Improved Basis-Set Incompleteness Potentials for Accurate Density-Functional Theory Calculations in Large Systems

The
accurate calculation of chemical properties using density-functional
theory (DFT) requires the use of a nearly complete basis set. In chemical
systems involving hundreds to thousands of atoms, the cost of the
calculations place practical limitations on the number of basis functions
that can be used. Therefore, in most practical applications of DFT
to large systems, there exists a basis-set incompleteness error (BSIE).
In this article, we present the next iteration of the basis-set incompleteness
potentials (BSIPs), one-electron potentials designed to correct for
basis-set incompleteness error. The ultimate goal associated with
the development of BSIPs is to allow the calculation of molecular
properties using DFT with near-complete-basis-set results at a computational
cost that is similar to a small basis set calculation. In this work,
we develop BSIPs for 10 atoms in the first and second rows (H, B–F,
Si–Cl) and 15 common basis sets of the Pople, Dunning, Karlsruhe,
and Huzinaga types. Our new BSIPs are constructed to minimize BSIE
in the calculation of reaction energies, barrier heights, noncovalent
binding energies, and intermolecular distances. The BSIPs were obtained
using a training set of 15 944 data points. The fitting approach
employed a regularized linear least-squares method with variable selection
(the LASSO method), which results in a much better fit to the training
data than our previous BSIPs while, at the same time, reducing the
computational cost of BSIP development. The proposed BSIPs are tested
on various benchmark sets and demonstrate excellent performance in
practice. Our new BSIPs are also transferable; i.e., they can be used
to correct BSIE in calculations that employ density functionals other
than the one used in the BSIP development (B3LYP). Finally, BSIPs
can be used in any quantum chemistry program that have implemented
effective-core potentials without changes to the software.