  The effective electric field experienced by the unpaired electron in the
ground state of PbF, which is a potential candidate in the search of electron
electric dipole moment due to some special characteristics, is calculated using
Z-vector method in the coupled cluster single- and double- excitation
approximation with four component Dirac spinor. This is an important quantity
to set the upper bound limit of the electron electric dipole moment. Further,
we have calculated molecular dipole moment and parallel magnetic hyperfine
structure constant (A$_\|$) of $^{207}$Pb in PbF to test the accuracy of the
wave function obtained in the Z-vector method. The outcome of our calculations
clearly suggests that the core electrons have significant contribution to the
"atom in compound (AIC)" properties.
