Resolving Finite-Size Errors in EOM-CCSD Band Gaps of Solids with Interacting-Bath Dynamical Embedding Theory

Abstract

Periodic equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD) has shown promise for quantitative calculations of band structures in solids. However, its steep computational scaling has limited calculations to relatively coarse $k$-point meshes, leading to sizable finite-size errors and discrepant estimates of thermodynamic-limit band gaps in recent benchmarks. In this work, we revisit EOM-CCSD band gaps for ten semiconductors and insulators using interacting-bath dynamical embedding theory (ibDET), a systematically improvable Green's function embedding framework that enables dense Brillouin-zone sampling at modest computational cost. By pushing the $k$-point sampling up to $10\times 10\times 10$, well beyond the system sizes accessible in canonical periodic EOM-CCSD calculations, we significantly reduce finite-size errors and obtain stable thermodynamic-limit extrapolations. We further compare $G_0{W}_0$@PBE, $G_0{W}_0$@HF, and EOM-CCSD on an equal footing using the same numerical settings in PySCF. We find that EOM-CCSD yields a mean absolute error of 0.32 eV relative to experimental band gaps for a test set of ten semiconductors and insulators, lower than that of $G_0{W}_0$@PBE. For ZnO, EOM-CCSD also accurately describes the Zn $3d$-band binding energy, despite overestimating the band gap. These results demonstrate that ibDET offers a practical route to high-accuracy many-body electronic structure calculations in periodic systems.

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