The relationship between the volumetric thermodynamic coefficients of liquid metals at the melting point and interatomic bond energy was studied. Using dimensional analysis, we obtained equations that connect cohesive energy with thermodynamic coefficients. The relationships were confirmed by experimental data for alkali, alkaline earth, rare earth, and transition metals. Cohesive energy is proportional to the square root of the ratio of melting point Tm divided by thermal expansivity αp. Thermal expansivity does not depend on the atomic size and atomic vibration amplitude. Bulk compressibility βT and internal pressure pi are related to the atomic vibration amplitude by an exponential dependence. Thermal pressure pth decreases with an increasing atomic size. Fcc and hcp metals with high packing density, as well as alkali metals, have the relationships with the highest coefficient of determination. The contribution of electrons and atomic vibrations to the Grüneisen parameter can be calculated for liquid metals at their melting point.