Hyperchromats with linear dependence of longitudinal chromatic aberration on wavelength

Optical lens systems that are characterized by a chromatic aberration of a predefined form are called hyperchromats. Our work describes a theory of hyperchromats with a linear dependence of longitudinal chromatic aberration on wavelength. The equations are derived for calculation of basic design parameters of these optical systems and some examples of hyperchromatic optical systems are shown. Mentioned optical systems can be used especially in 3D imaging systems and confocal microscopy.     

Syntheses, X-ray structures, photochemistry, redox properties, and DFT calculations of interconvertible fac- and mer-[Mn(SPS)(CO)3] isomers containing a flexible SPS-based pincer ligand

The lithium salt of the anionic SPS pincer ligand composed of a central hypervalent lambda4-phosphinine ring bearing two ortho-positioned diphenylphosphine sulfide side arms reacts with [Mn(CO)5Br] to give fac-[Mn(SPS)(CO)3]. This isomer can be converted photochemically to mer-[Mn(SPS)(CO)3], with a very high quantum yield (0.80+/-0.05). The thermal backreaction is slow (taking ca. 8 h at room temperature), in contrast to rapid electrode-catalyzed mer-to-fac isomerization triggered by electrochemical reduction of mer-[Mn(SPS)(CO)3]. Both geometric isomers of [Mn(SPS)(CO)3] have been characterized by X-ray crystallography. Both isomers show luminescence from a low-lying 3IL (SPS-based) excited state. The light emission of fac-[Mn(SPS)(CO)3] is largely quenched by the efficient photoisomerization occurring probably from a low-lying Mn-CO dissociative excited state. Density functional theory (DFT) and time-dependent DFT calculations describe the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of fac- and mer-[Mn(CO)3(SPS)] as ligand-centered orbitals, largely localized on the phosphinine ring of the SPS pincer ligand. In line with the ligand nature of its frontier orbitals, fac-[Mn(SPS)(CO)3] is electrochemically reversibly oxidized and reduced to the corresponding radical cation and anion, respectively. The spectroscopic (electron paramagnetic resonance, IR, and UV-vis) characterization of the radical species provides other evidence for the localization of the redox steps on the SPS ligand. The smaller HOMO-LUMO energy difference in the case of mer-[Mn(CO)3(SPS)], reflected in the electronic absorption and emission spectra, corresponds with its lower oxidation potential compared to that of the fac isomer. The thermodynamic instability of mer-[Mn(CO)3(SPS)], confirmed by the DFT calculations, increases upon one-electron reduction and oxidation of the complex.     

Configuration interaction calculations of the valence and the inner valence levels of the CS molecule

CI calculations were performed on the energies and relative intensities of the outer and inner valence levels of the CS molecule. Breakdown of the one-particle model is discussed in terms of CI, and the results are compared with the analogous investigations using the Green's function technique.     

Calculation of vibrational structure in the core and valence esca spectra of CO and N2

The vibrational excitations in the core and valence ESCA bands of CO and N₂ have been investigated by means of Franck—Condon (FC) analysis. FC factors obtained from optimized geometries and from the force constants of the neutral ground and ionized states are compared with those obtained from calculated ionized-state energy gradients. Geometries, force constants, and energy gradients are calculated both from frozen-orbital energies and from OS RHF wavefunctions. The differences between the results of the methods employed are discussed in the light of experimental data.     

Multiple equilibria and indifference-threshold points in a rational addiction model

Becker and Murphy (J Polit Econ 96(4):675–700, 1988) have established the existence of unstable steady states leading to threshold behavior for optimal consumption rates in intertemporal rational addiction models. In the present paper a simple linear-quadratic optimal control model is used to illustrate how their approach fits into the framework of multiple equilibria and indifference-threshold points. By changing the degree of addiction and the level of harmfulness we obtain a variety of behavioral patterns. In particular we show that when the good is harmful as well as very addictive, an indifference-threshold point, also known in the literature as a Skiba point, separates patterns converging to either zero or maximal consumption, where the latter occurs in the case of a high level of past consumption. This implicitly shows that an individual needs to be aware in time of these characteristics of the good. Otherwise, he/she may start consuming so much that in the end he/she is totally addicted.     

Photosynthesis-Inhibiting Activity of N-(Disubstituted-phenyl)-3-hydroxynaphthalene-2-carboxamides

A set of twenty-four 3-hydroxynaphthalene-2-carboxanilides, disubstituted on the anilide ring by combinations of methoxy/methyl/fluoro/chloro/bromo and ditrifluoromethyl groups at different positions, was prepared. The compounds were tested for their ability to inhibit photosynthetic electron transport (PET) in spinach (Spinacia oleracea L.) chloroplasts. N-(3,5-Difluorophenyl)-, N-(3,5-dimethylphenyl)-, N-(2,5-difluorophenyl)- and N-(2,5-dimethylphenyl)-3-hydroxynaphthalene-2-carboxamides showed the highest PET-inhibiting activity (IC₅₀ ~ 10 µM) within the series. These compounds were able to inhibit PET in photosystem II. It has been found that PET-inhibiting activity strongly depends on the position of the individual substituents on the anilide ring and on the lipophilicity of the compounds. The electron-withdrawing properties of the substituents contribute towards the PET activity of these compounds.     

New Reasons to Motivate Trope Theory: Endurantism and Perdurantism

In this paper, I argue that (non-presentist) endurantism is incompatible with the view that properties are universals. I do so by putting forward a very simple objection that forces the endurantist to embrace tropes, rather than universals. I do not claim that this is bad news for the endurantist—trope theory seems to me by all means more appealing than universals—rather, I would like to see this result as a further motivation to embrace tropes. I then also put forward a (more controversial) reason to believe that at least some versions of perdurantism also require tropes rather than universals.