  A linear-scaling algorithm is presented for computing the Hartree-Fock (HF)
exchange matrix using concentric atomic density fitting. The algorithm utilizes
the stronger distance dependence of the three-center electron repulsion
integrals along with the rapid decay of the density matrix to accelerate the
construction of the exchange matrix. The new algorithm is tested with
computations on systems with up to 1536 atoms and 15585 basis functions, the
latter of which represents, to our knowledge, the largest quadruple-zeta HF
computation ever performed. Our method handles screening of high angular
momentum contributions in a particularly efficient manner, allowing the use of
larger basis sets for large molecules without a prohibitive increase in cost.
