An improved generator coordinate Hartree-Fock (IGCHF) method is used to gen
erate Gaussian basis sets for the atoms from K (Z = 19) through Xe (Z = 54)
. The Griffin-Hill-Wheeler-HF equations are integrated using the integral d
iscretization technique. The ground state HF total energies obtained by us
are compared with those calculated with the original GCHF method and with o
ther approaches reported in the literature. The largest difference between
our energy values and the corresponding ones computed with a numerical HF m
ethod is equal to 6.003 mhartree for Kr (Z = 36).