Bending relaxation of H$_2$O by collision with para- and ortho-H$_2$

We extend our recent theoretical work on the bending relaxation of H$_2$O in collisions with H$_2$ by including the three water modes of vibration coupled with rotation, as well as the rotation of H$_2$. Our full quantum close-coupling method (excluding the H$_2$ vibration) is combined with a high-accuracy nine-dimensional potential energy surface. The collisions of para-H$_2$O and ortho-H$_2$O with the two spin modifications of H$_2$ are considered and compared for several initial states of H$_2$O. The convergence of the results as a function of the size of the rotational basis set of the two colliders is discussed. In particular, near-resonant energy transfer between H$_2$O and H$_2$ is found to control the vibrational relaxation process, with a dominant contribution of transitions with delta j2 = +2, +4. Finally, the calculated value of the H$_2$O bending relaxation rate coefficient at 295 K is found to be in excellent agreement with its experimental estimate.