code: def zero_point_energy(self, structure=None):
          
  
          freqs = self._positive_frequencies
          dens = self._positive_densities
  
          zpe = 0.5 * np.trapz(freqs * dens, x=freqs)
          zpe *= THZ_TO_J * const.Avogadro
  
          if structure:
              formula_units = structure.composition.num_atoms / structure.composition.reduced_composition.num_atoms
              zpe /= formula_units
  
          return zpe
docs: Zero point energy energy of the system. Only positive frequencies will be used.
          Result in J/mol-c. A mol-c is the abbreviation of a mole-cell, that is, the number
          of Avogadro times the atoms in a unit cell. To compare with experimental data the result
          should be divided by the number of unit formulas in the cell. If the structure is provided
          the division is performed internally and the result is in J/mol
  
          Args:
              t: a temperature in K
              structure: the structure of the system. If not None it will be used to determine the numer of
                  formula units
          Returns:
              Phonon contribution to the internal energy