(color online) The Euler angles (ϕ, θ, χ) define a relative orientation of the molecule-fixed coordinates (x, y, z) with respect to the space-fixed coordinates (X, Y, Z) for BaF depicted as a bar bell. The dotted blue line is the axis of nodes, which is the intersection of the XY and xy planes. The rotation–vibration motions of BaF in polar coordinates (r, ϕ, θ) is discussed. Also shown is an angular momenta coupling diagram for Hund’s case (b_βJ) in the state .