Suggested calculations using transition density matrices

It is suggested that certain transition density matrices, N-representable in a limit, be used in a variational calculation. It is noted that such trial matrices should yield reasonable values for the ground state energies of small atoms or molecules provided a set of overlap integrals is maximised.

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Zusammenfassung Es wird vorgeschlagen, bestimmte Übergangsdichtematrizen, die im Limit N-darstellbar sind, in einer Variationsrechnung zu benutzen. Es wird festgestellt, daß solche Näherungsmatrizen gute Werte für die Energie des Grundzustandes kleiner Atome oder Moleküle geben sollten, falls im Satz von Überlappungsintegralen maximiert wird.

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Résumé On propose d'utiliser dans un calcul variationnel certaines matrices densité de transition, N représentables à la limite. Ces matrices d'essai devraient fournir des valeurs raissonnables pour l'énergie de l'état fondamental dans les petits atomes et les petites molécules à condition de maximiser un ensemble d'intégrales de recouvrement.

     

Theoretical investigations of Fe porphyrins. V. Low-lying electronic states of bisammineporphinatoiron(III)

Ab initio CI calculations are reported on the lowest doublet, quartet, and sextet states of [Fe^III(P)(NH₃)₂]⁺. The low-spin ground state is calculated as (d_xy² (d_π)³ with d_xy(d_π)⁴ higher by 0.15 eV. The near-ir bands at ～1 eV observed in low-spin ferriheme proteins are attributed to (π → d_π) transitions. The lowest high-spin state is ⁶A_1g, and the near-ir transitions of the high-spin ferriheme proteins observed at ～1.2 eV are attributed to higher ⁶[tripsextet] excited states [i.e., ring triplet, metal sextet]. The 30-ps “triplet” transient populated with low quantum yield observed in laser-flash studies on Fe^III(TPP)CI [TPP = tetrapbenylporphyrin] may be an ¹[tripsextet] state.     

The phenolic oxidation of a β-methylchalcone

The phenolic oxidation of 2',4-dihydroxy-4'-methoxy-β-methylchalcone using alkaline potassium ferricyanide gives an aurone rather than an isoflavone. This result is discussed in the context of current theories regarding the biosynthesis of flavonoid and isoflavonoid compounds.     

Effective asymmetric synthesis of 1,2,9,9a-tetrahydrocyclopropa[c]benzo[e]indol-4-one (CBI)

A short, asymmetric synthesis of the 1,2,9,9a-tetrahydrocyclopropa[c]benzo[e]indol-4-one (CBI) analogue of the CC-1065 and duocarmycin alkylation subunits is detailed that employs an effective enzymatic desymmetrization reaction of prochiral diol 12 using a commercially available Pseudomonas sp. lipase. The optically active monoacetate (S)-13 is furnished in exceptional conversions (88%) and optical purity (99% ee) and serves as an intermediate for the preparation of either enantiomer of CBI. Similarly, the Pseudomonas sp. lipase resolved the racemic intermediate 19, affording advanced intermediates of CBI in good conversions and optical purity (99% ee), and provided an alternative approach to the preparation of optically active CBI derivatives.     

Tuning the band gap in hybrid tin iodide perovskite semiconductors using structural templating

Structural distortions within the extensive family of organic/inorganic hybrid tin iodide perovskite semiconductors are correlated with their experimental exciton energies and calculated band gaps. The extent of the in- and out-of-plane angular distortion of the SnI4(2-) perovskite sheets is largely determined by the relative charge density and steric requirements of the organic cations. Variation of the in-plane Sn-I-Sn bond angle was demonstrated to have the greatest impact on the tuning of the band gap, and the equatorial Sn-I bond distances have a significant secondary influence. Extended Hückel tight-binding band calculations are employed to decipher the crystal orbital origins of the structural effects that fine-tune the band structure. The calculations suggest that it may be possible to tune the band gap by as much as 1 eV using the templating influence of the organic cation.     

Rearrangement during cyclisation of some 3-(2-pyrrolyl) propionic acids and related compounds

Cyclisation of the title compounds leads to mixtures of the expected 4H-cyclopental[b]pyrrol-4-ones (1), the corresponding 6-ones (3) by a single rearrangement, and the cyclopenta[c]pyrrol-4-ones (4) by a double rearrangement, the proportions depending upon the substituents.The ¹H NMR spectra of 2-methyl-4H-cyctopenta[b]thiophen-6-one (3f) shows 6J long range $\text{CH}{}_3\text{CH}{}_2$ coupling, but this is absent in the corresponding pyrroles (3c,d). The ¹³C spectra of 1 and 3 cannot be interpreted on the basis of substituent chemical shifts in pyrroles and thiophens, and are clearly -CH = CH-X (X = NMe, NPh, S) bridged derivatives of cyclopent-2-enone.     

The effect of crown ethers on the alkylation of a cyclic β-keto ester

The effects of crown ethers (6 and 7) on the reactions of sodium (2a) and potassium enolates (2b) of 2-ethoxycarbonylcyclohexanone (1) with isopropyl iodide in dimethylsulfoxide and dimethoxyethane have been investigated. When the addition of crown ether promoted dissociation of ion pair 2 in either of the two solvents, the total rate of reaction (k_t) increased and the ratio of carbon- (3) to oxygen-alkylation (4 and 5) products decreased. The results are consistent with the involvement of both the ion pair and more dissociated species in alkylation and with greater reactivity for the latter.     

THE MOLECULAR WEIGHT OF HAEMATOPORPHYRIN DERIVATIVE, ITS GEL COLUMN FRACTIONS and SOME OF ITS COMPONENTS IN AQUEOUS SOLUTION

Abstract— The average molecular weights of haematoporphyrin derivative (HPD), the fractions of HPD that can he obtained by gel chromatography and of purified haematoporphyrin and protoporphyrin in aqueous solution have been determined by ultracentrifugation. The results show that HPD contains polymeric material with the excluded fraction from the gel column (HPD aggregate) having an average molecular weight of greater than 20000. The two remaining gel column fractions of HPD have lower molecular weights and their similarity indicates that these fractions do not separate because of molecular weight differences. Purified haematoporphyrin has a comparatively low molecular weight in aqueous solution but the data is not capable of discriminating between monomer, dimer or slightly higher oligomer. In contrast, protoporphyrin sediments to the bottom of the centrifuge tube under the conditions of sedimentation equilibrium indicating that it has an average molecular weight considerably greater than that of HPD aggregate.     

Elastic instabilities in cone- and -plate flow: Small gap theory

Consider the axisymmetric, inertialess cone- and -plate flow of a viscoelastic fluid. A perturbation method is used to obtain more tractable equations that describe the flow when the gap angle is small. A linear stability analysis of the base viscometric flow shows that there is a loss of stability when an elasticity parameter =DeWe, increases past a critical value. This purely elastic instability is of the oscillatory type. We obtain expressions for the critical elasticity number, frequency and wave number. The critical Deborah number varies as , the wave length as . and the wave speed as , where . is the gap angle. The most unstable mode exhibits infinitely many logarithmically-spaced roll cells which propagate inward towards the apex of the cone. These results are in agreement with experimental and numerical results.