Linear-scaling feasibility of mixed deformed-sinc and GTO basis sets

Determine whether a mixed basis that combines the deformed sinc basis set with Gaussian-type orbital (GTO) functions that resolve the nuclear cusp can be employed while preserving computational cost that scales linearly with the number of basis functions.

Background

The paper introduces a deformed periodic sinc basis with a pseudospectral diagonal approximation and a novel cyclic Knothe–Rosenblatt flow to construct curvilinear coordinates, achieving mean-field electronic structure calculations with cost that is log-linear in the number of basis functions. While this approach efficiently reduces basis size and retains desirable properties (e.g., spectral convergence with suitable pseudopotentials), high resolution near nuclei still requires many functions.

To further reduce basis size, the authors suggest augmenting the deformed sinc basis with sharp Gaussian-type orbitals (GTOs) to capture the nuclear cusp efficiently, a strategy used in other contexts. However, it is unclear whether such a hybridization can be implemented without sacrificing the favorable scaling of their approach, leading to the explicit open question about maintaining linear scaling with respect to the number of basis functions.