In Phonopy the thermal properties, free energy, heat capacity, and entropy, are calculated from their statistical thermodynamic expressions using phonon frequencies on a sampling mesh in the reciprocal space. According to the Phonopy documentation,

The unit systems of free energy, heat capacity, and entropy are kJ/mol, J/K/mol, and J/K/mol, respectively, where 1 mol means $N_A \times$ your input unit cell (not formula unit), i.e. you have to divide the value by number of formula unit in your unit cell by yourself. For example, in MgO (conventional) unit cell, if you want to compare with experimental results in kJ/mol, you have to divide the phonopy output by four.

First, what does $N_A$ stand for? I am confused with their statement in the documenation, in the example of MgO (conventional) unit cell, does '4' stand for the formula unit?

Second, suppose that I have the thermal properties of the same material in Bulk and monolayer form, both having one unit cell but with different number of atoms or ions in their unit cells, then should I normalize the values and divide by the number of atoms in the unit cell in order to compare the results?


1 Answer 1


$N_A$ stands for Avogadro's number. Energies are reported in kJ/mol, so they are technically for a mole of unit cells. Conversion factors to other units (kcal/mol, eV, Hartree, etc.) can be found or derived easily.

Phonopy reports all its quantities for the supplied unit cell. MgO has 8 atoms in its unit cell, so if you want to report values per MgO formula unit, you'll have to divide everything by 4.

If you wish to compare systems with different unit cells, you have to take care that you compare quantities that are equivalent. For example, normalized per atom (for single-element compounds), formula unit (multi-element compounds), or molecule (molecular crystals).

  • $\begingroup$ +1, I got that, thanks ~ $\endgroup$ Commented Jan 17 at 10:41
  • $\begingroup$ no problem, happy to help! $\endgroup$ Commented Jan 17 at 15:54

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