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Expressions for the anharmonic Helmholtz free energy contributions up to o( f ) ,valid for all temperatures, have been obtained using perturbation theory for a c r ystal in which every atom is on a site of inversion symmetry. Numerical calculations have been carried out in the high temperature limit and in the non-leading term approximation for a monatomic facecentred cubic crystal with nearest neighbour c entralforce interactions. The numbers obtained were seen to vary by a s much as 47% from thos e obtai.ned in the leading term approximati.on,indicating that the latter approximati on is not in general very good. The convergence to oct) of the perturbation series in the high temperature limit appears satisfactory.

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The thermal decomposition of 2,3-di~ethy l - J-hydr operox y- 1 - butene , p r epared f rol") singl e t oxygen, has been studied i n three solvents over the tempe r a ture r ange from 1500e to l o00e and t!1e i 111 t ial ~oncentrfttl nn r Ange from O. 01 M to 0.2 M. Analys i s of the kine tic data ind ica te s i nduced homolysis as the n ost probRble mode of d e composition, g iving rise to a 3/2 f S order dependence upon hy d.roperoxide concent :r8.tl on . Experimental activation e nergies for the decomposition were f ound to be between 29.5 kcsl./raole and 30.0 k cal./mole .• \,iith log A factors between 11 . 3 and 12.3. Product studies were conducted in R variety of solvents a s well as in the pr esence of a variety of free r adical initiators . Investigation of the kinetic ch a in length indicated a chain length of about fifty. A degenerat i ve chain branching mechanism 1s proposed which predicts the multi t ude of products which Rre observed e xperimentally as well as giving activation energies and log A factors si~il a r to those found experimentally .

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Kinetics and product studies of the decompositions of allyl-t-butyl peroxide and 3-hydroperoxy- l-propene (allyl hydroperoxide ) in tolune were investigated. Decompositions of allyl-t-butyl peroxide in toluene at 130-1600 followed first order kinetics with an activation energy of 32.8 K.cals/mol and a log A factor of 13.65. The rates of decomposition were lowered in presence of the radical trap~methyl styrene. By the radical trap method, the induced decomposition at 1300 is shown to be 12.5%. From the yield of 4-phenyl-l,2- epoxy butane the major path of induced decomposition is shown to be via an addition mechanism. On the other hand, di-t-butYl peroxyoxalate induced decomposition of this peroxide at 600 proceeded by an abstraction mechanism. Induced decomposition of peroxides and hydroperoxides containing the allyl system is proposed to occur mainly through an addition mechanism at these higher temperatures. Allyl hydroperoxide in toluene at 165-1850 decomposes following 3/2 order kinetics with an Ea of 30.2 K.cals per mole and log A of 10.6. Enormous production of radicals through chain branching may explain these relatively low values of E and log A. The complexity of the reaction is indicated a by the formation of various products of the decomposition. A study of the radical attack of the hydro peroxide at lower temperatures is suggested as a further work to throw more light on the nature of decomposition of this hydroperoxide.

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This research work has been planned with the intention of synthesizing optically active bicyclo[3,l,0]-hexan-2-one using chiral carbodiimides. Several carbodiimides have been prepared for practice and for attempts at asymmetric induction. The total synthesis of dibenzo[e,g]- (l:3)diazonine and the partial synthesis of l:13-dimethyldibenzo[e,g]- (l:3)diazonine are reported. Attempts to resolve 6,6f-dimethyl-2,2t-diphenic acid were not successful. The NMR spectra of carbodiimides and the related thioureas are compared. The reaction transition state of the 4-hydroxycyclohexanone with optically pure R,R(+)-di(a-phenylethyl)-carbodiimide has been considered. The ORD application to chiral cyclohexanones is discussed.

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This research work has been planned with the intention of proving the absolute configuration of lactobacillc acid. During the course of this work, attempts have been made to synthesize cis-2-carboxycyclopropane- l-.acetic acid as,v,a suitable resolvable material. As the results were not satisfactory, the synthesis of ci,s-2-carboxycyclopropane-l-propionic acid has been alternatively attempted by ring opening of bicyclo- [4.1.~-heptan-2-onewithout much success. Attempts to resolve or prepare bicyclo[ 4.1.~-hePtan-2-one optically active are also reported. On the other hand, a complete scheme is described for the possible synthesis of optically active lactobacillic acid. If only bicyclo- ~.1.~ -heptan-2-one can be resolved or prepared optically active, this described scheme can be applied smoothly to the synthesis of enant~omeric lactobacillic acid.