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The self-consistent procedure in electronic structure calculations isrevisited using a highly efficient and robust algorithm for solving thenon-linear eigenvector problem i.e. H({{\psi}}){\psi} = E{\psi}. This newscheme is derived from a generalization of the FEAST eigenvalue algorithm toaccount for the non-linearity of the Hamiltonian with the occupiedeigenvectors. Using a series of numerical examples and the DFT-Kohn/Sham model,it will be shown that our approach can outperform the traditional SCFmixing-scheme techniques by providing a higher converge rate, convergence tothe correct solution regardless of the choice of the initial guess, and asignificant reduction of the eigenvalue solve time in simulations.

Non-linear eigensolver-based alternative to traditional SCF methods