  We investigate ground state properties of singly charged chlorine (Cl$^-$)
and gold (Au$^-$) negative ions by employing four-component relativistic
many-body methods. In our approach, we attach an electron to the respective
outer orbitals of chlorine (Cl) and gold (Au) atoms to determine the Dirac-Fock
(DF) wave functions of the ground state configurations of Cl$^-$ and Au$^-$,
respectively. As a result, all the single-particle orbitals see the correlation
effects due to the appended electron of the negative ion. After obtaining the
DF wave functions, lower-order many-body perturbation methods, random-phase
approximation, and coupled-cluster (CC) theory in the singles and doubles
approximation are applied to obtain the ground state wave functions of both
Cl$^-$ and Au$^-$ ions. Then, we adopt two different approaches to the CC
theory -- a perturbative approach due to the dipole operator to determine
electric dipole polarizability and an electron detachment approach in the
Fock-space framework to estimate ionization potential. Our calculations are
compared with the available experimental and other theoretical results.
