A Diagnostic Analysis of B3LYP Thermochemical Errors: Physical Origins, System Dependence, and Practical Implications

Density functional theory remains a cornerstone of thermochemical modeling; however, its reliability depends critically on the interplay between functional form, basis-set representation, and the underlying physical interactions governing a given system. In this work, a diagnostic assessment of the B3LYP functional is presented, focusing on the identification of systematic error sources rather than on global statistical performance alone. Mean absolute errors reorganized from established benchmark datasets are used as a reference framework to analyze trends associated with molecular size, structural compactness, dispersion interactions, and electron density localization. Global thermochemical statistics show that B3LYP improves substantially over Hartree–Fock methods, yet exhibits only limited and non-monotonic sensitivity to basis-set extension beyond moderate polarization and diffuse functions. A persistent size-dependent error growth is identified for linear hydrocarbons, indicating cumulative deficiencies related to medium-range correlation effects. Branching-sensitive isomerization reactions reveal a pronounced overstabilization of linear isomers, which is significantly—but not completely—mitigated by the inclusion of empirical dispersion corrections, highlighting dispersion as a dominant but non-exclusive error source. In contrast, isomerizations involving nitrogen- and oxygen-containing molecules display strong sensitivity to diffuse basis functions, demonstrating that density localization and polarization effects dominate over dispersion in heteroatom-rich systems. These contrasting behaviors confirm that B3LYP errors arise from multiple, system-dependent physical origins that cannot be resolved by a single correction strategy. Overall, this study establishes a physically motivated diagnostic framework for interpreting B3LYP performance, emphasizing that functional reliability must be evaluated in relation to the dominant interactions of the target chemical system. The resulting classification provides practical guidance for method selection and expectation management in thermochemical applications.