====== Tanabe-Tsugano diagram d^10 configuration ======
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asked by [[mailto:riccardo.piombo@gmail.com|Riccardo Piombo]] (2020/03/05 18:37)
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<WRAP center box 100%>
Hi everyone,

While doing the Tanabe-Tsugano diagram of a transition metal (TM) complex, as the CuO square planar structure, I realized that when the electronic structure of the TM involves a d^n configuration with n<10 (in CuO n=9) everything's fine but when it involves an n=10 d^n configuration, as in the octahedral AgF case, my code gives me the following error: "bad argument #1 to 'pairs' (table expected, got user data)". 
Here is the part of the code to which the error refers:

<code>
H_Ag = OppUdd + OppCF_4d 

H_F  = OppUpp + OppCF_Ld 

H_Cluster = H_Ag + H_F
H_0 = H_Cluster + H_Zeeman + H_Hz_ext
H_0.Name = "Cluster hamiltonian without hopping Tpd

print("")
print("N-body states energies computation")
StartRestrictions1 = {NF, NB, {"1111111111 1111111111",n4d+nL,n4d+nL}}

Npsi_i = math.Binomial(NF,n4d+nL)
psiList_N = Eigensystem(H_0, StartRestrictions1, Npsi_i)
print(psiList_N)
--psiList_N = {psiList_N} 
file = assert(io.open("EnergyLevelDiagram", "w"))

print("")
print("Energy level diagram computation")
print("------------------------------------")
print("Loop on tuning parameter lambda")
print("")

lambda = 0.

for i=0, 25 do
  lambda = 0.1*i
  io.write(string.format("lambda = -%5.3f\n ",lambda))
  io.flush()
  file:write(string.format("%14.7E ",lambda))
  ---> lambda == tuning parameter
  H_pert = H_0 + lambda*(-1)*OppHopLd4d 
  Eigensystem(H_pert, psiList_N)
  for key,value in pairs(psiList_N) do   -------> ERROR IS HERE!!!
    print(key)
    energy = value * H_pert * value
    file:write(string.format("%14.7E ",energy))
  end
  file:write("\n")
end

</code>

The other way around if I uncomment the following line of code (the twelfth row from the beginning of the script):

<code>
psiList_N = {psiList_N} 
</code>

The calculation is successful but it gives me an empty diagram. Can everyone please help me?
Thanks in advance

P.S should the problem be linked with the fact that a d10 configuration is made by a single Slater determinant?
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