A combined density functional and ab initio quantum chemical study of the Brandi reaction

The Brandt reaction is the transformation of spiro[cyclopropane-1,5'-isoxaz olidines] into tetrahydropyridones under thermal conditions. According to c alculations performed by the restricted and unrestricted density functional theory and post-Hartree-Fock single- and multireference methods of ab init io quantum chemistry, the reaction proceeds through two biradical intermedi ates. These intermediates result from the homolytic cleavage of the N-O bon d of the isoxazolidine ring in the first step, and the homolytic cleavage o f one of the C-C bonds of the spiro-fused cyclopropane in the second. The a ctivation energy of the rate-determining first step of the parent reaction amounts to about 40 kcal mol(-1) at the RDFT/UDFT level of theory. This ene rgy is not much higher than the energy of the first biradical intermediate relative to the reactants, The relative energies calculated at the quadrati c Cl and coupled cluster ab initio level were of the same order of magnitud e. The effects of structural modification of spiro[cyclopropane-1,5'-isoxaz olidines] by substitution at carbon or nitrogen in the five-membered ring, introduction of a double bond into the five-membered ring and replacement o f the spiro-cyclopropane by spiro-cyclobutane axe discussed. The theoretica l results reflect Brandi's experimental findings on the reactivity of the c ompounds under conventional thermal or flash vacuum thermolysis conditions and his hypothesis about the reaction mechanism reasonably well.