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I am a beginner in Quantum Espresso When I want to calculate the total energy for Cu for example, I write the input file for primitive cell or conventional cell, what is the difference?

Thank you

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  • $\begingroup$ The absolute value of the total energy in Quantum ESPRESSO (or to my knowledge, any other existing DFT code) is not useful. You can either use primitive cells or conventional cells as long as you stick with your original choice for all subsequent calculations. The difference in the energy values doesn't matter because you cannot simply compare energy obtained from two different cell types. Related: this, this, this. $\endgroup$ Sep 16, 2023 at 7:25
  • $\begingroup$ However if you are using different cells, especially small ones, be careful to make sure the k point sampling is consistent so that you really are comparing like with like $\endgroup$
    – Ian Bush
    Sep 16, 2023 at 8:32

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The short answer is that, scientifically, it doesn't matter which cell you use, but you need to think about what you actually want to compute. In particular (as mentioned in the comments to your question):

  1. The total energy is not meaningful by itself, because it has an arbitrary zero. It is the differences in total energy between different calculations which are interesting, because these relate to actual observables. For example, the change in energy when you move an atom a small amount tells you the force acting on that atom.

  2. The total energy you compute will be the total energy for the simulation cell you used as input. When comparing energies between two systems, you will usually want to normalise the total energy to per atom (or possibly per unit volume), so that you can compare systems with different numbers of atoms.

For example, if cell A is a 2-atom primitive cell of a particular material phase, and cell B is the 8-atom conventional cell of a different phase (of the same material), you might be interested in knowing which phase has the lowest internal energy. Because cell B has four times the number of atoms that cell A has, you need to divide its total energy by four in order to compare it to the energy from cell A. In general, the simplest is to convert the energies to the energy per atom, in which case the energy from cell A would be divided by 2, and the energy of cell B would be divided by 8.

When comparing energies between two simulations, you do need to ensure both calculations are converged to the same accuracy so that the errors cancel when you take the difference.

This is the answer as far as the "science" goes; however, the computational demands of a larger cell will almost always be greater than those of the smaller cell. This is because the time taken by a conventional density functional theory programme (like QE) increases faster than linearly with the size of the simulated cell. Some parts of the calculation scale quadratically with the number of electrons, for example, and some parts scale cubically. In contrast, a larger simulation cell will use fewer k-points, so there is some saving in computational time there (though not enough to offset the increase in bands, plane-waves and atoms).

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