The H-R cleavage upon reaction MH + HR --> MH ... HR --> M(eta(2)-H-2)R, where MH represents 18-e transdihydrides Ru(H)(PH2CH2PH2)(2) (1), Ru(H)(H)(PH3)(4) (2), Ru(H)(H)(NH3)(4) (3); HR are HX (X = F, Cl) and HOR (R = H, CH3) is,studied using the DFT B3PW91/LANL2DZ level of theoretical calculations. The H-R bond splits upon interaction of the HR with 1 and 3 which possess a hydride H of high proton attracting power and significantly electropositive H of PH2 and NH3 groups. The basicity of the transition metal plays only a minor role in H-R splitting. The H-R cleavage proceeds via transfer of the H atom from R to hydride H in Ru-H ... H-R ... H-P(N), as an exothermic process without barrier or H ... H intermediate. The less acidic HOR yields a multi-H-bonded intermediate Ru-H ... H-O ...(H-P(N))(2), where the H-O bond cleaves with a low barrier. Such an energetically facile mechanism of H-R splitting was not found for 2, where H of PH3 is too inert to interact with R and a multi-H-bonded complex is not formed. The computed relative energies and barriers are in agreement with available experimental data.