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Functional and density-driven errors in density functional theory: quantum Monte Carlo benchmarks for solids
We introduce a systematic analysis of density functional approximation errors in solids by separating functional-driven from density-driven contributions using quantum Monte Carlo densities of silicon, sodium chloride, and copper as reference. Typically, functional errors dominate, but we identify important exceptions where density-driven errors exceed functional errors by factors of 2–3, notably for SOGGA11 and τ -HCTH in the semiconductor and the insulator. Material dependence is striking: 63% of func- tionals show error cancellation in silicon versus 18% in copper, and only five function- als surpass LDA accuracy for metallic copper even with exact densities. For silicon and sodium chloride, GILL or BECKE exchange combined with PBE, PW91, or P86 correlation achieves near-exact xc energies on QMC densities, while copper requires specialized functionals like PBEsol or PBELYP. High-quality densities consistently re- duce density-driven errors across all systems. Historical analysis reveals that 1990s GGA functionals outperform many modern meta-GGAs, contradicting expectations of systematic improvement along Jacob’s ladder. These results provide practical guidance for functional selection and highlight implications for machine learning potential devel- opment, where material-dependent error cancellation may compromise transferability.