You spin my subspace right round... - direct minimization in DFT for metallic systems

The article

Direct minimization technique for metals in density functional theory
Freysoldt, Boeck, Neugebauer
Phys. Rev. B 79, 241103(R) (2009)
http://link.aps.org/doi/10.1103/PhysRevB.79.241103

describes a method for the direct minimization of the expansion coefficients of the Kohn-Sham orbitals in a density functional theory scheme with simultaneous and consistent updates of occupation numbers and subspace rotations.
This extension to previous approaches allowed the authors to perform fast direct-minimization-DFT calculations for metallic systems (the convergence of which depends sensitively on changes in the Kohn-Sham Fermi surface during the iterations).
Since the KS orbitals have to be orthonormalized, the asymptotic complexity, however, is O(N³), i.e. the same as for self-consistent, iterative diagonalization of the KS Hamiltonian or any other KS orbital-based approach.