Supplementary information for
Electrochemical CO2 and CO Reduction on Metal-functionalized Porphyrin-like
Graphene
Vladimir Tripkovic, Marco Vanin, Mohammedreza Karamad, Mårten E.
Björketun, Karsten W. Jacobsen, Kristian S. Thygesen, and Jan Rossmeisl
Center for Atomic-scale Materials Design, Department of Physics,
Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
I.
CO2 AND CO CORRECTION
To arrive at the CO2 and CO corrections we have analyzed the same set of reactions as in the supplementary
material of ref. 18 in the paper, albeit using a somewhat different approach. We divided all the reactions into three
groups. First group included reactions that contained only CO2 , either free or within a more complex molecule such
as HCOOH or CH3 COOH. Similarly, the second group comprised all the reactions having CO. Finally, the third
group had both CO and CO2 . The first two groups were used to calculate CO2 and CO correction, while the third
group was used to check the accuracy of both corrections. The reactions in the three respective groups are listed below.
First group:
4H2 + CO2
CO2 + H2
3H2 + CO2
3H2 + CO2
10/3H2 + CO2
7/2H2 + CO2
3H2 + CO2
11/4H2 + CO2
2H2 + CO2
2H2 + CO2
→
→
→
→
→
→
→
→
→
→
CH4 + 2H2 O
HCOOH
CH3 OH + H2 O
1/2CH3 CH2 OH + 3/2H2 O
1/3C3 H8 + 2H2 O
1/2C2 H6 + 2H2 O
1/2C2 H4 + 2H2 O
1/4CH2 = CHCH = CH2 + 2H2 O
1/2CH3 COOH
1/2HCOOCH3 + H2 O
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
3H2 + CO
2H2 + CO
2H2 + CO
7/3H2 + CO
5/2H2 + CO
2H2 + CO
7/4H2 + CO
→
→
→
→
→
→
→
CH4 + H2 O
CH3 OH
1/2CH3 CH2 OH + 1/2H2 O
1/3C3 H8 + H2 O
1/2C2 H6 + H2 O
1/2C2 H4 + H2 O
1/4CH2 = CHCH = CH2 + H2 O
(11)
(12)
(13)
(14)
(15)
(16)
(17)
Second group:
Third group:
CO2 + H2
CO + H2 O
CO + H2
CO + H2
→
→
→
→
CO + H2 O
HCOOH
1/2CH3 COOH
1/2HCOOCH3
(18)
(19)
(20)
(21)
To get an estimate of the CO2 /CO correction, we have performed the sensitivity analysis on the reaction group 1
and 2. The results are shown in Fig. 1. The minimum in the diagram gives 0.43 eV correction for CO2 and 0.04 eV
for CO.
2
FIG. 1: The CO2 and CO enthalpy corrections obtained from the sensitivity analysis. The corrections are found in the minima
of the mean absolute error curves and amount to 0.43/0.04 eVs for CO2 (g)/CO(g).
The experimental, theoretical uncorrected, and theoretical corrected reaction enthalpies are listed in Tables I and
II, along with the absolute errors before and after the correction is applied.
As seen in Table I, the deduced
TABLE I: The first three columns denote the experimental reference enthalpies, theoretical calculated enthalpies and their
absolute differences, whilst the last two columns stand for the CO2 corrected theoretical values and the absolute differences
with respect to the reference values in the first column. All the values are given in eVs.
∆Href ∆Hunc abs error ∆Hcor abs error
-1.71 -1.27
0.44
-1.70
0.01
-0.55 -0.12
0.43
-0.55
0.00
-0.89 -0.45
0.44
-0.88
0.01
-1.30 -0.85
0.45
-1.28
0.02
-1.37 -0.94
0.43
-1.37
0.00
-0.66 -0.29
0.37
-0.72
0.06
-0.65 -0.25
0.40
-0.68
0.03
TABLE II: The first three columns denote the experimental reference enthalpies, theoretical calculated enthalpies and their
absolute differences, whilst the last two columns stand for the CO corrected theoretical values and the absolute differences with
respect to the reference values in the first column. All the values are given in eVs.
