Combining data-driven and quantum chemical approaches to evaluate Minnesota functionals (M06-2X, MN12-SX, and MN15) for the enthalpy of formation predictions.

contextThe accurate prediction of the standard enthalpy of formation (ΔHf°) is crucial for understanding molecular stability and reaction energetics, yet reliable experimental data are often unavailable for unstable or novel compounds. This work benchmarks three Minnesota density functionals (M06-2X, MN12-SX, and MN15) to evaluate their performance in predicting ΔHf° values for a diverse set of hydrocarbons via the atom equivalent method. Our results identify MN15 as the most accurate functional, particularly when zero-point energy (ZPE) corrections are included, achieving a mean absolute error of 1.70 kcal/mol. In contrast, MN12-SX exhibits significant sensitivity to ZPE corrections, limiting its reliability. To enhance predictive robustness, a machine learning model was developed, which demonstrated strong performance on acyclic systems but highlighted challenges in predicting strained cyclic molecules. This hybrid quantum-chemical and data-driven framework provides a validated pathway for improving the accuracy of thermochemical predictions.

methodsAll quantum chemical calculations were performed using the Gaussian 16 software package. The density functionals M06-2X, MN12-SX, and MN15 were employed in conjunction with the correlation-consistent polarized valence triple-zeta (cc-pVTZ) basis set. Single-point electronic energies and vibrational frequencies for ZPE corrections were computed at the same level of theory. Enthalpies of formation were derived using the atom equivalent method, where carbon and hydrogen energy equivalents were obtained via least-squares fitting to experimental data. Also, a machine learning workflow was implemented in Python using the scikit-learn library, wherein a random forest regressor was trained on molecular descriptors and experimental ΔHf° values, with model performance assessed via fivefold cross-validation.