I'm stumped as to how many optic branches (modes) are present if there are X number of molecules in a unit cell and Y number of atoms in each molecule. I know that each individual atom has 3 degrees of freedom and more generally in a single unit cell, there are 3 acoustic branches (modes) and 3*atoms-3 number of optic branches (modes). There should be a total of 3*atoms branches (modes) due to the degrees of freedom. I'm struggling to understand how to generalize this further to include molecules into the picture. Logically speaking, 3*molecules for all the degrees of freedom in a molecule, and 3*atoms for all the degrees of freedom of an atom. Maybe each molecule can be thought of as an individual unit cell inside a larger unit cell. Would there be a total number of 3*X*Y-3*X optical branches (modes)?