Correcting Basis Set Incompleteness in Wave Function Correlation Energy by Dressing Electronic Hamiltonian with an Effective Short-Range Interaction

We propose a general approach to reducing basis set incompleteness error in electron correlation energy calculations. The correction is computed alongside the correlation energy in a single calculation by modifying the electron interaction operator with an effective short-range electron-electron interaction. Our approach is based on a local mapping between the Coulomb operator projected onto a finite basis and a long-range interaction represented by the error function with a local range-separated parameter, originally introduced by Giner et al. [ <i>J. Chem. Phys.</i> 2018, 149, 194301]. Unlike the basis set incompleteness error correction proposed in that work, our method does not rely on short-range correlation density functionals. As a numerical demonstration, we apply the method with complete active space wave functions. Correlation energies are computed using two distinct approaches: the linearized adiabatic connection (AC0) method and <i>n</i>-electron valence state second-order perturbation theory (NEVPT2). We obtain encouraging results for the relative energies of test molecules, with accuracy in a triple-ζ basis set comparable to or exceeding that of uncorrected AC0 or NEVPT2 energies in a quintuple-ζ basis set.