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At least 19 records

Spin–Orbit Coupling Constants in Atoms and Ions of Transition Elements: Comparison of Effective Core Potentials, Model Core Potentials, and All-Electron Methods

The spin–orbit coupling constants (SOCC) in atoms and ions of the first- through third-row transition elements were calculated for the low-lying atomic states whose main electron configuration is [ n d] q ( q = 1–4 and 6–9, n = the principal quantum number), using four different approaches: (1) a nonrelativistic Hamiltonian used to construct multiconfiguration self-consistent field (MCSCF) wave functions utilizing effective core potentials and their associated basis sets within the framework of second-order configuration interaction (SOCI) to calculate spin–orbit couplings (SOC) using one-electron Breit–Pauli Hamiltonian (BPH), (2) a nonrelativistic Hamiltonian used to construct MCSCF wave functions utilizing model core potentials and their associated basis sets within the framework of SOCI to calculate SOC using the full BPH, (3) nonrelativistic and spin-independent relativistic Hamiltonians used to construct MCSCF wave functions utilizing all-electron (AE) basis sets within the framework of SOCI to calculate SOC using the full BPH, and (4) a relativistic Hamiltonian given by the exact two-component (X2C) transformation for construction of Kramers-restricted relativistic configuration interaction wave functions. In this investigation, these four approaches are referred to as ECP, MCP, AE, and X2C methods, respectively. The ECP, MCP, and AE methods are so-called two-step approaches (TSA), while the X2C method is a one-step approach (OSA). In the AE method, three different calculations—relativistic elimination of small components (RESC), third-order Douglas–Kroll–Hess (DKH3), and infinite-order two-component (IOTC) relativistic correction—were performed for the estimation of the scalar relativistic components in addition to those of the nonscalar relativistic (NSR) contributions. The calculated SOCC are compared to the available experimental data via the Landé interval rule. Although there are several exceptions, including states whose main configuration is [ n d] 5 , the average differences between the ECP and AE (IOTC) SOCC and between the ECP and the X2C SOCC are mostly less than 20%. The differences between the ECP and the experimental SOCC are even smaller. No serious discrepancy was found between the TSA and OSA predictions of SOCC for the first- and second-row transition elements in comparison to experiment. For atoms and ions of the third-row transition elements, the SOCC calculated through the Landé interval rule are not reliable. The low-energy spin-mixed (SM) states originating from a [5d]q configuration ( q = 2–4) have a larger energy lowering due to the SOC effects, in comparison with those for atoms and ions of the first- and second-row transition elements. For the spin-mixed (SM) states originating from a [5d]q configuration ( q = 6–8), the energy lowering of all 4 F 7/2 , 5 D 1 , and 5 D 3 states due to the SOC effects is smaller than those of the other SM states. Furthermore this difficulty, which also arises for the MCP, AE, and X2C (OSA) approaches, suggests that the LS-coupling scheme is inappropriate.

74 ATOMIC AND MOLECULAR PHYSICS↗

Transition elements based on transfinite interpolation

In this study the transfinite interpolation methodology, a 'blending-function' method in particular, is utilized for the formulation of transition elements. The method offers a formal way of meeting continuity requirements in a transition element. Element shape functions are derived by blending the continuity requirements of individual boundary segments. The blending directions are naturally orthogonal in rectangular domains therefore interpolation of the boundaries over rectangular 2D and 3D elements can be performed with minimal effort. In triangular domains, however, the choice of blending directions and interpolants is not straightforward. For that reason, two interpolation techniques are proposed for blending of the boundaries of triangular domains. A series of transition elements of various classes compatible with elements of different orders and dimensions is developed and the full potential of the transfinite interpolation, as it applies to element formulation, is explored.

Odabas, Onur R.↗

Transition element distribution in stony meteorites and in terrestrial and lunar rocks.

