First principle calculations for efficient transition metal contacts with monolayer MoS2-WSe2 are carried out for complementary device application. The four parameters analysed are exchange energy, density of states, entropy measurements, and effective potential periodicity at interface. Each characterises the electrical contact, as exchange energy establishes stable interface with minimum energy (contacts with strong bonding); density of states determines the charge polarity selection (electron or hole transport) and carrier flow rate through interfaces; entropy measurement reveal contacts with minimum phonon scattering rate (enhanced mobility); and effective potential continuity provides an alternative view of contact resistance from quantum mechanical perspective. Combining these results reveal that in specific crystallographic orientation among the 3d group: V, Cr, Co, and Ni; from 4d group: Tc, Ru, Pd, Ag and from 5d group: Ir, Pt, Au form suitable elemental electrodes for MoS2-WSe2 complementary FET applications. © 1980-2012 IEEE.