Relativistic effects in Sr, Dy, YbII and YbIII and search for variation of the fine structure constant

A possibility for fundamental constants to vary in time is suggested by theories unifying gravity with other interactions. In this article we examine proposals to use optical transitions of Sr, Dy, YbII and YbIII for the search of the time variation of the fine structure constant $\alpha$. Frequencies of atomic transitions are calculated using relativistic Hartree-Fock method and configuration interaction technique. The effect of variation of $\alpha$ on the frequencies is studied by varying $\alpha$ in computer codes. Accuracy of measurements needed to improve current best limit on the time variation of $\alpha$ is discussed.