In search of the electron electric dipole moment: relativistic correlation calculations of the P,T-violation effect in the ground state of HI$^+$

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