# pp hybridization

asked by Riccardo Piombo (2019/12/03 12:37)

Dear all,

I would like to simulate the energy diagram of a system formed by a Cu ion with 10 3d states surrounded by 4 planar Oxygens that hybridizing their 2p states give birth to a band of 5 Ligand-P states with the same symmetry of the 3d levels. It is clear to me how to insert the hybridization between d and P the states but how about the pp hybridization?

In particular I would like to simulate the case in which, when the P-d hybridization is zero, omitting the crystalline field on the d states then the pp hybridization separates the p states into four levels with energies:

Ea1u = Delta_pd + Tpp Eb1u = Delta_pd - Tpp Eb2u = Ea1u Eeu = Delta_pd

Schematically, at Tpd == 0, the energy diagram should be

d states

——- 5 3d states ——-

P states

——- Ea1u, Eb2u ——-

——- Eeu ——-

——- Eb1 ——-

I think that this is not right:

Delta_pd = -2.75 Tpp = -1.0 Ea1u = Delta_pd + Tpp Eb1u = Delta_pd - Tpp Eb2u = Ea1u Eeu = Delta_pd Akm_pp = PotentialExpandedOnClm("Oh",1,{Ea1u,Eb1u,Eb2u,Eeu}) hybrid_pp = NewOperator("CF", NF, IndexUp_Ld, IndexDn_Ld, Akm_pp) hybrid_pp.Name = "p-p hybridization"

Thanks in advance to all

## Answers

Dear Ricardo

The code you need is listed below. The basic idea is that the symmetry of the Hamiltonian acting on the d-shell is the same as for the Ligand d shell or for the hopping between them. If you expand this Hamiltonian on spherical harmonics you thus get the same expansion coefficients. Which coefficients are allowed you can find in the point-group tables.

Best wishes, Maurits

Thanks a lot professor, You've been very kind to me

Riccardo