Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is © the Owner Societies 2017
Atomic adsorption on graphene with a single vacancy: systematic DFT study through the Periodic Table of Elements Igor A. Pašti1, Aleksandar Jovanović1,2, Ana S. Dobrota1, Slavko V. Mentus1,3, Börje Johansson4, Natalia V. Skorodumova4,5 1University
of Belgrade – Faculty of Physical Chemistry, Studentski trg 12-16, 11158 Belgrade,
Serbia 2CEST
Kompetenzzentrum für elektrochemische Oberflächentechnologie GmbH, Viktor-Kaplan-
strasse 2, Section A, 2700 Wiener Neustadt, Austria 3Serbian
Academy of Sciences and Arts, Knez Mihajlova 35, 11000 Belgrade, Serbia
4Department 5Department
of Physics and Astronomy, Uppsala University, Box 516, 751 20 Uppsala, Sweden of Materials Science and Engineering, School of Industrial Engineering and
Management, KTH - Royal Institute of Technology, Brinellvägen 23, 100 44 Stockholm, Sweden
*corresponding author: Dr. Igor A. Pašti, associate professor University of Belgrade, Faculty of Physical Chemistry Studentski trg 12−16, 11158 Belgrade, Serbia e-mail:
[email protected] Phone: +381 11 3336 625 Fax: +381 11 2187 133
1. Electronic structure of SV-graphene system
Figure S1. DOS plots for SV-graphene (thick line) superimposed on DOS of pristine graphene (shaded area) using designated computational schemes.
2. Bonding of elements from different parts of the PTE at the SV site of graphene
Figure S2. Some examples of the ground state geometries obtained using PBE and PBE+D2. Carbon atoms are blue, while designated impurity atoms are given in different colors.
Table S1. Calculated distances of atoms adsorbed at SV−graphene from the graphene plane (in Å) H
He
element PBE PBE+D2 PBE+D3 vdW−DF2
0.023 0.023 0.026 0.284
Li
Be
1.687 1.730 1.690 1.583
0.842 0.856 0.855 0.798
3.274 3.038 3.037 2.988
B 0.043 0.047 0.033 0.028
C
N
O
F
0.000 0.000 0.000 0.000
0.010 0.009 0.010 0.006
0.315 0.316 0.316 0.327
1.654 1.655 1.653 1.542
Ne 2.877 2.705 2.763 2.782
Na
Mg
Al
Si
P
S
Cl
Ar
2.142 2.112 2.169 2.160
1.754 1.741 1.757 1.797
1.388 1.391 1.391 1.390
1.167 1.169 1.186 1.186
1.153 1.164 1.164 1.191
1.063 1.073 1.073 1.073
2.136 2.139 2.135 2.170
3.359 3.145 3.192 3.191
K
Ca
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
Ga
Ge
As
Se
Br
Kr
2.491 2.436 2.528 2.503
1.974 1.952 1.986 2.063
1.735 1.742 1.744 1.787
1.474 1.481 1.484 1.519
1.399 1.418 1.419 1.465
1.359 1.382 1.375 1.427
1.293 1.297 1.297 1.327
1.222 1.238 1.222 1.254
1.179 1.189 1.182 1.226
1.192 1.195 1.195 1.236
1.289 1.303 1.293 1.388
1.445 1.456 1.439 1.606
1.372 1.379 1.375 1.48
1.427 1.436 1.434 1.542
1.458 1.458 1.464 1.524
1.345 1.355 1.355 1.381
2.320 2.321 2.331 2.361
3.710 3.304 3.362 3.380
Rb
Sr
Y
Zr
Nb
Mo
Tc
Ru
Rh
Pd
Ag
Cd
In
Sn
Sb
Te
I
2.641 2.56 2.679 2.661
2.135 2.107 2.151 2.252
1.939 1.940 1.950 1.997
1.704 1.719 1.718 1.773
1.62 1.634 1.63 1.68
1.578 1.592 1.587 1.637
1.514 1.521 1.510 1.571
1.464 1.476 1.476 1.548
1.460 1.439 1.439 1.520
1.447 1.459 1.454 1.535
1.746 1.763 1.763 2.033
2.432 2.353 2.609 3.314
2.107 2.103 2.135 2.268
1.931 1.939 1.936 1.996
1.819 1.856 1.853 1.863
1.694 1.696 1.694 1.731
