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Impurity model with multiple ligand shells

asked by Ruiwen Xie (2021/11/26 10:47)

Dear Quanty developer,

When I was trying out the tutorial contributed by Robert Green in the workshop regarding the impurity model with multiple ligand shells (https://www.quanty.org/workshop/heidelberg/october_2019/programme, R. Green, tutorial on models beyond multiplet ligand field theory), I noticed that in the script comment,

-- Impurity model with multiple ligand shells
-- Utilizes an elliptical hybridization function

--Now the hybridization part of the Hamiltonian                 
if(LigandGeometry == "Chain") then
  --For the chain geometry, the 3d shell couples to the first ligand
  --and the chain of ligands are coupled with hopping t=Bandwidth/4

  Hamiltonian = Hamiltonian +
                  Veg * OppVeg + Vt2g * OppVt2g +  --hopping from 3d to first ligand
                  BandWidth / 4.0 * (OppVegL + OppVt2gL)  --ligand-ligand hopping

  XASHamiltonian = XASHamiltonian +
                  VegF * OppVeg + Vt2gF * OppVt2g +  --hopping from 3d to first ligand
                  BandWidth / 4.0 * (OppVegL + OppVt2gL)  --ligand-ligand hopping

My question is, is BandWidth/4, the factor 1/4, from the layout of hybridization operator (each shell has 4 neighbours)? And the comment line mentions elliptical hybridization function, from where I can see that it is elliptical? I do not get why it is elliptical from the current script.

Thanks a lot for your time!

Best Regards, Ruiwen

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