An example of polynomial expansion: The reaction of 3(5)-methyl-1H-pyrazole with chloroform and characterization of the four isomers

Abstract

The reaction in phase-transfer catalyzed conditions of 3(5)-methyl-1H-pyrazole with chloroform affords four isomers 333, 335, 355 and 555 in proportions corresponding to the polynomial expansion (a + b)3, with a = 0.6 and b = 0.4, a and b being 3-methyl and 5-methyl proportions. The up (u) and down (d) conformation of the pyrazolyl rings with regard to the Csp3–H atom was established by X-ray crystallography and by 1H-, 13C- and 15N-NMR in solution combined with gauge-including atomic orbitals (GIAO)/B3LYP/6-311++G(d,p) calculations. A comparison with other X-ray structures of tris-pyrazolylmethanes was carried out.