2.540 2.528 2.544 2.627
Xe 3.657 3.170 3.347 3.178
Cs
Ba
La
Hf
Ta
W
Re
Os
Ir
Pt
Au
Hg
Tl
Pb
Bi
Po
At
Rn
2.788 2.532 2.808 2.815
2.269 2.203 2.278 2.373
2.029 2.029 2.038 2.115
1.665 1.669 1.665 1.721
1.588 1.601 1.595 1.655
1.584 1.587 1.585 1.617
1.540 1.556 1.546 1.585
1.512 1.517 1.517 1.554
1.486 1.488 1.486 1.528
1.467 1.482 1.482 1.526
1.637 1.659 1.648 1.817
3.483 2.855 2.998 3.315
2.436 2.435 2.552 2.501
2.128 2.132 2.131 2.192
1.979 1.987 1.983 2.035
1.845 1.858 1.845 1.902
2.652 2.646 2.647 2.741
3.637 3.284 3.385 3.454
3. Adsorption energies at the single vacancy at graphene sheet
Table S2. Calculated adsorption energies of atoms in PTE on SV−graphene (in eV). H
Li
He
element PBE PBE+D2 PBE+D3 vdW−DF2
−3.29 −3.37 −3.33 −3.41
−0.01 −0.02 −0.03 −0.02
Be
B
C
−2.65
−6.17
−12.91
−15.60
−2.94
−6.30
−13.04
−15.70
−2.72 −2.59
−6.23 −6.29
−12.96 −11.76
−15.64 −15.60
N
O
−12.0 2 −12.1 1 −12.0 7 −9.51
F
Ne
−7.77
−4.55
nb
−7.85
−4.67
−0.04
−7.83 −5.41
−4.62 −2.43
−0.03 −0.04
Na
Mg
Al
Si
P
S
Cl
Ar
−1.88 −2.20 −2.00 −1.74
−1.70 −1.98 −1.80 −1.40
−5.15 −5.37 −5.23 −4.75
−8.21 −8.38 −8.28 −7.62
−8.31 −8.47 −8.41 −7.70
−7.13 −7.27 −7.25 −6.08
−2.85 −3.03 −3.01 −2.51
−0.00 −0.08 −0.09 −0.08
K
Ca
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
Ga
Ge
As
Se
Br
Kr
−2.09 −2.36 −2.22 −1.92
−3.18 −3.50 −3.27 −2.78
−6.48 −6.77 −6.59 −5.89
−8.03 −8.30 −8.14 −7.22
−7.27 −7.54 −7.38 −6.87
−6.16 −6.42 −6.28 −5.95
−6.18 −6.43 −6.31 −5.56
−7.10 −7.35 −7.23 −6.32
−7.68 −7.92 −7.79 −6.64
−6.64 −6.89 −6.78 −5.72
−3.61 −3.87 −3.75 −2.89
−1.05 −1.32 −1.18 −0.30
−3.96 −4.24 −4.07 −3.08
−6.30 −6.54 −6.39 −5.59
−6.62 −6.84 −6.74 −6.04
−5.60 −5.79 −5.74 −4.61
−2.20 −2.43 −2.39 −1.89
−0.01 −0.12 −0.12 −0.13
Rb
Sr
Y
Zr
Nb
Mo
Tc
Ru
Rh
Pd
Ag
Cd
In
Sn
Sb
Te
I
Xe
−2.06 −2.41 −2.23 −1.88
−2.83 −3.23 −2.93 −2.39
−6.21 −6.60 −6.32 −5.57
−8.34 −8.71 −8.45 −7.51
−8.15 −8.52 −8.26 −7.74
−7.29 −7.65 −7.43 −6.93
−8.26 −8.61 −8.47 −7.31
−8.81 −9.16 −8.99 −7.67
−8.34 −8.69 −8.49 −7.05
−5.27 −5.62 −5.44 −4.30
−1.72 −2.11 −1.89 −1.28
−0.10 −0.47 −0.34 −0.19
−2.12 −2.58 −2.28 −1.94
−4.28 −4.64 −4.39 −3.96
−4.98 −5.29 −5.01 −4.72
−4.24 −4.51 −4.42 −3.41
−1.67 −1.97 −1.89 −1.44
−0.03 −0.15 −0.16 −0.11
Cs
Ba
La
Hf
Ta
W
Re
Os
Ir
Pt
Au
Hg
Tl
Pb
Bi
Po
At
Rn
−2.20 −3.33 −2.37 −2.01
−3.38 −4.39 −3.49 −2.90
−6.70 −7.62 −6.81 −5.98
−8.60 −9.17 −8.71 −7.64
−8.99 −9.50 −9.13 −7.92
−8.52 −9.03 −8.72 −8.00
−8.13 −8.63 −8.37 −7.31
−9.29 −9.79 −9.53 −8.03
−9.28 −9.77 −9.45 −7.67
−7.08 −7.57 −7.34 −6.02
−2.40 −2.93 −2.60 −1.80
−0.03 −0.40 −0.29 −0.19
−2.12 −2.50 −2.38 −1.96
−3.31 −3.69 −3.46 −3.10
−4.06 −4.46 −4.19 −3.83
−3.38 −3.68 −3.58 −2.56
−1.41 −1.77 −1.67 −1.22
−0.00 −0.24 −0.18 −0.15
4. Magnetic properties of A@SV-graphene systems
