αdependence of transition frequencies for ions Si II, Cr II, Fe II, Ni II, and Zn II

We perform an improved calculation of the $\alpha$ dependence $(\alpha {=e}^2/hc)$ of the transition frequencies for ions, which are used in a search for the variation of the fine-structure constant $\alpha$ in space-time. We use the Dirac-Hartree-Fock method as a zero approximation and then the many-body perturbation theory and configuration-interaction methods to improve the results. The important problem of level pseudocrossing (as a function of $\alpha )$ is considered. Near the crossing point the derivative of the frequency over $\alpha$ varies strongly (including a change of sign). This makes it very sensitive to the position of the crossing point. We propose a semiempirical solution of the problem, which allows us to obtain accurate results.