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We present a spectrum-splitting approach to conduct all-electron Kohn-Shamdensity functional theory (DFT) calculations by employing Fermi-operatorexpansion of the Kohn-Sham Hamiltonian. The proposed approach splits thesubspace containing the occupied eigenspace into a core-subspace, spanned bythe core eigenfunctions, and its complement, the valence-subspace, and therebyenables an efficient computation of the Fermi-operator expansion by reducingthe expansion to the valence-subspace projected Kohn-Sham Hamiltonian. The keyideas used in our approach are: (i) employ Chebyshev filtering to compute asubspace containing the occupied states followed by a localization procedure togenerate non-orthogonal localized functions spanning the Chebyshev-filteredsubspace; (ii) compute the Kohn-Sham Hamiltonian projected onto thevalence-subspace; (iii) employ Fermi-operator expansion in terms of thevalence-subspace projected Hamiltonian to compute the density matrix,electron-density and band energy. We demonstrate the accuracy and performanceof the method on benchmark materials systems involving silicon nano-clusters upto 1330 electrons, a single gold atom and a six-atom gold nano-cluster. Thebenchmark studies on silicon nano-clusters revealed a staggering five-foldreduction in the Fermi-operator expansion polynomial degree by using thespectrum-splitting approach for accuracies in the ground-state energies of$\sim 10^{-4} Ha/atom$ with respect to reference calculations. Further,numerical investigations on gold suggest that spectrum splitting isindispensable to achieve meaningful accuracies, while employing Fermi-operatorexpansion.

Spectrum-splitting approach for Fermi-operator expansion in all-electron Kohn-Sham DFT calculations