Editing Density functional theory (section)

==Electron smearing==
The electrons of a system will occupy the lowest Kohn–Sham eigenstates up to a given energy level according to the [[Aufbau principle]]. This corresponds to the steplike [[Fermi–Dirac distribution]] at absolute zero. If there are several degenerate or close to degenerate eigenstates at the [[Fermi level]], it is possible to get convergence problems, since very small perturbations may change the electron occupation. One way of damping these oscillations is to ''smear'' the electrons, i.e. allowing fractional occupancies.<ref>{{cite journal|last1=Michelini|last2=Pis Diez|last3=Jubert|first1=M. C.|first2=R. |first3=A. H.|title=A Density Functional Study of Small Nickel Clusters|journal=International Journal of Quantum Chemistry|date=25 June 1998|volume=70|issue=4–5|page=694|doi=10.1002/(SICI)1097-461X(1998)70:4/5<693::AID-QUA15>3.0.CO;2-3}}</ref> One approach of doing this is to assign a finite temperature to the electron Fermi–Dirac distribution. Other ways is to assign a cumulative Gaussian distribution of the electrons or using a Methfessel–Paxton method.<ref>{{cite web|title=Finite temperature approaches – smearing methods|website=VASP the GUIDE|url=http://cms.mpi.univie.ac.at/vasp/vasp/Finite_temperature_approaches_smearing_methods.html|access-date=21 October 2016|archive-date=31 October 2016|archive-url=https://web.archive.org/web/20161031085240/http://cms.mpi.univie.ac.at/vasp/vasp/Finite_temperature_approaches_smearing_methods.html|url-status=dead}}</ref><ref>{{cite web|last1=Tong|first1=Lianheng|title=Methfessel–Paxton Approximation to Step Function|url=http://cms.mpi.univie.ac.at/vasp/vasp/Finite_temperature_approaches_smearing_methods.html|website=Metal CONQUEST|access-date=21 October 2016|archive-date=31 October 2016|archive-url=https://web.archive.org/web/20161031085240/http://cms.mpi.univie.ac.at/vasp/vasp/Finite_temperature_approaches_smearing_methods.html|url-status=dead}}</ref>