Computational Details:
As stated in the main text, density function theory using the generalized
gradient approximation (GGA-PBE) is used for this study. An energy cutoff of 400 eV
is used for the plane wave basis set. Graphene nanoribbons (GNRs) are represented
as periodic systems with 4 C pairs in the lateral (repeated) direction (shown
previously to be an efficient choice for Fe adsorption and defects on GNRs 1,2) and 5,
6, or 7 C pairs through the GNR width (n=5,6,7). A vacuum of greater than 15Å
between periodic ribbons is maintained in all directions to limit self-interactions.
Monkhorst-Pack k-point meshes of 9x1x1 were found to be sufficient to converge
cells to less than 1 meV for the total system in agreement with similar cell sizes in
previous studies1-3. This value is also the ionic convergence criteria used in all
simulations. Defect sites are labeled according to their distance from the GNR edge
(Figure 1 of the main text for n=7). In these calculations, atoms are treated as spin
polarized and edge C/N atoms and Fe atoms are initialized to have magnetic
moments
Vacancy formation energy is calculated using a graphene C reference state as
shown in Equation S1:
Fvac = EGNR+vac + EC,graphene - EGNR
S1
In the case of an edge vacancy, the edge H is retained as shown in Figure 1a of the
main text. In the case of pyridinic vacancies, a free N2 molecule in vacuum is used as
the nitrogen reference state and
defect formation energy is calculated using
Equation S2:
1
3
Fvac+3N = EGNR+vac+3N + 4EC,graphene - EGNR - EN2
2
S2
Formation energy for defects with Fe follow Equations S1 and S2 with the initial
energy being that of the GNR+defect+Fe system energy and including the
subtraction of the EFe,free reference state.
For Fe binding energy, a free Fe atom in vacuum is used as the Fe reference
state leading to Equations S3 (no N) and S4 (with N):
BEFe = EGNR+vac+Fe - EFe, free - EGNR+vac
S3
BEFeoverPyridinic = EGNR+vac+3N+Fe - EFe, free - EGNR+vac+3N
S4
Vacancy concentrations, cvac as a function of defect position, x, is given in Equation
S4:
é -F ( x ) ù
vac
cVac ( x ) µ expê
ú
RT
ë
û
S4
This equation applies to pyridinic vacancies as well.
Concentration of Fe/vacancies, cvac-Fe , as a function of position is likewise
proportional to the exponential of the defect formation energy. This is broken apart
into a term associated with the formation of the vacancy and a term associated with
the Fe binding energy. Thus, Equation S5 shows that the concentration of
Fe/vacancy defects is proportional to the vacancy concentration and the
2
exponential of the binding energy. This equation applies to Fe/pyridinic vacancies
as well.
é -F ( x )
ù
é -F ( x ) ù é -BE ( x ) ù
é -BE ( x ) ù S5
Fe/vac
vac
Fe
Fe
cFe/Vac ( x ) µ expê
ú = exp ê
ú exp ê
ú µ cvac ( x ) expê
ú
RT
ë
û
ë RT û ë RT û
ë RT û
Magnetic State Considerations:
In the case of Fe free defects, symmetry requires that only half of the GNR
width be explored dictating ferromagnetic, FM, and anti-ferromagnetic, AFM, initial
states for each symmetry inequivalent defect site on each GNR simulated. The
presence of Fe breaks the magnetic symmetry (as Fe’s magnetic moment may
couple to the nearest edge), necessitating exploration of the full width of sites in the
case of AFM edge systems and two FM states, one where Fe and the edge states are
aligned and one where the Fe and edge states are anti-aligned. Particular attention
is paid to simulating the same relaxed structure in these different magnetic
configurations states so as to avoid the meta-stable states that are prolific in these
systems. Each relaxed structure was initialized with all symmetry inequivalent
AFM/FM orderings and re-relaxed with the most stable structure at these different
magnetic states to find the true ground state. Such a treatment was found to
generate lower energy structures vs. relaxing initial defect structures with given
initial magnetic orderings.
In agreement with previous studies4,5, it is found that the AFM ordering of
edge states in the undefected GNRs yields the lowest energy. Also, as found
3
previously6, the discrepancy in energies between the AFM and non-magnetic (and
FM) states becomes larger as the GNR width is increased.
SI References:
1
2
3
4
5
6
R. C. Longo, J. Carrete, J. Ferrer, and L. J. Gallego, Physical Review B 81 (11),
115418 (2010).
R.C. Longo, J. Carrete, and L.J. Gallego, Journal of Chemical Physics 134 (2),
024704 (2011).
R. C. Longo, J. Carrete, and L. J. Gallego, Physical Review B 83 (23), 235415
(2011).
De-en Jiang, Bobby G. Sumpter, and Sheng Dai, The Journal of Chemical
Physics 126 (13), 134701 (2007).
Erjun Kan, Hongjun Xiang, Fang Wu, Changhoon Lee, Jinlong Yang, and
Myung-Hwan Whangbo, Applied Physics Letters 96 (10), 102503 (2010).
L. Pisani, J. A. Chan, B. Montanari, and N. M. Harrison, Physical Review B 75
(6), 064418 (2007).
4