Magneto-Structural Relationship of Tetragonally-Compressed Octahedral Iron(II) Complex Surrounded by a pseudo-S6 Symmetric Hexakis-Dimethylsulfoxide Environment

Since the octahedral high-spin iron(II) complex has the 5T2g ground term, the spin-orbit coupling should be considered in magnetic analysis; however, such treatment is rarely seen in recent papers, although the symmetry-sensitive property is of interest to investigate in detail. A method to consider the T-term magnetism was well constructed more than half a century ago. On the other hand, the method has been still improved in recent years. In this study, the octahedral high-spin iron(II) complex [Fe(dmso)6][BPh4]2 (dmso: dimethylsulfoxide) was newly prepared, and the single-crystal X-ray diffraction method revealed the tetragonal compression of the D4-symmetric coordination geometry around the iron(II) ion and the pseudo-S6 hexakis-dmso environment. From the magnetic data, the sign of the axial splitting parameter, Δ, was found to be negative, indicating the 5E ground state in the D4 symmetry. The DFT computation showed the electronic configuration of (dxz)2(dx2−y2)1(dyz)1(dxy)1(dz2)1 due to the tetragonal compression and the pseudo-S6 environment of dmso π orbitals. The electronic configuration corresponded to the 5E ground term, which was in agreement with the negative Δ value. Therefore, the structurally predicted ground state was consistent with the estimation from the magnetic measurements.

Nominal Equational Problems

We define nominal equational problems of the form $$\exists \overline{W} \forall \overline{Y} : P$$ ∃ W ¯ ∀ Y ¯ : P , where $$P$$ P consists of conjunctions and disjunctions of equations $$s\approx _\alpha t$$ s ≈ α t , freshness constraints $$a\#t$$ a # t and their negations: $$s \not \approx _\alpha t$$ s ≉ α t and "Equation missing", where $$a$$ a is an atom and $$s, t$$ s , t nominal terms. We give a general definition of solution and a set of simplification rules to compute solutions in the nominal ground term algebra. For the latter, we define notions of solved form from which solutions can be easily extracted and show that the simplification rules are sound, preserving, and complete. With a particular strategy for rule application, the simplification process terminates and thus specifies an algorithm to solve nominal equational problems. These results generalise previous results obtained by Comon and Lescanne for first-order languages to languages with binding operators. In particular, we show that the problem of deciding the validity of a first-order equational formula in a language with binding operators (i.e., validity modulo $$\alpha $$ α -equality) is decidable.

Composing on iPad as Middle Ground Education

In this article, I apply Biesta’s philosophical term “middle ground” as a theoretical basis for investigating music teaching where the students’ creative productions are part of their learning activities. The middle ground term illuminates how arts education depends on both incorporating the student’s desires and, at the same time, leading the student into encounters of responsibility with the material and socially-constructed world. I analyze how an educational design where secondary school students composed music with GarageBand on iPads can be characterized as middle ground education. The analysis is based on material from a microethnographic study in secondary school music lessons. From this, I discuss how middle ground education can be designed and propose the importance of students being given promotional challenges.

Electron-impact fine-structure excitation of Fe ii at low temperature

Fe ii emission lines are observed from nearly all classes of astronomical objects over a wide spectral range from the infrared to the ultraviolet. To meaningfully interpret these lines, reliable atomic data are necessary. In the work presented here we focused on low-lying fine-structure transitions, within the ground term, due to electron impact. We provide effective collision strengths together with estimated uncertainties as functions of temperature of astrophysical importance (10−100 000 K). Due to the importance of fine-structure transitions within the ground term, the focus of this work is on obtaining accurate rate coefficients at the lower end of this temperature range, for applications in low-temperature environments such as the interstellar medium. We performed three different flavours of scattering calculations: (i) an intermediate coupling frame transformation (icft) R-matrix method, (ii) a Breit–Pauli R-matrix (bprm) method, and (iii) a Dirac Atomic R-matrix Code (darc). The icft and bprm calculations involved three different autostructure target models each. The darc calculation was based on a reliable 20 configuration, 6069 level atomic structure model. Good agreement was found with our bprm and darc collision results compared to previous R-matrix calculations. We present a set of recommended effective collision strengths for the low-lying forbidden transitions together with associated uncertainty estimates.

Atomic data for IR and sub-mm wavelengths

Atomic spectra in the infrared and sub-mm wavelength regions can be divided into two broad categories: electric dipole-allowed transitions, and forbidden lines due to transitions within the ground term or between low-lying levels of the same parity. Both are of potential importance in the interpretation of astrophysical spectra. Allowed transitions can provide diagnostic information for stellar photospheres, particularly for elements that are not accessible in the visible region. Electric-dipole forbidden lines are important diagnostics of low-density plasmas, such as nebulae and the interstellar medium. In order to interpret astrophysical spectra, accurate atomic data are required. This paper summarizes the techniques for measuring atomic data and lists the most important compilations and databases.