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.