  We predict a quantum phase transition in fcc Ca under hydrostatic pressure.
Using density functional theory, we find at pressures below 80 kbar, the
topology of the electron charge density is characterized by nearest neighbor
atoms connected through bifurcated bond paths and deep minima in the octahedral
holes. At pressures above 80 kbar, the atoms bond through non-nuclear maxima
that form in the octahedral holes. This topological change in the charge
density softens the C' elastic modulus of fcc Ca, while C$_{44}$ remains
unchanged. We propose an order parameter based on applying Morse theory to the
charge density, and we show that near the critical point it follows the
expected mean-field scaling law with reduced pressure.
