373 research outputs found
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 scatterers. Wave-functions are expanded in a spherical-wave
basis on each scattering center and indexed up to a maximum orbital and
azimuthal number , while scattering matrices, which
determine spectral properties, are truncated at where phase
shifts are negligible. Historically, is set equal
to ; however, a more proper procedure retains free-electron and
single-site contributions for with 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 [ process
with rank ] and includes higher-order contributions via
linear algebra [ process with rank ].
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 CoPt, we present the
formalism and numerical results for accuracy and for the convergence of the
total energies, Fermi energies, and magnetic moments versus for a
given .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
Better Band Gaps with Asymptotically Corrected Local Exchange Potentials
We formulate a spin-polarized van Leeuwen and Baerends (vLB) correction to
the local density approximation (LDA) exchange potential [Phys. Rev. A 49, 2421
(1994)] that enforces the ionization potential (IP) theorem following Stein et
al. [Phys. Rev. Lett. 105, 266802 (2010)]. For electronic-structure problems,
the vLB-correction replicates the behavior of exact-exchange potentials, with
improved scaling and well-behaved asymptotics, but with the computational cost
of semi-local functionals. The vLB+IP corrections produces large improvement in
the eigenvalues over that from LDA due to correct asympotic behavior and atomic
shell structures, as shown on rare-gas, alkaline-earth, zinc-based oxides,
alkali-halides, sulphides, and nitrides. In half-Heusler alloys, this
asymptotically-corrected LDA reproduces the spin-polarized properties
correctly, including magnetism and half-metallicity. We also considered
finite-sized systems [e.g., ringed boron-nitirde (BN) and
graphene (C)] to emphasize the wide applicability of the method.Comment: 9 pages, 3 figure
Mixed valency and site-preference chemistry for cerium and its compounds: A predictive density-functional theory study
Cerium and its technologically relevant compounds are examples of anomalous mixed valency, originating from two competing oxidation states—itinerant Ce4+ and localized Ce3+. Under applied stress, anomalous transitions are observed but not well understood. Here we treat mixed valency as an “alloy” problem involving two valences with competing and numerous site-occupancy configurations. We use density-functional theory with Hubbard U (i.e., DFT+U) to evaluate the effective valence and predict properties, including controlling the valence by pseudoternary alloying. For Ce and its compounds, such as (Ce,La)2(Fe,Co)14B permanent magnets, we find a stable mixed-valent α state near the spectroscopic value of νs=3.53. Ce valency in compounds depends on its steric volume and local chemistry. For La doping, Ce valency shifts towards γ-like Ce3+, as expected from steric volume; for Co doping, valency depends on local Ce-site chemistry and steric volume. Our approach captures the key origins of anomalous valency and site-preference chemistry in complex compounds
- …