Orbitals in the non-relativistic case have the same quantum numbers n and l, but they vary in energy.

[Mhmd Al ahmad]

Dear Dirac users,

I have conducted a non-relativistic calculation on the iodine atom with the electron configuration [Kr] 4d^(10) 5s^(2) 5p^(5). In principle, the energy of the orbital depends on the quantum numbers n and l. Therefore, it is expected that all 5p orbitals would have the same energy. However, Dirac showed that only two of the p orbitals have the same energy. Could you please help me clarify this matter?

I have attached my output file below.

Thank you.

[Hans Jørgen Aagaard Jensen]

The 5p orbital energies have different energies,  because in restricted open-shell Hartree-Fock the orbital energy and the orbital itself depends on the occupation, unless you restrict them to be equal.

(Just as alpha- and beta-orbitals are different in open-shell unrestricted Hartree-Fock.)

 

You can achieve this averaging by including all six 5p spinors in the average-of-configurations open shell :

 

.CLOSED SHELL

30 18

.OPEN SHELL

1

5/0,6

 

Regards, Hans Jørgen.

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