In Search of the Electron Electric Dipole Moment: Relativistic Correlation Calculations of the $P,T$-Violating Effect in the Ground State of ${\mathrm{HI}}^{+}$

We report the first results of ab initio relativistic correlation calculation of the effective electric field on the electron, $E_{\mathrm{eff}}$, in the ground state of the ${\mathrm{HI}}^{+}$ cation. This value is required for interpretation of the suggested experiment on the search for the electron electric dipole moment. The generalized relativistic effective core potential, Fock-space relativistic coupled cluster with single and double cluster amplitudes (RCC-SD), and spin-orbit direct configuration interaction (SODCI) methods are used, followed by nonvariational one-center restoration of the four-component wave function in the iodine core. The RCC-SD value is $E_{\mathrm{eff}}=0.345\times {10}^{24}\mathrm{Hz}/e\mathrm{cm}$ and SODCI study gives $E_{\mathrm{eff}}=0.336\times {10}^{24}\mathrm{Hz}/e\mathrm{cm}$ (our final value). The structure of chemical bonding in ${\mathrm{HI}}^{+}$ is clarified, and a significant deviation of our value from that of Ravaine et al. [Phys. Rev. Lett. 94, 013001 (2005)] is explained.