Enhancement of the electron electric dipole moment in Eu${}^{2+}$

Recently, the ferroelectric Eu${}_{0.5}$Ba${}_{0.5}$TiO${}_3$ was suggested for experimental searches of the electron electric dipole moment. To analyze results of the experiment and interpret them in terms of fundamental constants, the effective electric field $E_{\mathrm{eff}}$  acting on unpaired electrons of the europium cation should be calculated. In the present paper we consider Eu${}^{2+}$ cation in the uniform external electric field $E_{\mathrm{ext}}$ as the first step and important starting point toward the calculation of $E_{\mathrm{eff}}$ in the real solid. We have performed high-level electronic structure correlation calculations using the coupled clusters theory compared to other approaches. The calculated value of the field enhancement coefficient is $K=E_{\mathrm{eff}}/E_{\mathrm{ext}}=-4.6$.