Finite-size Effects in periodic EOM-CCSD for Ionization Energies and Electron Affinities: Convergence Rate and Extrapolation to the Thermodynamic Limit

TL;DR

This paper analyzes how quasi-particle energies computed with EOM-CCSD methods converge as system size increases, deriving and confirming convergence rates to improve finite-size error corrections in periodic systems.

Contribution

It introduces a formal derivation of convergence rates for EOM-CCSD quasi-particle energies in periodic systems and validates these with numerical simulations.

Findings

Confirmed asymptotic convergence rates for different dimensional systems

Validated theoretical predictions with simulations on trans-Polyacetylene

Provided a basis for efficient finite-size error correction schemes

Abstract

We investigate the convergence of quasi-particle energies for periodic systems to the thermodynamic limit using increasingly large simulation cells corresponding to increasingly dense integration meshes in reciprocal space. The quasi-particle energies are computed at the level of equation-of-motion coupled-cluster theory for ionization (IP-EOM-CC) and electron attachment processes (EA-EOM-CC). By introducing an electronic correlation structure factor, the expected asymptotic convergence rates for systems with different dimensionality are formally derived. We rigorously test these derivations through numerical simulations for trans-Polyacetylene using IP/EA-EOM-CCSD and the G0W0@HF approximation, which confirm the predicted convergence behavior. Our findings provide a solid foundation for efficient schemes to correct finite-size errors in IP/EA-EOM-CCSD calculations.