∆Href
-2.14
-0.98
-1.32
-1.72
-1.80
-1.09
-1.08
∆Hunc abs error
-2.09
0.05
-0.94
0.04
-1.26
0.06
-1.67
0.05
-1.76
0.04
-1.10
0.01
-1.07
0.01
∆Hcor abs error
-2.13
0.01
-0.98
0.00
-1.30
0.02
-1.71
0.01
-1.80
0.00
-1.14
0.05
-1.11
0.03
CO2 correction improves considerably the reaction enthalpies containing CO2 molecule. On the other hand, the CO
correction is very small and therefore, it can be neglected. The CO2 correction does not improve the reaction enthalpies
for the reactions in Table III, except for the first reduction reaction in which case the error reduces significantly. All
the other reactions have CO2 group within a more complex molecule. Hence, it is straightforward to conclude that
the CO2 correction holds only for the CO2 (g) and not when CO2 group forms part of larger assemblies, such as
HCOOCH3 or CH3 COOH.
In Fig. 2 we show the most stable spin states for the clean metal-poprhyrins and when different intermediates are
adsorbed on the central metal atoms. We considered 4 different spin states 0,1,2 and 3 such that for the metals that
3
TABLE III: The first three columns denote the experimental reference enthalpies, theoretical calculated enthalpies and their
absolute differences, whilst the last two columns stand for the CO2 corrected theoretical values and the absolute differences
with respect to the reference values in the first column. All the values are given in eVs.
∆Href
0.43
-0.27
-1.10
-0.60
∆Hunc abs error
0.82
0.39
-0.49
0.22
-1.13
0.03
-0.79
0.19
∆Hcor abs error
0.39
0.04
-0.06
0.21
-0.70
0.40
-0.36
0.24
have one unpaired electron we performed calculations for spin 1 and 3 and for the metals with no unpaired electrons
we used spin 0 and 2. For the states with the adsorbed reaction intermediates we inferred the spin states by looking
at how many bonds a species makes to the porphyrine metal atom. For instance CHO∗ has one free bond which
adds one extra electron to the metal atom and hence, the spin should become opposite to the spin value on the clean
metal-funcionalized porphyrine-like graphene. The computed binding energies are compiled in Table. 3. For all the
species that contain the OH group, a correction of 0.3 eV for solvation effects was used.
FIG. 2: The most stable spin states used for different intermediates.
We have performed detailed density of states (DOS) analysis in this study. The total DOS, the projected density
of states onto the d states of the d metals and the distribution of the intermediates’ molecular states are summarized
in Figs. 4, 5 and 6. Additionaly, we have also analyzed using the same means the bonding of different intermediates
on Rh-porphyrin - the best catalyst we have found (see Fig. 7).
From Fig. 4 it is obvious that there are always occupied states at the Fermi level available to donate the charge
needed for reduction. From Fig. 5 we see that different intermediates, especially the C species are isoelectronic. Fig.
7 shows that the intermediates bind in a similar way to the metal atom - the peaks are located at nearly the same
positions. This is the reason why the binding energies will change similarly regardless of the Exchange-Correlation
Functional. The observation that they have virtually the same electronic structure with the HOMO level close to
the Fermi level explains why the slopes of the scaling relations in Figure 4 in the paper are all close to 1.0. If more
electrons were exchanged than the slope would have a value other than 1. The second observation that the peaks are
not broadened much is an indication of weak interactions, much weaker than in metals, which can be also ascertained
by comparing the respective binding energies.
4
FIG. 3: Free energy values of different intermediates. All energies are given in eVs.
5
FIG. 4: Total density of states.
6
:
FIG. 5: Projected density of states onto the d-orbitals of the d-metals in the porphyrin ring.
7
FIG. 6: Molecular density of states for different intermediates.
8
FIG. 7: Projected density of states on Rh d orbitals for the bare Rh-porphyrin and Rh-porphyrin with different intermediates.