Supporting Information Ab Initio Approach for Prediction of Oxide ...
Supporting Information Ab Initio Approach for Prediction of Oxide Surface Structure, Stoichiometry, and Electrocatalytic Activity in Aqueous Solution Xi Rong and Alexie M. Kolpak* Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States Corresponding Author *[email protected]
Determination of vacancy formation energy, As shown by Fig.1, the formation of surface A vacancy can be broken down into two steps. In the first step, the removal of a neutral atom of A from the surface leads to a change in free energy: (S1) and
where
are the free energies of the reference and reconstructed surfaces,
respectively, and
is the chemical potential of species A. In the second step, A reacts with
protons, electrons, and/or water molecules to form a solvated ion,
, the identity of which
depends on the environmental condition, as discussed below. (S2) Thus the free energy of the second step is: (S3) is the chemical potential of
where
,
and
are the number and chemical
potential of species i, and i = H2O, H+, and e−. The total free energy of formation for the surface reconstruction is therefore: (S4) It can be seen that A is the intermediate product from the reference surface to the reconstructed surface along with the solvated ion, This enables us to determine without affecting the value of
and
relative to
. Therefore,
is independent of
at standard temperature and pressure,
. The standard state of the metal atom is the respective bulk
metal at 25°C, while oxygen atoms are referred to O2(g) at 25°C and 1atm. Due to the overbinding of O2(g) within DFT1, we in practice express the latter such that the chemical potential of oxygen is the difference between the chemical potential of H2O(l) and H2(g) at 25°C and 1atm2. Under the above setup,
is computed directly from DFT with respect to the standard
state of A by approximating the free energy of solids by the DFT total energy3, and computing corrections for the zero-point energy and vibrational entropy for gas phase species and surface adsorbates . Our DFT calculations show that the corrections of the same adsorbate on different
.
surfaces are close to each other; thus, we use the values on the ideal MnO2 termination for all the considered surfaces in this work. As commonly practiced, H2O(l) at 25°C and 1atm is considered to be in equilibrium with H2O(g) at 25°C and 0.03 atm2; thus, the standard chemical potential of H2O(l) is equivalent to the DFT total energy of H2O(g) together with corrections for the zero-point energy (ZPE) and entropy4 at 25°C and 0.03 atm. All corrections relative to the DFT total energy are summarized in Table S1. Table S1. Corrections for zero-point energy and entropy at room temperature (ZPE-TS)/eV H2O(g)
0.10
H2(g)
-0.13
-O adsorbate
0.01
-OH adsorbate
0.23
-OOH adsorbate
0.15
is computed relative to the standard state of A by using the standard hydrogen electrode (SHE) as reference. At SHE, protons and electrons are in equilibrium with hydrogen gas at , ion concentration
standard state when electrode potential °
, and
. °
°
where
°
,
°
,
, and
°
°
(S5)
are the standard chemical potentials of hydrogen gas, proton, and
electron respectively. Under operational condition, we can correlate the chemical potentials of species in Eq.S3 to their standard states by °
(S6) °
(S7) °
(S8) °
Substitution of the above equations into Eq.S3 gives
(S9)
°
where
°
(S10)
is the standard hydrogen electrode free energy per A obtained from experiments5,
and the expression is
°
lists expressions of
for LaMnO3 component-related ion species at room temperature.
