多项式展开示例：3(5)-甲基-1-吡唑与氯仿的反应及四种异构体的表征。

Chemistry Department and QOPNA and LAQV-REQUIMTE, University of Aveiro, 3810-193 Aveiro, Portugal.

Departamento de Química Orgánica y Bio-Orgánica, Facultad de Ciencias, UNED, Paseo Senda del Rey, 9, E-28040 Madrid, Spain.

Molecules. 2019 Feb 4;24(3):568. doi: 10.3390/molecules24030568.

The reaction in phase-transfer catalyzed conditions of 3(5)-methyl-1-pyrazole with chloroform affords four isomers , , and 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 () and down () conformation of the pyrazolyl rings with regard to the Csp³⁻H atom was established by X-ray crystallography and by ¹H-, C- and N-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.

在相转移催化条件下，3(5)-甲基-1-吡唑与氯仿反应生成四个异构体[1a]-[1d]，其比例对应于多项式展开式(a + b)³，其中 a = 0.6，b = 0.4，a 和 b 分别为 3-甲基和 5-甲基的比例。吡唑环相对于 Csp³⁻H 原子的上（up）和下（down）构象通过 X 射线晶体学和溶液中的 ¹H、C 和 N-NMR 结合使用含相对论修正的原子轨道（GIAO）/B3LYP/6-311++G(d,p)计算来确定。并与其他三吡唑甲烷的 X 射线结构进行了比较。