Quantum chemistry coordinate system

Difference between the two is in rotation of the molecule. If you have body-centered coordinates it means that center of mass is in the 0 point of the system, but molecule can still rotate around it. It leads to confusion in calculations, because the molecule acquires spherical symmetry. To avoid that body-fixed coordinate system is used. This way the hole coordinate system rotates with the molecule, therfore the only type of movement that left is vibrations 

@amalgama Thank you! As far as I understand, the choice of a coordinate system helps us to separate various types of molecular movements - translational movement, rotations and vibrations

@_brauer_ Yes, this to system exclude translational movement and rotation. However vibrations are still present as long as we take temperature in consideration 

@amalgama I've got it, thank you) 

@_brauer_ to separate different types of movement it's also necessary to comply with Eckart's conditions

One thing I want to highlight is that rotation of the molecule as hole is withdrawn from the calculations, but intramuscular rotation still may be detected and counted. That's what microwave spectroscopy is for 

@amalgama is it about, for example, the rotation of substituents around the bond in organic molecules?

@marie-curie thanks for the addition)