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I am considering the relaxation for the following zigzag graphene nanoribbon.

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Here the boundary of the zigzag graphene(C: brown) nanoribbon has been passivated with one H atom. I have performed the spin-polarized and spin-unpolarized calculations with VASP. Surprisingly, I found that the spin-polarized calculation gives me lower total energy. Moreover, the total magnetic momentum can be traced back to the C atom passivated with H atom.

Should the zigzag graphene nanoribbon present a spin-polarized ground state? Although the boundary has been passivated. By the way, I have also passivated the boundary with 2 H atoms and then there is net total residual magnetic momentum. Should I use 2 H atoms to passivate the boundary of the zigzag graphene nanoribbon?

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This is consistent with some work we did on graphene nanoribbons a few years ago. We used LDA for this work, though from memory PBE gave similar results. This was using CASTEP, so different pseudopotentials to you and a different implementation of the plane-wave DFT method, so it can be considered independent verification.

Like you, we found that the bare zigzag edge was spin polarised fairly strongly (this is well studied now); passivating with one hydrogen per edge carbon reduced the spin polarisation enormously, but did not completely suppress it; and passivating with two hydrogens per edge carbon led to a non-spin-polarised ground state. The most stable edge structure was the two-hydrogen passivation. We published our findings here:

“Theoretical study of core-loss electron energy-loss spectroscopy at graphene nanoribbon edges”, Nobuyuki Fujita, Philip Hasnip, Matt Probert and Jun Yuan, J. Phys. Condens. Matter 27, 305301 (2015). https://doi.org/10.1088/0953-8984/27/30/305301

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