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.