How to get the crystal/ligand field splitting of d orbital of Fe complex using Quantum Espresso

Question

So I am working with Quantum Espresso (6.5) and we have built a few square planar Fe complexes (to be specific $\ce{Fe(NH_2)_2(OH)_2}$ cis and trans), and we ran scf (self consistent calculation) and pdos (projected density of state) calculations on it to get info on the atomic orbital occupancy and the magnetic moments. But this still doesn't give the energy splitting (d orbital splitting) order of the system. Can someone suggest some methods where we can get the crystal/ligand field splitting of d orbital of Fe using DFT (preferably using QE but other methods work too)?

Also is there a way to get this order from the occupancy of orbitals only?

PS: I understand WIEN2K would be of use here but because of some issue we won't be able to use that, so if there are other methods, do tell us.

EDIT: I did some asking around and apparently the order of energy can be found by using tight-binding-method or by group theory but I'm not really sure if someone can explain how those methods would work here.

I'd still prefer using quantum espresso for this though if somehow possible

Answer 1

You should take into account that for this type of square planar complex the set of 5 "d" orbilals of the iron atom are the ones that must be considered for the calculation. Usually, depending on the type of ligands (weak field or strong field) you can have a different orbital degeneracy for the "eg" and "t2g" orbitals, which are the energy levels that must be considered for the calculation of the field separation in a square planar complex (SP). Note that I have used the quotes for the label of the orbitals since they are the nomenclature that results from an octahedral complex from which 2 ligands of the z axis have been removed, the nomenclature for SP complexes does not follow these labels (e.g. they can be a, e, t2) The arrangement of these levels results in different configurations depending on the type of ligand and worsens a bit when there is metal-ligand hybridization (more covalent than ionic bonds). Example, array 1-2-2 , that is, the highest energy level "1", two degenerate levels "2" lowest in energy and "2" last two degenerate levels lowest in energy. In the literature there are many examples with 2-1-2 and 2-2-1 configurations as well. Your example has probably already been calculated. "Usually" the orbit that alone (1) is the dz2 and is not involved in the calculation of the ligand field separation delta. Finally, identify your "d" orbitals with a calculation of DOS in QE. Then order them in decreasing energy, look for the degenerate orbitals (same energy) and go to the formulas to make the calculation that you can find in the literature. Note: maybe someone has already developed a code that reads the output of QE and responds quickly, but be careful, check the occupancies of the orbitals, it is an extremely important theoretical aspect that you may need to consider based on the theory of LCAOs to ponder the energies of the orbitals.