Carbon doping switching on the hydrogen adsorption activity of NiO for hydrogen evolution reaction

Hydrogen evolution reaction (HER) is more sluggish in alkaline than in acidic media because of the additional energy required for water dissociation. Numerous catalysts, including NiO, that offer active sites for water dissociation have been extensively investigated. Yet, the overall HER performance of NiO is still limited by lacking favorable H adsorption sites. Here we show a strategy to activate NiO through carbon doping, which creates under-coordinated Ni sites favorable for H adsorption. DFT calculations reveal that carbon dopant decreases the energy barrier of Heyrovsky step from 1.17 eV to 0.81 eV, suggesting the carbon also serves as a hot-spot for the dissociation of water molecules in water-alkali HER. As a result, the carbon doped NiO catalyst achieves an ultralow overpotential of 27 mV at 10 mA cm−2, and a low Tafel slope of 36 mV dec−1, representing the best performance among the state-of-the-art NiO catalysts.


Supplementary Notes
Supplementary Note 1

Formation of nickel oxides
The dehydration of nickel oxalate dihydrate can result in nickel oxalate and water ( 2 4 • 2 2 → 2 4 + 2 2 ) and the subsequent decomposition of nickel oxalate leads to the generation of metallic Ni and carbon dioxide ( 2 4 → + 2 2 ). During the rapid decomposition of nickel oxalate, the carbon dopants can be retained in the Ni structure.
Furthermore, the residual water from the dehydration step can react with Ni at the decomposition temperature (2 2 + → + 2 ), leading to the formation of nickel oxides 14,15 .

Determination of stable surface
To determine the most stable surface termination, a surface phase diagram was plotted as a function of chemical potential of O species. In general, the surface energy is defined as the energy required to form new surface divided by the surface area.
where, is the energy for the whole relaxed slab, is the energy for the fixed bottom two layers, and are the chemical potential of nickel and oxygen, respectively, and and are the number of nickel and oxygen ions in the relaxed part. For NiO, the following chemical potential relation of Ni and O must be satisfied.
Since there are 8 Ni and 8 O in NiO bulk unit cell, we have Enforcing equation (1), (2) and (3) has allowed us to now write the surface energy as a function of Finally, we look to determine the range of . In an oxygen rich environment, oxygen will come from O2 gas and hence = 1 2 2 . In a nickel rich environment (oxygen poor), nickel will be produced from pure bulk Ni and so = According to equation (4), we plotted how surface energy changes with in the range shown in equation (5) in Supplementary Fig. 6.

Supplementary Note 3 Chemical environment of C-Ni1-xO-Air
In order to investigate the role of C in HER, C-Ni1-xO was annealed in the air at 400 o C for 10 min

Supplementary Note 4 Chemical environment of C-Ni1-xO after CV conditioning
By comparing the XPS results ( Supplementary Fig. 14) with those obtained from the C-Ni1-xO catalyst before conditioning (Fig. 3 The extra peaks (533 eV in O 1s, 286.8, 289.9, and 291.8 eV in C 1s spectra) observed for the conditioned sample are ascribed to the C-O and C-F/C-F2 structure from the residues of Nafion binder that was used in attaching the catalyst to the electrode [24][25][26][27] . The Nafion residues in the conditioned sample can also result in a C 1s peak at 288.6 eV due to its C-F2S structure 25 . This peak overlaps with that of O-C=O, which makes it difficult to estimate the atomic carbon concentration after conditioning. In order to exclude the influence of Nafion binder and confirm the coordination environment, XANES characterizations were carried out on the binder-free catalyst sample, i.e. C-Ni1-xO grown on nickel foam ( Supplementary Fig. 14b). The highlighted shaded areas of O K-edge and C K-edge spectra show the exact same characteristic peaks of C-Ni1-xO reported in Fig. 3. The results confirm that the O-C=O structure (carbon doping) are still presented in the conditioned sample. Taken together the XPS and XANES results, it is reasonable to conclude that the catalyst's composition is similar before and after conditioning. Furthermore, based on our XPS and XANES, it is reasonable to conclude that NiO layer is preserved after measurement.

