Density Functional Theory
Density Functional Theory (DFT) · Also known as: DFT, Kohn-Sham equations
Density Functional Theory (DFT) is a computational method for determining the properties of materials and molecules by modeling the ground state electron density. Developed by Walter Kohn and Lu Jeu Sham in the 1960s, DFT reduces the complexity of quantum chemistry from tracking individual electron coordinates to optimizing the total electron density, enabling efficient simulations of large molecular and condensed-matter systems.
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When to use it
DFT is used for electronic structure calculations of molecules, solids, surfaces, and interfaces. It is efficient for systems with 10–10,000 atoms and works well when the exchange-correlation functional accurately captures the physics. DFT is less reliable for systems with strong electron-electron correlations (e.g., transition metals, strongly correlated insulators) or for excited states.
Strengths & limitations
- Computationally efficient compared to post-Hartree-Fock methods, scales as O(N^3) for large systems.
- Remarkably accurate for ground state properties across diverse materials (band gaps, bond lengths, lattice constants).
- Flexible functional framework (LDA, GGA, hybrid) allows trading accuracy for computational cost.
- Applicable to molecules, surfaces, and extended solids with the same formalism.
- Well-established in codes (Gaussian, VASP, QUANTUM ESPRESSO) with decades of validation.
- Exchange-correlation functional is unknown and must be approximated, introducing systematic errors.
- Struggles with strongly correlated electron systems (Mott insulators, transition metal complexes).
- Systematically underestimates band gaps in semiconductors and insulators (typically by 30–50%).
- Poor description of van der Waals interactions; dispersion correction required for weak interactions.
- Cannot describe excited states directly; Time-Dependent DFT is an approximation with known failures.
Frequently asked
What is the difference between LDA, GGA, and hybrid functionals?
LDA (Local Density Approximation) uses only local density and is fast but less accurate. GGA (Generalized Gradient Approximation) includes density gradient information, improving accuracy at moderate cost. Hybrid functionals mix in Hartree-Fock exchange, offering better band gaps but at higher computational cost. Choice depends on your system and accuracy requirements.
Why does DFT underestimate band gaps?
The exact exchange-correlation functional (unknown) should exactly cancel the self-interaction error. Approximate functionals fail at this, systematically underestimating the energy difference between occupied and unoccupied states. Range-separated hybrids (CAM-B3LYP) improve this but at computational cost.
When should I use DFT vs. post-Hartree-Fock methods?
DFT is much faster and often sufficiently accurate for ground state properties of weakly-correlated systems. Use post-Hartree-Fock (MP2, CCSD) for high accuracy or strongly correlated systems, accepting higher computational cost.
What is a basis set and how does it affect DFT calculations?
A basis set is a set of mathematical functions used to expand the Kohn-Sham orbitals. Plane waves are common for periodic systems (solids), while Gaussian basis sets are typical for molecular calculations. Larger basis sets are more accurate but slower; convergence tests are essential.
Can DFT describe van der Waals interactions?
Standard DFT functionals cannot describe van der Waals interactions; they are too weak and require explicit correlation. Dispersion corrections (DFT-D2, DFT-D3) or non-local functionals (vdW-DF) add this physics, essential for physisorption and organic crystals.
Sources
- Kohn, W., Sham, L. J. (1965). Self-consistent equations including exchange and correlation effects. Physical Review, 140, A1133–A1138. DOI: 10.1103/PhysRev.140.A1133 ↗
- Hohenberg, P., Kohn, W. (1964). Inhomogeneous electron gas. Physical Review, 136, B864–B871. DOI: 10.1103/PhysRev.136.B864 ↗
- Burke, K. (2012). Perspective on density functional theory. The Journal of Chemical Physics, 136, 150901. DOI: 10.1063/1.4704546 ↗
How to cite this page
ScholarGate. (2026, June 3). Density Functional Theory (DFT). ScholarGate. https://scholargate.app/en/quantum-computing/density-functional-theory
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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- Time-Dependent DFTQuantum Computing↔ compare