Cu is a classic metal with high conductivity but usually exhibits poor catalytic activity. Here, we devise a highly efficient HER copper catalyst, which is modified by Zr via the formation of Cu-Zr intermetallic clusters (Figure 1(a)). Owing to the large electronegative difference between Cu and Zr, there forms structurally ordered Cu₅Zr intermetallic compound [41–44], one of the most thermodynamically stable phases with a face-centered cubic (fcc) structure in Cu-Zr system, in the Cu-rich component region [41–44]. On the basis of Cu₅Zr(111), first-principles density functional theory (DFT) calculations demonstrate that Zr atoms can effectively activate their surrounding negative-valence Cu atoms. As shown in partial density of states (PDOS) of Cu₅Zr(111) (Figure 1(b)), the center of d bands of the Cu₅Zr is shifted up toward the Fermi energy relative to bare Cu(111). Although surface Cu atoms tend to be oxidized into Cu(OH)₂ layer in the ambient surroundings, they are reduced to the metallic state in the HER potential range because of the Cu²⁺/Cu equilibrium potential of 0.61 V at \text{pH}=14 [45]. This is demonstrated by the DFT simulation on the Cu₅Zr(111), on which except for the Zr atoms, the Cu atoms do not adsorb hydroxyl group (HO{}^{\ast }) at 0 V vs. RHE (supplementary Figure S1). Distinguished from the hollow-site adsorption of Cu(111) (Figure 1(c)), the incorporation of Zr enables the Cu-Cu bridge sites of the Cu₅Zr(111) surface to adsorb hydrogen atoms, with a calculated HBE per H atom of -0.44 eV (Figure 1(d), supplementary Figure S2b and Table S1). While it is thermodynamically favorable to adsorb HO{}^{\ast } on the surface Zr atoms (Cu₅Zr-OH) in the HER potential range (Figure 1(e) and supplementary Figure S1), the hydroxylation does not adjust the optimal adsorption sites except for slightly weakening the HBE value to -0.36 eV (supplementary Figure S2d and Table S1). Such unique configuration is more favorable for the Cu₅Zr-OH(111) to accelerate the HER kinetics than the clean Cu₅Zr(111), suggesting a superior HER catalytic activity. This expectation is verified by the calculations of free-energy diagram for the HER reaction paths on the Cu₅Zr(111) facets with or without the hydroxylation of surface Zr atoms. As shown in Figure 1(f), the Cu₅Zr-OH(111) has an energy barrier of ~0.54 eV for the rate-limiting step of H{}^{\ast } adsorption/combination, much lower than the value of the Cu₅Zr (~0.67 eV).

With an aim at developing highly efficient and robust HER catalytic materials that should comprise sufficient available surface with high catalytic activity and have a rational structure with fast electron transfer and reliable steadiness [36], we construct self-supported monolithic NP Cu/Cu₅Zr electrodes with a hierarchical nanoporous architecture by a facile and scalable dealloying strategy [46, 47]. Therein, both the nanoporous microstructure and the components are controlled by hereditary effect of precursor Cu_20-xZr_xAl₈₀ (x=0, 1, 3, 5, and 20 at%) alloys during the dealloying processes [46]. Resembling the multiphase-structured Cu₂₀Al₈₀ alloy (supplementary Figure S3a), the Cu_20-xZr_xAl₈₀ (x=1, 3, and 5 at%) alloys are primarily composed of several-hundred-nanometer-wide α-Al and CuAl₂ phases with a quasiperiodic distribution, as illustrated by a scanning electron microscope (SEM) backscattered electron image for the Cu₁₇Zr₃Al₈₀ alloy (Figure 2(a)) and the corresponding energy-dispersive X-ray spectroscopy (EDS) elemental mappings (Figures 2(b)–2(d)). X-ray diffraction (XRD) characterization reveals that in addition to α-Al and CuAl₂ phases, there are intermetallic Cu₅Zr [48, 49], Al_9.83Zr_0.17 and Al₃Zr clusters that are embedded in Cu-rich and α-Al phases, respectively, with the incorporation of Zr components (supplementary Figures S3b–d and S4) [48, 49]. The multiphase structure enables the product of NP Cu/Cu₅Zr with a bimodal nanoporous structure, as that of bare NP Cu (supplementary Figure S5), in a two-step chemical dealloying process: the rapid dissolution of the α-Al phase embedded with Al_9.83Zr_0.17 and Al₃Zr to form large channels and the selective etching of the less-noble Al component from CuAl₂ alloy to generate small nanopores and expose Cu₅Zr clusters. As shown in a representative SEM image for the NP Cu/Cu₅Zr electrode dealloyed