An energy derivative analysis method for closed-shell self-consistent field (SCF) wave functions has been applied to the newly (theoretically and/or experimentally) discovered cis monobridged compounds Al2H2, Si2H2, Ga2H2, and Ge2H2. Monobridged stationary points for the B2H2 and C2H2 molecules were also considered for comparative purposes. At the stationary points. the first and second derivatives of the orbital, electronic, nuclear, and total energies for SCF wave functions were transformed from the Cartesian to the normal coordinate and to the mass-weighted normal coordinate systems. The energy derivative quantities in terms of the molecular vibrations provide crucial information concerning the structural stability of the monobridged dihydrides of group IIIA and group IVA atoms.