A descriptor of IB alloy catalysts for hydrogen evolution reaction

Alloying is regarded as one of the most promising strategies for boosting performance of catalysts for hydrogen evolution reaction (HER) due to the adjustable electronic structure and intermediate adsorption. However, there is no theory (including d‐band center theory) can accurately guide the preparation and design of alloy catalysts, and thus resulting all the reported alloy catalysts are obtained by time‐consuming and laborious experimental exploration. Herein, we proposed a mean d‐band center (εas) as a new accurate descriptor for alloy activity prediction. Theoretical simulation and experiment results revealed that this descriptor exhibits a strong scaling relation with H adsorption energy. Besides, the obtained Cu–Ag alloy displays an optimal overpotential of 223 mV at 10 mA/cm2 in 0.5 mol/L H2SO4, which is more than 300 mV lower than those of pristine Cu (530 mV) and Ag (569 mV) powder. Our work provides a new idea toward designing highly efficient HER catalysts and broadens the applicability of d‐band theory to activity prediction of alloys.


| INTRODUCTION
2][3] Electrochemical water splitting is an effective way of sustainable hydrogen production 4 and its efficiency highly depends on hydrogen evolution reaction (HER) catalysts. 5At present, Pt is still the most effective HER catalyst due to its high activity and appropriate intermediate adsorption energy, but its widespread application is limited by the scarcity and high cost. 2,6,7[10] Alloying, with the striking advantages of achievable continuous and precise adjustment through the electronic and strain effect [11][12][13][14] induced by the incorporation of a second metal, has been proven to be an effective way to adjust their d-band center to improve the H adsorption ability. 15,16Particularly, Cu-Ag alloy is metastable and high-energy due to the insolubility of Cu and Ag, which could improve the adsorption energy of intermediate effectively.8][19] However, conventional d-band center theory fails to precisely describe the adsorption energy due to the neglect of interaction between electrons of different element in alloy. 20Thus, it is uncapable to exploit efficient alloy catalysts under the guidance of conventional d-band center theroy.More recently, an attempt has been made to describe the d-band centers of the hollow site of alloys with different components, 20 but it still neglects the atomic interactions.
In this study, we proposed a new descriptor (ε as ) to represent the d-band center of hollow site in Cu-Ag alloys and established a linear relationship between ε as and H adsorption energy, which was verified via theoretical simulation and experiment results.The prepared Cu-Ag alloys show a volcano relationship between the ratio of Cu:Ag and HER activity.Besides, the obtained Cu 1 Ag 1 alloy exhibits the lowest overpotential of 223 mV at 10 mA/cm 2 in 0.5 mol/L H 2 SO 4 , which is more than 300 mV lower than those of pristine Cu (530 mV) and Ag (569 mV) powder.This study provides a new idea for designing highly efficient HER catalysts and broadens the applicability of d-band theory to activity prediction of alloys.

| Preparation of Cu-Ag alloys
The raw materials are commercial copper powder and silver powder (purity is 99.9%), put the raw material into the PTFE ball mill tank, the ratio of ball and material is 15:1, add two different diameters of 10 mm and 6 mm grinding balls, fill argon gas as a protective gas, in the QM-3SP4 planetary ball mill 400 r/min speed between the powder particles and grinding balls for a long time intense impact, collision, silver atoms are diffused in the copper matrix under the action of mechanical force to form an alloy.The products obtained by batching ratios Cu 100 at%; Cu 80 at%, Ag 20 at%; Cu 50 at%, Ag 50 at%; Cu 20 at%, Ag 80 at%, and Ag 100 at% were named Cu; Cu 3 Ag 1 , Cu 1 Ag 1 , Cu 1 Ag 3 , and Ag.

| Preparation of Cu+Ag
The raw copper powder and silver powder were mixed to obtain Cu+Ag.

| Preparation of A-CuAg
The annealing of Cu 1 Ag 1 powder was carried out in a tube furnace under argon protection at 400°C, leaving for 2 h, named A-CuAg.

| Characterizations
The morphology of the samples was examined with scanning electron microscopy (SEM, Hitachi S-4800).X-ray photoelectron spectroscopy (XPS) analysis was measured by an Axis Supra X-ray photoelectron spectrometer.The microstructure and morphology of the catalysts were observed by a JEOL 2100F transmission electron microscope (TEM, 200 kV).The crystal structure was analyzed through a Bruker D8 Advanced X-ray diffraction (XRD) with the Cu Kα radiation source.

