I'm using Quantum ESPRESSO in my calculations. And I'm a bit confused about the convergence for energy between two consecutive steps and the force allowed on each atom.

In my input file, I retained the default values as described in the Quantum ESPRESSO input file, i.e., etot_conv_thr=10^-4 a.u and forc_conv_thr=10^-3 a.u (Does 'a.u' mean atomic unit?)

In literature, they often express energy convergence in Ry or eV and force allowed on each atom in Ry/Å or eV/Å. Could someone assist me in converting these values, so I can verify if my results are accurate?


2 Answers 2


As correctly stated by @Camps,

[t]he atomic unit for energy is the Hartree ($E_h$).

The linked Wikipedia page in his answer explains what natural constants are assumed to be unity in order to get the stated definition.

However, the FAQ of Quantum Espresso states that

[u]nless otherwise specified, all PWscf input and output quantities are in atomic “Rydberg” units, i.e. energies in Ry, lengths in Bohr radii.

Therefore it seems that the unit of etot_conv_thr is $\mathrm{Ry}$ which differs by a factor of 2 from the Hartree and the unit of forc_conv_thr is $\mathrm{Ry/}a_0$, not $\mathrm{Ry/}Å$ as stated in the question. Keep in mind that in the FAQ, it is also stated that for the sub-package cp.x the Hartree is used:

Note that CP uses instead atomic “Hartree” units: energies are in Ha, not in Ry.

As far as I know, VASP as another example uses $\mathrm{eV}$ on some of its outputs. It therefore seems to be a good idea to check the unit convention for any (DFT) code that is being used in an investigation.


The atomic unit for energy is the Hartree ($E_h$) and it is equivalent to $4.3597447222071(85) \times 10^{−18} J$.

You can get more information about the atomic units visiting the Wikipedia page.

About converting, I like to use an online conversion tool named The Versatile Unit Converter which also has a widget app for Mac OS X.

The accuracy of your result should always be checked against experimental measured properties. For example, doesn't matter if you used LDA and a convergence value of $10^{-10}$ and the calculated energy gap continue to be underestimated.

  • $\begingroup$ When checking the FAQ quantum-espresso.org/faq/faq-self-consistency/#6, it is written that atomic Rydberg units are used, so that would be a factor of 2 different from Hartree units. I'm not sure what is correct here $\endgroup$
    – manju9
    Commented Feb 2 at 9:26
  • $\begingroup$ @manju9 Can you plz check the values of etot_conv_thr and forc_conv_thr in here quantum-espresso.org/Doc/INPUT_PW.html#idm123 $\endgroup$
    – Camilla
    Commented Feb 2 at 10:19
  • $\begingroup$ @manju9, one thing is what QE uses, and what atomic units are. $\endgroup$
    – Camps
    Commented Feb 2 at 13:25
  • 1
    $\begingroup$ @Camps Yes, but since the question was about help converting the specific values of the convergence threshold, it might be important to note that atomic units in Quantum Espresso might mean atomic "Rydberg" units as written in the FAQ $\endgroup$
    – manju9
    Commented Feb 2 at 14:25
  • $\begingroup$ @manju9 Does that mean etot_conv_thr=10^-4 a.u= 10^-4 Ry and forc_conv_thr=10^-3 a.u= 10^-3 Ry/Angstrom $\endgroup$
    – Camilla
    Commented Feb 2 at 15:20

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