We formulate the FB-ENM in the following order. First, we define the FB-ENM for a single reference molecular structure in a general form. Next, we construct the FB-ENM for multiple structures by merging the FB-ENMs of each structure. The merge defined here aims to enable barrier-free transitions between multiple reference molecular structures. Finally, we specifically define the constraints for each atom pair to ensure that the bond lengths, bond angles, and planar structures preserved between the reference molecular structures are also preserved during the transitions between the reference structures.