A systematic derivation procedure that greatly facilitates the application of the Taylor method to the integration of kinetic models is developed. In addition, an algorithm that gives the integration step as a function of the required level of accuracy is proposed. Using the Taylor method, application of this algorithm is immediate and largely reduces the integration time. In addition, a new method of integration of kinetic models, whose most important feature is the self-adaptability to the stiffness of the system along the integration process, is developed. This "stiffness-adaptive" Taylor method (SAT method) makes use of several algorithms, combining them to meet the particular requirements of the integration of each species along the integration process. In comparison with the Runge-Kutta-Felhberg, Runge-Kutta-Calahan, Taylor, and Gear methods, the SAT method is the best to integrate non-stiff and stiff kinetic systems, giving the best accuracy and the smallest computing time. 0 1992 by John Wiley & Sons, Inc.

The reaction of tetrahalo-p-benzoquinones with triphenylphosphoniocyclopentadienide yields 6-(triphenylphosphonio-3'-cyclopentadienyl) - 2,3,5-trihalocyclohexa-2,5-diene-1,4-dione (4a-d), a new class of zwitterionic dyes containing phosphorus. The rate-limiting step has been found to be the addition of the ylide to the quinone through a highly polar betaine intermediate. The elimination of hydrogen halide from the betaine, is of the E, or ElcB type for the bromanil system and of the El type for iodanil. SCF-AM1 calculations suggest that the ElcB path is energetically favoured relative to the El elimination path.

A general equation to derive kinetic models up to any order is given. This equation greatly facilitates the application of the Taylor series method to the integration of kinetic models up to very high orders. When dealing with non-stiff models, computing time is always reduced by increasing the integration order, at least up to the 20th order. When the model is stiff, the integration order should be optimized; however, a twelfth order is recommended to integrate weakly stiff models. The use of an algorithm which permits the immediate calculation of the integration step size required to maintain a given accuracy leads to further reductions in computing time. When implemented as recommended here, a high-order Taylor series method is more rapid and accurate than Runge-Kutta and predictor-corrector methods and can be advantageously used in combination with optimization methods to perform mechanism studies and in multicomponent kinetic determinations.

The kinetics and mechanism of the reaction of triphenylphosphoniocyclopentadienide 1 with tetrac h loro-pbenzoqu i none (c h loranil 2a) to yield 2,3,5tric h loro-6 -(3 -trip henylp hosp horany I idenecyclopenta-l,4-dienyl) -p-benzoquinone 3 in dichloromethane solution are reported. The rate Paper 1/02559G