How to set the initial spin for a fullerene molecule?

[yfchang]

Dear, I’d like to repeat a work published on the Chem. Phys. Lett. (2012, 535, 111-115) which reported the transport spin polarization of fullerene C28 (Td). But there are two problems need somebody’s help.
1.How to set the initial spin for this device? C28 (Td) has four unpaired electrons, what should I do to initialize the configuration in a SGGA calculation?
2.How to calculate the magnetic moment of one atom like reported in this work? I have noticed the answer form @zh like M = population-up  -  population-down. But for the example in http://quantumwise.com/publications/tutorials/mini-tutorials/141, the spin up population is 6.788, and the spin down population is 5.573 for the Vanadium atom, so the M should (6.788-5.573=1.215), why the result in this tutorial is 1.251? According another method to calculate the magnetic moment (M=(n*(n+2))^0.5), the result for this atom will be 1.97. What is the deferent between them?

[Anders Blom]

You can start by not setting any initial spin, then all atoms are initialized with maximum spin-polarization, corresponding to a ferromagnetic state. If there is supposed to be spontaneous spin-polarization between the C1,C2,C3 atoms you may need to flip the spin on those sites, but that information is not available in the paper you cite. Perhaps you can contact the authors for more information.

The 1.251 was a typo - thanks for spotting it, it has been fixed!

The sqrt(n) method I don't know about, isn't n here the electron density rather than the Mulliken population?

[yfchang]

Thank you very much!  The sqrt(n) method is taken from http://en.wikipedia.org/wiki/Magnetic_moment, the original form of it is M=g*(J*(J+1))^0.5, where J is the total angular momentum quantum number, g is the Landé g-factor. For free electron, g~2, so it change to M=(n*(n+2))^0.5, where n is the number of unpaired electron. So, what is the diffrent between the two magnetic moments calculated by subtract the spin up populations from the spin down populations and this method?

[zh]

Thank you very much!  The sqrt(n) method is taken from http://en.wikipedia.org/wiki/Magnetic_moment, the original form of it is M=g*(J*(J+1))^0.5, where J is the total angular momentum quantum number, g is the Landé g-factor. For free electron, g~2, so it change to M=(n*(n+2))^0.5, where n is the number of unpaired electron. So, what is the diffrent between the two magnetic moments calculated by subtract the spin up populations from the spin down populations and this method?

Please read the textbook of "Introduction to Atomic Physics" to understand the definition of magnetic moment (M), J, and m_z.   "J" cannot be replaced the number of unpaired electrons  simply.

For m calculated by the spin up populations from the spin down populations, it is  m_z.

[yfchang]

Thank you very much! I will read it.