In this paper, we investigate the possibility of using internal molecular vibrational and rotational modes of an open-shell molecule for one of the most important quantum algorithms: the Deutsch-Jozsa algorithm. The molecular system of interest is one of the representative open-shell molecules: 14 N 16 O. The gate pulses are constructed by utilizing multi-target optimal control theory (MTOCT). The gate fidelities of each quantum gate are more than 95.23%. Upon implementing the Deutsch-Jozsa algorithm combining these elementary gates, we obtained fidelity of at least 94.76%. This indicates that vibrational and rotational qubits of the open-shell 14 N 16 O molecule are about as promising for processing quantum algorithms as those of the closed-shell molecule 12 C 16 O that we studied earlier.