Combined 4-component and relativistic pseudopotential study of ThO for the electron electric dipole moment search

A precise theoretical study of the electronic structure of heavy atom diatomic molecules is of key importance to interpret the experiments in the search for violation of time-reversal (T) and spatial-parity (P) symmetries of fundamental interactions in terms of the electron electric dipole moment, eEDM, and dimensionless constant, k_T,P, characterizing the strength of the T,P-odd pseudoscalar-scalar electron-nucleus neutral current interaction. The ACME collaboration has recently improved limits on these quantities using a beam of ThO molecules in the electronic H³Δ₁ state [J. Baron et al., Science 343, 269 (2014)]. We apply the combined direct relativistic 4-component and two-step relativistic pseudopotential/restoration approaches to a benchmark calculation of the effective electric field, E_eff, parameter of the T,P-odd pseudoscalar-scalar interaction, W_T,P, and hyperfine structure constant in ^Δ3₁ state of the ThO molecule. The first two parameters are required to interpret the experimental data in terms of the eEDM and k_T,P constant. We have investigated the electron correlation for all of the 98 electrons of ThO simultaneously up to the level of the coupled cluster with single, double, and noniterative triple amplitudes, CCSD(T), theory. Contributions from iterative triple and noniterative quadruple cluster amplitudes for the valence electrons have been also treated. The obtained values are E_eff = 79.9 GV/cm, W_T,P = 113.1 kHz. The theoretical uncertainty of these values is estimated to be about two times smaller than that of our previous study [L. V. Skripnikov and A. V. Titov, J. Chem. Phys., 142, 024301 (2015)]. It was found that the correlation of the inner- and outer-core electrons contributes 9% to the effective electric field. The values of the molecule frame dipole moment of the ^Δ3₁ state and the H³Δ₁ →X¹Σ⁺ transition energy of ThO calculated within the same methods are in a very good agreement with the experiment.