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I'm new here so please forgive me if I lack proper stack exchange etiquette. So, I was wondering if anyone here could provide insight on a problem that I am running into with with a Hartree-Fock calculation. I wrote a code from scratch that attempts to calculate the HF energy and basis for a 1D potential that is supposed to model the nucleon-nucleon two body interaction:

$$ V(x)= 60 e^{-25x^2} - 15 e^{-1.56x^2} $$

If I run the code for so called "spinless" fermions, it converges and gives results similar to those given in literature on this potential. However, if I add any spin degrees of freedom to the problem, the SCF procedure does not converge. Instead it arrives at a group of two or more sets of eigenvectors which when used to calculate the new fock-matrix will eventually reproduce one another. I want to believe that this is because I am trapped in a local minimum in the HF functional. So my main question is: Have any of you ever encountered such a problem with a basic HF code? Considering that in some cases I get good results and in other cases no results, I feel that the problem lies in the physics of the potential, rather than in my code. Is this a reasonable statement in your eyes?

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