24 resultados para Macaulay, Thomas Babington Macaulay, 1st baron, 1800-1859.


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To evaluate the dynamical effects of the screened interaction in the calculations of quasiparticle energies in many-electron systems a two-delta-function generalized plasma pole model (GPP) is introduced to simulate the dynamical dielectric function. The usual single delta-function GPP model has the drawback of over simplifications and for the crystals without the center of symmetry is inappropriate to describe the finite frequency behavior for dielectric function matrices. The discrete frequency summation method requires too much computation to achieve converged results since ab initio calculations of dielectric function matrices are to be carried out for many different frequencies. The two-delta GPP model is an optimization of the two approaches. We analyze the two-delta GPP model and propose a method to determine from the first principle calculations the amplitudes and effective frequencies of these delta-functions. Analytical solutions are found for the second order equations for the parameter matrices entering the model. This enables realistic applications of the method to the first principle quasiparticle calculations and makes the calculations truly adjustable parameter free.

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The analytical expressions of quasi-first and second order homogeneous catalytic reactions with different diffusion coefficients at ultramicrodisk electrodes under steady state conditions are obtained by using the reaction layer concept. The method of treatment is simple and its physical meaning is clear. The relationship between the diffusion layer, reaction layer, the electrode dimension and the kinetic rate constant at an ultramicroelectrode is discussed and the factor effect on the reaction order is described. The order of a catalytic reaction at an ultramicroelectrode under steady state conditions is related not only to C(Z)*/C(O)* but also to the kinetic rate constant and the dimension of the ultramicroelectrode; thus the order of reaction can be controlled by the dimension of the ultramicroelectrode. The steady state voltammetry of the ultramicroelectrode is one of the most simple methods available to study the kinetics of fast catalytic reactions.

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The conditions for quasi-first and second order homogeneous catalytic reactions and their variation with each other at an ultramicrodisk electrode in the steady state are discussed in this paper. The order of reaction can be controlled by changing the dimension of the ultramicroelectrode: the second order reaction can be changed to quasi-first by decreasing the dimension of the ultramicroelectrode. An example of this is given. The main factor effect on the reaction order is the dimension of the ultramicroelectrode. The K4Fe(CN)6-aminopyrine system is selected to confirm the theory, the experiments showing that the system is a second order reaction at a 432 mum microelectrode, and a quasi-first order reaction at a 19 mum ultramicroelectrode. The kinetic constant of the system can be determined by applying the previous theory of homogeneous catalytic reaction.

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The reaction of EuCl3, AlCl3 and C6Me6 in toluene gives the Eu(II) complex [Eu(eta-6-C6Me6)(AlCl4)2]4; X-ray crystal determination shows the molecule to be a cyclotetramer, in which the four Eu(C6Me6)AlCl4 units are connected via four groups of eta-2-AlCl4.