We predict that ultralong-range Rydberg bi-molecules form in collisions between polar molecules in cold and ultracold settings. The collision of $Lambda$-doublet nitric oxide (NO) with long-lived Rydberg NO($nf$, $ng$) molecules forms ultralong-range Rydberg bi-molecules with GHz energies and kilo-Debye permanent electric dipole moments. The Hamiltonian includes both the anisotropic charge-molecular dipole interaction and the electron-NO scattering. The rotational constant for the Rydberg bi-molecules is in the MHz range, allowing for microwave spectroscopy of rotational transitions in Rydberg bi-molecules. Considerable orientation of NO dipole can be achieved. The Rydberg molecules described here hold promise for studies of a special class of long-range bi-molecular interactions.
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