For deviations in the fractional coordinates of molecules in the asymmetric unit cell, the geometry and energy of the crystal structure can be invariant to certain translations of the entire asymmetric unit cell in one or more fractional coordinate directions, subject to space group symmetry. To ensure that these degenerate geometric representations are evaluated identically, fractional coordinates are measured relative to a reference atom in the asymmetric unit cell. This is arbitrarily taken as the first atom listed in the asymmetric unit cell. N r,s denotes the total number of atoms in the asymmetric unit cell (including atoms from other molecules if Z ′ > 1). The vector of all fractional coordinates in the asymmetric unit cell, rs , contains 3N r,s elements for the fractional coordinates of each atom in 3 dimensions, x, ŷ, and ẑ. These are used to calculate the vector Y s of 3(N r,s -1) elements containing relative fractional atomic coordinates: