An extensive diabatic investigation of the NaRb species has been carried out for all excited states up to the ionic limit Na -Rb 1 . An ab initio calculation founded on the pseudopotential, core polarization potential operators and full configuration interaction has been used with an efficient diabatization method involving a combination of variational effective hamiltonian theory and an effective overlap matrix. Diabatic potential energy curves and electric dipole moments (permanent and transition) for all the symmetries R 1 , P, and D have been studied for the first time. Thanks to a unitary rotation matrix, the examination of the diabatic permanent dipole moment (PDM) has shown the ionic feature clearly seen in the diabatic 1 R 1 potential curves and confirming the high imprint of the Na -Rb 1 ionic state in the adiabatic representation. Diabatic transition dipole moments have also been computed. Real crossings have been shown for the diabatic PDM, locating the avoided crossings between the corresponding adiabatic energy curves.charge transfer, diabatic curves, effective Hamiltonian theory, electric dipole moments 1 | I N TR ODU C TI ON Cold and ultracold molecules have been the object of quest and considerable interest bringing new opportunities and a wide diversity of applications. Indeed, a key role is played by these molecules when they interact with microwave fields in various fields: microwave trap [1,2] ; adjusting molecule-molecule interaction so as to have new quantum phases [3][4][5] ; probing the dynamics of quantum phase transitions [6,7] ; as well as the use of ultracold molecules in quantum computing. [6,8,9] Furthermore, for materials with nonclassical mechanical comportment, the survey of elasticity [10] is stretched out through the modelisation of rheological phenomena by a new system, which can be delivered from the association of ultracold molecules into chains. Studies of polar molecular systems are of special interest because they give rise to suggested experiences for measuring the lifetime of long-lived energy levels, the Electron permanent electric Dipole Moment (EDM) as well as the impact of dipole-dipole interactions on the specifications of the molecular species'. [11] Besides, affordable novel qualitative regimes formerly unaccessible by ultracold homonuclear (nonpolar) samples [12][13][14] have been yielded thanks to ultracold polar systems interacting with each other through greatly electric anisotropic dipole-dipole forces. Considerable interest has been directed toward the formation of ultracold and cold molecules. Thus, extensive endeavor has been devoted to exploit the alkali-metal dimers characteristics to produce these cold specimen, maybe by consistent process [15][16][17] and photoassociation spectroscopy. [18,19] Many of these procedures imply optical excitement, either in their production or in the steps of detection, so the possession of a proper specification of many excited states of the alkali-metal dimer is necessary. Otherwise, in view of the importance of the NaRb...