Good- Γ numbers: A shell-optimized route to the thermodynami

Single-particle finite-size errors remain a central obstacle in quantum Monte Carlo simulations of periodic systems, conventionally reduced via twist averaging. Here, we introduce good- Γ (GG) particle numbers as system sizes N at which the Γ -point Hartree-Fock energy of the high-density two-dimensional uniform electron gas (2D UEG) lies anomalously close to its thermodynamic-limit (TL) value. All results in this work concern the 2D UEG in its high-density Fermi-liquid regime, r s = 1 – 4 . We systematically investigate the kinetic- and exchange-energy errors, Δ KE ( N ) and Δ EX ( N ) , that underlie this one-body finite-size-error cancellation across four densities and both spin polarizations. We then compare diffusion Monte Carlo energies extrapolated to the TL from GG- N sequences against twist-averaged extrapolations at the same densities and polarizations, finding agreement to within a fraction of a millihartree in every case, independent of whether a 1 / N or an N − 5 / 4 extrapolation form is used.