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Within the field of modern molecular physics laser synthesis and cooling has seen a surge of attention. Due to their attractive properties, heteronuclear alkali metal dimers have been singled out as especially advantageous diatomics. In particular, the LiRb molecule has a large permanent dipole moment in both ground and excited electronic states which not only allows for easy manipulation by external electric field but also makes it possible to use as a base material for quantum computers. Recently, few laser schemes for the assembly and cooling of the LiRb molecule have been proposed, found and probed. However, a systematical searching of the most efficient optical pathways for conversion of ultracold Li and Rb atoms into the stable ground molecular state, indispensably requires highly accurate term values, and radiative and electric properties of the ”intermediate” excited states, especially possessing strong ”mixed” singlet-triplet character. We accomplished a comprehensive deperturbation analysis of the spin-orbit coupled A1S+ ~ b3P and D1P ~ d3P complexes of the LiRb molecule exploiting the recent spectroscopic observations[1-3] and our own electronic structure estimates. The large scale ab initio calculations were performed within the framework of a pure Hund’s coupling case ”a” for both singlet and triplet state manifolds converging to the lowest three dissociation limits. The adiabatic potential energy curves (PECs), spin-orbit (SO) and angular coupling matrix elements as well as the permanent and transition dipole moments were calculated in a wide range of inter-atomic distances. Most obtained electronic matrix elements demonstrate a pronounced dependence on inter-atomic distance due to strong configuration interaction occurring in the chemical bond domain. The predicted SO splitting in the triplet b3P and d3P states are found to be in good agreement with their experimental counterparts [2]. The rigorous coupledchannel (CC) deperturbation model was used to describe the spin-orbit and spin-rotational interactions in mutually perturbed states of the A1S+ ~ b3P and D1P ~ d3P complexes of LiRb on the spectroscopic level (~ 0:01 cm^-1) of accuracy. The adjusted fitting parameters of the developed CC model (such as PECs and SO matrix elements) were then applied for the simulation of the stimulated Raman a3S+ ! [A1S+ b3P]=[D1P ~ d3P] ! X1S+ processes which can lead to efficient formation of ultracold LiRb molecules in their absolute ground state vX = 0; JX = 0. The work was supported by the RFBR grant Nr. 16-03-00529a. References [1] A. Altaf, S. Dutta, J. Lorenz, J. Perez-Rios, Y.P. Chen, D. S. Elliott, J. Chem. Phys. 142, 114310, (2015). [2] I. Stevenson, D. Blasing, A. Altaf, Y. P. Chen, D. S. Elliott, J. Chem. Phys., 145, 224301, (2016). [3] I. Stevenson, D. B. Blasing, A. Altaf, Y. P. Chen, D. S. Elliott, Phys. Rev. A 94, 062503, (2016).