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 developingfast and accurate quantum mechanical methods for modeling largemolecular systems. In this work, by utilizing a machine learningregression technique, we have developed new low-cost quantummechanical approaches to model large molecular systems. Thedeveloped approaches rely on using one-electron Gaussian-typefunctions called atom-centered potentials (ACPs) to correct for thebasis set incompleteness and the lack of correlation effects in theunderlying minimal or small basis set Hartree-Fock (HF)methods. In particular, ACPs are proposed for ten elementscommon in organic and bioorganic chemistry (H, B, C, N, O, F, Si,P, S, and Cl) and four different base methods: two minimal basissets (MINIs and MINIX) plus a double-zeta basis set (6-31G*)incombination with dispersion-corrected HF (HF-D3/MINIs, HF-D3/MINIX, HF-D3/6-31G*) and the HF-3c method. The newACPs are trained on a very large set (73 832 data points) of noncovalent properties (interaction and conformational energies) andvalidated additionally on a set of 32 048 data points. All reference data are of complete basis set coupled-cluster quality, mostlyCCSD(T)/CBS. The proposed ACP-corrected methods are shown to give errors in the tenths of a kcal/mol range for noncovalentinteraction energies and up to 2 kcal/mol for molecular conformational energies. More importantly, the average errors are similar inthe training and validation sets, confirming the robustness and applicability of these methods outside the boundaries of the trainingset. In addition, the performance of the new ACP-corrected methods is similar to complete basis set density functional theory (DFT)but at a cost that is orders of magnitude lower, and the proposed ACPs can be used in any computational chemistry program thatsupports effective-core potentials without modification. It is also shown that ACPs improve the description of covalent andnoncovalent bond geometries of the underlying methods and that the improvement brought about by the application of the ACPs isdirectly related to the number of atoms to which they are applied, allowing the treatment of systems containing some atoms forwhich 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 energiesof systems with hundreds to thousands of atoms.