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xirainbow

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[资源] 【分享】Getting the bulk energy in surface calculation

In first-principles calculations, there is a subtle complication in getting the bulk energy. One way (the more obvious way) is to get it from a bulk calculation. The problem with this method is that you will be using different k-points for your supercell calculations and bulk calculations. This can lead to inaccurate surface energies.

   A definition is to take the change in energy when you add a new layer of atoms to your supercell with the vacuum. That is(见附件)

   If everything is converged (slab size, vacuum size) then adding a layer to the supercell is just like adding a layer to the bulk.
   Think about it this way. Assume you have an enormous vacuum and an enormous slab in a 1x1x100000 cell. Before you add an atom (which is the SAME as adding a layer given this cell), you have 2 surfaces, a vacuum, and a bulk. After you add an atom (add a layer) you still have 2 surfaces, a vacuum, and a bulk, but the bulk has one more atom (layer). In other words, it is the same as adding an atom to the bulk, from which you can obtain the bulk energy
Why do we do this? Remember that first-principles calculations are all about canceling errors. When you calculate the bulk directly, you use different k-points than when you calculate the slab. By calculating the energy of 1 Al atom by adding a layer to a supercell (shrinking the vacuum size by layer, and keeping the total cell geometry the same) the errors arising from incomplete kpoint meshes will cancel. In the limit of infinite k-points the answers should be the same. But nobody has time to calculate energies of infinite kpoints.

   A general rule of thumb is that kpoints/atom is constant (but that the distribution of kpoints along kx, ky, and kz will depend on crystal geometry!!). ( I do not get the last statement