  Linear scaling density matrix methods typically do not provide individual
eigenvectors and eigenvalues of the Fock/Kohn-Sham matrix, so additional work
has to be performed if they are needed. Spectral transformation techniques
facilitate computation of frontal (homo and lumo) molecular orbitals. In the
purify-shift-and-square method the convergence of iterative eigenvalue solvers
is improved by combining recursive density matrix expansion with the folded
spectrum method [J. Chem. Phys. 128, 176101 (2008)]. However, the location of
the shift in the folded spectrum method and the iteration of the recursive
expansion selected for eigenpair computation may have a significant influence
on the iterative eigenvalue solver performance and eigenvector accuracy. In
this work, we make use of recent homo and lumo eigenvalue estimates [SIAM J.
Sci. Comput. 36, B147 (2014)] for selecting shift and iteration such that homo
and lumo orbitals can be computed in a small fraction of the total recursive
expansion time and with sufficient accuracy. We illustrate our method by
performing self-consistent field calculations for large scale systems.
