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Nowadays the rigorous coupled-channel (CC) deperturbation analysis is the well-established procedure for accurate representation of strongly interacting electronic states. The practical implementation of the CC approach is based on the explicit knowledge of the potential energy curves, non-adiabatic electronic matrix elements and transition dipole moments as function of internuclear distance. The high level ab initio electronic structure calculation is apparently the most straightforward way of generating all required matrix elements. The close energies of the K and Rb atoms in their first excited 2P states indispensably lead to the high density of the strongly coupled molecular states. Moreover, for KRb molecule the spin-orbit (SO) coupling effect becomes comparable with the vibrational spacing even for small and intermediate interatomic distances where smooth transformation between pure (a) to (c) Hund's coupling cases take places. We present the spin-orbit, angular and radial coupling matrix elements among all strongly coupled electronic states converging to the lowest three dissociation limits of KRb molecules. The non-adiabatic matrix elements have been obtained in a wide range internuclear distances by using of both shape and energy consistent small (9-electrons) effective core pseudopotentials (ECP). The dynamic correlation has been accounted for a large scale multi-reference configuration interaction method which was applied for only two valence electrons keeping the rest frozen, i.e. in a full valence (2-electrons) CI scheme. The angular independent core-polarization potentials (CPP) were employed together with the above small core ECPs to take into account for implicitly the residual core-valence effect. The relevant adiabatic potential energy curves and electric dipole transition moments were evaluated as well. All electronic structure calculations were performed in the framework of a quasi-relativistic (a) Hund's case coupling scheme by means of the MOLPRO program package [1]. The possible application of the ab initio functions for modelling of the energy and radiative properties of the spin-orbit A~b complex of KRb is discussed [2,3]. The reliability of the results is fragmentally probed by a comparison with preceding calculations. This work was supported by the Russian Foundation for Basic Researches (grant N13-03-00466-a). [1] MOLPRO, Version 2010.1, a package of ab initio programs, H.-J. Werner, P. J. Knowles et al. [2] J.-T. Kim et al., New J. Phys. 2009, 11, 055020. [3] E. A. Pazyuk et al., ECAMP11 2013.