Ab initio studies of structural features not easily amenable to experiment: Part 20. Structural aspects of ethyl groups

The molecular structures of a number of stable conformations of ethanol, ethylamine, methylethyl ether, methylethylamine and of the ethyl anion have been determined by ab initio geometry optimizations using Pulay's Force method on the 4–21G level. The calculated geometries characterize the extent to which structural groups in a molecule are sensitive to asymmetries in their environment. Characteristic structural trends are consistently found for the CH bond distances and CCH angles in the C₂H₅ groups of trans-ethanol, trans-methylethyl ether and in the ethyl anion. They differ from those previously found for C₂H₅ groups in hydrocarbons. There is qualitative disagreement between the trends calculated for CH bond distances in trans-ethanol and trans-methylethyl ether and those found in the microwave substitution structures of these compounds. Since the substitution parameters are unresolved because of relatively large experimental or model uncertainties, it is presently impossible to decide whether this discrepancy is the result of computational or experimental deficiency. The methyl groups in methylethyl ether and methylethylamine exhibit the characteristic structural distortions which are usually found for CH₃ groups adjacent to electron lone pairs. The CC bond distances in C₂H₅ in the systems studied here are sensitive to the conformational arrangement of ethyl relative to the rest of a system in a way which can be rationalized by orbital interactions involving antibonding orbitals on sp³-hybridized carbon atoms. The calculated conformational stabilities agree qualitatively with experimental trends, except in the case of ethanol where the trans — gauche energy difference is small (about 0.1 kcal mol^?1) and within the uncertainties of the calculations. Our conformational energies for CH₃CH₂NH₂ are in disagreement with a previous ab initio investigation based on a comparison of unoptimized standard geometries. In general, the agreement between calculated structural parameters and corresponding reliable experimental values is very good in all comparable cases.     

Mass spectra of the coordination compounds of nickel with the tetradentate Schiff bases of S-substituted thiosemicarbazides with 2,4-pentanedione and 3-oxo-2,4-pentanedione

The mass spectra of the coordination compounds of nickel(II) with the bis-S-substituted thiosemicarbazones of 2,4-pentanedione (R₂H₂L) with the general formula [NiR₂HL]X and of 3-oxo-2,4-pentanedione (H₂R₂LO) with the general formula NiR₂LO were studied. A distinguishing feature of the mass spectra of [NiR₂HL]X is the absence of molecular ion peaks. The initial point of fragmentation is the [M - HX] ions. The strongest lines in spectra of NiR₂LO are those due to the elimination of R and R-H. At the first stage the fragmentation of all the investigated compounds takes place mainly through only one of the thiosemicarbazide residues. At the second stage the 2,4-pentanedione (3-oxo-2,4-pentanedione) residue is eliminated, after which the remaining thiosemicarbazide part dissociates. A significant part of the fragmentation paths was confirmed by the peaks of the metastable ions and also by the mass spectra of the deuterated analogs.Institute of Chemistry, Academy of Sciences of the Moldavian SSR, Kishinev. Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 27, No. 2, 205–211, March–April, 1991. Original article submitted August 19, 1986.     

Trees in tournaments

Letf(n) be the smallest integer such that every tournament of orderf(n) contains every oriented tree of ordern. Sumner has just conjectures thatf(n)=2n–2, and F. K. Chung has shown thatf(n)(1+o(1))nlog₂ n. Here we show thatf(n)12n andf(n)(4+o(1))n.     

Uniformly non-l n (1) Musielak-Orlicz sequence spaces

We give a necessary and sufficient condition for the uniformly non-l _n ⁽¹⁾ property of Musielak-Orlicz sequence spacesl ^Φ generated by a sequence Φ=(ϕ_n:n⩾l) of finite Orlicz functions such that for eachn∈ℕ. As a result, forn ₀⩾2, there exist spacesl ^Φ which are only uniformly non-l _n ⁽¹⁾ forn⩾n ₀. Moreover we obtain a characterization of uniformly non-l _n ⁽¹⁾ and reflexive Orlicz sequence spaces over a wide class of purely atomic measures and of uniformly non-l _n ⁽¹⁾ Nakano sequence spaces. This extends a result of Luxemburg in [19]. Submitted in memory of Professor W. Orlicz     

Random walk on a disordered directed Bethe lattice

The random walk of a particle on a directed Bethe lattice of constant coordinanceZ is examined in the case of random hopping rates. As a result, the higher the coordinance, the narrower the regions of anomalous drift and diffusion. The annealed and quenched mean square dispersions are calculated in all dynamical phases. In opposition to the one-dimensional (Z=2) case, the annealed and quenched mean quadratic dispersions are shown to be identical in all phases.We shall employ indifferently the expressions Bethe lattice or infinite Cayley tree to denote an infinite ramified lattice of constant coordinanceZ.^{(4, 5)}