A nonzero value of permanent electric dipole moment of electron (eEDM) implies manifestation of interactions which are not symmetric with respect to both spatial and time inversions (P,T-odd interactions). The observation of the eEDM at a level significantly greater than 10-38 e*cm would indicate the presence of a New physics beyond the standard model; popular extensions of the standard model predict the magnitude of eEDM at the level of 10-26 10-30 e*cm . In 1970th it was shown that diatomic molecules containing heavy elements are very promising for such experiments. In the systems one can achieve a strong effective electric field (Eeff) acting on unpaired electrons that leads to the enhanced effect. However, the interpretation of the experiments in terms of eEDM requires knowledge of the magnitude of Eeff, which cannot be measured, and is the task of relativistic quantum chemistry.
We have developed a method, which allows to significantly simplify the relativistic treatment of heavy-atom compounds. It can be used for calculation of properties such as Eeff, hyperfine structure constants, etc. in atoms, molecules and crystals. This approach includes relativistic correlation calculation of valence electronic structure using generalized relativistic effective core potential approach followed by the non-variational restoration of four-component electronic structure in the vicinity of heavy atom nucleus.
We present here the status and application of the method to the most actual molecules to search for the New physics. Among the systems are ThO  molecule on which the best limit on eEDM is obtained by ACME collaboration: eEDM < 8.7x10 -29e*cm . The limit can be used to estimate restriction on the masses of intermediate supersymmetric particles, which can be involved to induce eEDM . The 229ThO molecule can be used to search for P,T-odd nuclear magnetic quadrupole moment of Th . For interpretation of such experiment, we have calculated corresponding parameters. Also we discuss other prospective systems such as ThF+ which is considered by E. Cornell group for the eEDM measurement.
This work is supported by the SPbU Fundamental Science Research grant from Federal Budget No. 0.38.652.2013 and the RFBR Grant No. 13-02-01406. L.S. is also grateful to the President of RF grant no MK-5877.2014.2 and Dmitry Zimin "Dynasty" Foundation.