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I tried calculating total energy using SCF calculations after optimization with quantum espresso. Still, I don't know how to optimize total energy in the standard state instead of isolated atoms.

If there is a way to isolate atoms? What is the difference between a free atom and an isolated atom?

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    – Camps
    Dec 13, 2023 at 14:05

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From the tag you used, I assume that you are trying to do the isolated atom calculation in Quantum ESPRESSO. However, I would suggest you doing it with PySCF, NWchem, SIESTA or other code that uses a localized basis set instead of a plane wave basis set code like QE or VASP. I have tried this type of calculation using QE. This requires a very large supercell (i.e., very high vacuum) to remove the spurious image-image interaction and it also requires other corrections. So, QE or plane wave codes are computationally very inefficient in this case and they also require huge memory.

If you have to use QE, then consider the following suggestions:
  • Put the atom at the center and set an initial supercell size of around 10 Angstrom and run a simple SCF calculation. Then increase the supercell size a little bit and check if the energy changes. Try increasing the supercell size until the energy converges within your preferred threshold.
  • Don't forget to use the tag assume_isolated in the &CONTROL block. You can use assume_isolated='makov-payne' or assume_isolated='martyna-tuckerman'. See this documentation for details.
  • You need a very high k-mesh and high memory. Always a good practice is to check convergence for ecutwfc and K_POINTS but if you just want a good starting guess, use QE input generator.
Better alternatives:

Localized basis set can handle this type of isolated atom case very efficiently with much less memory requirements. I used PySCF and it was very fast in my case. There are simple tutorials to run SCF or DFT calculation using localized basis sets such as GTO. But you are not limited to PySCF. There are other free alternatives such as SIESTA or commercial ones such as Gaussian. A complete list can be found here.

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In quantum mechanical calculations, it is common to study systems in their isolated or standard state, rather than as individual atoms. The isolated or standard state refers to the state of an atom or molecule in an environment where it is not influenced by any external factors, such as other atoms or molecules. This allows for a more accurate representation of the system's behavior in a bulk or condensed phase.

In the context of electronic structure calculations like those performed with quantum espresso, the total energy of a system is typically optimized by considering the interactions between atoms in a periodic arrangement, such as in a crystal lattice or a supercell. This approach takes into account the long-range interactions and periodicity of the system, which are important for accurately describing the properties of materials.

To study isolated atoms, one can use a supercell with a sufficiently large vacuum region, effectively isolating the atoms from their periodic neighbors. By increasing the size of the supercell and the vacuum region, the interactions between periodic replicas of the system become negligible, and the system can be treated as effectively isolated.

Regarding the difference between a free atom and an isolated atom, this lies in the context in which they are considered. A free atom typically refers to an atom completely devoid of any external influence, including other atoms or the surrounding environment, but may still be subject to certain constraints or interactions, such as boundary conditions or periodicity in the case of supercells.

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