The authors' recently suggested approach (1984) for calculating the Helmholtz free energy, including the usual high-order pseudopotential perturbation corrections for the nearly-free-electron-like liquid metals, is critically examined and is now improved so as to be applicable in principle to any sp-type disordered metal in its liquid phase. It appears that the mean atomic volume, the packing density parameter and the related thermal quantities can now be predicted from first principles with reasonable accuracy by the presently described variational thermodynamic calculation for nearly all the sp-type liquid metals.