ON THE EVALUATION OF TURNOVER FREQUENCIES IN UNICYCLIC HOMOGENEOUS CATALYSIS - EXPERIMENTAL, NUMERICAL, AND STATISTICAL ASPECTS

Transition-metal homogeneous catalysis provides a means for the chemos elective, regioselective and stereoselective synthesis of fine chemica ls, and the turnover frequency TOF(x, T, P) can be used as a measure o f the specific activity of unicyclic homogeneous catalytic systems. Gi ven an appropriate in situ spectroscopic method for the experimental m easurement of both the organometallic and organic reactant concentrati ons, various numerical approaches for the evaluation of TOF(x, T, P) a re considered. First, the associated problem of spectrophotometric cal ibration is investigated, particularly as it regards the use of infrar ed spectroscopy. Clearly, accurate calibrations are a pre-requisite to the calculation of TOF(x, T, P), and the propagation of error becomes an important issue. Accordingly, a practical guide to calibration is suggested which takes into account some of the particular difficulties associated with transition-metal systems. Secondly, differencing and quadrature methods are compared against spline fitting techniques for the evaluation of TOF(x, T, P). Realistic confidence intervals for the resulting estimate of TOF(x, T, P) are derived for each of the method s and comparisons are drawn on this basis. Attention is given to both the presence of error in the explanatory variable of the resulting reg ressions as well as the error correlation structures arising from deri vative and integral approximations. Asymptotic properties of the estim ation schemes are also discussed. Overall, the central difference meth od was found most suitable for the analysis of the present experimenta l data due to its ease of use and desirable statistical properties. Ty pical sources of error and the magnitude of these errors, from the ana lysis of real in situ infrared spectroscopic measurements of the homog eneous rhodium catalyzed hydroformylation of alkenes to yield aldehyde s, are discussed in detail. (C) 1998 Elsevier Science B.V. All rights reserved.