Functional and Density-Driven Errors in Density Functional Theory: Quantum Monte Carlo Benchmarks for Solids

Abstract

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 functionals show error cancellation in silicon versus 18% in copper, and only five functionals 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 reduce 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 development, where material-dependent error cancellation may compromise transferability.