  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 it 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.
ACME collaboration has recently obtained and improved limits on these
quantities using a beam of ThO molecules in the $H^3\Delta_1$ state [Science
343, 269 (2014)]. We apply the combined direct 4-component and two-step
relativistic pseudopotential/restoration approaches to a benchmark calculation
of the effective electric field, Eeff, parameter of the T,P-odd
pseudoscalar$-$scalar interaction, $W_{T,P}$, and HFS constant in $^3\Delta_1$
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 theory. Contributions from iterative triple and
noniterative quadruple cluster amplitudes for the valence electrons have been
also treated. The obtained values are Eeff=79.9 GV/cm, $W_{T,P}$=113.1 kHz. The
theoretical uncertainty of these values we estimate as about two times smaller
than that of our previous study [JCP, 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
$^3\Delta_1$ state and the $H^3\Delta_1\to X^1\Sigma^+$ transition energy of
ThO calculated within the same methods are in a very good agreement with the
experiment.
