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Extensions of Szegö's theory of orthogonal polynomials,III

Let {ø _n (dμ)} be a system of orthonormal polynomials on the unit circle with respect to a measuredμ. Szegö's theory is concerned with the asymptotic behavior ofø _n (dμ) when logμ′∈L ¹. In what follows we will discuss the asymptotic behavior of the ratioø _n (dμ ₂)/ø _n (dμ ₁) on the unit circle whendμ ₁ anddμ ₂ are close in a sense (e.g.,dμ ₂=gdμ ₁, where g≥0 is such thatQ(e ^it )g(t) andQ(e ^it )/g(t) are bounded for a suitable polynomialQ) and μ ₁ ^′ >0 almost everywhere or (a somewhat weaker requirement) lim _n→∞Φ _n (dμ ₁,0)=0 for the monic polynomial Φ _n . The asymptotic behavior of the same fraction outside the unit circle was discussed in an earlier paper.     

Donor—acceptor interactions of substituted benzenes with molecular chlorine and carbon disulfide

CNDO molecular orbital calculations have been performed to analyze donor—acceptor interactions between molecular chlorine and benzene, toluene, mesitylene and hexamethylbenzene and the, as yet, unreported chlorine—hexafluorobenzene and carbon disulfide—benzene pairs. The stabilization energy and the dipole moment and its derivative (?p/?R_CICI) calculated for the benzene—chlorine complex are in good agreement with the estimated experimental values. The trends in the experimental stabilization energies and the Cl-Cl vibrational frequencies with increasing methyl substitution appear to be well reproduced by the calculations. The charge transferred from the benzene donor is polarized toward the outer chlorine atom or sulfur atom. For hexafluorobenzene-chlorine the direction of electronic charge polarization is reversed from that of the benzene and methylbenzene complexes. The calculated results are discussed within the framework of Muliiken's simplified resonance theory for complexes.     

Conformational preferences of 34 valence electron A2X4 molecules: An ab initio Study of B2F4, B2Cl4, N2O4, and C2O

Ab initio molecular orbital structures and energies of B₂F₄, B₂Cl₄, N₂O₄, and C₂O have been calculated for both perpendicular D_2d and planar D_2h rotamers. The experimental trend toward greater preference for the D_2d forms in going from B₂F₄ to B₂Cl₄ is reproduced. N₂O₄ favors the planar conformation, although the rotation barrier is overestimated at the theoretical levels used. The oxalate dianion is calculated to be more stable in the D_2d conformation; the experimental planar arrangement in the solid may be due to crystal packing forces. The preferences for one conformation over another are small; analysis indicates that different effects may predominate in each case: π stabilization for B₂F₄, hyperconjugation for B₂Cl₄, lone-pair interactions for N₂O₄, and electrostatic repulsions for C₂O.     

Reactions of tetrahydro-as-triazine-3(2H)-thiories with α, β-difunctional compounds

The results of allowing tetrahydro-as-triazine-3(2H)-thiones to react with various α,β-diiunctional compounds, such as, α-bromoethyl p-toluenesulfonate, chloroacetaldehyde, α-bromophenylacet-uldehyde, phenaeyl bromide, chloroacetonitrile, α-bromophenylaeelonitrile, and α-cyanobenzyl p-toluenesulfonate are discussed. These condensations give either a 5H-thiazolo[3,2-b]-as-triazine or a 2H-thiazolo[2,3-c]-as-triazine.     

A 13C- and 195Pt-NMR. Study of the Complexes trans-PtCl2 (amine) (CH2CH2)

¹³C- and ¹⁹⁵Pt-NMR. spectra for the complexes trans-PtCl₂(amine)(CH₂?CH₂) have been measured. For amine = (S)-N-methyl-α-methylbenzylamine the two diastereomers present may be distinguished from the values ³J(Pt,C). The ¹⁹⁵Pt-chemical shift is shown to be sensitive to subtle differences stemming from intramolecular non-bonded interactions.     

Thin-layer chromatographic separation of serotonin from epinephrine and norepinephrine

A thin-layer chromatographic procedure is reported for the separation of serotonin from epinephrine and norepinephrine. The method involves the use of ethylenediaminetetraacetic acid-impregnated silica gel G plates and n-butanol-ethanol-acetic acid-water (8:2:1:3) as developer. Serotonin is well separated from both epinephrine and norepinephrine. Epinephrine and norepinephrine overlapped slightly but were both detectable. The procedure is thus applicable to the separation of all three biogenic amines in spite of the absence of an absolutely clear separation of epinephrine from norepinephrine.