The magnetic properties of M@SV-graphene systems are given in Table S3. The applied computational schemes agree well considering predicted magnetic moments. However, this property is rather sensitive to the computational treatment and it has been shown for the case of Fe that the use of DFT+U gives rise to a magnetic ground state which is not the case with PBE and, as we show, vdW-DF2.1 For a detailed analysis of bonding in the case of Fe, which can be further translated to the cases of Ru and Os, the reader is referred to ref. (1). However, in spite the problems in prediction of magnetism in M@SV-graphene systems associated with PBE, it can be concluded that the adsorption of foreign atoms into SV site alters magnetic properties of SV-graphene to a great extent. Our results suggest that large fraction of considered atoms results with non-magnetic ground states, while some elements (alkaline and earth alkaline metals, elements in the middle of the d-block, metals in groups 11 and 12) give magnetic systems with appreciable magnetic moments.
Table 3. Ground state magnetizations of A@v−G systems (in Bohr magnetons, μB). H
He
element PBE PBE+D2 PBE+D3 vdW−DF2
2.74 2.74 2.74 2.48
1.36 1.36 1.36 1.38
Li
Be
B
C
N
O
F
Ne
0.82 0.82 0.82 2.20
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
1.36 1.37 1.36 1.38
Na
Mg
Al
Si
P
S
Cl
Ar
0.98 0.98 0.98 0.98
1.94 1.94 1.94 1.89
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.01 0.00 0.00 0.39
1.36 1.37 1.37 1.45
K
Ca
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
Ga
Ge
As
Se
Br
Kr
1.00 1.00 1.00 0.99
1.89 1.9 1.89 1.82
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
1.01 1.01 1.01 1.01
2.01 2.02 2.01 2.05
2.84 2.83 2.84 2.76
0.00 0.00 0.00 0.00
0.28 0.28 0.28 0.00
0.00 0.00 0.00 0.00
0.87 0.77 0.93 0.94
1.00 1.18 1.12 1.78
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
1.36 1.37 1.37 1.38
Rb
Sr
Y
Zr
Nb
Mo
Tc
Ru
Rh
Pd
Ag
Cd
In
Sn
Sb
Te
I
Xe
1.00 1.00 1.00 1.00
1.96 1.96 1.96 1.93
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.97 0.97 0.97 0.97
1.98 1.98 1.98 1.99
0.94 0.94 0.93 0.95
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
1.02 1.00 1.00 0.95
1.69 1.72 1.50 1.31
2.33 2.34 2.30 2.22
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.02 0.07 0.15 0.60
1.37 1.42 1.39 1.41
Cs
Ba
La
Hf
Ta
W
Re
Os
Ir
Pt
Au
Hg
Tl
Pb
Bi
Po
At
Rn
1.00 1.00 1.00 1.00
1.97 1.98 1.96 1.94
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.75 0.77 0.76 0.63
1.97 1.97 1.97 1.99
0.94 0.93 0.94 1.02
0.00 0.00 0.00 0.00
0.71 0.71 0.71 0.00
0.00 0.00 0.00 0.00
1.00 1.00 1.00 0.59
1.34 1.40 1.38 1.35
0.81 0.80 0.82 0.77
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.37 0.36 0.41 0.71
1.37 1.41 1.40 1.46
An interesting situation is seen in the case of adsorption of noble gases. In all cases we observe magnetism which is in magnitude very close to that of the pure SV-graphene substrate. For this reason we checked spin polarization in these systems (see a representative picture in Fig. S3) and confirmed that the magnetism is due to the vacancy itself. Due to very weak interactions of noble gases with the vacancy it is almost unaffected compared to the pure SV-graphene.
Figure S3. Distribution of spin polarization (ρspin up – ρspin down) for the ground states of Ar at graphene single vacancy calculated at the PBE level (the isovalues are ±0.006 e Å−3).
5. Correlation of adsorption energies
Figure S4. Correlation between the calculated adsorption energies of investigated elements on pristine graphene and SV-graphene, for the four methods applied.
