  A way to account for correlations between the chemically active (valence) and
innermore (core) electrons in the framework of the generalized relativistic
effective core potential (GRECP) method is suggested. The "correlated" GRECP's
(CGRECP's) are generated for the Hg and Pb atoms. Only correlations for the
external twelve and four electrons of them, correspondingly, should be treated
explicitly in the subsequent calculations with these CGRECP's whereas the
innermore electrons are excluded from the calculations. Results of atomic
calculations with the correlated and earlier GRECP versions are compared with
the corresponding all-electron Dirac-Coulomb values. Calculations with the
above GRECP's and CGRECP's are also carried out for the lowest-lying states of
the HgH molecule and its cation and for the ground state of the PbO molecule as
compared to earlier calculations and experimental data. The accuracy for the
vibrational frequencies is increased up to an order of magnitude and the errors
for the bond lengths (rotational constants) are decreased in about two times
when the correlated GRECP's are applied instead of earlier GRECP versions
employing the same innercore-outercore-valence partitioning.