Table S2. A
°
°
°
°
. Based on Eq.S10, Table S2
of LaMnO3 component-related ion species at T= 25°C
Aqueous species
/eV5
/eV
Mn2+ Mn(OH)+ Mn(OH)2 HMnO2− Mn
Mn3O4 Mn2O3 MnO2 MnO42− MnO4−
La
La3+ La2O3
O
H 2O
[H2O(l)/H2(g) as reference]
H 2O
[O2(g) as reference]
Formation energy of surface reconstruction: a general form Similar to vacancy formation, the mechanism of atomic adsorption is the process of the electrochemical formation of a neutral atom from the most stable ion species, followed by the adsorption of the atom on surface. Other more complicated surface reconstructions such as change of orientation and termination, and presence of steps and kinks can be constructed as a series of process involving loss and adsorption of atoms from a reference surface to form a new surface, since the change of Gibbs free energy is independent of mechanism. The general equation for the reconstruction formation is therefore given by the formation energy with respect
to the standard state of the exchanged atom and the electrochemical reaction free energy with respect to SHE, as shown in Eq.S11, where
, the number of exchanged atoms, is positive for
vacancy formation and negative for adsorption. °
(S11)
Equilibrium condition of bulk/surface/solvents for LaMnO3 By comparing values of
in Table S2 as a function of USHE and pH, we generate Pourbaix
diagrams of La and Mn in aqueous solution, as shown by Fig.S1a and 1b respectively. The Pourbaix diagrams are identical to Ref 7.
Figure S1. Computed Pourbaix diagrams for La (left side) and Mn (right side) in aqueous solution; concentrations of neutral and charged ions are fixed at 1 and 10-6 M, respectively. Under the equilibrium condition of LaMnO3 in aqueous solution, the formation energy of bulk LaMnO3 is zero with respect to the most stable component-related ions in Fig. S1. (S12) where
is free energy change from the standard state of i (La ,Mn or O) to the most stable
solvated ions, as shown in Table S2, and
is the formation energy of LaMnO3 from the
standard state of i, which is obtained from experiments6. As shown by Fig. S2, the dashed lines represent the equilibrium conditions of LaMnO3 with the concentration of charged solvated ions varying from 10-6 to 10-12 M. The area bounded
by the lines is the stable bulk region, in which the formation of LaMnO3 from the solvated ions is spontaneous. For simplicity, the phase diagram and boundaries in Fig.4 are determined assuming 10-6 M concentration of charged ion species, as typical in Pourbaix diagrams7. While varying the concentration from 10-6 to 10-12 causes Mn vacancies in the surface to become favorable at lower URHE and decreases the bulk stability region, we find that it does not qualitatively affect the results.
Figure S2. LaMnO3 bulk stability region for different molar concentrations (indicated by the red numbers) of solvated species.
DFT Computational details Calculations are performed using VASP8 with PAW pseudopotentials9 and the RPBE-GGA10 functional. An energy cutoff of 500 eV and a 2x2x1 k-point mesh are used for all calculations. Supercells are composed of 7-atomic-layer-thick slabs separated by ~20 Å of vacuum perpendicular to the surface to prevent spurious interactions due to periodic boundary conditions. A (2×2) in-plane supercell is employed (see Fig. 2). Structures are relaxed until forces on each atom are less than 10-4 eV/Å. Our computed value of the lattice constant is 5.56x5.67x7.77 Å, compared to the experimental value of 5.54x5.70x7.72 Å11. Using the total DFT energy of O2 from the tabulated formation enthalpy of water and DFT energies of H2O(g) and H2(g)12, we find that the formation energies of LaMnO3 and MnxOy are in good agreement with experiments13-14 (< 6% error), providing sufficient accuracy in the calculation of free energies.
We consider only [001] surfaces, as these are observed experimentally. Along the (001) direction, LaMnO3 consists of alternaing LaO and MnO2 atomic phalnes, with nominal charges of +1 and -1, respectively. Both polar and non-polar slabs can therefore be constrcuted. However, as polar fields are energetically costly, they are likely compensated in realistic catalyst systems15; thus we consider only non-polar slabs. Figure S3 shows the optimized supercell of ideal MnO2 terminated surface.
Figure S3. Optimized supercell of ideal MnO2 terminated surface
Considered surfaces in this paper We compute the total Gibbs free energy of a range of possible reconstructed surfaces derived from the ideal MnO2 and LaO (001) terminations, including various combinations and concentrations of oxygen vacancy, cation vacancies, cation adsorbates, as summarized in the Fig. S4. We then consider OER/ORR intermediates (i.e., -OH, -O, and –OOH adsorbates) on these surfaces at different coverages, as listed in Table S3. Finally, the formation energies of all the considered surfaces are determined with respect to the ideal MnO 2 terminated surface in Fig. S3 and solvated ions by the developed method.
