We present a rigorous method for accurate ab initio calculations of the electron electric-dipole-moment $\mathcal{P},\mathcal{T}$-odd interaction constant $W_d$. The approach uses configuration interaction wave functions and Dirac four-component spinors as one-particle basis functions, and the interaction constant $W_d$ is obtained as an expectation value over these correlated wave functions. We apply the method to the HfF${}^{+}$ molecular ion and determine spectroscopic constants for four low-lying electronic states. For one of these states ($\Omega =1$) we determine the effective electric field ($E_{\mathrm{eff}}=W_d\Omega$), which amounts to 23.3 GV/cm, correlating 34 valence and outer atomic core electrons and using wave-function expansions with nearly $5\times {10}^8$ coefficients.

• Received 21 February 2013

DOI:https://doi.org/10.1103/PhysRevA.88.032514