Although it may seem that the need to use generalized coordinates in the AFED method is a disadvantage, it has been shown in Appendices A and B that this is less of a disadvantage that one might expect. In Appendix A, it is shown that it is only necessary to transform the coordinates and not the momenta, which considerably simplifies the problem of working in generalized coordinates. In Appendix B, a simple scheme is developed to integrate the equations of motion in spherical polar coordinates when a distance (radial) coordinate is the reaction coordinate. The implementation of such transformations is often simpler than the implementation of a constraint procedure for a generalized coordinate as would be required by the bluemoon method [5, 6].
As another example, consider the case of a dihedral angle, an important reaction coordinate for studying backbone motion in long chain molecules and proteins. A simple transformation scheme can be developed obtaining a coordinate system in which a dihedral angle is an explicit coordinate. This transformation will involve the four atomic position vectors needed to define a dihedral angle. To this end, consider a united-atom model of butane, shown in Fig. 5 below:
or CH 
unit
is treated as a single pseudoatom. The position vector of each atom is indicated.
In this model, each CH or CH group is treated as a single pseudoatom
and is, thus, ideal for illustrating the transformation scheme. The transformation
consists, first, in transforming 
to a coordinate frams in which 
is at the origin. Following this, a rotation matrix which places the
vector along the z-axis and (r2-r1)
X (r2-r3) along the y-axis.
When this is done, the spherical
polar coordinates of the new position are introduced. The azimuthal
angle is, then, the required dihedral angle. Complete details on how
to construct the transformation and an illustrative example can
be found in Ref. [15]. Such a scheme is not, however, limited to
united-atom models, as has been shown in Ref. [16]
