An efficient step size control for continuation methods

In solving a nonlinear equation by the use of a continuation method one of the crucial problems is the choice of the step sizes. We present a model for the total computational cost of a standard numerical continuation process and solve the problem of optimal step size control for this model. Using the theoretical results as a basis, we develop an adaptive step size algorithm for Newton's method. This procedure is computationally inexpensive and it gives quite satisfactory results compared to some other numerical experiments found in the literature.     

Asymmetric strecker synthesis of alpha-amino acids via a crystallization-induced asymmetric transformation using (R)-phenylglycine amide as chiral auxiliary

[reaction: see text]. Diastereoselective Strecker reactions based on (R)-phenylglycine amide as chiral auxiliary are reported. The Strecker reaction is accompanied by an in situ crystallization-induced asymmetric transformation, whereby one diastereomer selectively precipitates and can be isolated in 76-93% yield and dr > 99/1. The diastereomerically pure alpha-amino nitrile obtained from pivaldehyde (R1 = t-Bu, R2 = H) was converted in three steps to (S)-tert-leucine in 73% yield and >98% ee.     

Combinatorial Chemistry for Ligand Development in Catalysis: Synthesis and Catalysis Screening of Peptidosulfonamide Tweezers on the Solid Phase

On the basis of a pyrrolidine tweezer 1, a library of peptidosulfonamide tweezers (15a-e, 16a-e) was synthesized on the solid phase. This library was screened in a simultaneous substrate screening procedure for the ability to enantioselectively catalyze the Ti(O-i-Pr)(4)-mediated addition of diethylzinc to aldehydes. One of the best solid-phase tweezer catalyst (i.e., 16d, giving an ee of 32% in solid-phase catalysis) was resynthesized in solution (compounds 20 and 21). The now homogeneous solution-phase catalysis showed even better enantioselectivity (i.e., up to 66%).