Hypochromic and hyperchromic effects on the vibronic structure of molecular crystal spectra. The dimer model

It is shown on model calculations that crystal-field mixing of Frenkel excition states in molecular crystals lead not only to a redistribution of their relative intensities but also to changes in the vibrational structure of weak exciton bands.     

The electronic absorption study of imide anion radicals in terms of time dependent density functional theory

The absorption spectra of the N-(2,5-di-tert-butylphenyl) phthalimide (1-), N-(2,5-di-tert-butylphenyl)-1,8-naphthalimide (2-) and N-(2,5-di-tert-butylphenyl)-perylene-3,4-dicarboximide (3-) anion radicals are studied in terms of time dependent density functional theory (TDDFT). For these anion radicals a large number electronic states (from 30 to 60) was found in the visible and near-IR regions (5000-45,000 cm(-1)). In these regions the TD/B3LYP treatment at the 6-1+G* level is shown to reproduce satisfactorily the empirical absorption spectra of all three anion radicals studied. The most apparent discrepancies between purely electronic theory and the experiment could be found in the excitation region corresponding to D0-->D1 transitions in the 2- and 3- molecules. For these species we argue that the structures seen in the lowest energy part of the absorptions of the 2- and 3- species are very likely due to Franck-Condon (FC) activity of the totally symmetric vibrations not studied in this Letter.     

Non-linear electrical effect in graded-electron concentration silicon

A gradient of carrier concentration in semiconductors can create a double-frequency internal electric field which is parallel to this gradient and perpendicular to the applied a.c. field. This warm-carrier effect was measured in silicon specimens with a gradient of electron concentration, at 77 and 300 K, under applied fields from 1 to 10 V m^-1 and within the frequency range of 0.3–20 kHz. A comparison between experimental data and a theoretical model is discussed.     

A characterization of strong measure zero sets

We show that a setXυR has strong measure zero iff for every closed measure zero setFυR,F+X has measure zero. Supported by KBN grant PB 2 1017 91 01.     

On sums of Darboux and nowhere constant continuous functions

We show that the property

(P)

for every Darboux function there exists a continuous nowhere constant function such that is Darboux

follows from the following two propositions:

(A)

for every subset of of cardinality there exists a uniformly continuous function such that ,

(B)

for an arbitrary function whose image contains a non-trivial interval there exists an of cardinality such that the restriction of to is uniformly continuous,

which hold in the iterated perfect set model.

     

Two stars

The authors investigate an operation * on the subsets of ${\mathcal{P}(\mathbb{R})}$ . It is connected with Borel’s strong measure zero sets as well as strongly meager. The results concern the behaviour of the family of countable sets when * is applied.     

State mixing and cd spectra of chiral molecules consisting of two identical chromophores

A study is reported of the effect of electronic state mixing on circular dichroism spectra of chiral molecules containing two identical chromophores. The CD spectrum of dimethyl-1,1'-bianthry1-2,2' dicarboxylate is intepreted in terms of such mixing between the ¹L_a and ¹B_b states of the anthracene moicty.