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!
Edited On 7:02:46 AM PDT - Fri, Jun 8th 2018 by Kwaldner

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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!

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The negative is just a computational flag to indicate that you want the extra electrons to be beta electrons not alpha electrons.
Edited On 12:05:02 PM PDT - Fri, Jun 8th 2018 by Sean

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


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