ABSTRACT:The generalized relativistic effective core potential GRECP method is analyzed from theoretical and computational points of view. The Hamiltonian in the frozen-core approximation is compared with the Hamiltonian containing the GRECP operator. It is demonstrated that the GRECP operator can be derived from rather natural physical grounds and the procedure of the GRECP generation can be justified theoretically. The accuracy of the RECP approximations in the simulation of the interactions and densities in the valence and outer-core regions is analyzed. The reliability of the simulation of the interaction with the inner-core electrons removed from the calculations with the GRECP is also studied. The importance of additional nonlocal terms both with the potentials for the outer-core pseudospinors and with the potentials depending on the occupation numbers of the outermost core shells in the expression for the GRECP operator is demonstrated in calculations on the Ag, Ba, Hg, Tl, and U atoms. The difference between the outer core and valence potentials was investigated. It is shown that in the valence region the two-component pseudospinors coincide with the large components of four-component spinors in calculations for the same configuration states with a very high accuracy. Problems of Gaussian approximation caused by rather singular shapes of the potentials are considered. To attain a required high accuracy of approximation of the numerical potentials by Gaussians, serious additional efforts were undertaken.

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.

An experiment to search for the electron electric dipole moment (eEDM) on the metastable H 3 1 state of ThO molecule was proposed and now prepared by the ACME Collaboration [http://www.electronedm.org]. To interpret the experiment in terms of eEDM and dimensionless constant k T, P characterizing the strength of the T,P-odd pseudoscalar-scalar electron-nucleus neutral current interaction, an accurate theoretical study of an effective electric field on electron, E eff , and a parameter of the T,P-odd pseudoscalar-scalar interaction, W T ,P , in ThO is required. We report our results for E eff (84 GV/cm) and W T ,P (116 kHz) together with the hyperfine structure constant, molecule frame dipole moment, and H 3 1 → X 1 + transition energy, which can serve as a measure of reliability of the obtained E eff and W T ,P values. Besides, our results include a parity assignment and evaluation of the electric-field dependence for the magnetic g factors in the -doublets of H 3 1 .