I wish to calculate the values of the orbital angular momentum of excited electronic states, using Molpro. So $\langle L_x \rangle$, $\langle L_y \rangle$, and $\langle L_z \rangle$. (Specifically for my case, I'm looking for the projection on the z-axis in a diatomic molecule. But I guess the answer should apply generally for all projections.) This should ideally be done at the
MRCI level. But feel free to share procedures if they exist in other programs too.
I can find one mention of these operators in the documentation, called
LOP taken together, or
LZ, individually. However they are listed with parity
-1, and: "Expectation values are only nonzero for symmetric operators (
parity=1)". Still, the electronic state must have some angular momentum. For instance, in
CASSCF I can calculate the $\langle L_x^2 \rangle$, $\langle L_y^2 \rangle$, and $\langle L_z^2 \rangle$ with the card
EXPEC2,LXX,LYY,LZZ. But then the sign of the projected angular momentum is lost, and I wish to compare signs for the different excited states.