KKR Method
Korringa-Kohn-Rostoker Method · Also known as: KKR, multiple scattering
The Korringa-Kohn-Rostoker (KKR) method is a powerful multiple-scattering approach for calculating electronic band structures and properties of periodic and disordered solids. Developed in the late 1940s, KKR treats electrons as scattering from atomic potentials in a muffin-tin geometry, enabling efficient calculations for both crystalline and amorphous systems.
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When to use it
KKR is suitable for periodic systems, especially those with complex structures or multiple scattering. It is particularly powerful for disordered alloys via the coherent potential approximation (CPA).
Strengths & limitations
- Efficient for large unit cells and complex structures.
- Naturally handles disorder via CPA without supercells.
- Excellent for magnetic systems and spin-dependent properties.
- Green's function formalism provides flexibility for defects.
- Well-suited for transport and response properties.
- Muffin-tin approximation breaks down for highly localized electrons.
- Assumes spherical symmetry inside MT spheres; may be inaccurate near atoms.
- Requires careful choice of MT sphere radii and interstitial parameters.
- Less transparent than plane-wave DFT for visualization and intuition.
- Implementation more complex; fewer commercial packages.
Frequently asked
What is the muffin-tin approximation and when is it valid?
MT approximation assumes spherically symmetric potential inside non-overlapping spheres centered on atoms, with constant potential outside. It is valid for spherically symmetric charge distributions; it breaks down for anisotropic bonds or rough potentials.
How does KKR handle disorder?
The coherent potential approximation (CPA) replaces a random alloy with a single effective medium, allowing disorder to be included without supercells. CPA is very efficient but assumes short-range correlations are weak.
What are structure constants?
Structure constants encode how an electron wave scattered from one atom propagates to and rescatters from another, depending on geometry. They generalize the free-electron Green's function to the crystal structure.
Is KKR better than DFT for disordered systems?
For disordered systems, KKR+CPA is more efficient than supercell DFT, allowing for realistic disorder without massive computational cost. For ordered systems, DFT is more widely used and flexible.
What basis functions are used in KKR?
Inside MT spheres, solutions of the radial Schrödinger equation (partial waves) are used. In the interstitial, plane waves or other basis sets can be employed, depending on the code.
Sources
- Korringa, J. (1947). On the calculation of the energy of a Bloch wave in a metal. Physica, 13, 392–400. DOI: 10.1016/0031-8914(47)90013-X ↗
- Gyorffy, B. L. (1972). Coherent potential approximation for random substitutional binary alloys. Physical Review B, 5, 2382–2384. link ↗
- Vosko, S. H., Wilk, L., Nusair, M. (2003). Accurate spin-dependent electron liquid correlation energies. Canadian Journal of Physics, 58, 1200–1211. link ↗
How to cite this page
ScholarGate. (2026, June 3). Korringa-Kohn-Rostoker Method. ScholarGate. https://scholargate.app/en/quantum-computing/kkr-method
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