Basis Set Convergence and Empirical Approaches for Obtaining Accurate Diagonal Born-Oppenheimer Corrections from an...

The Born-Oppenheimer (BO) approximation is fundamental to computational chemistry because it drastically simplifies the time-independent Schrödinger equation, making calculations for molecular systems computationally feasible. Accurate determination of the diagonal Born-Oppenheimer correction (DBOC) is essential for achieving benchmark accuracy in high-level thermochemical applications. Here, we establish the DBOC200HC database, consisting of 200 structurally diverse hydrocarbons with up to 18 carbon atoms (e.g., triamantane (C₁₈H₂₄)), including aliphatic, aromatic, antiaromatic, cyclic, noncyclic, and caged systems. Reference DBOCs are determined near the coupled-cluster singles and doubles complete basis set limit (CCSD/CBS) using additivity schemes based on HF/cc-pVQZ and CCSD/cc-pVnZ (n = D, T) calculations. Given the computational expense associated with CCSD/CBS calculations for large hydrocarbons, it is important to develop reliable yet computationally economical approximations. Several such approaches are assessed using the DBOC200HC database. While scaled Hartree-Fock methods offer limited improvement, methods incorporating first-order Møller-Plesset perturbation theory (MP1) perform significantly better. Specifically, calculating the DBOC at the MP1/cc-pVDZ level of theory and scaling the MP1 correlation component (ΔE_DBOC^MP1 = E_DBOC^MP1 - E_DBOC^HF) by an empirical factor of 1.5447 yields the best balance between accuracy (RMSD = 0.026 kJ/mol) and computational cost (practically the same cost as HF/cc-pVDZ). This exceptionally low RMSD suggests that highly accurate DBOCs for use in high-level thermochemical protocols can be obtained via the scaled MP1 approach, without resorting to computationally more demanding levels of theory such as MP2 or CCSD. To validate our results, we further test the empirical methods optimized over the DBOC200HC database on an independent database of 12 larger hydrocarbons, including systems like dodecahedrane (CH)₂₀.