  Tetrahedral liquids such as water and silica-melt show unusual thermodynamic
behavior such as a density maximum and an increase in specific-heat when cooled
to low temperatures. There is a debate in the literature whether these
phenomena stem from a phase transition into a low-density and high-density
liquid phases, which occur in the supercooled regime. Here we consider a model
of tetrahedral liquids for which we construct a volume-constrained statistical
mechanical theory which quantifies the local structure of the liquid. We
compare the theory to molecular dynamics simulations and show that the theory
can rationalize the simulations semi-quantitatively. We show that the anomalous
density and specific heat behavior arise naturally from this theory without
exhibiting a liquid-liquid phase-transition. We explain that this theory may or
may not have a phase transition, depending on the volume and temperature
dependence of the energy and entropy which are sensitive to small changes in
the parameters of the model.
