  Following Vasisht et al's identification of the second critical point
(Tc2,Pc2) for liquid silicon in the Stillinger-Weber (S-W) model for silicon,
we study the variation of Tc2,Pc2 with tetrahedral repulsion parameter in an
extension of the earlier "potential tuning" study of this system. We use the
simple isochoric cooling approach to identify the location of the second
critical point as a function of the "tuning" or "tetrahedrality", parameter
{\lambda}, and identify two phenomena of high interest content. The first is
that the second critical point pressure Pc2, becomes less negative as {\lambda}
decreases from the silicon value (meaning the drive to high tetrahedrality is
decreased) and reaches zero pressure at the same value of lambda as earlier
found to mark the onset of glassforming ability in an earlier study of this
tunable system. The second is that, as the Tc,2 approaches the temperature of
the liquid-gas spinodal, {\lambda}>22, the behavior of the temperature of
maximum density TMD switches from the behavior seen in most current water pair
potential models (locus of TMDs has a maximum), to the behavior seen in
empirical engineering multiparameter equations of state (EoS) (and also by two
parameter Speedy isothermal expansion EoS) for water, according to which the
locus of TMDs of HDL phase has no maximum, and the EoS for HDL has no second
critical point. At {\lambda}= 23 the behavior is isomorphic with that of the mW
model of water, which is now seen to conform to the "critical point free"
scenario for water.
