A thermodynamic state in which the internal energy is equal to zero is a contractual thing. When choosing this state, we are guided by the convenience of calculations. For example for perfect gases we assume that the internal energy is equal to zero at temperature 0K. In engineering calculations we are dealing with changes of energy rather than its absolute values. In such cases, the total internal energy value (measured from its true zero) is not significant.

A confined particle must have a kinetic energy greater than zero owing to the uncertainty principle. If confined within a region of size L, the root-mean-square uncertainty delta p in its momentum must be at least h/(4 pi L). Its root-mean-square average momentum p must be at least as great as this uncertainty, corresponding to a minimum kinetic energy, even at absolute zero on the order of (delta p)^2/2m = h^2/[16(pi^2)mL^2], where m is the mass of the particle. This is the zero-point kinetic energy. For an unconfined particle, say an isolated gas atom or molecule in intergalactic space, L is essentially infinity and the zero-point kinetic energy is zero. In any case, the total energy of a particle of mass m is E = mc^2, so this sets an absolute scale for energy, not merely for changes in energy. [m includes the mass equivalent of any kinetic energy, be it zero-point kinetic energy or otherwise, namely (kinetic energy)/c^2, as well as the mass equivalent of potential energies (self-gravitational potential energy makes a negative contribution).]

 Thank you with your answers. Refer please also question: "At zero point, if internal energy nonzero, will it mean nonzero inertia?"

Since zero-point energy E equals zero-point mass m = E/c^2, if E is nonzero then it does contribute to inertia, as any mass does.

Thanks for all, 

I'am agree with the answer of Leszek Malinowski  and Jack Denur. In engineering calculations, we don't need to know at O K the internal energy is 0 or not. Besides, in general case, we are interested to calculate energy variation and not absolute anergy in such point. 

Best wishes!

kind regards!

The two are related but probably not identical. Internal energy is a better term than free energy for the ZPE. Vacuum may have internal energy that is in excess of ZPE. In this regard ZPE is only one case in a larger system.

With CMB everywhere there is no way to achieve zero temperature. So ZPE is theoretical and ideal.