The Colour of Dyes and Steric Hindrance in Their Molecules

Abstract

AbstmcL Extending our recent proof of the cosmic no-hair theorem for Bianchi models in power-law inflation, we prove a more general cosmic no-hair theorem for all 0 < X < fi, where X is the coupling constant of an exponential potential of an inflaton +, exp(-Xrcc$). For any initially expanding Bianchi-type model except type IX, we find that the isotropic idationary solution is the unique attractor and that anisotropies always enhance inflation. For Bianchi IX, this conclusion is also true, if the initial ratio of the vacuum energy A.@ to the maximum 3-cumature (3) R,, is larger than 1/[3(1-Xz/2)] and its time derivative is initially positive. It t u n s out that the sufficient condition for inflation in Bianchi twe-IX spacetims with cosmological constant A, which is a special case of the theorem (A = 0), becomes less restrictive than Wald's one. For type lX, we also show a recollapse theorem. PACS numbers: 9880,0450 0264-9381/93/040703+32SO7.50 @ 1993 IOP Publishing Lid 703 704inflationary models were systematically investigated in the conformal frame. They found that new inflation as well as chaotic inflation with a massive inflaton allow not only natural initial data but also natural coupling constants. Such approaches may hence give us a natural inllationary model.Apart from the naturalness of inflationary models, we have another question about naturalness of an inflationary solution, namely whether inflation is the unique attractor in the most general spacetime with cosmological constant or vacuum energy. In the discussion about inflation, we usually assume Friedmann-Robertson-Walkertype spacetimes. Although we have not so far known anything about the initial state of the Universe, the ansatz of isotropy and homogeneity of the Universe might be also justified by inflation. In order to show it, we have to study whether or not inflation really occurs even in anisotropic and/or inhomogeneous spacetimes and whether the spacetime is isotropized and homogenized during inflation. This problem is related to the so-called cosmic no-hair conjecture.In the most general inhomogeneous case, however, the analysis is very difficult, and hence a numerical approach may be the only way to show whether or not it is true [6], except for perturbation analysis [7].However, in an anisotropic but homogeneous case, if a positive cosmological constant exirts, we have the cosmic no-hair theorem proved by Wald [SI, which tells us that all initially-expanding Bianchi models except type IX approach the de Sitter spacetime in one expansion time. For type IX, some spacetimes recollapse, and we know just a sufficient condition for inflation [8-10]. In the old or new inflationary models, the false vacuum energy is almost a constant, and thus behaves as a positive cosmological constant. This theorem is, therefore, applied. This theorem was also extended to chaotic inflationary models 191.A natural question may arise, namely whether or not this theorem is extendible to power-law inflationary models [Ill. This question becomes more important in ...

Further Studies on the Oxidation State of Iron in μ-Oxo Dimeric Phthalocyanine Complexes

“…In this case the geometry of form '690' probably differs from those of other phthalocyanine and porphyrin m-oxo-bridged complexes [2,3,61,63]. Similar results have been found for some cyanine dyes, where, depending on the interchromophoric angle, hypsochromic or bathochromic shifts of the long-wavelength band in the electronic spectra have been observed [57,64]. The second case where the bathochromic shift of the Q-band for form '690' could be observed is when one parallel phthalocyanine ligand is shifted in the xyplane with respect to the other ligand (slipped-stacked orientation, Fig.…”

“…The Mössbauer spectra of 57 Fe have been recorded with an NGRS-4 spectrometer at 300 K. A 57 Co source in a chromium matrix has been used. A criterion of goodness of fit (w 2 ) has been calculated for each spectrum.…”

“…It is well known that in general for two nearly parallel phthalocyanine chromophores the Q-band is hypsochromically shifted in comparison with that for the monomer analogues (PcM or PcMX) owing to dipole-dipole exciton coupling [49,56,57,58,59,60]. Thus the Q-band has been observed at 627 nm for PyPcMn-O-MnPcPy [26,48] R is an unsubstituted or a tetra-4-tert-butyl-or tetra-4-ethylsubstituted phthalocyanine [46,[51][52][53][54][55].…”

“…Now it should be discussed what is responsible for the unusual electronic spectrum of form '690'. The simplest way to estimate the geometry of two interacting chromophores is to use exciton interaction theory [56][57][58][59][60]62]. According to this theory, two important reasons could lead to the bathochromic shift of the Q-band for form '690'.…”

Structure and electronic absorption spectra of cyanine dyes – derivatives of tetrazolo- and triazoloisoindole

“…Our dyes had unusually high logarithms of extinction as for monomethine cyanine. Taking into account the traditions of the famous Ukrainian Kiprianov-Babichev school on the study of the dependence of absorption spectra on the structure of cyanine dyes [13][14][15], we have studied the electronic structure and absorption spectra of dyes 1 and 2.…”