Potential tuning in the S-W system. (i) Bringing Tc,2 to ambient   pressure, and (ii) colliding Tc,2 with the liquid-vapor spinodal
  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. 
C. Austen Angell and Vitaliy Kapko
cond-mat.dis-nn