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Supplementary material: The atomic structures of the
adsorbed clusters on Cu (100) and Ni (111) surfaces and
the temperature and magnetic effects on the stabilities of
the clusters
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In the main manuscript, we discuss the relative stabilities of adsorbed Cn and CnHn
clusters on Cu (111), Cu (100), and Ni (111) surfaces for n=1, 2, 3, and 6. The atomic
structures of these clusters on Cu (111) surface are shown in Figure 1 of the main
manuscript. Here, atomic structures of the adsorbed Cn and CnHn clusters on Cu (100),
and Ni (111) surfaces are shown in Figure S1.
Our simulation results in the main manuscript are obtained by comparing the total
energies of various structures at temperature of 0K and with PBE functional. Here, we
discuss the influence of dispersion forces and finite temperature effects on our main
results, the role of H on assisting the formation of C6 ring structures. As shown in Figure
S2, after including dispersion forces (with optB88-vdW functional)
[1]
, the binding
between adsorbed clusters and metal surface will be enhanced about 0.1~0.2 eV per
carbon atom. But the relative stabilities between chain and ring structures are almost the
same. Then, the influence of finite temperature effects is also studied. The vibrational
contribution to free energy (Fvib) is calculated as Fvib=ZPE-TS, where ZPE is the zero
point energy of the adsorbed cluster, S is the vibrational entropy at finite temperature T.
We set T as 1000 K, and calculate the Fvib with PHON package [2]. As shown in Figure S3,
after considering the finite temperature effect at 1000K, our conclusion about the role of
H is still valid.
Metal Ni is ferromagnetic (FM) at low temperature and paramagnetic (PM) at high
temperature, with a Curie temperature of 611K. At the graphene growth temperature
(800~1400K), Ni is supposed to be PM. So our results in the main manuscript are based
on non-spin-polarized DFT calculations. Here, we discuss the influence of PM on the
relative stabilities of the adsorbed clusters on Ni surface. Constrained spin-polarized DFT
(SDFT) calculations are employed, with local magnetic moment of 0.5µB
[3]
. The
constrained total energy functional can be written as
∑ 𝐸̃ = 𝐸 + 𝐸𝑝 = 𝐸 + 𝜆 ∑𝑖(𝑠𝑖 − 𝑠𝑖0 )2 ,
where 𝐸 is the DFT energy, 𝐸𝑝 is the penalty energy, 𝑠𝑖 is the magnetic moment vector of
atom i, and 𝑠𝑖0 is the desired magnetic moment vector. We set 𝜆 as 10 [4]. The direction of
desired magnetic moments of each Ni atom is randomly determined. We take 3 sets of
magnetic snapshots, and calculate the formation energies of adsorbed C6 and C6H6 on
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Ni(111) surfaces. The results are shown in Figure S4, we can see that after considering
the effects of local magnetic moments of PM Ni, the binding energy between the cluster
and the metal surface increases less than 0.1eV per carbon atom; and the relative
stabilities between the C ring and chain structures are almost the same.
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Figure S1. Representative atomic structures of most stable -Cn and -CnHn clusters on (a) and (b) Cu (100) and (c) and
(d) Ni(111) surface. Light blue (green, brown, red) balls are Cu (Ni, C, H) atoms.
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Figure S2. The calculated formation energies (per carbon atom) of the most favored -C6Hx (x=0, 3, 5, 6) in ring or
chain structure on Cu(111) surface, with (a) PBE and (b) optB88-vdW functionals, respectively.
Figure S3. The calculated formation energies (per carbon atom) of the most favored -C6Hx (x=0, 3, 5, 6) in ring or
chain structure on Cu(111) surface are shown. The results without and with finite temperature effects (ZPE-TS) are
shown in (a) and (b), respectively.
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Figure S4. The calculated formation energies (per carbon atom) of the most favored -C6Hx (x=0 and 6) in ring or
chain structure on Ni(111) surface. The results from non-spin-polarized DFT calculations and constrained SDFT
calculations are shown in (a) and (b), respectively. For constrained SDFT calculations, 3 sets of magnetic snapshots are
considered.
References
1.
J. Klimeš, D. R. Bowler, and A. Michaelides, J. Phys.: Cond. Matt. 22, 022201 (2010).
2.
D. Alfe, Computer Physics Communications 180, 2622-2633 (2009)
3.
A. V. Ruban, S. Khmelevskyi, P. Mohn and B. Johansson , Phys. Rev. B 75, 054402 (2007).
4.
F. Körmann, P. W. Ma, S. L. Dudarev, et al., J. Phys.: Cond. Matt. , 28, 076002 (2016).
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