| Electrochemical measurements
The HER activity was measured using a CHI660E electrochemical workstation in Ar (HER)-saturated 0.5 mol/L H 2 SO 4 electrolytes (reference electrode: KClsaturated Hg/HgCl 2 electrode, counter electrode: graphite rod).The 0.5 mol/L H 2 SO 4 solution was purged with Ar for about 60 min to exclude air.Typically, 5 mg of catalyst and 8 mg of carbon black were suspended in 500 μL of isopropanol, 500 μL of deionized water, and 20 μL of Nafion solution (5 wt%, Du Pont) to form a homogeneous ink assisted by ultrasound.Then the 7 μL of homogeneous ink was spread onto the surface of the glassy carbon by a micropipette and dried at room temperature.All of the potentials versus SCE were converted to the reversible hydrogen electrode (RHE) using the equation E (vs.RHE) = E (vs.SCE) + E θ SCE + 0.0592 pH.Before the electrochemical tests, 40 cycles of cyclic voltammetry (CV) at a scan rate of 50 mV/s were performed to stabilize the catalyst, then the linear sweep voltammetry (LSV) curves were recorded at a scan rate of 2 mV/s, and all of the polarization curves were the steady ones after several scans.Electrochemical impedance spectroscopy (EIS) measurements were performed from 100 kHz to 0.01 Hz.

| Calculation methods
All DFT calculations were performed using Vienna Ab initio Simulation Package (VASP). 21The projector augmented wave (PAW) pseudopotential 22 with the PBE generalized gradient approximation (GGA) exchange-correlation function 23 was utilized in the computations.The cutoff energy of the plane waves basis set was 550 eV, and a Monkhorst-Pack mesh of 3 × 3 × 1 was used in K-sampling in the adsorption energy calculation.The long-range dispersion interaction was described by the DFT-D3 method.All atoms were fully relaxed with the energy convergence tolerance of 10 −5 eV per atom, and the final force on each atom was < 0.01 eV/Å.All periodic slabs have a vacuum layer of at least 15 Å.The bottom layer of atoms is fixed at their optimized bulk-truncated positions during geometry optimization, and the rest of atoms could relax.
The adsorption energy of reaction intermediates can be computed using the following Equations: (1) and ( 2): (1) where ΔE ZPE is the zero-point energy change; and ΔS is the entropy change.In this work, the values of ΔE ZPE and ΔS were obtained by vibration frequency calculation.