Discussion of the distribution of the transition elements (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn) among the individual minerals of stony meteorites, and comparison with data on comparable lunar and terrestrial minerals. As an example of meteorite distribution patterns, data on the Modoc meteorite are presented. For the lunar rocks, microprobe data are used, along with published information from other investigators. For comparison with terrestrial igneous rocks, Skaergaard intrusion rocks are used. They present some striking analogies in mineralogy and petrology with the lunar igneous rocks and are thus peculiarly suitable for this cross comparison.

Mason, B.↗

Evaluation of discretization procedures for transition elements in adaptive mesh refinement

Three transition interpolation schemes for use in h-or r-refinement have been analyzed in terms of accuracy, implementation ease and extendability. They include blending-function interpolation, displacement averaging, and strain matching at discrete points along the transition edge lines. The results suggest that the choice of matching depends strongly on the element formulations, (viz. displacement or assumed strain, etc.) and mesh refinement criteria employed, and to a lesser extent the choice of computer architecture (serial vs. parallel) and the equation solution procedures. A recommended pairing of some of the elements with the choice factors is suggested.

Park, K. C.↗

Multi-principal element transition metal dichalcogenides via reactive fusion of 3D-heterostructures

Transition metal dichalcogenides combining multiple principal elements in their structures are synthesized via mechanochemical exfoliation and spontaneous reassembly of binary precursors into 3D-heterostructures that are converted into single-phase layered materials by high-temperature reactive fusion. As a result, physical and chemical events enabling these transformations are summarized in the form of a conceivable reaction mechanism.

36 MATERIALS SCIENCE↗

Analysis of over-magnetization of elemental transition metal solids from the SCAN density functional

Current investigations have revealed that the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation exchange-correlation functional significantly over-magnetizes elemental Fe, Co, and Ni solids. For the paradigmatic case, bcc Fe, the error relative to experiment is ≳ 20 % . A comparative analysis of magnetization results from SCAN and its deorbitalized counterpart, SCAN-L, leads to identification of the source of the discrepancy. It is not from the difference between Kohn-Sham (SCAN-L) and generalized Kohn-Sham (SCAN) procedures. The key is the iso-orbital indicator α (the ratio of the local Pauli and Thomas-Fermi kinetic energy densities). Its deorbitalized counterpart α L has more dispersion in both spin channels with respect to magnetization in an approximate region between 0.6 and 1.2 bohrs around an Fe nucleus. The overall effect is that the SCAN switching function evaluated with α L reduces the energetic disadvantage of the down channel with respect to up compared to the original α , which in turn reduces the magnetization. This identifies the origin of the SCAN magnetization error as insensitivity of the SCAN switching function to α values in the approximate range 0.5 ≲ α ≲ 0.8 and oversensitivity for α ≳ 0.8 .

36 MATERIALS SCIENCE↗

Emergence of californium as the second transitional element in the actinide series

Abstract A break in periodicity occurs in the actinide series between plutonium and americium as the result of the localization of 5 f electrons. The subsequent chemistry of later actinides is thought to closely parallel lanthanides in that bonding is expected to be ionic and complexation should not substantially alter the electronic structure of the metal ions. Here we demonstrate that ligation of californium(III) by a pyridine derivative results in significant deviations in the properties of the resultant complex with respect to that predicted for the free ion. We expand on this by characterizing the americium and curium analogues for comparison, and show that these pronounced effects result from a second transition in periodicity in the actinide series that occurs, in part, because of the stabilization of the divalent oxidation state. The metastability of californium(II) is responsible for many of the unusual properties of californium including the green photoluminescence.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Heterostructures with InGaAs/GaAs quantum dots doped with transition elements: II. Study of the circularly polarized luminescence

Optical and transport properties of the heterostructure with the InAs/GaAs quantum dots doped with manganese or chromium atoms in the course of growth using metal-organic vapor phase epitaxy (MOVPE) are analyzed. Circularly polarized luminescence was obtained due to doping of quantum dots with the Mn or Cr atoms. The sign of the degree of circular polarization was found to depend on the dopant. The effect is interpreted using specific features of the radiative recombination in quantum dots in the presence of resident electrons and holes.

77 NANOSCIENCE AND NANOTECHNOLOGY↗