Exchange-correlation functionals in density functional theory

6 problems

• A practical functional that obeys the flat-plane condition

  Partially resolved

  The exact energy changes in straight lines when a fraction of an electron is added or when spin is fractionally shared, and approximate functionals bend those lines. Bending one way spreads electrons out too much; bending the other way mistreats stretched bonds.

• System-independent functional giving fundamental gaps of molecules and solids

  Open

  Standard functionals underestimate the energy needed to add or remove an electron, which sets how well a material conducts or absorbs light. Fixes exist but each must be retuned for each material.

• Transferability of machine-learned functionals beyond their training chemistry

  Open

  Functionals fitted by machine learning to accurate data now beat hand-made ones on molecules similar to their training set. It is unknown whether they stay accurate for metals, transition-metal compounds and solids they never saw.

• Reliable energy ranking of molecular crystal polymorphs

  Open

  The same molecule can pack into several crystal forms with almost equal energies, and which form appears changes how a drug dissolves. Calculations still struggle to rank these forms correctly.

• Certified chemical accuracy for systems of a thousand atoms

  Open

  Chemists want energies correct to within 1 kcal/mol (about 0.043 eV), small enough to predict which reaction or crystal form wins, but the methods that reach this cost grows so fast that they fail beyond tens of atoms. The goal is a method that keeps this accuracy for proteins, crystals and surfaces and states its own error bar.

• A density functional free of self-interaction that keeps thermochemical accuracy

  Open

  Common approximations let an electron feel a push from its own charge, which spreads electrons out too much and spoils predictions of reaction barriers and charge transfer. Corrections that remove this self-repulsion usually make ordinary bond energies worse, and no approximation yet fixes the first without hurting the second.