On the Ewald method and the quartic Helmholtz free energy of an anharmonic metallic crystal

Thesis (M. Sc.) - Brock University, 1978.

An analysis of decoupling procedures in generating thermal Green's functions of O([lambda]â ´) by the Zubarev equation of motion method

The Zubarev equation of motion method has been applied to an anharmonic crystal of O( ,,4). All possible decoupling schemes have been interpreted in order to determine finite temperature expressions for the one phonon Green's function (and self energy) to 0()\4) for a crystal in which every atom is on a site of inversion symmetry. In order to provide a check of these results, the Helmholtz free energy expressions derived from the self energy expressions, have been shown to agree in the high temperature limit with the results obtained from the diagrammatic method. Expressions for the correlation functions that are related to the mean square displacement have been derived to 0(1\4) in the high temperature limit.

The application of the structural correlation method to determine the reaction coordinate for a putative ring closure reaction

The cr ystal structure of the compound 2-benzoylethylidene-3-(2,4- dibromophenyl)-2,3-dihydro-5-phenyl-l,3,4-thiadiazole* C23H16Br2NZOS (BRMEO) has been determined by using three dimensiona l x-ray diffraction data. The crys tal form is monoclinic, space group P21/c, a = 17.492(4), o -.t' 0 R 0 b =: 16.979(1), c = 14.962(1) A, "X. =o= 90 ',= 106.46(1) , z = 8, graphite-monochromatized Mo~ rad iation, Jl= 0.710J3~, D = 1.62g/cc and o D = 1.65g/cc. The data were col lected on ~ Nonius CAD-4 c diffractometer. The following atoms were made anisotropic: Br, S, N, 0, C7, and C14-C16 for each i ndependent molecu le ; the rest were left isotropic. For 3112 independent refl ec tions with F > 6G\F), R == 0.057. The compound has two independent molecules within the asymmetric unit. Two different conformers were observed which pack well together. /l The S---O interaction distances of 2.493(6) and 2 . 478(7) A were observed for molecules A and B respectively. These values are consistent with earlier findings for 2-benzoylmethylene-3-(2,4-dibromophenyl)- ~~ 2,3-dihydro-5-phenyl-l,3,4-thiadiazole C22H14Br2N20S (BRPHO) and 2-benzoylpropylidene-3-(2,4-dibromophenyl)-2,3-dihydroiii ,'r 5-phenyl-l,3,4-thiadiazole C24H18Br2N20S (BRPETO ) where S---O distances are l ess than the van der Waals (3.251\) but greater than those expected for () a single bond (1.50A). From the results and the literature it appears obvious that the energy/reaction coordinate pathway has a minimum between the end structures (the mono- and bicyclic compounds). * See reference (21) for nomenclature.