Nonadiabatic corrections to electric quadrupole transition rates in H$_2$

We derive formulas and perform calculations of nonadiabatic corrections to rates of electric quadrupole transitions in the hydrogen molecule. These corrections can be represented in terms of the quadrupole moment curve $D^{(1)}(R)$, similarly to the Born-Oppenheimer one, $D^{(0)}(R)$, derived originally by Wolniewicz. Numerical results change E2 transition rates for the fundamental band by as much as 0.4 - 12\% depending on rotational quantum numbers.