The rotation search should be restricted to an appropriately chosen asymmetric unit (Rao et al., 1980). Table 1 lists asymmetric units for cross-rotation functions for search models without internal symmetry. P_{1} is the rotated Patterson function of the search model and P_{2} is the observed Patterson function. The Laue group of P_{1} is “-1”. The Laue group of P_{2} is determined by the space group of the crystal.

Laue Group  Crystal System  Euler Angles

Lattman Angles

-1 triclinc 0 ≤ θ_{1} < 2π, 0 ≤ θ_{2} ≤ π, 0 ≤ θ_{3} < 2π

0 ≤ θ_{−} ≤ 2π, 0 ≤ θ_{2} ≤ π, 0 ≤ θ_{+} < 4π

2/m (b unique) monoclinic (b-u) 0 ≤ θ_{1} < 2π, 0 ≤ θ_{2} ≤ π/2, 0 ≤ θ_{3} < 2π

0 ≤ θ_{−} ≤ 2π, 0 ≤ θ_{2} ≤ π/2, 0 ≤ θ_{+} < 4π

2/m (c unique) monoclinic (c-u)  0 ≤ θ_{1} < 2π, 0 ≤ θ_{2} ≤ π, 0 ≤ θ_{3} < π

0 ≤ θ_{−} ≤ π, 0 ≤ θ_{2} ≤ π, 0 ≤ θ_{+} < 4π

mmm orthorhombic 0 ≤ θ_{1} < 2π, 0 ≤ θ_{2} ≤ π/2, 0 ≤ θ_{3} < π

0 ≤ θ_{−} ≤ π, 0 ≤ θ_{2} ≤ π/2, 0 ≤ θ_{+} < 4π

4/m tetragonal 0 ≤ θ_{1} < 2π, 0 ≤ θ_{2} ≤ π, 0 ≤ θ_{3} < π/2

0 ≤ θ_{−} ≤ π/2, 0 ≤ θ_{2} ≤ π, 0 ≤ θ_{+} < 4π

4/mmm tetragonal 0 ≤ θ_{1} < 2π, 0 ≤ θ_{2} ≤ π/2, 0 ≤ θ_{3} < π/2

0 ≤ θ_{−} ≤ π/2, 0 ≤ θ_{2} ≤ π/2, 0 ≤ θ_{+} < 4π

-3 trigonal 0 ≤ θ_{1} < 2π, 0 ≤ θ_{2} ≤ π, 0 ≤ θ_{3} < 2π/3

0 ≤ θ_{−} ≤ 2π/3, 0 ≤ θ_{2} ≤ π, 0 ≤ θ_{+} < 4π

-3m trigonal 0 ≤ θ_{1} < 2π, 0 ≤ θ_{2} ≤ π/2, 0 ≤ θ_{3} < 2π/3

0 ≤ θ_{−} ≤ 2π/3, 0 ≤ θ_{2} ≤ π/2, 0 ≤ θ_{+} < 4π

6/m hexagonal 0 ≤ θ_{1} < 2π, 0 ≤ θ_{2} ≤ π, 0 ≤ θ_{3} < π/3

0 ≤ θ_{−} ≤ π/3, 0 ≤ θ_{2} ≤ π, 0 ≤ θ_{+} < 4π

6/mmm hexagonal 0 ≤ θ_{1} < 2π, 0 ≤ θ_{2} ≤ π/2, 0 ≤ θ_{3} < π/3

0 ≤ θ_{−} ≤ π/3, 0 ≤ θ_{2} ≤ π/2, 0 ≤ θ_{+} < 4π

Table 1: Asymmetric Units of Cross-Rotation Functions.