| RESULTS AND DISCUSSION
The  24 Cu should possess the strongest H* adsorption energy (ΔG H* ).However, as shown in Figure 1B, the Cu-Ag alloys exhibit lower G Δ H * than that of pure Cu (0.207 eV) and Ag (0.322 eV), and Cu 1 Ag 1 displays the lowest ΔG H* (0.128 eV).The ΔG H* of top and bridge site was calculated which is higher than that of hollow site (Figure S2).The electron transfer between copper and silver was calculated and it was found that the number of electron transfer increases with the increase of the proportion of dissimilar atoms (Table S1).The relationship between the ΔG H* and the d-band center of these five samples is a volcano rather than the predicted linear relationship (Figure 1C).This contradiction should be attributed to the neglect of interaction between the alloying elements in the conventional DFT calculation, that is, mean-field behavior. 25Therefore, proposing an available and simple descriptor to couple the ΔG H* and d-band of alloy is crucial but challenging for designing HER catalysts.
To address this issue, we first prepared Ag, Cu 1 Ag 3 , Cu 1 Ag 1 , Cu 3 Ag 1 , and Cu samples via ball-milling method, which correspond to the models in Figure S1.As shown in Figure 2A, the Cu and Ag possess the Cu phase (PDF No. 04-0836) and Ag phase (PDF No. 04-0783), respectively.Since copper and silver are not solid soluble, there is no standard PDF card.Cu 3 Ag 1 is shifted to the right compared to Cu, and Cu 1 Ag 3 is shifted to the left compared to Ag, which is the same as the trend of XRD calculated theoretically (Figure S3).The main peak of Cu 1 Ag 1 is in the middle and has the largest broadening compared to Cu 3 Ag 1 and Cu 1 Ag 3 .According to the scanning electron microscope (SEM) image in Figure 2B, Cu 1 Ag 1 displays a micron-sized lamellar structure, which gradually becomes smaller with the extension of ball milling time (shown in Figure S4).The high-resolution transmission electron microscope (HRTEM) image (Figure 2C) shows that surface possess an interplanar distance of 0.219 nm, which is between the Cu(111) plane (0.209 nm), and the Ag(111) plane (0.236 nm).The TEM-EDS mapping (Figure 2D) shows that Cu and Ag elements are homogeneously distributed in the Cu 1 Ag 1 sample, which is consistent with the SEM-EDS mapping in Figure S5.With the extension of ball milling time, the characteristic peaks of Cu and Ag gradually disappear, also indicating that Cu 1 Ag 1 alloy is formed successfully (Figures S6 and S7).
On the other hand, the H adsorption energies of Cu-Ag alloys are qualitatively measured by experiment through the hydrogen temperature programmed desorption (H 2 -TPD) method.The peak positions in the TPD spectra are corresponding to the H 2 desorption temperature.Just as predicted by the d-band center theory, pure Cu exhibit a higher desorption temperature (259°C) than that of pure Ag sample (Figure 3B), indicating the interaction between Cu and H 2 is stronger than that of Ag.Whereas, the positions of the spectral peaks of Cu-Ag alloys are all lagged, indicating an enhanced interaction between the hydrogen and the alloy surface.With the increase of Ag content, the desorption temperature increases from 415°C for Cu 3 Ag 1 to 457°C for Cu 1 Ag 1 , and then decrease to 426°C for Cu 1 Ag 3 .Moreover, the Cu 1 Ag 1 exhibit two desorption peaks at 685°C and 708°C (Figure S8), further proving its high H adsorption ability.The desorption peak area, which can reflect the H 2 -adsorbing capacity, [28][29][30][31][32] also shows the same trend as desorption temperature, and the maximum H 2 -adsorbing capacity is about 0.355 mmol/g of Cu 1 Ag 1 .Figure 3C shows the overall trend of H 2adsorption ability and capacity.Thus, there is a volcanic relationship between the VBS-measured d-band center and H adsorption ability (Figure 3D), consistent with the results of DFT calculation.
The superior H adsorption ability of Cu-Ag alloys should result in a higher HER performance.and Ag-based catalysts in Table S2. Figure 4C shows that Cu 1 Ag 1 has the lowest Tafel slope of 89 mV/dec, indicating its fastest kinetics among all the samples.The overpotential shows a trend of first decreasing and then increasing of the overpotential, consistent with calculated and actual G Δ H * results in Figure 1B,C.Except for high activity, long-term durability is another essential merit for an ideal electrocatalyst.As shown in Figure 4D, the current-dependent time relation (i-t curve) reveals that Cu 1 Ag 1 can work continuously for more than 20 h without any current decrease at −0.45 V versus RHE.The inset in Figure 4D is the LSV curves before and after an accelerated durability test of 1000 cycles, indicating that the HER properties of Cu 1 Ag 1 hardly change after 1000 cycles.
To further clarify the role of alloying on the enhancement of performance, an annealed sample (denoted as A-CuAg) was prepared by heat-treating Cu 1 Ag 1 alloy and a mixed sample (denoted as Cu+Ag) was prepared for comparison (Figure S9).As expected, Cu 1 Ag 1 peaks disappeared, replaced by peaks of pure Cu and Ag (Figure S10), indicating both A-CuAg and Cu+Ag only contain Cu and Ag phase.X-ray photoelectron spectroscopy (XPS) measurements were obtained to analyze the valence states of Cu and Ag (Figure S11).In all samples, both Ag and Cu elements present metallic states (Ag 0 and Cu 0 ), but only the Cu 2p peak and Ag 3d peak for Cu 1 Ag 1 were skewing, suggesting the electron transfer between Cu and Ag in Cu-Ag alloy in comparison with A-CuAg and Cu+Ag.As shown in Figure S12A, A-CuAg and Cu +Ag required an overpotential of 470 mV and 541 mV at 10 mA/cm 2 , respectively, which are significantly higher than that of Cu 1 Ag 1 (223 mV), consistent with Tafel slopes (Figure S12C), electrochemical impedance spectroscopy (EIS) (Figure S12D), electrochemical active surface area (ECSA) (Figure S12E) and intrinsic activity (Figure S12F), indicating the critical effect of alloying on HER activity.To further clarify the role of alloying, the HER performance of various Cu 1 Ag 1 alloy catalysts with different ballmilling time were tested (Figure S13).With the extension of milling time, the alloy formed gradually and the overpotential decreased.
The experimental results imply that the above volcano relationship (Figure 1C) between the d-band center of alloy and HER performance is actual.Based on the mean-field theory, [33][34][35] the integral geometric d-band center of the alloy is inappropriate to descript the adsorption ability of the hollow site due to alloying and the difference of the three atomic species around the hollow site.( ) by the low root-mean-square error (RMSE) of 0.02 eV.Hence, ε as is a valid descriptor of HER performance, validating the descriptor role of d-band center.
To verify the universality of ε as , we theoretically calculated the DOS and DFT for different ratios of Cu-Au alloys (Figure S14).The trend of the DOS of Cu-Au alloys with composition is consistent with that of Cu-Ag alloys, that is as the ratio of Au increases, the d-band centers of Cu and Au shift upward and the d-band centers of the alloys shift downward (Figure S15).Cu 1 Au 1 (Cu:Au = 1:1) displays the lowest ΔG H* (0.106 eV) among all the Cu-Au alloys with different ratio of Cu and Au (Figure S16).Moreover, the ε as is applied for Cu-Au alloys and a good linear relationship between ε as and ΔG H* is also obtained in Figure S17 (R 2 = 0.93, RMSE = 0.02 eV).Increasing of ε as results in stronger binding of H* and a lower ΔG H* .As a new operator of ΔG H* , the proposing of ε as broadens the d-band center theory and provides guidance for prediction and design of alloy catalysts.

