Renormalization group and high-temperature series for the two-dimensional ising model

We employ high-temperature series to investigate a two-parameter class of renormalization group transformations for the two-dimensional Ising model on the triangular lattice. For the static case we identify an optimal organization of the high-temperature expansion and an optimal transformation matrix and thus find, in second order, =0.96 and the magnetic eigenvaluey=2-/2=1.76.From recursion relations for flip rates we find the dynamic exponent to be the same for all transformations in our two-parameter class,z=2.32.Our fixed-point flip rates do not describe a Markov process even though the corresponding master equation for the single-event probability displays no explicit memory effects. The non-Markovian nature shows up only in a violation of the Markovian detailed balance conditions.     

Nachweis von C (15)-epimeren Coleonen C und D in der Natur und ihre Bedeutung für den sterischen Verlauf der Bildung des Spirocyclopropanrings

Natural Occurrence of C(15)-Epimeric Coleons C and D and its Significance to the Stereochemistry of the Formation of a Spirocyclopropanring In a previous paper some evidence was presented for a predominant occurrence of epimeric coleons ((15S)-coleon C ((15 S)- 1a ), and (15S)-coleon D ((15S)- 2a )) in Plectranthus lanuginosus [1], The proposed structures have now been proven by careful comparison of their physical data with those of the already described C(15)-epimers whose structures were deduced by X-ray analysis of a derived cis-diketone 3 [5], Examination of the epimeric purity of coleons possessing a 2-hydroxy-1-methylethyl side-chain (coleons C , D , H , I , I ′ and derivatives) isolated from seven different species (Coleus, Plectranthus and Solenostemon) has shown that these coleons always occur as a mixture of C(15)-epimers, although in most cases with one predominant epimer. The consequences for the stereochemistry of the postulated in vivo formation of the methyl-substituted spirocyclopropane substructure is discussed.     

Some diels—alder reactions of η1-bonded cyclopentadienylmetal compounds

Bis(cyclopentadienyl)mercury readily undergoes Diels—Alder reactions with RCCR (R = CO₂Me or CF₃), CF₃CFCFCF₃, CF₃CFCF₂, (CF₃)₂CC(CN)₂, C₂(CN)₄ and Ph$\text{NCONNC}$O to give stable adducts characterised by¹H, ¹⁹F and ¹³C NMR, spectroscopy. Similar reactions of CF₃CCCF₃ and CF₃CFCFCF₃ with the cyclopentadiene derivatives Me₃MC₅H₅ and (Me₃M)₂C₅H₄ (M = Si, Sn) are also described.     

Flache T1-Stabilität in der Strati-fizierung verseller Entfaltungen

Let 0 be the local ring of a simple singularity defined over the complex numbers and the dimension of its versal deformation space. Than it is well known that any nearby singularity in this space is also simple and has smaller unfolding dimension in the hierarchy of simple singularities. In particular this implies that the =max-stratum consists just of one point namely the given singularity. We want to generalize this concept as we are interested in families of varieties with formal unchanged singularities. For this we introduce in quite generality the notion of flat T¹-stabi1ity which may be checked for any k- algebra 0 where k is for simplicity an algebraically closed field of à priori arbitrary characteristics. We call 0 formal flat T¹ stable or for short flat T¹-stable if the following is true: if R is any deformation of 0 over an Artin local finite k-algebra A and if T¹(R/A,R) is A-flat than R is isomorphic to the trivial deformation . T¹(R/A,R) is the first cotangent module of R over A with values in R. Obviously the simple singularities A_k, D_k, E₆, E₇, E₈ fulfill this criterion over C but we look also at fibres of arbitrary stable map germs, generic singularities of algebraic varieties where we have to modify this notion in order to deal with wild ramification and to quasihomo-genous hypersurface singularities where it functorializes because in this case T¹ commutes with arbitrary base change. The notion of flat T¹-stable singularities is closely related to questions of existence of equisingular families and is used in[12] and [5], [6] to stratify certain Hilbert schemes.     

π Coordination de diazoalcanes sur le dicyclopentadienylvanadium (II)

The X-ray crystal and molecular structure of η⁵-cyclopentadienyl-η¹-2,4-diphenylcyclobut-1-en-3-oneiron dicarbonyl (I) was determined (monoclinic crystals, a 9.2371(9), b 26.4502(9), c 8.2450(7) Å, β 115.502(6)°, Z = 4, space group P2₁ /c, 1902 unique reflections, R = 0.068). Molecule I contains the η¹-cyclobut-1-en-3-one ligand with three sp² and one sp³ carbon atoms in a four-membered cycle, σ-bonded to the CpFe(CO)₂ fragment (bond distance FeC 1.935(6) Å).     

PHOTOCHEMICAL AND FREE RADICAL INITIATED REACTIONS OF 1,3-DIMETHYLTHYMINE WITH ETHANOL

The photochemically induced reaction of 1,3-dimethylthymine (DMT) with ethanol gives four major alcohol adducts. These have been identified as l,3-dimethyl-6-(1-hydroxy-1-ethyl)thymine ( 1 ), 1,3-dimethyl-5-(2-hydroxy-l-pyl)uracil ( 2 ), and the cis and trans isomers of 5,6-dihydro-l,3-di-methyl-6-(l-hydroxy-l-ethyl) thymine ( 3 and 4 ). The compounds 3 and 4 have been shown to be identical to the adducts produced in y-ray irradiated ethanolic aqueous solutions of DMT. Cyclobutane dimers of DMT are also found in the photochemical reaction mixture. Reaction of 1-hydroxyethyl radicals with DMT, initiated by decomposition of di-t-butyl peroxide, leads to formation of the same alcohol adducts, as well as to DMT adducts containing two molecules of ethanol. The acetone sensitized reaction of DMT with ethanol gives 1,3, and 4, along with a variety of adducts incorporating the acetone sensitizer.     

