X-ray crystal structure and molecular mechanics calculations of (2,6-iso-dipropyl-phenylamide) dimethyl (tetra-methylcyclopenta-dienyl) silane titanium dichloride

Crystal and molecular structure of (2.6-dipropylphenylamide) dimethyl (tetra-methyl cyclopentadienyl) silane titanium dichloride (I) was fully characterized by X-ray diffraction. The crystal is obtained from a mixture of ether/hexane as orthorhombic. with a = 12.658 (3) Angstrom. b = 16.62 (3) Angstrom. c = 11.760 (2) Angstrom. V = 2474.2 (9) Angstrom(3). Z = 4, space group Pnma. R = 0.0399; Componud I compose of the pi-bounded ring with its dimethylsilyl-dipropyl phenyl amido group and the two terminal chloride atoms coordinated to central metal to form a so-called constrained geometry catalyst (CGC) structure. The result of molecular mechanics (MM) calculations on compound I shows that bond lengths and bond angles from the MM calculation are comparable to the data obtained from the X-ray diffraction study. The relation of the structure of CGCs and their catalytic activity by MM calculations is also discussed.

Outer wave number spectrum and statistical distribution of apparent wave number vector

Based on the ray theory and Longuet-Higgins's linear,model of sea waves, the joint distribution of wave envelope and apparent wave number vector is established. From the joint distribution, we define a new concept, namely the outer wave number spectrum, to describe the outer characteristics of ocean waves. The analytical form of the outer wave number spectrum, the probability distributions of the apparent wave number vector and its components are then derived. The outer wave number spectrum is compared with the inner wave number spectrum for the average status of wind-wave development corresponding to a peakness factor P = 3. Discussions on the similarity and difference between the outer wave number spectrum and inner one are also presented in the paper. (C) 2002 Elsevier Science Ltd. All rights reserved.