Correction of the basis set error due to the absence of the electron-electron cusp in the wave function by using an adiabatic correction

This article proposes an analytical method to address the slow convergence of electronic structure calculations caused by the inability of finite one-particle basis sets to describe the electron-electron cusp. An equivalence is made between a calculation using a finite basis set with the physical Coulomb interaction and a calculation using a complete basis set with a model interaction (specifically, the error-function screened Coulomb potential characterized by a range-separation parameter $μ$). By leveraging the adiabatic connection formalism, a simple, parameter-free correction formula is derived. It depends only on the on-top pair density and a locally defined range-separation parameter ($μ$) derived from the basis set itself. This `adiabatic connection based basis set error correction' (ABC) is derived from the asymptotic expansion of the wave function at large $μ$ for small inter-electronic distances. Therefore it is applicable to both ground and excited states without the restriction imposed by the Hohenberg-Kohn theorem. Numerical tests illustrate that the method achieves chemical accuracy using smaller basis sets than typically required.

Source: arXiv:2606.07350v1 - http://arxiv.org/abs/2606.07350v1 PDF: https://arxiv.org/pdf/2606.07350v1 Original Link: http://arxiv.org/abs/2606.07350v1