When DFT band structure is obtained, how do we know whether it is calculated with respect to vacuum level or any other? I heard that these band structures can be calculated w.r.t. vacuum level where atomic wave function becomes zero or the zero potential between atoms. I don't understand these two cases. Also I don't know to which of these my calculated bands structure corresponds to?
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The "zero" of energy is arbitrary, it doesn't affect any properties (total energy is not an observable). In particular, in a plane-wave DFT simulation you will almost always be using a pseudopotential, which will change all the band energies by a pseudopotential-dependent rigid shift.
If you want to calculate where your band energies are with respect to any given state, for example the vacuum, then the usual approach is to compute the energy of that other state, and simply subtract it from the band-energies. In a 2D slab calculation, for example, the mean potential will decay into the vacuum (between the periodic slab images), and it will reach a plateau at the vacuum energy. (NB it is usually more numerically stable to average the potential over the plane parallel to the slab.)
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$\begingroup$ Thanks @Phil for answer. Later on I will be calculating work function, and therefore the information on reference energy is required. $\endgroup$– AbPhysCommented May 26 at 5:22
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$\begingroup$ How does one compute the energy of "the other state" - vacuum? I tried to think through your answer @Phil for last few days, but couldn't grasp much. I appreciate if you could elaborate more. $\endgroup$– AbPhysCommented May 31 at 4:32