Say, I have two crystal structures of a particular organic molecule, the crystal structures are basically identical, apart from a rotation and redefinition of the lattice vectors/angles, a simple result of different choices during the structure refinement process after the xray or neutron experiment for structure determination. As a practical example consider triclinic (P-1) malonic acid for which two structures have been published:
one (MALNAC02) with: a,b,c, alpha,beta,gamma=5.156,5.341,8.407,71.48,76.12,85.09
the other (MALNAC) with a,b,c, alpha,beta,gamma=5.33,5.14,11.25,102.7,135.17,85.17
If I wanted to convert one structure to the other so that they perfectly overlap (apart from a trivial translation step), by rotating it successively through one or more of the cartesian (x,y,z) axis through appropriate angles, how would I find these angles?
I understand there are different ways to do this, other than the successive rotation around the cartesian axes (use a rotation matrix or Eulerian angles) but here I need to know these angles (around the cartesian axes), also I know there is not only one unique version of these angles - but I am fine with having just one of them.