  The Materials Project crystal structure database has been searched for
materials possessing layered motifs in their crystal structures using a
topology-scaling algorithm. The algorithm identifies and measures the sizes of
bonded atomic clusters in a structure's unit cell, and determines their scaling
with cell size. The search yielded 826 stable layered materials, which are
considered as candidates for the formation of two-dimensional monolayers via
exfoliation. Density-functional theory calculates the exfoliation energy of
each material and 681 monolayers are found to exhibit exfoliation energies
below those of certain already-extant two-dimensional materials, indicating the
possibility of exfoliating them from bulk phases. The crystal structures of
these two-dimensional materials provide templates for future theoretical
searches of stable two-dimensional materials. The optimized structures and
other data for all 826 monolayers are provided at https://materialsweb.org .
