In the way of a comment I only can repeat what has been explained
several times in this mailing list:
Take care to calculate all energies you want to compare with exactly the
same parameters: same structural unit cell, same number of k-vectors,
same Rkmax etc. and be careful to check that

Thank you Dr Pieper for the detailed and fruitful information.
For my compound with the hexagonal structure, I know beforehand the
magnetic ground structure which is still hexagonal with magnetic order
AF1, but for the 2 other magnetic structures for AF2 and AF3 , they become
orthorhombic.
Since

Of course inclusion of SO interactions may lead to another magnetic
ground state. For example, at least in principle it certainely will do
so if the symmetry of your Hamiltonian including SO breaks some symmetry
of the ground state you found without SO. So you might want to look
wether or not

Thanks Dr pieper for the rich information within your answer.
Perhaps I didn't formulated my question well . I am not interesting exactly
to the ground state energy , but to the magnetic ground state. As I
mentionned before , I want to determine the magnetic ground state from 5
configurations:

My 2 cents to this: Not a particularly meaningful question.
The only meaningful thing about energies, as in eigenvalues of the
Hamiltonian, is their DIFFERENCE. The evolution with time of the state
of an isokated quantum system (SchrÃ¶dinger picture) is completely
governed by the differences

Hello again
I am waiting for an answer to my question .
My question is about the effect of the inclusion of the Spin-Orbit Coupling
on the ground state energy.
I want to know if the SO affect the ground state energy also or It only
causes the splitting of the degenerate state energies.
Any

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