Extending Hirshfeld‐I to bulk and periodic materials

In this work, a method is described to extend the iterative Hirshfeld‐I method, generally used for molecules, to periodic systems. The implementation makes use of precalculated pseudopotential‐based electron density distributions, and it is shown that high‐quality results are obtained for both molecules and solids, such as ceria, diamond, and graphite. The use of grids containing (precalculated) electron densities makes the implementation independent of the solid state or quantum chemical code used for studying the system. The extension described here allows for easy calculation of atomic charges and charge transfer in periodic and bulk systems. The conceptual issue of obtaining reference densities for anions is discussed, and the delocalization problem for anionic reference densities originating from the use of a plane wave basis set is identified and handled. © 2012 Wiley Periodicals, Inc.     

Reply to ‘comment on “extending Hirshfeld‐I to bulk and periodic materials”’

The issues raised in the comment by Manz are addressed through the presentation of calculated atomic charges for NaF, NaCl, MgO, SrTiO $$_3$$ , and La $$_2$$ Ce $$_2$$ O $$_7$$ , using our previously presented method for calculating Hirshfeld‐I charges in solids (Vanpoucke et al., J. Comput. Chem. doi: 10.1002/jcc.23088). It is shown that the use of pseudovalence charges is sufficient to retrieve the full all‐electron Hirshfeld‐I charges to good accuracy. Furthermore, we present timing results of different systems, containing up to over 200 atoms, underlining the relatively low cost for large systems. A number of theoretical issues are formulated, pointing out mainly that care must be taken when deriving new atoms in molecules methods based on “expectations” for atomic charges. © 2012 Wiley Periodicals, Inc.     

Comparisons between singularity categories and relative stable categories of finite groups

We consider the relationship between the relative stable category of and the usual singularity category for group algebras with coefficients in a commutative noetherian ring. When the coefficient ring is self-injective we show that these categories share a common, relatively large, Verdier quotient. At the other extreme, when the coefficient ring has finite global dimension, there is a semi-orthogonal decomposition, due to Poulton, relating the two categories. We prove that this decomposition is partially compatible with the monoidal structure and study the morphism it induces on spectra.     

The basic bundle gerbe on unitary groups

We consider the construction of the basic bundle gerbe on SU(n)$SU\left(n\right)$ introduced by Meinrenken and show that it extends to a range of groups with unitary actions on a Hilbert space including U(n)$U\left(n\right)$ and _Up(H)$U_p\left(H\right)$, the Banach Lie group of unitaries differing from the identity by an element of a Schatten ideal. In all these cases we give an explicit connection and curving on the basic bundle gerbe and calculate the real Dixmier–Douady class. Extensive use is made of the holomorphic functional calculus for operators on a Hilbert space.     

Light beats the spread: “non‐diffracting” beams

“Non‐diffracting” beams do not spread as they propagate. This property is useful in many areas. Here, the theory, generation, properties, and applications of various “non‐diffracting” beams, including the Bessel beam, Mathieu beam, and Airy beam is reviewed. Applications include imaging, micromanipulation, nonlinear optics, and optical transfection.     

First experiments on the Australian Synchrotron Imaging and Medical beamline,including investigations of the effective source size in respect of X‐ray imaging

The Imaging and Medical beamline at the Australian Synchrotron achieved `first light' in December 2008. Here, the first experiments performed on the beamline are reported, which involved both X‐ray imaging and tomography studies for a range of samples. The use of a plastic‐edge phantom for quantitative measurements of contrast and resolution proved to be very instructive and helped to confirm certain parameter values such as the effective horizontal source size, detector resolution and average X‐ray energy for the polychromatic beam.     

Isoscalar monopole strength in 100Mo: an indicator for static triaxial deformation in the ground state

We perform deformation constraint symmetry-unrestricted three-dimensional time-dependent density functional theory (TDDFT) calculations for the isoscalar monopole (ISM) mode in ¹⁰⁰Mo. Monopole moments are obtained as a function of time using time propagating states based on different deformations. A Fourier transform is then performed on the obtained response functions. The resulting ISM strength functions are compared with experimental data. For the static potential-energy-surface (PES) calculations, the results using the SkM* and UNEDF1 energy-density functionals (EDFs) show spherical ground states and considerable softness in the triaxial deformation. The PES obtained with the SLy4 EDF shows static triaxial deformation. The TDDFT results based on different deformations show that a quadrupole deformation (characterized by \begin{document}$ \beta_2 $\end{document}) value of 0.25–0.30 gives a two-peak structure of the strength functions. Increasing triaxial deformation (characterized by γ) from 0\begin{document}$ ^{\circ} $\end{document} to 30\begin{document}$ ^{\circ} $\end{document} results in the occurrence of an additional peak between the two, making the general shape of the strength functions closer to that of the data. Our microscopic TDDFT analyses suggest that ¹⁰⁰Mo is triaxially deformed in the ground state. The calculated isoscalar \begin{document}$ Q_{20} $\end{document} and \begin{document}$ Q_{22} $\end{document} strength functions show peaks at lower energies. The coupling of these two modes with the ISM mode is the reason for the three-peak/plateau structure in the strengths of ¹⁰⁰Mo.