Experimental design on the simplex

Optimum experimental designs depend on the design criterion, the model and the design region. The talk will consider the design of experiments for regression models in which there is a single response with the explanatory variables lying in a simplex. One example is experiments on various compositions of glass such as those considered by Martin, Bursnall, and Stillman (2001). Because of the highly symmetric nature of the simplex, the class of models that are of interest, typically Scheff´e polynomials (Scheff´e 1958) are rather different from those of standard regression analysis. The optimum designs are also rather different, inheriting a high degree of symmetry from the models. In the talk I will hope to discuss a variety of modes for such experiments. Then I will discuss constrained mixture experiments, when not all the simplex is available for experimentation. Other important aspects include mixture experiments with extra non-mixture factors and the blocking of mixture experiments. Much of the material is in Chapter 16 of Atkinson, Donev, and Tobias (2007). If time and my research allows, I would hope to finish with a few comments on design when the responses, rather than the explanatory variables, lie in a simplex. References Atkinson, A. C., A. N. Donev, and R. D. Tobias (2007). Optimum Experimental Designs, with SAS. Oxford: Oxford University Press. Martin, R. J., M. C. Bursnall, and E. C. Stillman (2001). Further results on optimal and efficient designs for constrained mixture experiments. In A. C. Atkinson, B. Bogacka, and A. Zhigljavsky (Eds.), Optimal Design 2000, pp. 225–239. Dordrecht: Kluwer. Scheff´e, H. (1958). Experiments with mixtures. Journal of the Royal Statistical Society, Ser. B 20, 344–360. 1

The curvature of the conical intersection seam: an approximate second-order analysis

We present a method for analyzing the curvature (second derivatives) of the conical intersection hyperline at an optimized critical point. Our method uses the projected Hessians of the degenerate states after elimination of the two branching space coordinates, and is equivalent to a frequency calculation on a single Born-Oppenheimer potential-energy surface. Based on the projected Hessians, we develop an equation for the energy as a function of a set of curvilinear coordinates where the degeneracy is preserved to second order (i.e., the conical intersection hyperline). The curvature of the potential-energy surface in these coordinates is the curvature of the conical intersection hyperline itself, and thus determines whether one has a minimum or saddle point on the hyperline. The equation used to classify optimized conical intersection points depends in a simple way on the first- and second-order degeneracy splittings calculated at these points. As an example, for fulvene, we show that the two optimized conical intersection points of C2v symmetry are saddle points on the intersection hyperline. Accordingly, there are further intersection points of lower energy, and one of C2 symmetry - presented here for the first time - is found to be the global minimum in the intersection space

Síntesi, caracterització i avaluació com a catalitzadors de nous complexos quirals de platí

The oxidative addition proved to be a useful method to prepare platinum (II) hydridotiolate by reaction of tetrakis(triphenylphosphine)platinum(0) with aminothiolate and phosphinothiolate ligands like cysteamine, cysteine ethyl and methyl Esther, 2-(diphenylphosphino)ethanetiol and 2-(diphenylphosphino)propanetiol. The complexes are square-planar and the aminothiolate or phosphinothiolate ligands are chelated to platinum (II). The hydrido ligand is trans to the sulfur and the other coordination position is occuped by a triphenylphosphine ligand. The complexes are mononuclear and they show low symmetry. The only symmetry element, the plan is broke if the ligand is branched, obtaining asymmetric complexes C1. If the ligand has electronic or esteric impediments the reaction doesn't run and the starting products are recovered. This was observed with N,N-dimethylcysteamine and penicylamine methyl esther ligands. In the special case of orthoaminotiophenol the hydridotiolate was obtained but the ligand was not chelated. The aminothiolate complexes don't show solution equilibrium. Otherwise, the complexe with 2-(diphenylphosphino)ethanetiol show an isomerisation equilibrium which forms cis isomer as a minor component. The complexe with 2-(diphenylphosphino)-propanetiol shows a conformational equilibrium between chair and twist forms. The complexes have been tested as catalyst precursors in hydroformylation and hydrosilylation reactions. The hydroformylation reaction runs only in presence of SnCl2 as cocatalyst. Catalytic activity depends on the presence of triphenylphosphine and, with less magnitude, CO and H2 pressure. We also studied the enantioselectivity using a chiral complexe. In the hydrosililation reaction, catalysts run with good results (<90%) using triethylsilane as silicon hydride. Dehydrogenative addition product has been also found in this reaction.

Isomerism and C-H, C-C, O-O, C-O bond activation studies by transition metals

Aquesta tesi és el reflex que de la cooperació entre grups experimentals i grups teòrics s'aconsegueix l'assoliment d'objectius inassolibles de forma individual. A partir de la DFT s'expliquen processos inorgànics i organometàl·lics de gran valor biològic i/o industrial. La tesi està enfocada especialment a l'estudi de complexos mononuclears i binuclears de coure, on té lloc l'activació d'enllaços C-H, C-C, i O-O. L'estudi de complexos octaèdrics de ruteni ha permès dur a terme extensos estudis isomèrics i racionalitzar les propietats espectroscòpiques dels mateixos. A més a més, estudis més puntuals respecte clusters de coure, l'estudi de la reacció de Pawson-Khand, l'estudi d'enllaços Pt-Pt en complexos trimèrics de platí, a més a més de l'estudi de la isomeria de complexos de Ni i Pt.