question about multiplicity


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I have a system which I am trying to run a broken symmetry calculation. The two fragments are antiferromagnetically-coupled.

The first fragment has charge -1 and S=9/2.

The second fragment has charge -1 and also S=9/2.

The overall molecule has charge -2 and S=0.

When my input specifies the first fragment with charge= -1 multiplicity= -10, second fragment with charge=-1 multiplicity= 10, and overall molecule with charge= -2 multiplicity= 1, I do not get any error.

However, when my input specifies the first fragment with charge= -1 multiplicity= -8, second fragment with charge=-1 multiplicity= 10, and overall molecule with charge= -2 multiplicity= 1, I get an error.

Does anyone know why this is so?

I thought multiplicity is 2S+1, and so if I treat the first fragment as spin up and second fragment as spin down, the second scenario should work and not the first?

Thanks so much for any help!

Forum Regular
Multiplicity is 2S+1

First scenario:
Fragment 1; charge = -1, multiplicity = -10 so 9 unpaired beta electrons [2(9/2)+1 = 10]
Fragment 2; charge = -1, multiplicity = 10 so 9 unpaired alpha electrons [2(9/2)+1 = 10]
Total should then be charge = -2 and multiplicity = 1 since we have even number of alpha and beta electrons [2(0/2)+1 = 1]
You specified charge = -2 and multiplicity = 1 for the total, so the calculation works

Second scenario:
Fragment 1, -1 charge, multiplicity = 8 so 7 unpaired alpha electrons [2(7/2)+1 = 8]
Fragment 2, -1 charge, multiplicity = 10 so 9 unpaired alpha electrons [2(9/2)+1 = 10]
Total should then be -2 charge and multiplicity = 17 since we have 16 unpaired alpha electrons [2(16/2)+1 = 17]
You specified charge = -2 and multiplicity = 1 for the total, so the calculation fails
(Even if you had a typo in your post and meant to write multiplicity = -8 for the first fragment, the total would still not be multiplicity = 1 since you would have two more alpha electrons than beta electrons, [2(2/2)+1 = 3])

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Many thanks for the help! I am still struggling with how 9 unpaired beta electrons can give a negative multiplicity of -10, and not -8, since 2(-9/2)+1=-8 ?

Thanks so much!

Forum Regular
The negative is just a computational flag to indicate that you want the extra electrons to be beta electrons not alpha electrons.

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That is helpful, and now makes a lot of sense. Thanks so much!


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