6. Dissolution potentials of metals from the SV site of graphene We have calculated electrode potentials for the reaction Mz+ + SV-graphene + ze− → M@SV-graphene
(S1)
o denoted hereafter as E M z /M@SV -graphene . The potentials were calculated on the basis of the standard
electrode potential ( E Mo z /M ) for the reaction: Mz+ + ze− → M(s)
(S2)
assuming a galvanic cell where anode is made of pure metal M and the cathode is made of SVgraphene, where the half-reaction is given by Eq. (S1). Activity of Mz+ ions is assumed to be one. Assuming that there are no volume changes during the reaction and that the entropy contribution o can be disregarded, E M z /M@SV -graphene is given by:
E Mo z /M@SV -graphene E Mo z /M
E ads E coh zF
(S3)
In the above equation F if Faraday constant while Eads and Ecoh should be expressed in [J mol−1] The calculated potentials (Table S4) are referred to the Standard Hydrogen Electrode (SHE) at 25°C. o Table S4. Calculated values of E M z /M@SV -graphene for the four methods applied. Where the half-
reaction (S2) can take place with different z we always took the most negative E Mo z /M . Elements are assembled as they appear in the groups of the PTE, with the increasing atomic number. E Mo z /M@SV -graphene / V metal Li Na K Rb Cs Be Mg Ca Sr Ba Sc Y
E Mo z /M / V −3.0401 −2.71 −2.931 −2.98 −3.206 −1.847 −2.372 −2.868 −2.889 −2.912 −2.077 −2.372
z 1 1 1 1 1 2 2 2 2 2 3 3
PBE −2.02 −1.94 −1.78 −1.77 −1.81 −0.42 −2.28 −2.20 −2.33 −2.17 −1.22 −1.76
PBE+D2 −1.73 −1.62 −1.51 −1.42 −0.68 −0.36 −2.14 −2.04 −2.13 −1.67 −1.12 −1.63
PBE+D3 −1.95 −1.82 −1.65 −1.60 −1.64 −0.39 −2.23 −2.15 −2.28 −2.12 −1.18 −1.72
vdW-DF2 −2.08 −1.82 −1.95 −1.95 −2.00 −0.36 −2.43 −2.40 −2.55 −2.41 −1.41 −1.97
La Ti Zr Hf V Nb Ta Cr Mo W Mn Tc Re Fe Ru Os Co Rh Ir Ni Pd Pt Cu Ag Au Zn Cd Hg Al Ga In Tl Sn Pb As Sb Bi Te Po
−2.379 −1.63 −1.45 −1.55 −1.13 −1.099 −0.60 −0.74 no data no data −1.185 no data 0.30 −0.44 0.60 no data −0.28 0.76 no data −0.25 0.915 1.188 0.337 0.7996 1.52 −0.7618 −0.40 0.85 −1.662 −0.53 −0.34 −0.34 −0.13 −0.126 no data no data 0.308 −0.9 no data
3 2 4 4 2 3 3 3
−1.64 −0.04 −0.93 −1.01 −0.15 −0.91 −0.30 −0.05
−1.33 0.10 −0.84 −0.87 −0.01 −0.78 −0.13 0.03
−1.60 0.02 −0.90 −0.98 −0.10 −0.87 −0.26 −0.01
−1.88 −0.45 −1.14 −1.25 −0.35 −1.04 −0.66 −0.12
2
0.45
0.57
0.51
0.14
3 2 3
0.33 0.97 1.29
0.50 1.10 1.41
0.41 1.04 1.35
0.06 0.58 0.91
2 3
1.37 1.62
1.49 1.74
1.42 1.67
0.85 1.19
2 2 2 2 1 3 2 2 2 3 3 3 1 2 2
0.85 1.61 1.81 0.40 −0.43 1.26 −0.91 −0.93 0.53 −1.08 −0.15 −0.47 −0.10 0.44 0.51
0.98 1.78 2.05 0.53 −0.04 1.44 −0.78 −0.75 0.72 −1.00 −0.05 −0.32 0.28 0.62 0.70
0.92 1.69 1.94 0.47 −0.26 1.33 −0.85 −0.81 0.66 −1.05 −0.11 −0.42 0.16 0.50 0.59
0.39 1.12 1.28 0.04 −0.87 1.06 −1.29 −0.89 0.61 −1.21 −0.44 −0.53 −0.26 0.28 0.41
3 2
0.93 0.13
1.07 0.26
0.98 0.22
0.86 −0.29
Supplementary references 1
E. J. G. Santos, A. Ayuela, D. Sanchez-Portal, New J. Phys., 2009, 12, 53012.
