  Very recently, we have introduced correlation consistent effective core
potentials (ccECPs) derived from many-body approaches with the main target
being its use in explicitly correlated methods but also in mainstream
approaches. The ccECPs are based on reproducing excitation energies for a
subset of valence states, i.e., achieving a near-isospectrality between the
original and pseudo Hamiltonians. In addition, binding curves of dimer
molecules have been used for refinement and overall improvement of
transferability over a range of bond lengths. Here we apply similar ideas to
the second row elements and study several aspects of the constructions in order
to find the optimal (or nearly-optimal) solutions within the chosen ECP forms
with $3s,3p$ valence space (Ne-core). New constructions exhibit accurate
low-lying atomic excitations and equilibrium molecular bonds (on average within
$\approx$ $0.03$ eV and $3$ m\AA), however, the errors for Al and Si oxide
molecules at short bond lengths are notably larger for both ours and existing
ECPs. Assuming this limitation, our ccECPs show a systematic balance between
the criteria of atomic spectra accuracy and transferability for molecular
bonds. In order to provide another option with much higher uniform accuracy, we
also construct He-core ECPs for the whole row with typical discrepancies of
$\approx$ 0.01 eV or smaller.
