## 2 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Reaction Product and Solvent** & **DFT/ Basis Set** & **1H-1** & **7H-1** & **2** & **Salt 1** & \
\begin{tabular}{c} **Iminium** \\ **Salt 1** \\ \end{tabular} & **Animal 1** &
\begin{tabular}{c} **Transition** \\ **State 1** \\ \end{tabular} & **3** \\ \hline \multirow{4}{*}{**3a**} & B3 LYP/ & 0.4 & 0 & \(-\)13.6 & 2.1 & 5.6 & \(-\)5.0 & 11.6 & \(-\)11.8 \\  & 6-31+G(d) & _0.4_ & \(0\) & _1.0_ & _3.8_ & _8.6_ & 11.9 & 28.2 & 5.2 \\ \cline{1-1}  & B3 LYP-D3/ & 0.5 & 0 & \(-\)16.5 & 1.8 & 4.5 & \(-\)13.6 & 1.9 & \(-\)21.7 \\  & 6-31+G(d) & _0.5_ & \(0\) & _\(-\)1.8_ & 3.9 & 7.5 & 3.2 & 19.1 & \(-\)4.0 \\ \hline \multirow{4}{*}{**3a**} & B3 LYP-D3/ & _0.3_ & 0 & \(-\)17.1 & 3.1 & 1.4 & \(-\)16.4 & \(-\)0.9 & \(-\)24.9 \\  & 6–311+G(d,p) & \(0\) & _0.9_ & _\(-\)2.6_ & _4.9_ & _4.3_ & _1.0_ & _16.1_ & \(-\)7.0 \\ \hline \multirow{4}{*}{**3a**} & B3 LYP/ & 0.2 & 0 & \(-\)13.9 & 3.8 & 7.3 & \(-\)5.0 & 11.8 & \(-\)11.0 \\  & 6-31+G(d) & \(0\) & \(0\) & _0.6_ & _6.6_ & _10.2_ & _11.7_ & _28.4_ & _5.8_ \\ \cline{1-1}  & B3 LYP-D3/ & 0.3 & 0 & \(-\)16.8 & 3.5 & 6.1 & \(-\)17.7 & 2.2 & \(-\)20.8 \\ \cline{1-1}  & 6-31+G(d) & _0.4_ & \(0\) & _\(-\)2.0_ & _6.0_ & _9.3_ & 3.7 & 19.5 & \(-\)3.1 \\ \hline \multirow{4}{*}{**3b**} & B3 LYP/ & 0.2 & 0 & \(-\)13.9 & 3.1 & 3.2 & \(-\)10.4 & 7.1 & \(-\)16.0 \\  & 6-31+G(d) & \(0\) & \(0\) & _0.6_ & _6.1_ & _5.4_ & _5.3_ & _22.7_ & _0.3_ \\ \cline{1-1}  & B3 LYP-D3/ & 0.3 & 0 & \(-\)16.8 & 3.1 & 2.6 & \(-\)17.4 & \(-\)0.9 & \(-\)24.1 \\ \cline{1-1}  & 6-31+G(d) & _0.4_ & \(0\) & _\(-\)2.0_ & _6.3_ & _5.2_ & _\(-\)0.9_ & _15.8_ & _\(-\)7.6_ \\ \hline \multirow{4}{*}{**3a**} & \(\omega\)B97X-Dand/ & 0 & 0.1 & \(-\)19.7 & 1.5 & 3.9 & \(-\)18.6 & 3.6 & \(-\)27.4 \\  & 6-31+G(d) & \(0\) & \(1\) & _\(-\)4.8_ & 3.1 & _7.0_ & \(-\)0.1 & 21.3 & \(-\)8.6 \\ \cline{1-1}  & 6-31+G(d,p) & \(0\) & _1.5_ & _\(-\)6.3_ & _4.1_ & _3.6_ & _3.7_ & _17.9_ & \(-\)13.3 \\ \hline \multirow{4}{*}{**3a**} & \(\omega\)B97X-Dand/ & 0 & 0.3 & \(-\)20.1 & 3.4 & 5.6 & \(-\)18.5 & 3.9 & \(-\)26.5 \\ \cline{1-1}  & 6-31+G(d) & \(0\) & _1.2_ & \(-\)6.2 & _6.6_ & _8.8_ & \(0\) & _21.7_ & \(-\)8.7 \\ \hline \end{tabular}
\end{table} 
Table 1: The relative electronic (plain text) and Gibbs free (italics) energies (kcal/mol) of subsequent stages of the tandem Mannich—electrophilic amination reactions calculated by DFT/PCM methods. It should be pointed out that in all cases, except for pure B3 LYP functional, the formation of product **3** is thermodynamically favoured over the reversible production of hemiamimal **2**. Moreover, the heterocyclic system of **2** is virtually planar with the amino N7 atom of the 5-isoxazolone fragment showing a pyramidal arrangement of its bonds with the sum of the three valence angles equal to 334.4\({}^{\circ}\). This value is consistent with relatively long bonds formed by N7 to O8 and C6 (1.446 and 1.393 A, respectively). Our survey of the Cambridge Structural Database (CSD) [17] showed that for N-substituted 5-isoxasolones the N-C bond lengths range from 1.33 to 1.43 A. Such a broad range of the values shows that the amino N atom can with ease change its hybridization state. In our previous work, we have reported that isoxazolone 1 reacts with iminium salt derived from L-proline only in the presence of a base, e.g., triethylamine (Scheme 2) [5]. Hence, the investigated tandem reaction is a base-promoted process, which in the case of L-proline transformation leads to single diastereoisomer **3c**. In order to investigate the nature of the diastereospecific reaction, we have completed theoretical calculations for the reaction paths that lead to both products. Surprisingly, it was found that the thermochemical factors do not favor formation of any of the examined diastereoisomers **3c** (Table 2).