The user can then choose the Wyckoff site combinations from which to sample the structure space. As a default setting, the AXS algorithm includes all possible Wyckoff site combinations in the structure search. For each Wyckoff site combination that satisfies the atom count constraint, we attempt to consider all structures which satisfy the associated symmetry constraints. We generate the search space of Wyckoff positions by constraining candidate positions to lie on a 3-dimensional grid. Symmetrically equivalent positions associated with the candidate position are also generated. Each individual candidate position will therefore contain a number of atoms equal to the multiplicity of the special Wyckoff site. The grid density, H, is defined by the user in units of grid points per Å( Å-1 ) and is the same in all three dimensions. These candidate atomic positions are generated for each Wyckoff position in the valid combination. These candidate positions, which span the degrees of freedom of each Wyckoff position at the user-specified density, are then compared pairwise against candidates of every other Wyckoff position to check for overlap in atomic positions. This collision tolerance parameter which defines atomic overlap, d tol, is specified by the user. Once every individual candidate position is checked against all others candidates from distinct Wyckoff sites, we assemble all possible valid sets of candidate positions into structures which span the degrees of freedom of the Wyckoff sites.