CM frame kinetic energy for a molecule

[kelly0303]

Hello! When the kinetic energy of a molecule is written in its CM frame we get the formula attached. The first term is the kinetic energy of the CM frame with respect to the lab frame, the second term is the kinetic energy associated with the distance between the nuclei and the last term is the kinetic energy of the electrons with respect to the CM. Can someone help me understand what the 3rd term is? It seems like all the possible motions are taken into account so I am not sure what that is (it comes out naturally from the mathematical derivation, but I am not sure what it is physically). Thank you!

 

[DrClaude]

Are you sure about the significance of the last term? What to the indices $i$ and $j$ sum over?

The 3rd term contains all the rotational terms. Further development of this term will lead to the rotational energy (rotational of the molecular frame wrt the lab frame) and a Coriolis term.

 

[kelly0303]

Are you sure about the significance of the last term? What to the indices $i$ and $j$ sum over?

The 3rd term contains all the rotational terms. Further development of this term will lead to the rotational energy (rotational of the molecular frame wrt the lab frame) and a Coriolis term.

The last term is the kinetic energy of the electrons with respect to the molecule center of mass and the i and j indices are over the electrons. Actually the rotation of the molecule comes from the second term where R is the internuclear distance.