Figure S4. Top-down view of optimized surface structures, without OER/ORR intermediates considered in this work Our DFT results show that the stable attachable site for intermediates is atop of Mn for MnO2 termination, and bridge of La-La for LaO termination. For each bare surface in Fig. S4, the adsoprtion enthalpies per site EO, EOH, EOOH of –O, -OH, and –OOH, repectively, are calculated with respect to the total energies of H2O(g) and H2(g) from DFT2.
Table S3. Summary of considered coverage and the corresponding adsorption enthalpies per site for the surfaces in Fig. S4; * represents the adsorption site adjacent to the vacancy, while # represents that diagonal to the vacancy Surface
Coverage
EO/eV
EOH/eV
EOOH/eV
1.
¼
1.83
0.57
3.78
½
1.89
0.53
3.77
¾
1.86
0.54
3.68
1
1.74
0.52
3.66
2.
¼*
1.24
-0.01
3.40
3.
¼#
1.18
0.22
3.38
¼*
1.90
0.31
3.59
¾
1.42
0.25
3.45
¼
0.90
0.01
3.25
½
1.06
0.02
3.29
7.
½
1.30
0.43
3.64
9.
¼
1.35
0.36
3.60
½
1.28
0.35
3.61
12.
¼
0.99
0.20
3.35
13.
¼
0.28
-
-
14.
¼
1.15
-0.23
3.16
15.
¼
-0.39
-0.97
4.31
½
-
-1.03
-
1
-
-0.64
-
¼
1.63
0.00
-
½
-
-0.04
-
1
-
0.22
-
4.
16.
Figure S5. Top-down view of optimized surface structures of R1, R2, R3 and R4 in Fig. 4
Thermodynamic equivalent aqueous condition to T=1100K and
atm in
atmosphere At standard condition (T=25°C,
atm,
atm), the Gibbs free energy change for 5
H2(g)+O2(g)=H2O(l) is 1.23 per electron transfer , namely URHE=1.23V. At T=1100K and atm, the relative chemical potential of O2(g) to its standard state is -1.73eV per molecule from the ideal gas approximation,
. This shifts URHE to 0.80V (1.23-
1.73/4=0.80V) if the change of chemical potential is attributed to shift of URHE.
Reaction mechanisms of OER and ORR
Figure S6. OER and ORR on the MnO2 termination with ¼ ML [Mn]vac. All other surfaces follow the same reaction mechanism, in which intermediates of –OH, –O, –OOH are involved and located atop of Mn atoms. All the geometries of surfaces shown in the figure are optimized. and
are the Gibbs formation energies of reaction steps based on Ref 2.
Identification of active sites and the corresponding ϕ for Fig. 5 For each stable surface, we calculate the value of ϕ for each distinguishable reaction site and for site concentrations of ¼ to 1 ML. The sites that give the lowest values of ϕ are taken as the current dominating sites and used to plot ϕ as a function of USHE and pH in Figs. 5b and 5d. Our DFT results show that adsorption strength on the surfaces of A0, A1, R1, R2, R3, R4, which have geometrically identical Mn in the surface, is little affected by the locations of active sites and number of coverage. For B2, however, adsorption strength adjacent to the Mn vacancy site is stronger than that diagonal to the vacancy. This is because the farther of Mn away from the vacancy, the less influence of its electronic structure exhibits, as shown by the d orbital band centers in Fig. S7. Due to comparatively large ϕ of the adjacent site, we plot ϕ of the diagonal site, which gives 0.2V smaller OER overpotential than the ideal MnO2 termination.
Thus,
consideration of realistic surface structure under operational condition can reduce the discrepancy between overpotentials predicted by DFT and experiments.