DFT Calculation Details
For the QE calculation part, ultrasoft pseudopotential with kinetic energy cutoffs of 40 Ry for wavefunction and 240 Ry for charge density is implemented. In order to capture the correct antiferromagnetic ordering of Ni along the (111) direction, a 2 × 2 × 2 supercell must be used.
Integration over the Brillouin zone is performed using a 4 × 4 × 4 k-point mesh. In order to improve k-point integration, a cold smearing of 0.002 Ry is used 28  In order to study the surface of NiO, the bulk unit cell was converted from its fcc unit cell to simple cubic unit cell, and then this cell was expanded to a √5 × √2 × 1 supercell for the (111) surface or a 2 × 2 × 1 supercell for the (100) surface. A vacuum region of 15 Å is added to effectively separate two adjacent slabs and avoid spurious interactions. The convergence of surface energy over the number of layers was tested and it was found that the energy difference between 5-layer slab and 7-layer slab is smaller than 1 meV Å -2 , so 5-layer slab is used. In order to mimic the properties of bulk, the bottom two layers of (111) surface were fixed with bulk positions, while the remaining structure relaxed as the surface. Due to the inversion symmetry breaking, a dipole field correction was applied along the vacuum direction. For all slab calculations, a 2 × 2 × 1 kpoint mesh was used with a smearing of 0.005 Ry to help the convergence.

Calculation of ∆
∆ is the most commonly used indicator to compare the activity between different sites toward hydrogen adsorption since it correlates well with experimental exchange current densities, and an optimal hydrogen adsorption corresponds to ∆ = 0 (too positive or negative ∆ leads to too weak or strong hydrogen adsorption) 29 . We calculated ∆ with the following equation, proposed by Nørskov et al 30,31 .
where, ∆ is the change in the total energy change after H adsorbs on the surface, ∆ is the change of entropy, ∆ is the change of zero point energy and ∆ is the solvation energy difference between surface with H and bare surface.

H adsorption profile on p-surface and o-surface
The ∆ of all possible hydrogen adsorption sites on both surfaces have been calculated to give insights into the effect of Ni vacancy on the activity toward hydrogen adsorption. With respect to p-surface, we found that only the bridge site (i.e. H bonding with two Ni, Supplementary Fig. 7) is favorable for H adsorption with a ∆ value of −0.192 eV (Supplementary Table 2). On the other hand, for the o-surface, in addition to Ni #1 ( Supplementary Fig. 8a), both the exposed third  Fig. 8b) give a slightly positive ∆ of 0.152 eV (Supplementary surface area compared to that of p-surface.

Calculation of ECSA
The ECSA was calculated based on a method reported in literature 32 . A series of CV (from 20 to 120 mV s -1 with an interval of 20 mV s -1 ) were collected in a non-faradaic reaction potential window from 0.2 V to 0.1 V vs. RHE. A linear plot of the janodic -jcathodic versus scan rate was obtained accordingly and the slope is proportional to the ECSA. The ECSA can be calculated through the following equation: Where represents the areal capacitance (i.e. the slope of Supplementary Fig. 14), A is the geometric area of the working electrode (0.5 cm 2 ), and is the referential area capacitance of flat electrode (here we use 40 μF cm -2 for Ni based catalysts and 30 μF cm -2 for Pt suggested by Jaramillo et al. 33,34 ).

Energy barrier calculation
For the energy barrier calculation, the IS and FS for Heyrovsky step on both o-surface and Csurface were relaxed. The number of required IMs for NEB calculations was tested for the Heyrovsky reaction over o-surface and C-surface. It was found that 8 IMs and 6 IMs are enough to converge the barriers for o-surface and C-surface, respectively. After the exact saddle point was found by DIMER calculation, we did phonon calculation for all atoms in the system (except for the layers whose atoms are fixed) to check the number of imaginary frequencies in the system and confirmed there is only one imaginary frequency, whose direction is along the reaction pathway.
All these indicate that they are the real saddle points.

Coordinates files
The coordinates files for pristine NiO surface, octopolar NiO surface and C doped NiO surface (the atoms with "0 0 0" after their coordinates are fixed at the NiO bulk positions, in order to recover the bulk properties at the bottom layer of the slab) are shown below.