  Localized representation of the Kohn-Sham subspace plays an important role in
quantum chemistry and materials science. The recently developed selected
columns of the density matrix (SCDM) method [J. Chem. Theory Comput. 11, 1463,
2015] is a simple and robust procedure for finding a localized representation
of a set of Kohn-Sham orbitals from an insulating system. The SCDM method
allows the direct construction of a well conditioned (or even orthonormal) and
localized basis for the Kohn-Sham subspace. The SCDM algorithm avoids the use
of an optimization procedure and does not depend on any adjustable parameters.
The most computationally expensive step of the SCDM method is a column pivoted
QR factorization that identifies the important columns for constructing the
localized basis set. In this paper, we develop a two stage approximate column
selection strategy to find the important columns at much lower computational
cost. We demonstrate the effectiveness of this process using the dissociation
process of a BH$_3$NH$_3$ molecule, an alkane chain and a supercell with 256
water molecules. Numerical results for the large collection of water molecules
show that two stage localization procedure can be more than 30 times faster
than the original SCDM algorithm and compares favorably with the popular
Wannier90 package.
