Quaternion transformation of molecular orientation

For comparing two molecules, since the most general positional relationship is the combination of a translation and a rotation, where the translational component can be removed by referring both molecules to their centres of gravity, a rotation taking one to the other must be found. Rather than using a 3 × 3 rotation matrix, it is better to represent the rotation by a unit quaternion, since the equations to be solved to find, by least squares, the best quaternion, are linear.