Correlation between the atomic and electronic structure
Figure S7. d orbital band center of cation relative to the Fermi level in the surface layer without intermediate adsorbates as a function of: (a) O:Mn stoichiometry in the surface, (b) –O adsorption energy, and (c) –OH adsorption energy. * represents the adsorption site adjacent to the vacancy, while # represents that diagonal to the vacancy. It can seen that the increased O:Mn ratio in the surface layer decreases d orbital occupation on the remaining Mn sites, thereby increasing adsorption strength of –O, -OH, and –OOH.
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
Wang, L.; Maxisch, T.; Ceder, G. Oxidation Energies of Transition Metal Oxides within the GGA+U Framework. Phys. Rev. B 2006, 73, 6. Man, I. C.; Su, H. Y.; Calle-Vallejo, F.; Hansen, H. A.; Martinez, J. I.; Inoglu, N. G.; Kitchin, J.; Jaramillo, T. F.; Norskov, J. K.; Rossmeisl, J. Universality in Oxygen Evolution Electrocatalysis on Oxide Surfaces. ChemCatChem 2011, 3, 1159-1165. Kotomin, E. A.; Mastrikov, Y. A.; Heifets, E.; Maier, J. Adsorption of Atomic and Molecular Oxygen on the LaMnO3(001) Surface: Ab Initio Supercell Calculations and Thermodynamics. Phys. Chem. Chem. Phys. 2008, 10, 4644-4649. Assael, M. J.; Trusler, J. P. M.; Tsolakis, T. F. Thermophysical Properties of Fluids: An Introduction to Their Prediction; Imperial College Press: London, U.K.; 1996. Wagman, D. D. E., W.H.; Halow, I.; Parker, V.B.; Bailey, S.M.; Schumm, R.H. Selected Values of Chemical Thermodynamic Properties; National Bureau of Standards: Washington, U.S.A.; 1968-1971. Jacob, K. T.; Attaluri, M. Refinement of Thermodynamic Data for LaMnO3. J. Mater. Chem. 2003, 13, 934-942. Pourbaix, M. Atlas of Electrochemical Equilibria in Aqueous Solutions; National Association of Corrosion Engineers: Houston, U.S.A.; 1974. Kresse, G.; Furthmuller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169-11186. Blochl, P. E. Projector Augmented-Wave Method. Phys. Rev. B 1994, 50, 17953-17979. Hammer, B.; Hansen, L. B.; Norskov, J. K. Improved Adsorption Energetics within Density-Functional Theory Using Revised Perdew-Burke-Ernzerhof Functionals. Phys. Rev. B 1999, 59, 7413-7421. Norby, P.; Andersen, I. K.; Andersen, E. K.; Andersen, N. The Crystal Structure of Lanthanum Manganate (III), LaMnO3, at Room Temperature and at 1273 K under N2. J. Solid State Chem. 1995, 119, 191-196. Martinez, J. I.; Hansen, H. A.; Rossmeisl, J.; Nørskov, J. K. Formation Energies of Rutile Metal Dioxides Using Density Functional Theory. Phys. Rev. B 2009, 79, 045120. Jacob, K.; Attaluri, M. Refinement of Thermodynamic Data for LaMnO3. J. Mater. Chem. 2003, 13, 934-942. Jacob, K.; Kumar, A.; Rajitha, G.; Waseda, Y. Thermodynamic Data for Mn3O4, Mn2O3 and MnO2. High Temp. Mater. Processes (London) 2011, 30, 459-472. Noguera, C. Physics and Chemistry at Oxide Surfaces; Cambridge University Press: Cambridge, U.K.; 1996.
