# Energy level diagram for d3 system in CrCl3 using ligand field theory

asked by Chamini Shammi Pathiraja (2023/01/22 04:20)

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)

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

1)
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 * OppVt2gNpsi=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”

, 2023/01/24 21:45

Hi, when I use all the states from d3L0 to d4L1, it takes forever for the calculation. How can I just use the states for d3L0 and L4L1 and calculate the ELD diagram?

Thank you, Chamini

, 2023/01/24 23:20

Dear Chamini,

Indeed Quanty is not written with the idea to calculate all eigenstates in the Hilbert space, but focuses on the lowest “few”.

You should set NTri to 120 + 210*10, or even less and add restrictions to the function Eigensystem such that you only allow for d3, d4 and d5 configurations.

Best wishes, Maurits

, 2023/02/01 03:53, 2023/02/02 01:38

Hi Maurits,

I have edited the code and added the restrictions as below.


StartRestrictions = {NF, NB, {"1111111111 1111111111",13,13}}
Restrictions = {NF, NB, {"1111111111 0000000000",3,4}}
   Npsi_d3L0 = Binomial(10,3)
Npsi_d4L1 = Binomial(10,4)*Binomial(10,1)
Npsi = Npsi_d3L0 + Npsi_d4L1
psiList = Eigensystem(Hamiltonian0, StartRestrictions, Npsi,{{"restrictions",Restrictions}})

Can you please let me know if this is correct? I have only used the d3L0 and D4L1 states. The reason I'm asking is that still, it's taking a very long time.

Thank you, Chamini

, 2023/02/03 02:04

Hi Maurits, I also have another question. In the workshop 2022 tutorial files, I looked into the NIO ELD quanty code using ligand field theory. In that code, the Hamiltonian has two parts Hamiltonian0 and Hamiltonian1. ANd inside the loop for 10Dq, we multiply the whole Hamiltonian1 by the new 10Dq value within the loop. But here, the operator of the 10Dq hasn't been used anywhere.

But in the documentation in quanty website, you have first written only the Hamiltonian0 and then inside the for loop for the 10Dq values, we add the 10Dq value*oporator to generate the new hamiltonian.

Which one of these is correct?

Chamini