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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 anextension of the earlier "potential tuning" study of this system. We use thesimple isochoric cooling approach to identify the location of the secondcritical point as a function of the "tuning" or "tetrahedrality", parameter{\lambda}, and identify two phenomena of high interest content. The first isthat the second critical point pressure Pc2, becomes less negative as {\lambda}decreases from the silicon value (meaning the drive to high tetrahedrality isdecreased) and reaches zero pressure at the same value of lambda as earlierfound to mark the onset of glassforming ability in an earlier study of thistunable system. The second is that, as the Tc,2 approaches the temperature ofthe liquid-gas spinodal, {\lambda}>22, the behavior of the temperature ofmaximum density TMD switches from the behavior seen in most current water pairpotential models (locus of TMDs has a maximum), to the behavior seen inempirical engineering multiparameter equations of state (EoS) (and also by twoparameter Speedy isothermal expansion EoS) for water, according to which thelocus of TMDs of HDL phase has no maximum, and the EoS for HDL has no secondcritical point. At {\lambda}= 23 the behavior is isomorphic with that of the mWmodel of water, which is now seen to conform to the "critical point free"scenario for water.

Potential tuning in the S-W system. (i) Bringing Tc,2 to ambient pressure, and (ii) colliding Tc,2 with the liquid-vapor spinodal