Correcting basis-set errors due to the absence of the electron-electron cusp using an adiabatic connection

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. (Small Gaussian basis set errors are often constructed or used with the objective to reduce computational effort, and may contain other sources of errors.) A model correspondence is established 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 correction formula is derived. It does not contain any fitting to reference experimental or calculated data. 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" 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 (energy errors <1 kcal/mol) using smaller basis sets than typically required.