Impurities and Alloys

Callaway, Joseph

doi:10.1016/b978-0-12-155203-9.50010-9

Cited by 8 publications

(12 citation statements)

References 84 publications

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“… 26 Third, the wavefunction for a periodic material can be described in terms of Bloch waves, where each one-particle Bloch wave has the form in eqn (18) . 55 …”

Section: Resultsmentioning

confidence: 99%

“…Because the cell periodic functions { u n ( k⃑ , r⃑ )} have the same periodicity as the unit cell, they can be expanded in terms of a basis set of planewaves commensurate with the unit cell. 55 Fourth, a planewave basis set systematically approaches completeness as the cutoff energy is raised. 26 All commensurate planewaves with kinetic energy below this cutoff energy are included in the basis set.…”

Section: Resultsmentioning

confidence: 99%

“…The k -points { k⃑ } sample the primitive cell in reciprocal space (aka ‘the first Brillouin zone’). 55 More k -points corresponds to a finer integration mesh in reciprocal space. A sufficiently large number of k -points is needed to achieve accurate integrations.…”

Section: Resultsmentioning

confidence: 99%

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Introducing DDEC6 atomic population analysis: part 4. Efficient parallel computation of net atomic charges, atomic spin moments, bond orders, and more

2018

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The DDEC6 method is one of the most accurate and broadly applicable atomic population analysis methods. It works for a broad range of periodic and non-periodic materials with no magnetism, collinear magnetism, and non-collinear magnetism irrespective of the basis set type. First, we show DDEC6 charge partitioning to assign net atomic charges corresponds to solving a series of 14 Lagrangians in order. Then, we provide flow diagrams for overall DDEC6 analysis, spin partitioning, and bond order calculations. We wrote an OpenMP parallelized Fortran code to provide efficient computations. We show that by storing large arrays as shared variables in cache line friendly order, memory requirements are independent of the number of parallel computing cores and false sharing is minimized. We show that both total memory required and the computational time scale linearly with increasing numbers of atoms in the unit cell. Using the presently chosen uniform grids, computational times of $9 to 94 seconds per atom were required to perform DDEC6 analysis on a single computing core in an Intel Xeon E5 multiprocessor unit. Parallelization efficiencies were usually >50% for computations performed on 2 to 16 cores of a cache coherent node. As examples we study a B-DNA decamer, nickel metal, supercells of hexagonal ice crystals, six X@C 60 endohedral fullerene complexes, a water dimer, a Mn 12 -acetate single molecule magnet exhibiting collinear magnetism, a Fe 4 O 12 N 4 C 40 H 52 single molecule magnet exhibiting non-collinear magnetism, and several spin states of an ozone molecule. Efficient parallel computation was achieved for systems containing as few as one and as many as >8000 atoms in a unit cell. We varied many calculation factors (e.g., grid spacing, code design, thread arrangement, etc.) and report their effects on calculation speed and precision. We make recommendations for excellent performance. † Electronic supplementary information (ESI) available: ESI documentation includes a pdf le containing: the 14 charge partitioning Lagrangians (S1); spin partitioning Lagrangian and ow diagram (S2); equations for bond order analysis (S3); algorithm for total electron density grid correction (S4); table and description listing big arrays and in which modules they are allocated and deallocated (S5); table and description of computational parameters (S6); description of how to use the enclosed reshaping sub routines (S7); and description of how to use the enclosed spin functions (S8). Additionally ESI includes a zip format archive containing: the system geometries; Jmol readable xyz les containing DDEC6 NACs, atomic multipoles, electron cloud parameters, ASMs, SBOs, and r-cubed moments; DDEC6 bond orders and overlap populations; a Fortran module containing reshaping subroutines; and a Fortran module containing spin functions. See

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“… 26 Third, the wavefunction for a periodic material can be described in terms of Bloch waves, where each one-particle Bloch wave has the form in eqn (18) . 55 …”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Introducing DDEC6 atomic population analysis: part 4. Efficient parallel computation of net atomic charges, atomic spin moments, bond orders, and more

2018

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“…The interactions between the lattice points could lead to the formation of electronic band structures. 8 As a result, the properties of inorganic crystals show a strong dependence on their size, especially in the nanoscale, the so called quantum size effect. 9 The molecular interactions in organic crystals cause their properties to be distinct from those of individual molecules.…”

Section: Introductionmentioning

confidence: 99%

Luminescent zero-dimensional organic metal halide hybrids with near-unity quantum efficiency

et al. 2018

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“…The linear MO response is described by the off-diagonal element of the permittivity tensor calculated by 43 , 44 (SI units): The imaginary part of the permittivity tensor is obtained by the Kramers–Kronig relations. The summations run over occupied (labeled i as initial states) and unoccupied states ( f standing for final).…”

Section: Ab Initio Descriptionmentioning

confidence: 99%

Band structure analysis of the magneto-optical effect in bcc Fe

Stejskal

Veis

Hamrle

2021

Sci Rep

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Magneto-optical effects are among the basic tools for characterization of magnetic materials. Although these effects are routinely calculated by the ab initio codes, there is very little knowledge about their origin in the electronic structure. Here, we analyze the magneto-optical effect in bcc Fe and show that it originates in avoided band-crossings due to the spin-orbit interaction. Therefore, only limited number of bands and k-points in the Brillouin zone contribute to the effect. Furthermore, these contributions always come in pairs with opposite sign but they do not cancel out due to different band curvatures providing different number of contributing reciprocal points. The magneto-optical transitions are classified by the dimensionality of the manifold that is formed by the hybridization of the generating bands as one- or two-dimensional, and by the position relative to the magnetization direction as parallel and perpendicular. The strongest magneto-optical signal is provided by two-dimensional parallel transitions.

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Impurities and Alloys

Cited by 8 publications

References 84 publications

Introducing DDEC6 atomic population analysis: part 4. Efficient parallel computation of net atomic charges, atomic spin moments, bond orders, and more

Introducing DDEC6 atomic population analysis: part 4. Efficient parallel computation of net atomic charges, atomic spin moments, bond orders, and more

Luminescent zero-dimensional organic metal halide hybrids with near-unity quantum efficiency

Band structure analysis of the magneto-optical effect in bcc Fe

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