ac Stark effect in ThO $H^3{\mathrm{\Delta }}_1$ for the electron electric-dipole-moment search

A method and a code for calculations of diatomic molecules in the external variable electromagnetic field have been developed. The code is applied for calculation of systematics in the electron's electric-dipole-moment search experiment on ThO $H^3{\mathrm{\Delta }}_1$ state related to geometric phases, including dependence on the $\mathrm{\Omega }$ doublet, rotational level, and external static electric field. It is found that systematics decrease cubically with respect to the frequency of the rotating transverse component of the electric field. Calculation confirms that experiment on ThO $H^3{\mathrm{\Delta }}_1$ state is very robust against systematic errors related to geometric phases.