  We report ab initio correlated relativistic calculations of the effective
electric field W_d acting on the electron in two excited electronic states of
PbO, required for extracting the electric dipole moment of the electron from an
ongoing experiment at Yale, which has the potential of improving accuracy for
this elusive property by several orders of magnitude. The generalized
relativistic effective core potential and relativistic coupled cluster methods
are used, followed by nonvariational one-center restoration of the
four-component wavefunction in the heavy atom core. W_d is -3.2\times 10^24
Hz/ecm for the a(1) state and -9.7\times 10^24 Hz/ecm for the B(1) state.
Comparison of calculated and experimental values of the hyperfine constant
A_{\parallel} provides an accuracy check for the calculation.
