Exchange-Correlation Functionals
In Kohn-Sham density functional theory the exchange-correlation functional is the one approximated term, and its choice controls the accuracy of computed structures and energies. The local density approximation (LDA) depends only on the local density and typically overbinds, giving lattice constants and volumes that are too small. Generalized gradient approximations (GGAs) add the density gradient: PBE is widely used for chemistry and tends to give volumes that are too large, while PBEsol and AM05 were designed for solids and usually give lattice constants between LDA and PBE. Hybrid functionals and DFT + U are used where self-interaction error in localized d or f electrons matters. Because no functional is uniformly best, comparing several can bracket the uncertainty in a computed quantity. See DFT + U and the Hubbard U and DFT convergence.
Functional error as a limit of DFT in catalysis (2012)
Kitchin’s 2012 preface on trends in computational catalysis argued that DFT alone cannot answer every catalysis question, partly because the approximate exchange-correlation functional can limit accuracy. He pointed to the construction of new functionals by large-scale fitting to databases of energies, with chemisorption applications, as one of the methodological efforts needed to improve DFT accuracy (Kitchin 2012). Summary: kitchin2012.
Functional dependence of oxide polymorph energetics (2014)
Mehta, Salvador and Kitchin computed equations of state for six polymorphs of TiO2, VO2, RuO2, IrO2 and SnO2 with LDA, PBE, PBEsol and AM05. Every LDA volume was smaller than the corresponding PBE volume, and PBEsol and AM05 volumes were similar and closest to experiment. Relative polymorph energies depended on the functional most when the polymorphs differed strongly in volume (for example, pyrite versus columbite ordering in RuO2 and IrO2, or the pyrite and fluorite energies of TiO2), and less for polymorphs of similar volume. For TiO2, GGA functionals placed anatase below rutile, opposite to experiment, and the authors point to zero-point or DFT + U corrections as possible remedies. They propose using the spread across functionals as bounds on the energy differences relevant to synthesis (Mehta et al. 2014). Summary: mehta2014.
Exact exchange fraction and TiO2 rutile-anatase ordering (2015)
Curnan and Kitchin varied the exact exchange fraction in PBE0 and HSE06 for rutile and anatase TiO2. Both start anatase-favoring (about -0.081 eV/TiO2 at zero exact exchange), cross to the experimental rutile-favoring order at fractions of about 0.72 (PBE0) and 0.78 (HSE06), peak, and revert toward the Hartree-Fock limit; the non-monotonic trend tracked cell volumes and c/a ratios. With GGA plus U, PBE, PW91 and AM05 recovered the full four-polymorph ordering over similar U windows, PBEsol only over a narrow one, and LDA not at all. Because no first-principles rule fixes the exchange fraction and the resulting errors (about 0.07 to 0.13 eV/TiO2) are as large as polymorph energy differences, the authors judged hybrid functionals unreliable for predictive polymorph selection (Curnan 2015). Summary: curnan2015.
Benchmarking functionals for catalysis (2016)
Bligaard et al. stress that benchmarking DFT functionals against higher-level theory and against careful experiments is needed to approach the chemical accuracy (about 1 kcal/mol for activation energies) that catalysis requires, which current methods do not reach (Bligaard et al. 2016). Experimental benchmarks exist for small adsorbates on single-crystal late transition metal surfaces, including systems with substantial van der Waals contributions, but are scarce for metal oxides, carbides and nitrides, whose large system sizes also make high-level calculations prohibitively expensive. Summary: bligaard2016.
BEEF-vdW versus PBE for coverage-dependent atomic adsorption (2016)
Comparing BEEF-vdW adsorption energies of seven atomic adsorbates on Pt(111) and Pd(111) with earlier PBE values showed that BEEF-vdW binds less strongly, most noticeably at low coverage, with the two converging near 1 ML (Thirumalai 2016). Because PBE tends to overbind, the authors read the gap not as a physical vdW effect but as evidence that quantitative coverage-dependent trends depend on the choice of functional. Summary: thirumalai2016.
Functional dependence of strain and interface energies (2017)
For TiO2 films on SrTiO3 and BaTiO3, Xu, Salvador and Kitchin compared PBE, PBEsol and BEEF-vdW. Biaxial strain penalties from BEEF-vdW and PBEsol were mostly within 10% of PBE, with larger deviations for more anisotropic strain. Interface energies were nearly functional independent for a weakly reconstructed interface (under 3.5% variation for anatase (001) on (001)) but varied by 36 to 46% for a heavily reconstructed one with many oxygen vacancies, with PBEsol consistently giving the highest values. Despite this, the dependence was systematic on a given facet and the predicted stable polymorph did not change between functionals (Xu et al. 2017). Summary: xu2017.
PBE errors in Cu-Au alloy and metal surface energies (2022)
In simulating segregation in Cu-Pd-Au alloys, Yang and co-workers found that Au surface enrichment in CuAu was overestimated relative to experiment and attributed it to PBE. Literature PBE formation energies of Cu3Au, CuAu and CuAu3 are substantially less negative than experimental values (for example -56 versus -93 meV/atom for CuAu), so the Cu-Au interaction is underestimated, and PBE mean surface energies are below experiment for Cu, Pd and especially Au (0.87 versus 1.51 J/m2). The authors conclude this part of the discrepancy can only be fixed with a more accurate functional (Yang et al. 2022). Summary: yang2022; see also Surface segregation.
Reference data quality for machine learning on metal complexes (2023)
Garrison and coworkers found that graph networks could not fit the TPSSh/def2-SVP energies of a subset of tmQM complexes (mainly Fe, Ru and Os), even when those structures were in the training set, although the DFT calculations themselves converged without any warning sign. Recomputing all energies with the range-separated hybrid meta-GGA ωB97M-V and the diffuse-augmented def2-SVPD basis removed this systematic error and lowered model errors, which the authors take as evidence that the original level of theory did not describe all complexes consistently (Garrison et al. 2023). Summary: garrison2023.
PBE versus PBEsol plus D3 in segregation simulations (2024)
Training separate surrogates on PBE and on PBEsol with D3 dispersion, Broderick et al. (2024) found that PBEsol-based simulations matched experimental segregation in AgAuCu and AuCuPd at least as well as, and usually better than, PBE. The remaining disagreement, chiefly overpredicted Au segregation, was traced to the functionals underestimating the Au surface energy, an error PBEsol reduces but does not remove. Summary: broderick2024.