Theoretical study of thorium monoxide for the electron electric dipole moment search: electronic properties of H(3)Δ(1) in ThO.

Recently, improved limits on the electron electric dipole moment, and dimensionless constant, kT,P, characterizing the strength of the T,P-odd pseudoscalar-scalar electron-nucleus neutral current interaction in the H(3)Δ1 state of ThO molecule were obtained by the ACME collaboration [J. Baron et al., Science 343, 269 (2014)]. The interpretation of the experiment in terms of these fundamental quantities is based on the results of theoretical study of appropriate ThO characteristics, the effective electric field acting on electron, Eeff, and a parameter of the T,P-odd pseudoscalar-scalar interaction, WT,P, given in Skripnikov et al. [J. Chem. Phys. 139, 221103 (2013)] by St. Petersburg group. To reduce the uncertainties of the given limits, we report improved calculations of the molecular state-specific quantities Eeff, 81.5 GV/cm, and WT,P, 112 kHz, with the uncertainty within 7% of the magnitudes. Thus, the values recommended to use for the upper limits of the quantities are 75.8 GV/cm and 104 kHz, correspondingly. The hyperfine structure constant, molecule-frame dipole moment of the H(3)Δ1 state, and the H(3)Δ1 → X(1)Σ(+) transition energy which, in general, can serve as a measure of reliability of the obtained Eeff and WT,P values are also calculated. In addition, we report the first calculation of g-factor for the H(3)Δ1 state of ThO. The results are compared to the earlier experimental and theoretical studies, and a detailed analysis of uncertainties of the calculations is given.