A linear multistep numerical integration scheme for solving systems of ordinary differential equations with oscillatory solutions

In ^[1], a set of convergent and stable two-point formulae for obtaining the numerical solution of ordinary differential equations having oscillatory solutions was formulated. The derivation of these formulae was based on a non-polynomial interpolant which required the prior analytic evaluation of the higher order derivatives of the system before proceeding to the solution. In this paper, we present a linear multistep scheme of order four which circumvents this (often tedious) initial preparation. The necessary starting values for the integration scheme are generated by an adaptation of the variable order Gragg-Bulirsch-Stoer algorithm as formulated in ^[2].     

Organometallic Reactions and Syntheses : Volume 6, E. I. Becker and M. Tsutsui,ed., Plenum Publishing Corporation., New York/ London, 1977, xii + 314 pages $47.40

The (Me₃Si)₃C group causes very large steric hindrance to nucleophilic displacement at a silicon atom to which it is attached, and (Me₃Si)₃CSiMe₂Cl is even less reactive than t-Bu₃SiCl towards base. The compounds (Me₃Si)₃CSiMe₂X (X = Cl, Br, or I) are cleaved by MeOH/MeONa to give (Me₃Si)₂CHSiMe₂OMe, possibly via the silaolefin (Me₃Si)₂ CSiMe₂, and the correspondLug (Me₃Si)₃ CSiPh₂X compounds undergo the analogous reaction even more readily. The halides (Me₃Si)₃CSiR₂X (X = Cl or Br) and (Me₃Si)₃CSiCl₃ do not react with boiling alcoholic silver nitrate, but the iodides (Me₃Si)₃CSiR₂I are rapidly attacked.     

Thermal expansion in (La0.62Pb0.38)MnO3: Possible evidence for a coupling between elastic and magnetic exchange forces

Using single-crystal, automated diffractometer techniques, the linear coefficient of thermal expansion has been determined for La_0.62Pb_0.38MnO₃ from 298 to 627 K. The linear coefficient of thermal expansion is observed to undergo a change from 7.2 × 10^?5 Å/K for T < T_c to 10.8 × 10^?5 Å/K for T > T_c. It is concluded that while the rhombohedral distortion in the (La, Pb)MnO₃ system can be understood qualitatively on the basis of ionic size and polarizability considerations alone, the quantitative systematics of the distortion parameters and the change in the linear thermal expansion coefficient at T_c indicate a significant coupling between the elastic and magnetic exchange forces.     

Kinetics of nucleophilic attack on coordinated organic moieties. XVIII. Nucleophilicity of anions towards the tricarbonyl-(η-benzene) manganese (I) cation.

Kinetic results for the addition of OH^? to [Mn(CO)₃(η-C₆H₆)]⁺ (I) in water (eq. 1, X  OH) obey the expression k_obs  k_OH[OH^?], and give a k_OH value of 290 mol^?1 dm³ s^?1 at 20.0°C and ionic strength of 0.25 mol dm^?3. The analogous reaction of NaCN with I in water fits the two-term expression k_obs = k_OH[OH^?] + k_CN[CN^?], and leads to a k_CN value of 0.8 mol^?1 dm³ s^?1 at 20.0°C and ionic strength of 0.25 mol dm^?3. Interestingly, the related reaction (eq. 1, X  N₃) is too rapid to follow by stopped-flow spectrophotometry, indicating the overall rate trend N₃^? » OH^? » CN^?. This unusual nucleophilicity order, unexpected on the basis of both basicity and polarizability, is similar to that previously observed for anion addition to free carbonium ions.     

Gas chromatography in qualitative analysis. Part 14. Molecular retention index as an alternative system for the characterization of gas chromatographic stationary phases

Summary The limitations of methods for the characterization of stationary phases, which require the use of a base or reference stationary phase, are considered. In order to overcome these problems, a new method of column characterization, based upon measurements of molecular retention index and ΔMe values for selected functional groups, is proposed. ΔMe values are shown to be dependent upon liquid phase composition, nature of the support and liquid phase loading.     

Orientation of nucleophilic substitution in π-cation radicals or π-dications from meso-substituted metalloporphyrins

Treatment of meso-substituted metalloporphyrins [meso -substituent = OCOCF₃, OCOCH₃, OMe, CHO, CN, Cl; metal = Zn(II) or Cd(II)] with thallium(III) trifluoroacetate, followed by an acidic work-up, gives the corresponding β-substituted α-oxophlorins which were either characterised as such or else further derivatised. In all cases the major (or only) disubstitution product has the αβ orientation at the meso positions, indicating that the existing meso substituent directs the incoming one (trifluoroacetate) into the flanking, rather than opposite, meso position of the intermediate π-cation radical or π-dication. In contradistinction, meso substituted zinc(II) porphyrins which are able to lose protons (e.g. α-oxophlorins or α-aminoporphyrins) react with thallium(III) trifluoroacetate, and after a work-up with HCl the corresponding γ-chloro-α-oxophlorin or γ-chloro-α-aminoporphyrin is obtained.     

Inverse gas chromatography in the study of polymer degradation. Part 2. Oxidation of sulphurated squalene as a model for the oxidative degradation of natural rubber vulcanizates

Summary Inverse gas chromatography with sulphurated olefinic stationary phases and air as carrier gas has been found to yield characteristic shifts of retention data. The resulting plots of retention index versus reaction time obtained for a range of squalene vulcanizates have been found to be similar to those given by oxygen absorption measurements. Furthermore the chromatographic oxidation curves have been found to be consistent with the known oxidation behaviour of the various sulphur networks formed on vulcanization. This paper is dedicated to the memory of Dr.Graham Moore (1924–1968).