The Eschweiler–Clarke (the amine methylation) reaction was investigated by density functional theory (DFT) calculations. First, a reaction model of H₃CNH₂ + HC(O)OH + CH₂O + (H₂O)₃ → (H₃C)₂NH + CO₂ + (H₂O)₄ was employed for geometry optimizations. Geometries and activation free energies of transition states (TSs) by eight DFTs, B2PLYP-D3, B3LYP, B3LYP-D, BP86-D, PBE0-D, M06-2X, wB97X-D, and APF-D, along with MP2 were compared. Four elementary processes were obtained. The rate-determining step is of the hydride-transfer TS, H₃CN⁺HCH₂ + HCO₂⁻ → H₃CNHCH₃ + CO₂. Whereas BP86-D and APF-D gave underestimated energies, M06-2X was found to be a reasonable DFT to trace the present reaction. Second, by the use of M06-2X/6-311++G**, hydride-shift TSs were examined for various sizes of the water cluster (H₂O)_n, and the controversial two mechanisms were evaluated. It was suggested that the first formic acid contributes to formation of the iminium ion H₃CN⁺HCH₂ and the second formic acid works for the hydride transfer. The Eschweiler–Clarke reaction was described by the scheme, R¹R²NH + H₂CO + (HCOOH)₂ + (H₂O)_n → R¹R²NCH₃ + CO₂ + HCO₂⁻ + H₃O⁺(H₂O)_n.

中文翻译：

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Eschweiler-Clarke反应中氢化物位移的密度泛函理论研究

通过密度泛函理论 (DFT) 计算研究了 Eschweiler-Clarke（胺甲基化）反应。首先，H ₃ C  NH ₂  + HC(O)OH + CH ₂ O + (H ₂ O) ₃  → (H ₃ C) ₂ NH + CO ₂  + (H ₂ O) _{4 的反应模型}是用于几何优化。8 个 DFT、B2PLYP-D3、B3LYP、B3LYP-D、BP86-D、PBE0-D、M06-2X、wB97X-D 和 APF-D 以及 MP2 的几何形状和过渡态 (TS) 的激活自由能是比较的。获得了四个基本过程。速率决定步骤是氢化物转移 TS, H ₃ C N ⁺ HCH ₂  + HCO ₂ ⁻  → H ₃ C  NH  CH ₃  + CO ₂。尽管 BP86-D 和 APF-D 给出了低估的能量，但发现 M06-2X 是一个合理的 DFT 来追踪当前的反应。其次，通过使用 M06-2X/6-311++G**，针对不同大小的水团簇 (H ₂ O) _n检测氢化物位移 TS ，并对有争议的两种机制进行评估。有人提出第一个甲酸有助于形成亚胺离子 H ₃ C  N ⁺ HCH ₂第二种甲酸用于氢化物转移。Eschweiler-Clarke 反应由以下方案描述，R ¹ R ² NH + H ₂ CO + (HCOOH) ₂  + (H ₂ O) _n  → R ¹ R ² NCH ₃  + CO ₂  + HCO ₂ ⁻  + H ₃ O ⁺ (H ₂ O) _n。