Accurate Density Functional Theory Forces for Charged Noncovalent Complexes

Force accuracy is essential for training machine-learned force fields based on density functional theory (DFT) data and for reliably modeling noncovalent interactions (NCIs). Despite this importance and the sensitivity of forces to the underlying density functional approximation, a gap remains in benchmarking DFT force accuracy for NCIs. Here, we assess the force performance of dispersion-enhanced DFT against CCSD(T) references for representative charged NCI dimers. While conventional dispersion-enhanced density functional approximations (DFAs) exhibit substantial force errors for charged systems, the recently proposed (r²SCAN+MBD)@HF, which combines r²SCAN, many-body dispersion, and Hartree-Fock densities in a synergistic manner, systematically reduces these errors [Zhao, H.; Lőrincz, B. D.; Henkes, T.; Berta, D.; Nagy, P. R.; Tkatchenko, A.; Vuckovic, S. Sci. Adv. 2026, 12, eadz8521]. The improvements in force accuracy of (r²SCAN+MBD)@HF over other DFT approaches are most pronounced for strongly charged dimers, extend to vibrational frequencies, and propagate to improved vibrational spectra from machine-learned force field-based molecular dynamics simulations. This work supports (r²SCAN+MBD)@HF as a promising and high-quality reference level for training machine-learned force fields for the studied charged NCI cases and motivates its broader application to more complex ionic environments.