Transferable Atom-Centered Potentials for the Correction of Basis Set Incompleteness Errors in Density-Functional Theory

Recent
progress in the accurate calculation of noncovalent interactions
has enabled density-functional theory (DFT) to model systems relevant
in biological and supramolecular chemistry. The application of DFT
methods using atom-centered Gaussian basis sets to large systems is
limited by the number of basis functions required to accurately model
thermochemistry and, in particular, weak intermolecular interactions.
Basis set incompleteness error (BSIE) arising from the use of incomplete
basis sets leads to erroneous intermolecular energies, bond dissociation
energies, and structures. In this article, we develop a correction
for BSIE in DFT calculations using basis set incompleteness potentials
(BSIP). BSIPs are atom-based one-electron potentials (ACPs) with the
same functional form as effective core potentials (ECP) that are designed
to correct the effects of BSIE in properties that are linear mappings
of the energy. We present a systematic way of developing general,
error-correcting ACPs and apply this technique to generate BSIPs for
eight common elements in organic and biological systems (H, C, N,
O, F, P, S, and Cl). Two BSIPs were optimized for use with the scaled
MINI (MINIs) and MINIs­(d) basis sets and were designed to correct
for the impacts of BSIE on noncovalent binding energies and intra/intermolecular
geometries. BSIPs developed for use with 6-31G*, pc-1, and 6-31+G**
basis sets also correct for the effects of BSIE on bond dissociation
energies, which enables the study of chemical reactions in very large
systems. BSIPs can be used with any density functional in any electronic
structure program that implements ECPs. Our BSIPs add very little
to the computational cost provided an efficient ECP implementation
is used. Our results support the use of BLYP-D3/MINIs-BSIP as a computationally
inexpensive and more accurate alternative to other approaches (e.g.,
B3LYP/6-31G* and BP86/6-31G*) in protein and supramolecular structural
studies.