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.     

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.     

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.     

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.     

Optical Spectra of Oligofurans: A Theoretical Approach to the Transition Energies,Reorganization Energies,and the Vibronic Activity

There is experimental evidence of high vibronic activity that accompanies the allowed transition between the ground state and the lowest electronic singlet excited state of oligofurans that contain two, three, and four furan rings. The absorption and emission spectra of the three lowest oligofurans measured at liquid nitrogen temperature show distinct fine structures that are reproduced using the projection-based model of vibronic coupling (with Dushinsky rotation included) parameterized utilizing either Density Functional Theory (DFT, with several different exchange-correlation functionals) or ab initio (CC2) quantum chemistry calculations. Using as a reference the experimental data concerning the electronic absorption and fluorescence for the eight lowest oligofurans, we first analyzed the performance of the exchange-correlation functionals for the electronic transition energies and the reorganization energies. Subsequently, we used the best functionals alongside with the CC2 method to explore how the reorganization energies are distributed among the totally symmetric vibrations, identify the normal modes that dominate in the fine structures present in the absorption and emission bands, and trace their evolution with the increasing number of rings in the oligofuran series. Confrontation of the simulated spectra with the experiment allows for the verification of the performance of the selected DFT functionals and the CC2 method.     

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.

     

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.     

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.     

Easily prepared chiral scorpionates: tris(2-oxazolinyl)boratoiridium(i) compounds and their interactions with MeOTf

Optically active C 3-symmetric monoanionic ligands are uncommon in organometallic chemistry. Here we describe the synthesis of readily prepared tris(4 S-isopropyl-2-oxazolinyl)phenylborate [To (P)] and fluxional, zwitterionic four- and five-coordinate iridium(I) compounds [Ir(To (P))(eta (4)-C 8H 12)] ( 4) and [Ir(To (P))(CO) 2] ( 5). The highly fluxional nature of 4 and 5 makes structural assignment difficult, and the interaction between the iridium(I) center and the [To (P)] ligand is established by solid-state and solution (15)N NMR methods that permit the direct comparison between solution and solid-state structures. Although iridium cyclooctadiene 4 is a mixture of four- and five-coordinate species, the dicarbonyl 5 is only the five-coordinate isomer. The addition of electrophiles MeOTf and MeI provides the oxazoline N-methylated product rather than the iridium methyl oxidative addition product. N-Methylation was unequivocally proven by through-bond coupling observed in (1)H- (15)N HMBC experiments.     

Direct and indirect optical transitions in Zn3P2

Absorption measurements were made on single crystals of Zn₃P₂ at temperatures of 300, 80 and 5 K, and photo-voltage spectral responses-were measured at 300 K for Au- and In---Zn₃P₂ contacts. Interband absorption was interpreted as a process involving three mechanisms: (1) indirect transitions from the valence band at the Γ point, (2) either excitations from acceptor level to the conduction band at the Γ point, or second indirect transitions associated with the creation of excitons, and (3) band-to-band direct transitions at the Γ point. The effect of the lighting configuration on spectral PV plots is also discussed, and the origin of two peaks of PV responses is interpreted as being in accordance with optical data. The indirect energy gap has been estimated as 1.315eV at 300 K and 1.335 eV at 80 and 5 K, and the direct one as 1.505, 1.645 and 1.685 eV at 300, 80 and 5 K, respectively.