Theoretical investigation into the potential of halogenated methanes to undergo reductive metabolism

The density-functional theory (DFT)-based computational chemistry software package DMol was used to provide insight into the reductive potentials of a series of halomethanes. It is known that certain members of this series are readily reduced in vivo via catalysis by cytochrome P450. DMol was used to calculate the electron affinities of these molecules to be used as measures of their reduction potentials. Our results are consistent with experimental electrochemical reduction potentials and indicate that electron affinity is dependent upon the number and type of halogens present in the molecule. Calculated bond lengths and angles also compared favorably with experimental results and estimates derived from other ab initio methods of calculation. Concurrent with this study was the observation of a linear empirical relationship between electron affinity and the lowest unoccupied molecular orbital energy. It is possible that these values could be used as indicators of reductive potentials and ultimately of metabolic rates for use in PB–PK models designed to predict the dose associated with the toxicity of molecules of this and other classes. © John Wiley & Sons, Inc.     

A Leibniz differentiation formula for positive operators

Is is shown that for n→+∞ the Leibnizian combination L′_n(fg)−fL′_n(g)−gL′_n(f) converges uniformly to zero on a compact interval W if the positive operators L_n belong to a certain class (including Bernstein, Gauss-Weierstrass and many others), and if the moduli of continuity of f,g satisfy ω_W(f;h)ω_W(g;h)=o(h) as h→0+. A counterexample shows that Lipschitz conditions are not appropriate to bring about a second-order version of this formula.