Cohesive-Energy Bookkeeping in Density-Functional Theory: How Much of the Error Is the Atomic Reference? A Decomposition by Material Class and a Per-Element Shift Test

The cohesive energy is computed as isolated-atom energy minus solid energy, so its error sums an atomic-reference part and a solid part, yet benchmarks report one mean absolute error per functional. Using two published benchmark sets (9 solids with LDA, PBE, PBEsol and SCAN; 12 elemental metals with PBE, PBEsol and SCAN), this paper decomposes cohesive-energy errors by material class and tests an additive per-element shift model. The model reduces the mean absolute error in-sample from 0.517 to 0.021 eV/atom (LDA), 0.133 to 0.018 (PBE), 0.194 to 0.020 (PBEsol) and 0.239 to 0.009 (SCAN); under leave-one-solid-out cross-validation the reductions are 64%, 37%, 45% and 52%. Elemental silicon and carbon errors alone predict the silicon carbide error to within 0.10 eV/atom for all four functionals. All numbers are produced by the deposited script from the deposited data table, transcribed from Jana, Patra and Samal (2018) and Jana, Sharma and Samal (2018).