Ab-initio calculation method is employed to determine the potential functions and the unknown parameters in pair-potential-based mean filed model for metals. Using the mean fields constructed from the potential functions, the vibration free volumes of atoms of metals Al, Cu, Ni, Na, and K at melting points are evaluated. The results indicate that the widely used hypothesis that the ratio of vibration free volume to the primitive cell volume of atoms in melting curve is a constant, is not correct. We provide a ratio model which can be usd to obtain much more accurate results of melting curve.