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 bioorganic 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
(73 832 data points) of noncovalent properties (interaction
and conformational energies) and validated additionally on a set of
32 048 data points. All reference data are 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 noncovalent 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 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 that supports effective-core
potentials without modification. It is also shown that ACPs improve
the description of covalent and noncovalent 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.