Determination of vacancy formation energy, As shown by Fig.1, the formation of surface A vacancy can be broken down into two steps. In the first step, the removal of a neutral atom of A from the surface leads to a change in free energy: (S1) and
where
are the free energies of the reference and reconstructed surfaces,
respectively, and
is the chemical potential of species A. In the second step, A reacts with
protons, electrons, and/or water molecules to form a solvated ion,
, the identity of which
depends on the environmental condition, as discussed below. (S2) Thus the free energy of the second step is: (S3) is the chemical potential of
where
,
and
are the number and chemical
potential of species i, and i = H2O, H+, and e−. The total free energy of formation for the surface reconstruction is therefore: (S4) It can be seen that A is the intermediate product from the reference surface to the reconstructed surface along with the solvated ion, This enables us to determine without affecting the value of
and
relative to
. Therefore,
is independent of
at standard temperature and pressure,
. The standard state of the metal atom is the respective bulk
metal at 25°C, while oxygen atoms are referred to O2(g) at 25°C and 1atm. Due to the overbinding of O2(g) within DFT1, we in practice express the latter such that the chemical potential of oxygen is the difference between the chemical potential of H2O(l) and H2(g) at 25°C and 1atm2. Under the above setup,
is computed directly from DFT with respect to the standard
state of A by approximating the free energy of solids by the DFT total energy3, and computing corrections for the zero-point energy and vibrational entropy for gas phase species and surface adsorbates . Our DFT calculations show that the corrections of the same adsorbate on different
.
surfaces are close to each other; thus, we use the values on the ideal MnO2 termination for all the considered surfaces in this work. As commonly practiced, H2O(l) at 25°C and 1atm is considered to be in equilibrium with H2O(g) at 25°C and 0.03 atm2; thus, the standard chemical potential of H2O(l) is equivalent to the DFT total energy of H2O(g) together with corrections for the zero-point energy (ZPE) and entropy4 at 25°C and 0.03 atm. All corrections relative to the DFT total energy are summarized in Table S1. Table S1. Corrections for zero-point energy and entropy at room temperature (ZPE-TS)/eV H2O(g)
0.10
H2(g)
-0.13
-O adsorbate
0.01
-OH adsorbate
0.23
-OOH adsorbate
0.15
is computed relative to the standard state of A by using the standard hydrogen electrode (SHE) as reference. At SHE, protons and electrons are in equilibrium with hydrogen gas at , ion concentration
standard state when electrode potential °
, and
. °
°
where
°
,
°
,
, and
°
°
(S5)
are the standard chemical potentials of hydrogen gas, proton, and
electron respectively. Under operational condition, we can correlate the chemical potentials of species in Eq.S3 to their standard states by °
(S6) °
(S7) °
(S8) °
Substitution of the above equations into Eq.S3 gives
(S9)
°
where
°
(S10)
is the standard hydrogen electrode free energy per A obtained from experiments5,
and the expression is
°
lists expressions of
for LaMnO3 component-related ion species at room temperature.
Table S2. A
°
°
°
°
. Based on Eq.S10, Table S2
of LaMnO3 component-related ion species at T= 25°C
Aqueous species
/eV5
/eV
Mn2+ Mn(OH)+ Mn(OH)2 HMnO2− Mn
Mn3O4 Mn2O3 MnO2 MnO42− MnO4−
La
La3+ La2O3
O
H 2O
[H2O(l)/H2(g) as reference]
H 2O
[O2(g) as reference]
Formation energy of surface reconstruction: a general form Similar to vacancy formation, the mechanism of atomic adsorption is the process of the electrochemical formation of a neutral atom from the most stable ion species, followed by the adsorption of the atom on surface. Other more complicated surface reconstructions such as change of orientation and termination, and presence of steps and kinks can be constructed as a series of process involving loss and adsorption of atoms from a reference surface to form a new surface, since the change of Gibbs free energy is independent of mechanism. The general equation for the reconstruction formation is therefore given by the formation energy with respect
to the standard state of the exchanged atom and the electrochemical reaction free energy with respect to SHE, as shown in Eq.S11, where
, the number of exchanged atoms, is positive for
vacancy formation and negative for adsorption. °
(S11)
Equilibrium condition of bulk/surface/solvents for LaMnO3 By comparing values of
in Table S2 as a function of USHE and pH, we generate Pourbaix
diagrams of La and Mn in aqueous solution, as shown by Fig.S1a and 1b respectively. The Pourbaix diagrams are identical to Ref 7.
