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To determine the lattice parameter of a material, I did a VC-RELAX calculation using Quantum ESPRESSO, and I also applied the Birch-Murnaghen equation to obtain the optimized lattice parameter. However, I noticed that the results are slightly different by 0.0926 Angstrom.

Now, I am a bit confused about which value to consider for my subsequent calculations, and I wonder why they are not exactly the same?

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  • $\begingroup$ Does the Birch-Murnaghen give you all the cell parameters a, b and c for, let say, a triclinic cell? $\endgroup$
    – Camps ♦
    Jul 25 at 19:20
  • $\begingroup$ @Camps No. Birch-Murnaghen equation can give optimized lattice parameter, optimized total energy and optimized Bulk Modulus. $\endgroup$
    – Camilla
    Jul 25 at 19:34
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    $\begingroup$ Well, if it cannot return ALL the cell parameters, then the best option is going with VC-RELAX calculation. $\endgroup$
    – Camps ♦
    Jul 25 at 19:45
  • $\begingroup$ Could you please describe how exactly you applied BM equation? Is it some kind of computation type in QE? Did you run geometry optimization with fixed cell parameters over some range? $\endgroup$
    – Ivan Chernyshov
    Jul 27 at 22:02
  • $\begingroup$ @IvanChernyshov Sure. I used PWTK, a scripting interface for Quantum ESPRESSO (QE). To begin, I created an SCF file using PWTK (which is similar to the one we use in QE but with some differences, see this link please: pwtk.ijs.si/tutorial.html). Additionally, I created another file specifically for the equation of state. When launching the calculation in the terminal, the EOS file utilizes the first SCF file and automatically generates multiple output files by varying the lattice parameter. This process allows for the determination of different types of EOS, among them BM. $\endgroup$
    – Camilla
    Aug 1 at 11:10

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I will personally recommend to use the result (lattice parameter) after the fit with the Birch-Murnaghan equation, that what people do especially the bulk modulus will be included as a result and compared to experimental data. Your obtained energies are sampled with discrete lattice parameters, except the case when your step is very small, your derived lattice parameter will always be approximate. The BM equation is continuous and has an identifiable minimum.

However, I noticed that the results are slightly different by 0.0926 Angstrom.

The error is relatively small, you may find it large compared to experimental results for example, but it is really small compared to the non-negligible error induced by an approximate exchange correlation functional.

I wonder why they are not exactly the same?

A macroscopic classical and a microscopic quantum result will never be in perfect agreement.

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