====== Energy level diagram for d3 system in CrCl3 using ligand field theory ======
;;#
asked by [[mailto:cpathira@CougarNet.UH.EDU|Chamini Shammi Pathiraja]] (2023/01/22 04:20)
;;#
== ==
<WRAP center box 100%>
I have been trying to plot the energy level diagram for d3 in CrCl3 using ligand field theory. When I use the crystal field, since the Npsi is 120, it gives me the outcome without any error. But d3 ligand filed energy level diagram quanty script doesn't run properly.

This is what I used as the parameters. Can you please let me know if I did anything wrong.

nd = 3
-- parameters from experiment (core level PES)
U       =  3.5
Delta   =  3.8
-- parameters obtained from JPCL
F2dd    = 11.6 * 0.58
F4dd    =  7.271 * 0.785
tenDq   =  1.55
tenDqL  =  0.103
Veg     =  1.992
Vt2g    =  1.320
zeta_3d =  0.048*0.5
Bz      =  0.000001

ed      = (10*Delta-nd*(19+nd)*U/2)/(10+nd)
eL      = nd*((1+nd)*U/2-Delta)/(10+nd)
F0dd    = U+(F2dd+F4dd)*2/63

Hamiltonian0 =  F0dd*OppF0_3d + F2dd*OppF2_3d + F4dd*OppF4_3d + zeta_3d*Oppldots_3d + Bz*(2*OppSz_3d + OppLz_3d)
             + ed * OppN_3d + eL * OppN_Ld
Hamiltonian1 = tenDqL*OpptenDq_Ld + Veg * OppVeg + Vt2g * OppVt2g
            
Npsi=Binomial(20,nd+10)
StartRestrictions = {NF, NB, {"1111111111 0000000000",nd,nd}, {"0000000000 1111111111",10,10}}
psiList = Eigensystem(Hamiltonian0, StartRestrictions, Npsi)

file = assert( io.open("EnergyLevelDiagram", "w"))

for i=0, 300 do
  lambda = 0.01*i
  io.write(string.format("%5.3f ",lambda))
  io.flush()
  file:write(string.format("%14.7E ",lambda))
  Hamiltonian=Hamiltonian0 + lambda * Hamiltonian1
  Eigensystem(Hamiltonian, psiList)
  for key,value in pairs(psiList) do
    energy = value * Hamiltonian * value
    file:write(string.format("%14.7E ",energy))
  end
  file:write("\n")
end
</WRAP>

~~DISCUSSION|Answers~~