Figure S1. Computed Pourbaix diagrams for La (left side) and Mn (right side) in aqueous solution; concentrations of neutral and charged ions are fixed at 1 and 10-6 M, respectively. Under the equilibrium condition of LaMnO3 in aqueous solution, the formation energy of bulk LaMnO3 is zero with respect to the most stable component-related ions in Fig. S1. (S12) where
is free energy change from the standard state of i (La ,Mn or O) to the most stable
solvated ions, as shown in Table S2, and
is the formation energy of LaMnO3 from the
standard state of i, which is obtained from experiments6. As shown by Fig. S2, the dashed lines represent the equilibrium conditions of LaMnO3 with the concentration of charged solvated ions varying from 10-6 to 10-12 M. The area bounded
by the lines is the stable bulk region, in which the formation of LaMnO3 from the solvated ions is spontaneous. For simplicity, the phase diagram and boundaries in Fig.4 are determined assuming 10-6 M concentration of charged ion species, as typical in Pourbaix diagrams7. While varying the concentration from 10-6 to 10-12 causes Mn vacancies in the surface to become favorable at lower URHE and decreases the bulk stability region, we find that it does not qualitatively affect the results.
Figure S2. LaMnO3 bulk stability region for different molar concentrations (indicated by the red numbers) of solvated species.
DFT Computational details Calculations are performed using VASP8 with PAW pseudopotentials9 and the RPBE-GGA10 functional. An energy cutoff of 500 eV and a 2x2x1 k-point mesh are used for all calculations. Supercells are composed of 7-atomic-layer-thick slabs separated by ~20 Å of vacuum perpendicular to the surface to prevent spurious interactions due to periodic boundary conditions. A (2×2) in-plane supercell is employed (see Fig. 2). Structures are relaxed until forces on each atom are less than 10-4 eV/Å. Our computed value of the lattice constant is 5.56x5.67x7.77 Å, compared to the experimental value of 5.54x5.70x7.72 Å11. Using the total DFT energy of O2 from the tabulated formation enthalpy of water and DFT energies of H2O(g) and H2(g)12, we find that the formation energies of LaMnO3 and MnxOy are in good agreement with experiments13-14 (< 6% error), providing sufficient accuracy in the calculation of free energies.
We consider only [001] surfaces, as these are observed experimentally. Along the (001) direction, LaMnO3 consists of alternaing LaO and MnO2 atomic phalnes, with nominal charges of +1 and -1, respectively. Both polar and non-polar slabs can therefore be constrcuted. However, as polar fields are energetically costly, they are likely compensated in realistic catalyst systems15; thus we consider only non-polar slabs. Figure S3 shows the optimized supercell of ideal MnO2 terminated surface.
Figure S3. Optimized supercell of ideal MnO2 terminated surface
Considered surfaces in this paper We compute the total Gibbs free energy of a range of possible reconstructed surfaces derived from the ideal MnO2 and LaO (001) terminations, including various combinations and concentrations of oxygen vacancy, cation vacancies, cation adsorbates, as summarized in the Fig. S4. We then consider OER/ORR intermediates (i.e., -OH, -O, and –OOH adsorbates) on these surfaces at different coverages, as listed in Table S3. Finally, the formation energies of all the considered surfaces are determined with respect to the ideal MnO 2 terminated surface in Fig. S3 and solvated ions by the developed method.
Figure S4. Top-down view of optimized surface structures, without OER/ORR intermediates considered in this work Our DFT results show that the stable attachable site for intermediates is atop of Mn for MnO2 termination, and bridge of La-La for LaO termination. For each bare surface in Fig. S4, the adsoprtion enthalpies per site EO, EOH, EOOH of –O, -OH, and –OOH, repectively, are calculated with respect to the total energies of H2O(g) and H2(g) from DFT2.
