Accurate Estimation of the Diagonal Born–Oppenheimer Corrections of Hydrogen-Bearing Molecules: The Comparison of Different Density Functional Methods

To achieve accurate molecular properties, rigorous consideration of corrections to the Born-Oppenheimer approximation (BOA) is warranted. This work employs a finite difference method to calculate the Diagonal Born-Oppenheimer Correction (DBOC) at various levels of density functional theory (DFT). These calculations are systematically compared with the reference values obtained at CCSD/aug-cc-pVTZ level. DBOC values are calculated for H₂, H₂O, H₂O₂, H₂S, HCl, HCN, HF, HNC, NH₃, CH₄, OH, NH₂, and CH₃ molecules. Systematic examinations are performed using six exchange-correlation functionals (SVWN, PBE, B3LYP, PBE0, ωB97XD, M06-2X) combined with six basis sets (6-31G(d,p), 6-31++G(d,p), 6-311G(d,p), 6-311++G(d,p), cc-pVTZ, aug-cc-pVTZ). Compared with those "reference values", our analysis reveals significant error cancellation phenomena for specific functional/basis set combinations. Notably, minimal basis sets such as 6-31G(d,p) prove sufficient for DBOC computation across all small molecules examined. The introduction of diffuse functions demonstrates negligible improvement in accuracy while substantially increasing computational expense and occasionally introducing numerical instability. Furthermore, our results indicate that meta-GGA functionals (e.g., M06-2X, ωB97XD) require increased integration grid density to ensure numerical precision. Based on comparative accuracy and computational efficiency, the B3LYP/6-311G(d,p) and PBE/6-311G(d,p) levels are recommended for DBOC calculations involving hydrogen atoms for these small molecule systems. The finite difference method employed in this study, relying on wave function calculations, demonstrates broad applicability. The implementation is also quite simple, i.e., requiring handling the wave function data and the overlap integral calculations, making it a highly simple and efficient method for calculating DBOC. While this methodology proves effective for the current molecular set, extension to more complex systems necessitate further investigation into functional and basis set dependencies.