Polyatomic vibration-rotation interaction ($B_{\mathbf{v}}=B_e-{\sum }_i{\alpha }_i(v_i+d_i/2)$)

The first-order dependence of a polyatomic rotational constant on vibrational occupations $v_i$, where $d_i$ is the degeneracy of normal mode $i$. The factor $d_i/2$ accounts for all of that mode's zero-point energy. A single band's change in rotational constant generally determines one ${\alpha }_i$, rather than every zero-point correction needed for $B_e$.