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Among other alkali diatomics the KRb molecule demonstrates a high density of the low-lying electronic states arisen from close energy of the K and Rb atoms in their first excited 2 P states. The adiabatic states are mutually per- turbed due to the pronounced spin-orbit effect induced by heavy Rb atom and strong configuration interaction. A global deperturbation analysis is appar- ently required to represent the observed energies and radiative properties of the excited KRb states with the spectroscopic accuracy. Here we present R-depended spin-orbit matrix elements ab initio calculated between all electronic states converging to the lowest four dissociation lim- its. The relevant quasi-relativistic matrix elements accompanied by the adia- batic potential energy curves were evaluated for a wide range of internuclear distances and density grid in the basis of the spin-averaged wave functions corresponding to pure Hund’s coupling case (a). Both shape and energy con- sistent small (9-electrons) effective core pseudopotentials were used to monitor a sensitivity of the matrix elements to the particular basis set. The dynamic correlation has been taken accounted by a large scale multi-reference configura- tion interaction method which was applied for only two valence electrons. The l-independent core-polarization potentials of the both atoms were employed to take into account the residual core-valence effect. The achieved accuracy of the present ab initio functions is discussed by a com- parison with preceding calculations 1 and their empirical counterparts 2 corre- sponding to the observed spin-orbit splitting between different Ω-components of the triplet (1) 3 Σ + and (1-3) 3 Π states. All electronic structure calculations were performed with the Molpro package 3 . The present work was supported by the RFBR under Grant No. 13-03-00466- a.