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

## TL;DR

This paper introduces a new method to reduce errors in electron correlation energy calculations caused by incomplete basis sets.

## Contribution

A novel approach to basis set incompleteness error correction is proposed, avoiding reliance on short-range correlation density functionals.

## Key findings

- The method modifies the electron interaction operator with an effective short-range interaction.
- Encouraging results were obtained for relative energies of test molecules using complete active space wave functions.

## Abstract

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. [
J. Chem. Phys.
2018, 149, 194301
30466264
10.1063/1.5052714]. 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 n-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.