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Is it possible to incorporate the empty d-orbitals of a p-block element (suppose it is chlorine) into a VASP calculation? If yes, what is the standard procedure to incorporate these orbitals.

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If I understand the question, you want to add Hubbard U correction to d orbitals on chlorine atoms? I think you can get bands with d-orbital character by including enough empty bands, but I don't think there is any point. The Hubbard U correction term only adds an energy penalty between occupied orbitals and the d-orbitals will not be occupied (unless you add lots of electrons). An analogous argument is true with e.g. the Hartree potential; the unoccupied states don't contribute to the density and don't alter the potential.

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    $\begingroup$ Thanks for your contributions. I just wanted to know if anything special is neededt to be specified in the VASP input to probe the participation of d-orbitals in chemical bonding. As mentioned by @SusiLehtola that plain waves always include empty orbital, is the answer I was looking for. Once again thank you for clearing. $\endgroup$ Aug 31 '20 at 19:51
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The empty orbitals are always included in plane wave calculations. The plane waves don't conform to atomic symmetry, and can be seen to contain contributions of arbitrary angular momentum.

If you were to use an atomic basis set, then you would need to put in D basis functions explicitly; however, this is pretty much always done in practice at least in the quantum chemistry community, since you need D fuctions to describe polarization of the P orbitals. Typically, a polarized double-zeta basis will have D functions for Cl, a triple-zeta basis will also have F functions, and a quadruple-zeta basis will have G functions.

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    $\begingroup$ @SusiLehtola You might have to increase NBANDS so that there enough bands above the Fermi level to reach the ang. mom. character that you want. You can check which bands have l=2 character by putting LORBIT=11 in the INCAR file and looking in PROCAR. This will show the projections of the wave function (band) onto the spherical harmonics at each atomic site for each k-point. $\endgroup$ Aug 27 '20 at 20:34
  • $\begingroup$ @TySterling Well that's a different thing, right: then you're looking at excited states that have some sort of atomic d character. But the point is that d orbitals and higher contribute even to the ground state, and you don't have to do any special tricks to describe the ground state correctly with plane waves other than properly adjust your Ecut. $\endgroup$ Aug 28 '20 at 7:18
  • $\begingroup$ you are probably right, maybe I don't quite understand this. But here is what I am thinking: Increasing ECUT simply increases how well a particular state is approximated by plane waves. The lowest band in a hyrdogen crystal, for instance, should be of l=0 character only. All of the electrons are contributed from s states. The unoccupied higher energy states should have p,d,f,... etc. character in higher energy bands, but the lowest band should only be filled with l=0 states from the s orbitals. Adding more planewaves simply makes the filled states 'look' better $\endgroup$ Aug 28 '20 at 14:24
  • $\begingroup$ A plane wave contains infinitely many angular momentum states, see en.wikipedia.org/wiki/Plane_wave_expansion. Although a H atom in isolation has spherical symmetry, it loses it straight away in a crystal. The ground state is no longer expressible as s states on the atoms, but you also need p, d, f, g, h, etc character as well. $\endgroup$ Aug 29 '20 at 8:58
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    $\begingroup$ I think we are equivocating what each other is saying. I believe the author is asking about adding Hubbard U correction to chlorine d orbitals, i.e. they want to know how to include (approximately) d orbitals on a specific atom. In PAW, this is reasonable as the regions near the atoms are approximated as spherical and l is a good quantum number in that region. The 'd-orbital' in this case would be the projection of the total KS state onto the l=2 spherical harmonics around that atom, but there would be no wave functions with this character unless bands high enough in energy are included. $\endgroup$ Aug 31 '20 at 14:45

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