Serially improved GTOs for molecular applications (SIGMA): Basis sets from H to Ne.

A new approach for generating Gaussian basis sets is reported and tested for atoms from H to Ne. The basis sets thus calculated, named SIGMA basis sets, range from DZ to QZ sizes and have the same composition per shell as Dunning basis sets but with different treatment of the contractions. The standard SIGMA basis sets and their augmented versions have proven to be very suitable for providing good results in atomic and molecular calculations.

Accurate Hellmann-Feynman forces from density functional calculations with augmented Gaussian basis sets.

The Hellmann-Feynman (HF) theorem provides a way to compute forces directly from the electron density, enabling efficient force calculations for large systems through machine learning (ML) models for the electron density. The main issue holding back the general acceptance of the HF approach for atom-centered basis sets is the well-known Pulay force which, if naively discarded, typically constitutes an error upward of 10 eV/Å in forces. In this work, we demonstrate that if a suitably augmented Gaussian basis set is used for density functional calculations, the Pulay force can be suppressed, and HF forces can be computed as accurately as analytical forces with state-of-the-art basis sets, allowing geometry optimization and molecular dynamics to be reliably performed with HF forces.