Density functional theory

Density functional theory is a quantum theory that uses electron density as its central variable to calculate energies and properties of many-electron systems.

Hohenberg–Kohn theorems: Theorems establishing that a system’s ground-state energy and properties are determined by its electron density. They justify replacing the many-electron wavefunction with electron density as the theory’s central variable.
Many-body problem: The problem of predicting interacting properties of systems containing many coupled particles. Density functional theory addresses the electronic version without explicitly solving the full interacting wavefunction.
Computational materials science: The use of computation and physical models to predict and understand materials. Density functional theory is a standard tool for modeling materials’ atomic structures and properties.
Quantum Monte Carlo: A family of stochastic methods for approximating quantum many-body properties using Monte Carlo sampling. Some quantum Monte Carlo methods can benchmark density functional energies at substantially greater computational cost.
Band-gap problem: The frequent underestimation of semiconductor and insulator fundamental gaps by common approximate density functionals. It is a prominent limitation when density functional calculations are used to predict electronic excitations.
Kohn–Sham method: A formulation that maps an interacting electron system onto auxiliary noninteracting electrons with the same density. It turns density-based theory into tractable one-electron equations.
Schrödinger equation: The equation governing the quantum state and energy of a nonrelativistic system. Ground-state density functional theory is built to recover the ground-state energy of this quantum problem.
Molecular geometry optimization: A computational search for molecular coordinates that minimize an energy or satisfy another structural criterion. Density functional energies and forces are commonly used to locate stable molecular structures.
Coupled cluster: A wavefunction-based electronic-structure method that accounts for electron correlation through an exponential excitation operator. It often provides accurate molecular benchmarks where density functional results depend on functional choice.
Self-interaction error: An error in approximate electronic methods where an electron interacts spuriously with its own charge distribution. It can distort density functional predictions of ionization, charge transfer, and localized electrons.

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