  We investigate the ultracold collisions of rotationally excited dipolar
molecules in free-space, taking the hetero-nuclear bi-alkali molecule of KRb as
an example. We show that we can sharply tune the elastic, inelastic and
reactive rate coefficients of lossy molecular collisions when a second
rotationally excited colliding channel crosses the threshold of the initial
colliding channel, with the help of an applied electric field, as found by
Avdeenkov et al. for non-lossy molecules [Phys. Rev. A 73, 022707 (2006)]. We
can increase or decrease the loss processes whether the second channel is above
or below the initial channel. This is seen for both bosonic and fermionic
molecules. Additionally, we include the electric quadrupole and octopole moment
to the dipole moment in the expression of the long-range multipole-multipole
interaction. We found that for processes mediated by the incident channel like
elastic and loss collisions, the inclusion of quadrupole and octopole moments
are not important at ultralow energies. They are important for processes
mediated by state-to-state transitions like inelastic collisions.
