Fast and accurate quantum mechanical modeling of large molecular systems using small basis set Hartree–Fock methods corrected with atom-centered potentials

There has been significant interest in developing fast and accurate quantum mechanical methods for modeling large molecular systems. In this work, by utilizing a machine-learning regression technique, we have developed new low-cost quantum mechanical approaches to model large molecular systems. The developed approaches rely on using one-electron Gaussian-type functions called atom-centered potentials (ACPs) to correct for the basis set incompleteness and the lack of correlation effects in the underlying minimal or small basis set Hartree-Fock (HF) methods. In particular, ACPs are proposed for ten elements common in organic and bio-organic chemistry (H, B, C, N, O, F, Si, P, S, and Cl) and four different base methods: two minimal basis sets (MINIs and MINIX) plus a double-ζ basis set (6-31G*) in combination with dispersion-corrected HF (HF-D3/MINIs, HF-D3/MINIX, HF-D3/6-31G*), and the HF-3c method. The new ACPs are trained on a very large set (73832 data points) of non-covalent properties (interaction and conformational energies) and validated additionally on a set of 32048 data points. All reference data is of complete basis set coupled-cluster quality, mostly CCSD(T)/CBS. The proposed ACP-corrected methods are shown to give errors in the tenths of a kcal/mol range for non-covalent interaction energies and up to 2 kcal/mol for molecular conformational energies. More importantly, the average errors are similar in the training and validation sets, confirming the robustness and applicability of these methods outside the boundaries of the training set. In addition, the performance of the new ACP-corrected methods is similar to complete basis set DFT but at a cost that is orders of magnitude lower, and the proposed ACPs can be used in any computational chemistry program that supports effective-core potentials without modification. It is also shown that ACPs improve the description of covalent and non-covalent bond geometries of the underlying methods and that the improvement brought about by the application of the ACPs is directly related to the number of atoms to which they are applied, allowing the treatment of systems containing some atoms for which ACPs are not available. Overall, the ACP-corrected methods proposed in this work constitute an alternative accurate, economical, and reliable quantum mechanical approach to describe the geometries, interaction energies, and conformational energies of systems with hundreds to thousands of atoms.