  Relativistic many-body methods at different levels of approximations are
employed to gain insights into the passage of the electron correlations from
lower to higher levels in the accurate determination of the electric dipole
polarizability ($\alpha_d$) and electric dipole moment (EDM) due to the
electron-nucleus tensor-pseudotensor (T-PT) and nuclear Schiff moment (NSM)
interactions of the $^{199}$Hg ground state. Moreover, plausible reasons for
the differences in the previous calculations are pointed out. Comparison
between the calculated and experimental results of $\alpha_d$ indicates that
our EDM calculations are about 3\% accurate which in combination with the
measured value of $^{199}$Hg EDM yield limits for the T-PT coupling constant
$C_T < 2.31 \times 10^{-9}$ and the NSM $S<1.55 \times 10^{-12}|e|fm^3$. From
this limit of $S$ and the latest nuclear structure calculation, we get improved
limits for the strong CP violating parameter $\theta_{QCD} < 2.12 \times
10^{-10}$ and the combined up and down quark chromo-EDMs $(-0.004 \tilde{d}_u +
0.020 \tilde{d}_d) < 1.15 \times 10^{-27} |e| cm$.
