The mechanism of the reductive cleavage of organic halides (RX) by pentacyanocobaltate(II) Co(CN)53− was investigated by means of the extended Hückel MO theory. First, the molecular structure of Co(CN)53− was considered to be the square-pyramidal C4V configuration, without H2O as its sixth ligand. Secondly, the order of the observed rate constants for the Co(CN)53−+RX→Co(CN)5X3−+R. reaction was found to be in satisfactory accordance with that of the calculated binding energies of the R-X bond. Thirdly, the reductive cleavage of RX by Co(CN)53− proceeds by the aid of the predominant electron-migration from the highest-occupied, lone-pair halogen-orbital to the singly-occupied dz2 Co-orbital and from the highest-occupied dxz (or dyz) Co-orbital to the lowest-unoccupied, antibonding pσ* orbital of the R–X bond. Finally, the mode of the interaction between Co(CN)53− and RX was precisely discussed in terms of the homolytic cleavage of the R–X bond.

The correlation between the gas-phase proton affinities of aliphatic oxygenated compounds (alcohols, acids, and esters and their electronic structures was investigated by means of an INDO-MO theory. There appears to be a satisfactory linear-dependence of the proton affinities with the energy difference between the parent molecule and the energetically most stable protonated species and with the bond energy of the oxygen-proton bond, although the above energies are overestimated in comparison with the proton affinities. The proton affinities are also predicted with a sufficient accuracy using the first ionization potential and the electron density of the oxygen atom (especially, the % p-character in the oxygen lone-pairs) of the parent molecule.

A new technique using the polynomials approximation and the trapezoidal average method, has been proposed for estimating kinetic rate constants. It is implemented by minimizing the error of the concentration (of a product) obtained from the polynomial-approximated least square-error analysis of the observed concentrations during the initial reaction stage relative to that obtained theoretically from the trapezoidal average of the calculated concentration (of a product) on the basis of the law of mass action. The technique is useful for easily and exactly estimating the rate constants in systems of linear or nonlinear differential equations. A kinetic model, A→ B\ightleftarrowsC, was used to illustrate and develop the present technique.

A new technique is proposed for estimating the rate constants in systems of linear or nonlinear differential equations, using a polynomial approximation of the observed concentrations of species participating in the reaction and an iterative search technique. The method is implemented by minimizing the errors of the concentrations (of species), as computed by the theoretical equations derived from the linear differential equations or by the trapezoidal averaging simulation, relative to those calculated by the polynomial approximation. The present technique requires the concentrations (at the initial reaction stage) of s-2 species (the s species takes part in the reaction). Two kinetic example, A\ightleftarrowsB\ightleftarrowsC and S+E\ightleftarrowsES→P, have been used to illustrate and develop the present technique.

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