How big should a defected supercell be? DFT

In summary, when studying defects using plane-wave basis density functional theory, it is important to use a supercell that is large enough to avoid any interactions between the defect and its periodic images. This can be achieved by checking that the wave vector components of the defect's wave function are smaller than the reciprocal lattice vectors of the supercell. Bloch's Theorem can be used as an approximation for this calculation.
  • #1
muonneutrino91
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When studying defects using plane-wave basis density functional theory, it is necessary to ensure that the size of the supercell in which the defect is located is large enough to ensure that there is no interaction between the defect in question, and the periodically repeated defects that are a part of the analysis.

One could simply increase the size of the supercell until convergence in final energy, but I know for certain that there is a way of approximating this by making use of Blochs Theorem, but I cannot for the life of me remember how to figure this out.

Can anyone offer guidance on this? Many thanks
 
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  • #2
. Bloch's Theorem states that any wave function can be written as a superposition of plane waves with wave vector components that are integral multiples of the reciprocal lattice vectors. This suggests that in order to study defects, we can calculate the wave functions of the defect in a sufficiently large supercell so that the wave functions overlap with their periodic images, resulting in a converged energy result. To ensure this, one must check that the wave vector components of the defect's wave function are smaller than the magnitude of the reciprocal lattice vectors of the supercell.
 

1. How is the size of a defected supercell determined in DFT calculations?

The size of a defected supercell in DFT calculations is typically determined by considering the size of the defect, the desired level of accuracy, and the available computational resources. Generally, a larger supercell will provide a more accurate representation of the defect, but it will also require more computational resources and time.

2. What is the minimum size for a defected supercell in DFT calculations?

The minimum size for a defected supercell in DFT calculations is typically determined by the size of the defect and the convergence criteria of the calculations. In general, the supercell should be large enough to accommodate the defect and its surrounding atoms, and also large enough for the calculated properties to converge with respect to the supercell size.

3. Is there a maximum size for a defected supercell in DFT calculations?

There is no specific maximum size for a defected supercell in DFT calculations, but the size should be chosen based on the available computational resources and the desired level of accuracy. In some cases, a supercell may become too large to be practically calculated, and alternative methods such as continuum models may be used.

4. How does the size of a defected supercell affect the accuracy of DFT calculations?

The size of a defected supercell can greatly affect the accuracy of DFT calculations. A larger supercell will provide a more accurate representation of the defect, but it will also require more computational resources and time. In some cases, a smaller supercell may be sufficient for obtaining accurate results, but it is important to carefully consider the size for each specific case.

5. Are there any guidelines for choosing the size of a defected supercell in DFT calculations?

There are no specific guidelines for choosing the size of a defected supercell in DFT calculations, as it will depend on the specific system and desired level of accuracy. However, it is generally recommended to start with a smaller supercell and gradually increase the size until the calculated properties converge. It is also important to consider the symmetry of the system and the nature of the defect when choosing the supercell size.

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