Some formal properties of ensemble density functionals

Formal properties of ensemble density functionals are examined. Expressions for the difference between energy functionals where the particle number differs by one are constructed in terms of their first functional derivatives for the universal energy functional, the electron–electron repulsion energy functional, and the interacting kinetic energy functional. Equations that must be satisfied by second and higher order functional derivatives are derived. It is also shown that the shape of ${\delta V_{ee}[\rho]\over\delta\rho({\bf r})}$ and ${\delta K[\rho]\over\delta\rho({\bf r})}$ , the functional derivatives of the mutual electron–electron repulsion, and kinetic energy, respectively, are separately particle number independent for particle numbers between successive integers. © 2013 Wiley Periodicals, Inc.     

On the importance of intramolecular hydrogen bond cooperativity in d‐glucose – an NMR and QTAIM approach

The idea that hydrogen bond cooperativity is responsible for the structure and reactivity of carbohydrates is examined. Density functional theory and gauge‐including atomic orbital calculations on the known conformers of the α and β anomers of d ‐glucopyranose in the gas phase are used to compute proton NMR chemical shifts and interatomic distances, which are taken as criteria for probing intramolecular interactions. Atom–atom interaction energies are calculated by the interacting quantum atoms approach in the framework of the quantum theory of atoms in molecules. Association of OH1 in the counterclockwise conformers with a strong acceptor, pyridine, is accompanied by cooperative participation from OH2, but there is no significant change in the bonding of the two following 1,2‐diol motifs. The OH6 ^... O5 (G?g+/cc/t and G+g?/cc/t conformers) or OH6 ^... O4 (Tg+/cc/t conformer) distance is reduced, and the OH6 proton is slightly deshielded. In the latter case, this shortening and the associated increase in the OH6–O4 interaction energy may be interpreted as a small cooperative effect, but intermolecular interaction energies are practically the same for all three conformers. In most of the pyridine complexes, one ortho proton interacts with the endocyclic oxygen O5. Analogous results are obtained when the clockwise conformer, G?g+/cl/g?, detected for the α anomer, and a hypothetical conformer, Tt/cl/g?, are complexed with pyridine through OH6. Generally, the cooperative effect does not go beyond the first two OH groups of a chain. Copyright © 2017 John Wiley & Sons, Ltd.     

One color,pulsed excited-state upconversion in YAG:Tm3+

One color red laser pumping of YAG:Tm³⁺ crystals results in a strong upconverted near ultraviolet and blue fluorescence from the excited¹ D ₂ and¹ G ₄ multiplets. It is found that under pulsed-pumping conditions the quasi-resonant excited-state absorption from the³ H ₄ multiplet is the responsible process. Analysis of the upconverted emission confirmed previous results on³ H ₄ level assignments as well as on inhomogeneous line broadening in the YAG structure.     

Explicit difference approximations of Du Fort-Frankel type of the one-dimensional diffusion equation

Summary It is shown that the well-known Du Fort-Frankel difference approximation of the one-dimensional diffusion equation is a special case of a more general difference equation, which is also stable for any choice of the difference grid. Results computed with the aid of a smoothing formula, are given.

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Zusammenfassung Dieser Artikel zeigt, daß das bekannte Du Fort-Frankel Differenzenverfahren zur Lösung der eindimensionalen Wärmeleitungsgleichung ein Spezialfall eines allgemeineren Differenzenverfahrens ist, das auch bei willkürlicher Wahl des Differenzengitters stabil ist. Ein Beispiel, das mit Hilfe eines Glättungsverfahrens durchgerechnet wurde, folgt.

     

Performance of iterative methods for Newtonian and generalized Newtonian flows

We consider the use of accelerated gradient-type iterative methods for solution of Newtonian and certain non-Newtonian (power-law and Bingham models) viscous flow problems. The formulations are based on penalty and mixed finite element methods, and such factors as the effect of the penalty parameter, asymmetry, continuation and preconditioning are examined.