The electronic structures with spin-orbit effects of the zirconium nitride ZrN molecule are investigated by the methods of multireference single and double configuration interaction. The potential energy curves are calculated along with the spectroscopic constants for the lowest-lying 34 spin-orbit states Ω in ZrN. A good agreement is displayed by comparing the calculated spectroscopic constants with those available experimentally. The permanent dipole moments are calculated along with the vibrational energies. New results are obtained in this work for 29 spin-orbit states and their spectroscopic constants calculated.
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