Enhanced sensitivity to variation of the fine structure constant and m_p/m_e in diatomic molecules

Sensitivity to temporal variation of the fundamental constants may be strongly enhanced in transitions between narrow close levels of different nature. This enhancement may be realized in a large number of molecules due to cancelation between the ground state fine structure omega_f and vibrational interval omega_v (omega=omega_f - n omega_v is close to zero, delta omega/omega= K (2 delta alpha/alpha +0.5 delta mu/mu), K >>1, mu=m_p/m_e). The intervals between the levels are conveniently located in microwave frequency range and the level widths are very small. Required accuracy of the shift measurements is about 0.01-1 Hz. As examples, we consider molecules Cl_2+, CuS, IrC, SiBr and HfF+.