Random Versus Systematic Errors in Reaction Enthalpies Computed Using Semi-empirical and Minimal Basis Set Methods

The connectivity-based hierarchy (CBH) protocol for computing accurate reaction enthalpies developed by Sengupta and Raghavachari is tested for fast <i>ab initio</i> methods (PBEh-3c, HF-3c, and HF/STO- 3G), tight-binding DFT methods (GFN-xTB, DFTB, and DFTB-D3), and NDDO-based semiempirical methods (AM1, PM3, PM6, PM6-DH+, PM6-D2, PM6-D3H+, PM6-D3H4X, PM7, and OM2) using the same set of 25 reactions as in the original study. For the CBH-2 scheme, which reflects the change in the immediate chemical environment of all the heavy atoms, the respective MUE relative to G4 for PBEh-3c, HF-3c, HF/STO-3G, GFN-xTB, DFTB-D3, DFTB, PM3, AM1, PM6, PM6-DH+, PM6-D3, PM6-D3H+, PM6-D3H4X, PM7, and OM2 are 1.9, 2.4, 3.0, 3.9, 3.7, 4.5, 4.8, 5.5, 5.4, 5.3, 5,4, 6.5, 5.3, 5.2, and 5.9 kcal/mol, with a single outlier removed for HF-3c, PM6, PM6-DH+, PM6-D3, PM6-D3H4X, and PM7. The increase in accuracy for the NDDO-based methods is relatively modest due to the random errors in predicted heats for formation.