| CONCLUSION
In conclusion, we proposed a new descriptor (ε as ) to present the d-band center of the real adsorption site in Cu-Ag alloy and revealed the linear relationship between the ε as and H adsorption energy.At the same time, the prepared Cu-Ag alloys show a volcano relationship between the ratio of Cu:Ag and HER activity.The lowest overpotential is only 223 mV at 10 mA/cm 2 in 0.5 mol/L H 2 SO 4 , which is more than 300 mV lower than those of pristine Cu (530 mV) and Ag (569 mV) powder.This work paves a new avenue for designing highly efficient HER catalysts and broadens the applicability of d-band theory to activity prediction of alloys.
typical d-band configuration of Cu-Ag alloys with different ratio of Cu:Ag are given by the density function theory (DFT) computation.The ratio of Cu:Ag are fixed at 3:1, 1:1, 1:3, and the corresponding sample were named as Cu 3 Ag 1 , Cu 1 Ag 1 , Cu 1 Ag 3 .Pure Cu and Ag were selected for comparison.Based on the atomic models of Cu, Cu 3 Ag 1 , Cu 1 Ag 1 , Cu 1 Ag 3 , and Ag in Figure S1, the d-band configuration is given in Figure 1A.The spectra reveal that the d-band center gradually shift upwards from Ag to Cu as the ratio of Ag decrease.Based on the generally accepted d-band theory,

