  Motivated by the ideas of using cold alkaline earth atoms trapped in an
optical lattice for realization of optical atomic clocks, we investigate
theoretically the perturbative effects of atom-atom interactions on a clock
transition frequency. These interactions are mediated by the dipole fields
associated with the optically excited atoms. We predict resonance-like features
in the frequency shifts when constructive interference among atomic dipoles
occur. We theoretically demonstrate that by fine-tuning the coherent
dipole-dipole couplings in appropriately designed lattice geometries, the
undesirable frequency shifts can be greatly suppressed.
