* TIMO FLEIG*, Laboratoire de Chimie et Physique Quantiques, Université Paul Sabatier Toulouse 3, Toulouse, France.

A new and rigorous method for accurate ab-initio calculations of the electron electric dipole moment \calP,T-odd interaction constant is presented. The approach uses string-based Configuration Interaction wavefunctions\footnote\beginminipage[t]15.0cm S.~Knecht, H.~J.~Å.~Jensen and T.~Fleig *J.~Chem.~Phys.* \underline\textbf132, 014108 (2010)

T.~Fleig, H.~J.~Å.~Jensen, J.~Olsen and L.~Visscher *J.~Chem.~Phys.* \underline\textbf124, 104106 (2006) \endminipage and Dirac four-component spinors as one-particle basis functions, and the \calP,T-odd constant is obtained as an expectation value over these correlated wavefunctions. The method has been applied to the HfF^{+} molecular ion to determine spectroscopic constants for four low-lying electronic states. For one of these states (
= 1) we have determined a new accurate benchmark value for the effective electric field E_{ eff} correlating 34 valence and outer atomic core electrons and using wavefunction expansions with nearly 5
10^{8} coefficients. For the
= 1 state of the ThO molecule the first ab-initio result for the electron EDM interaction constant is presented.

Aspects of modern all-electron relativistic many-body approaches applicable to both atoms and molecules will be discussed, including perspectives for the treatment of other interesting candidate systems and \calP- or \calP,T-non-conserving effects in molecular systems.