Diagonal a3Σ1+-a3Σ1+ and off–diagonal X1Σ0++-a3Σ0-+ magnetic hyperfine structure (HFS) matrix elements were calculated ab initio for the LiRb and LiCs molecules in a wide range of internuclear distances using the multi–reference Fock space coupled clusters method with generalized relativistic effective core potentials to describe the four–component valence wavefunctions near the nuclei. At large distances, both HFS functions vary little, though they may fluctuate by as much as 12 to 24% in the intermediate range. The plateau exhibited by the a3Σ1+-a3Σ1+ HFS function at 4–5 Å, could be attributed to pronounced spin–orbit coupling of the intersecting a3Σ+ and b3Π states.
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