The cross-validation errors for each reference species that could be calculated using the automatic isodesmic reaction procedure specified by Equation ( ) with RC2, RC3, or RC4 type constraints (Figure ) indicate that performance across different restriction levels remains largely similar. Interestingly, the number of species found for RC2 and RC3 across various levels of theory is very close, suggesting that most of the reactions found probably satisfy at least RC3 conditions or higher. This observation implies that the majority of the automatically generated isodesmic reactions are of high quality and adhere to more stringent constraint levels. However, it is important to recognize that more stringent constraint levels are not always desirable or beneficial. Although higher-order constraint levels, such as RC4, can potentially lead to slightly improved accuracy in some cases (e.g., method A, E, H, K, L), they also significantly reduce the number of species that can be solved using the IDR approach. For the cases shown in Figure , the number of species that could be solved to have matching isodesmic reactions is often more than halved when using RC4 constraints compared to RC3 and RC2. This substantial reduction in the number of solvable species highlights the trade-off between the level of constraint and the applicability of the IDR approach. As the constraints become more stringent, the likelihood of finding a valid isodesmic reaction can decrease dramatically, significantly limiting the number of species that can be analyzed using this method. Given the similar performance across all restriction levels and the significant reduction in the number of solvable species for RC4, coupled with the observation that RC3 and RC2 tend to yield a similar number of reactions, applying RC3 constraints appears to be the optimal choice when using the IDR approach in general.