F
I G U R E 1 Theoretical calculations on electronic states and adsorption energies of Cu-Ag alloys in different ratios.(A) The partial of density of states (PDOS) of Ag, Cu 1 Ag 3 , Cu 1 Ag 1 , Cu 3 Ag 1 , and Cu.(B) adsorption energies of H* (ΔG H* ) on Cu-Ag alloy surfaces in different ratios.(C) the relationship between d-band center and ΔG H* .
, we experimentally measured the actual H adsorption ability and d-band center, respectively.The d-band center positions of Cu-Ag alloys are experimentally estimated by valence band spectra (VBS) of X-ray photoelectron spectroscopy measurement.As shown in F I G U R E 2 Morphology and structure of the Cu 1 Ag 1 catalyst.(A) XRD patterns of Cu-Ag alloys in different atomic ratios.(B) Scanning electron microscopy (SEM) image of Cu 1 Ag 1 .(C) HRTEM image of Cu 1 Ag 1 .(D) TEM image and combined EDS mappings of Cu 1 Ag 1 showing elemental distribution of Cu (red) and Ag (green), the scale bar: 100 nm.HRTEM, high-resolution transmission electron microscope; TEM, transmission electron microscope; XRD, X-ray diffraction.
Figure 4A displays the linear sweep voltammetry (LSV) curves for Ag, Cu 1 Ag 3 , Cu 1 Ag 1 , Cu 3 Ag 1 , and Cu in N 2 -saturated 0.5 mol/L H 2 SO 4 .Cu 1 Ag 1 only required an overpotential of 223 mV to reach a current density of 10 mA/cm 2 , which is much lower than those of Cu (530 mV), Cu 3 Ag 1 (412 mV), Cu 1 Ag 3 (338 mV), and Ag (569 mV) (Figure 4B), as well as the recently reported Cu-based F I G U R E 3 Experimental measurement on electronic states and adsorption energies of Cu-Ag alloys in different ratios.(A) Valence band spectra (VBS) of alloys in different ratios as measured by high-resolution X-ray photoelectron spectroscopy.(B) Hydrogen temperature programmed desorption (TPD) spectra of samples with H 2 adsorbed.(C) The H 2 -adsorption capacity and H 2 -desorption temperature in different ratios.(D) The relationship between d-band center and H 2 -desorption temperature.

F
I G U R E 4 HER activity and durability in Ar-saturated 0.5 mol/L H 2 SO 4 aqueous electrolyte.(A) Polarization curves of Cu, Cu 3 Ag 1 , Cu 1 Ag 1 , Cu 1 Ag 3 , and Ag in 0.5 mol/L H 2 SO 4 with a scan rate of 5 mV/s, without insulation resistance compensation.(B) Overpotential of alloys with different atomic ratios.(C) Corresponding Tafel plots of the polarization curves in (A).(D) Long-term stability of Cu 1 Ag 1 at a potential of −0.45 V versus RHE.
Figure 5A shows the PDOS of three atoms around the hollow active site in Cu 3 Ag 1 , Cu 1 Ag 1 , and Cu 1 Ag 3 .It can be seen that the d-band center of the Cu atoms in Cu-Ag alloys are higher than that of pure Cu (−2.52 eV) with the order of Cu 3 Ag 1 (−2.10 eV) < Cu 1 Ag 1 (−2.04 eV) < Cu 1 Ag 3 (−1.92eV), while the Ag atoms display much lower d-band center than that of neighboring Cu atoms, indicating that the high adsorption ability of hollow sites is mainly contributed by Cu atoms.Thus, Cu 1 Ag 1 possesses the lowest H adsorption ability due to the high proportion of Cu atoms.Considering that H* adsorbed on hollow site could bond with Cu and Ag simultaneously (Figure 5B), an extended d-band center (ε as ) to represent the d-band center of several atoms around the hollow site is proposed, and the corresponding formula is shown below.

( 4 )
Since the d-band center of Cu is higher than that of Ag, we use the d-band center of Cu as a benchmark to consider the d-band centers of several atoms around the adsorption site.ε Cu denotes the d-band center of Cu; ε Ag enotes the d-band center of Ag; ε Cu 1 indicates the d-band center of Cu atom #1 around the hollow site; ε Cu 2 indicates the d-band center of another Cu atom #2 around the hollow site; ε Ag 1 indicates the d-band center of Ag atom #1 near adsorption site; ε Ag 2 indicates the d-band center of another Ag atom #2 around the hollow site the effect of silver on copper.Figure 5C shows the relationship of adsorption energies of H* (ΔG H* ) with the d-band center of hollow site (ε as ).ε as shows a strong linear correlation with ΔG H* (R 2 = 0.93) and its reliability is further confirmed F I G U R E 5 Theoretical calculations on electronic states and adsorption energies of Cu-Ag alloys in different ratios.(A) The PDOS of three atoms around the active site in Cu 3 Ag 1 , Cu 1 Ag 1 , and Cu 1 Ag 3 .(B) The selected illustrations of the calculated surface sites for hydrogen (H) adsorption.The blue spheres are Cu, gray spheres are Ag and pink spheres are H. (C) The relationship of ε as and adsorption energies of H*(ΔG H* ).