Table S3. Summary of considered coverage and the corresponding adsorption enthalpies per site for the surfaces in Fig. S4; * represents the adsorption site adjacent to the vacancy, while # represents that diagonal to the vacancy Surface
Coverage
EO/eV
EOH/eV
EOOH/eV
1.
¼
1.83
0.57
3.78
½
1.89
0.53
3.77
¾
1.86
0.54
3.68
1
1.74
0.52
3.66
2.
¼*
1.24
-0.01
3.40
3.
¼#
1.18
0.22
3.38
¼*
1.90
0.31
3.59
¾
1.42
0.25
3.45
¼
0.90
0.01
3.25
½
1.06
0.02
3.29
7.
½
1.30
0.43
3.64
9.
¼
1.35
0.36
3.60
½
1.28
0.35
3.61
12.
¼
0.99
0.20
3.35
13.
¼
0.28
-
-
14.
¼
1.15
-0.23
3.16
15.
¼
-0.39
-0.97
4.31
½
-
-1.03
-
1
-
-0.64
-
¼
1.63
0.00
-
½
-
-0.04
-
1
-
0.22
-
4.
16.
Figure S5. Top-down view of optimized surface structures of R1, R2, R3 and R4 in Fig. 4
Thermodynamic equivalent aqueous condition to T=1100K and
atm in
atmosphere At standard condition (T=25°C,
atm,
atm), the Gibbs free energy change for 5
H2(g)+O2(g)=H2O(l) is 1.23 per electron transfer , namely URHE=1.23V. At T=1100K and atm, the relative chemical potential of O2(g) to its standard state is -1.73eV per molecule from the ideal gas approximation,
. This shifts URHE to 0.80V (1.23-
1.73/4=0.80V) if the change of chemical potential is attributed to shift of URHE.
Reaction mechanisms of OER and ORR
Figure S6. OER and ORR on the MnO2 termination with ¼ ML [Mn]vac. All other surfaces follow the same reaction mechanism, in which intermediates of –OH, –O, –OOH are involved and located atop of Mn atoms. All the geometries of surfaces shown in the figure are optimized. and
are the Gibbs formation energies of reaction steps based on Ref 2.
Identification of active sites and the corresponding ϕ for Fig. 5 For each stable surface, we calculate the value of ϕ for each distinguishable reaction site and for site concentrations of ¼ to 1 ML. The sites that give the lowest values of ϕ are taken as the current dominating sites and used to plot ϕ as a function of USHE and pH in Figs. 5b and 5d. Our DFT results show that adsorption strength on the surfaces of A0, A1, R1, R2, R3, R4, which have geometrically identical Mn in the surface, is little affected by the locations of active sites and number of coverage. For B2, however, adsorption strength adjacent to the Mn vacancy site is stronger than that diagonal to the vacancy. This is because the farther of Mn away from the vacancy, the less influence of its electronic structure exhibits, as shown by the d orbital band centers in Fig. S7. Due to comparatively large ϕ of the adjacent site, we plot ϕ of the diagonal site, which gives 0.2V smaller OER overpotential than the ideal MnO2 termination.
Thus,
consideration of realistic surface structure under operational condition can reduce the discrepancy between overpotentials predicted by DFT and experiments.
Correlation between the atomic and electronic structure
Figure S7. d orbital band center of cation relative to the Fermi level in the surface layer without intermediate adsorbates as a function of: (a) O:Mn stoichiometry in the surface, (b) –O adsorption energy, and (c) –OH adsorption energy. * represents the adsorption site adjacent to the vacancy, while # represents that diagonal to the vacancy. It can seen that the increased O:Mn ratio in the surface layer decreases d orbital occupation on the remaining Mn sites, thereby increasing adsorption strength of –O, -OH, and –OOH.
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
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