Täthetsfunktionaler

Density functionals are mathematical functions used in density functional theory (DFT) to approximate the exchange-correlation energy of a many-electron system. DFT is a quantum mechanical method that aims to calculate the ground-state properties of atoms, molecules, and solids by focusing on the electron density rather than the much more complex many-electron wavefunction. The total energy of the system is expressed as a functional of the electron density, and a crucial component of this functional is the exchange-correlation energy.

The exact form of the exchange-correlation functional is unknown and is the subject of ongoing research. Therefore, approximations are employed. These approximations are often categorized into "rungs" of a "Jacob's Ladder," where higher rungs represent more sophisticated and generally more accurate functionals. Common types of density functionals include the local density approximation (LDA), generalized gradient approximations (GGAs), meta-GGAs, hybrid functionals, and double-hybrid functionals.

LDA functionals depend only on the electron density at a given point. GGAs include the gradient of the density, capturing some of the non-uniformity of the electron distribution. Meta-GGAs incorporate the kinetic energy density or the Laplacian of the density. Hybrid functionals mix a portion of exact (Hartree-Fock) exchange with DFT exchange. Double-hybrid functionals further improve accuracy by including a fraction of second-order perturbation theory correlation. The choice of density functional significantly impacts the accuracy of DFT calculations for various properties like binding energies, reaction barriers, and electronic structures.