Basis Set Convergence and Empirical Approaches for Obtaining Accurate Diagonal Born–Oppenheimer Corrections from an Extensive Database of 200 Structurally Diverse Hydrocarbons

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 (ΔEDBOCMP1 = EDBOCMP1 – EDBOCHF) 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.