated at $L_{tr}=(l,m)_{tr}$ where phase shifts $\delta_{l>l_{tr}}$ are negligible. Historically, $L_{max}$ is set equal to $L_{tr}$; however, a more proper procedure retains free-electron and single-site contributions for $L_{max}>L_{tr}$ with $\delta_{l>l_{tr}}$ set to zero [Zhang and Butler, Phys. Rev. B {\bf 46}, 7433]. We present a numerically efficient and accurate \emph{augmented}-KKR Green's function formalism that solves the KKR secular equations by matrix inversion [$\mathcal{R}^3$ process with rank $N(l_{tr}+1)^2$] and includes higher-order $L$ contributions via linear algebra [$\mathcal{R}^2$ process with rank $N(l_{max}+1)^2$]. Augmented-KKR yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. For fcc Cu, bcc Fe and L$1_0$ CoPt, we present the formalism and numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus $L_{max}$ for a given $L_{tr}$.Comment: 7 pages, 5 figure

Nudged-elastic band method with two climbing images: finding transition states in complex energy landscapes

The nudged-elastic band (NEB) method is modified with concomitant two climbing images (C2-NEB) to find a transition state (TS) in complex energy landscapes, such as those with serpentine minimal energy path (MEP). If a single climbing image (C1-NEB) successfully finds the TS, C2-NEB finds it with higher stability and accuracy. However, C2-NEB is suitable for more complex cases, where C1-NEB misses the TS because the MEP and NEB directions near the saddle point are different. Generally, C2-NEB not only finds the TS but guarantees that the climbing images approach it from the opposite sides along the MEP, and it estimates accuracy from the three images: the highest-energy one and its climbing neighbors. C2-NEB is suitable for fixed-cell NEB and the generalized solid-state NEB (SS-NEB).Comment: 3 pages, 4 figure

Coexistence pressure for a martensitic transformation from theory and experiment: revisiting the bcc-hcp transition of iron under pressure

The coexistence pressure of two phases is a well-defined point at fixed temperature. In experiment, however, due to non-hydrostatic stresses and a stress-dependent potential energy barrier, different measurements yield different ranges of pressure with a hysteresis. Accounting for these effects, we propose an inequality for comparison of the theoretical value to a plurality of measured intervals. We revisit decades of pressure experiments on the bcc - hcp transformations in iron, which are sensitive to non-hydrostatic conditions and sample size. From electronic-structure calculations, we find a bcc - hcp coexistence pressure of 8.4 GPa. We construct the equation of state for competing phases under hydrostatic pressure, compare to experiments and other calculations, and address the observed pressure hysteresis and range of onset pressures of the nucleating phase.Comment: 8 pages, 1 figure, 202 citation

Better band gaps for wide-gap semiconductors from a locally corrected exchange-correlation potential that nearly eliminates self-interaction errors

This work constitutes a comprehensive and improved account of electronic-structure and mechanical properties of silicon-nitride (Si3N4) polymorphs via van Leeuwen and Baerends (LB) exchange-corrected local density approximation (LDA) that enforces the exact exchange potential asymptotic behavior. The calculated lattice constant, bulk modulus, and electronic band structure of Si3N4 polymorphs are in good agreement with experimental results. We also show that, for a single electron in a hydrogen atom, spherical well, or harmonic oscillator, the LB-corrected LDA reduces the (self-interaction) error to exact total energy to ~10%, a factor of three to four lower than standard LDA, due to a dramatically improved representation of the exchange-potential.Comment: 6 pages, 3 figure