The first genuine observation of fluorescent mononuclear phthalocyanine aggregates

An initial photophysical study of a tetra-solketal-substituted zinc phthalocyanine is reported; at low temperature this compound exhibits very strong aggregation, and a new red shifted emission peak is observed, lambda max approximately 750 nm, attributed to a fluorescent phthalocyanine dimer.     

Fragmentation of N-linked glycans with a matrix-assisted laser desorption/ionization ion trap time-of-flight mass spectrometer

N-Linked glycans were ionized from several matrices with a Shimadzu-Biotech AXIMA-QIT matrix-assisted laser desorption/ionization quadrupole ion trap time-of-flight mass spectrometer. [M+Na]+ ions were produced from all matrices and were accompanied by varying amounts of in-source fragmentation products. The least fragmentation was produced by 2,5-dihydroxybenzoic acid and the most by alpha-cyano-4-hydroxycinnamic acid and 6-aza-2-thiothymine. Sialic acid loss was extensive but could be prevented by formation of methyl esters. Fragmentation produced typical low-energy-type spectra dominated by ions formed by glycosidic cleavages. MS(n) spectra (n = 3 and 4) were used to probe the pathways leading to the major diagnostic ions. Thus, for example, an ion that was formed by loss of the core GlcNAc residues and the 3-antenna was confirmed as being formed by a B/Y rather than a C/Z mechanism. The proposed structures of several cross-ring cleavage ions were confirmed and it was shown that MS3 spectra could be obtained from as little as 10 fmol of glycan.     

Unrestricted perfect pairing: the simplest wave-function-based model chemistry beyond mean field

The perfect pairing (PP) approximation from generalized valence bond theory is formulated in an unrestricted fashion for both closed- and open-shell systems using a coupled cluster ansatz. In the model chemistry proposed here, active electron pairs are correlated, but the unpaired or radical electrons remain uncorrelated, leading to a linear number of decoupled cluster amplitudes which can be solved for analytically. The alpha and beta spatial orbitals are variationally optimized independently. This minimal treatment of electron-electron correlation noticeably improves upon symmetry-breaking problems and other pathologies in Hartree-Fock (HF) theory and may be computed using the resolution of the identity approximation at only a factor of several times more effort than HF itself. PP also generally predicts improved molecular structures over HF. This compact, correlated wave function potentially provides a useful starting point for dynamical correlation corrections.     

Porphyrins

Extended Hückel calculations are reported for tetravalent porphin complexes of Si(OH)₂, Ge(OH)₂, GeCl₂, and SnCl₂ and divalent complexes of Ge, Sn, and Pb. Divalent Ge porphin is expected to be planar and have the extra two electrons in the ring. Divalent Sn and Pb porphins are expected to be non-planar and have the extra two electrons on the metal. The possibility of a charge transfer transition a ₁(p _z )e _g ^* () is noted, and its identication in available spectra of Sn and PbTPP is made. The electronic structure of the tetravalent species is similar to other metalloporphyrins except for the possibility of low lying ligand to porphin charge transfer states in the hydroxy complexes.

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Zusammenfassung Für die vierwertigen Porphin-Komplexe des Si(OH)₂, Ge(OH)₂, GeCl₂ und SnCl₂ und die zweiwertigen Komplexe des Ge, Sn und Pb werden Berechnungen nach der erweiterten Hückel-methode durchgeführt. Von dem zweiwertigen Ge-Porphin wird erwartet, da\ es planar ist und da\ sich die beiden zusÄtzlichen Elektronen im Ring befinden, wÄhrend von den zweiwertigen Sn- und Pb-Porphinen zu erwarten ist, da\ sie nicht planar sind und die beiden zusÄtzlichen Elektronen sich am Metall befinden. Auf die Möglichkeit eines Charge-Transfer-übergangs a ₁(p _z )e _g ^* () wird hingewiesen, und dieser übergang wird in gemessenen Spektren von Sn und PbTPP identifiziert. Die Elektronenstruktur der vierwertigen Verbindung ist denjenigen anderer Metallporphyrine Ähnlich, au\er der Möglichkeit niedrig liegender Ligand-Porphin-Charge-Transfer-ZustÄnde in den Hydroxy-Komplexen.

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Résumé Calculs de type Hückel étendu pour des complexes tétravalents de la porphine avec Si(OH)₂, Ge(OH)₂, GeCl₂ et SnCl₂ et des complexes divalents avec Ge, Sn et Pb. La porphine de Ge divalente est prévue plane avec les deux électrons supplémentaires dans le cycle. Les porphines divalentes de Sn et Pb sont prévues non planes avec les deux électrons supplémentaires sur le métal. On remarque la possibilité d'une transition de transfert de charge a ₁(p _z)e _g ^* () et on l'identifie dans les spectres disponsibles pour Sn et PbTPP. La structure électronique des espèces tétravalentes est semblable à celle des autres métalloporphyrines à l'existence possible près dans les complexes hydroxy d'états de transfert de charge de basse énergie entre le ligand et la porphine.

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Paper XX: Ake, R. L, Gouterman, M.: Theoret. chim. Acta (Berl.) 17, 408–416 (1970).