Quasiparticle Energies That Will Not Be Computed: A Calibrated Release for 2D Semiconductors

The $G_0W_0$ approximation is the practical reference for quasiparticle energies, but it costs two to four orders of magnitude more than semilocal density functional theory, and at that price most of the data will never be computed. The Computational 2D Materials Database contains 16,905 entries, of which 339 have $G_0W_0$ results. We release predicted quasiparticle band gaps and vacuum-aligned band edges, each with a calibrated 90% interval, for 3,534 two-dimensional semiconductors that have no $G_0W_0$ calculation, at a cost of one hybrid functional calculation per material. Two findings support the release. First, the limiting resource is the number of materials rather than the number of electronic states, because labels are generated one material at a time. A tabular foundation model given $10^{4}$ material-stratified rows predicts the correction to within 0.101 eV, 27% below a gradient boosting baseline tuned for the same metric on all $1.9\times10^{6}$ rows; holding the row budget fixed while varying only the material count separates the two: a 185-fold increase in rows yields 0.003 eV, whereas going from 10 to 192 materials yields 0.19 eV. Second, the predictive quantiles remain calibrated in the regime where a screening model operates, widening by up to a factor of 3.9 on unseen elements and unseen stoichiometry classes while marginal coverage holds at the nominal level, so each released row carries its own stated uncertainty. Neither learned structural embeddings nor explicit spin descriptors improve upon tabular features.