from the precursor Cu₁₇Zr₃Al₈₀ alloy (Figure 2(e)), it displays a uniform bimodal nanoporous structure consisting of large channels with ~300 nm in width and small nanopores with the diameter of ~18 nm (supplementary Figure S6). The small nanopore structure is further verified by N₂ adsorption/desorption isotherm (supplementary Figure S7a), which signifies a size distribution with maximum centered at ~18 nm (supplementary Figure S7b). Figure 2(f) shows a typical high-resolution transmission electron microscope (HRTEM) image of Cu/Cu₅Zr ligaments, where high-density intermetallic Cu₅Zr clusters with diameter of ~3-6 nm can be identified by their distinct contrasts and lattices. Atomic resolution high-angle annual-dark-field scanning transmission electron microscope (HAADF-STEM) image viewed along the [111] zone axis illustrates that these Cu₅Zr clusters are exposed and in situ anchored on the NP Cu skeleton with a seamless interfacial structure (Figure 2(g)), enhancing the stability of electroactive Cu₅Zr clusters and their electron transfer with conductive Cu skeleton. The hybrid structure of NP Cu/Cu₅Zr is further verified by the corresponding fast Fourier transform (FFT) patterns (inset of Figure 2(g)) and the XRD patterns (Figure 2(h)) with two sets of diffraction characteristics [48]. In the XRD patterns, the weak diffraction peaks at 2\theta =37.0, 43.7, and 45.7 are assigned to the (220), (311), and (222) planes of fcc Cu₅Zr clusters (JCPDS 40-1322) (inset of Figure 2(h)) [48], apart from the obvious ones attributed to monometallic Cu (JCPDS 04-0836). X-ray photoelectron spectroscopy (XPS) analysis reveals the presence of Zr and Cu with an atomic ratio of 92/5, in addition to a little residual Al according to inductively coupled plasma mass spectroscopy (ICP-MS) and EDS (supplementary Figure S8 and Table S2). The deviation of Zr/Cu ratio from the initial value in the precursor alloy confirms the fact that those Al_9.83Zr_0.17 and Al₃Zr are removed with the dissolution of α-Al phase. Because of electron donation from Zr to Cu (inset of Figure 2(j)), the Zr 3d XPS spectrum shows the chemical state of Zr²⁺ in addition to the Zr⁴⁺ that is due to the oxidation of surface Zr atoms (Figure 2(i)) [50]. This is in contrast with the observation of solid Cu/Cu₅Zr bulk alloy with negligible Cu₅Zr clusters exposed at the surface (supplementary Figures S9a and b), of which the primary chemical state of Zr²⁺ is attributed to the electron transfer from Zr to Cu (supplementary Figure S9c). As a result, Cu exhibits the chemical state of Cu^δ- in addition to Cu⁰ and Cu⁺ that correspond to the Cu atoms locating at the internal and surface of Cu ligaments, respectively (Figure 2(j) and supplementary Figure S9d) [34, 51]. Similar dealloying processes also take place in the precursor Cu_20-xZr_xAl₈₀ alloys with x=1 (Cu₁₉Zr₁Al₈₀) or 5 (Cu₁₅Zr₅Al₈₀), which gives rise to almost the same bimodal nanoporous structure (supplementary Figures S10a and S11a) except for their distinct Cu/Zr compositions of 97/1 (supplementary Figure S10b) and 80/16 (supplementary Figure S11b), respectively. In contrast, the precursor alloy with x=20 (i.e., Zr₂₀Al₈₀) produces NP Zr with a single-modal nanoporous structure during the chemical dealloying (supplementary Figure S12).

To assess the electrocatalytic HER activity of NP Cu/Cu₅Zr, all nanoporous catalytic materials are directly used as working electrodes for electrochemical measurements in N₂-saturated 1 M KOH aqueous electrolyte, based on a classic three-electrode configuration with a saturated calomel electrode (Hg/Hg₂Cl₂, SCE) and a graphite rod as the reference electrode and the counter electrode, respectively. All potentials are calibrated with respect to the RHE. Supplementary Figure S13 shows the first four polarization curves of NP Cu/Cu₅Zr electrode. In agreement with DFT simulation result, there takes place an irreversible reduction reaction of Cu hydroxide to metallic Cu at the potential of -0.17 V vs. RHE during the first HER measurement. This enables metallic surface Cu atoms to take part in the subsequent HER. In the plot of geometry area-normalized current density versus iR-corrected potential, Figure 3(a) shows the representative HER polarization curves of self-supported NP Cu/Cu₅Zr hybrid electrode and NP Cu and Zr monometallic electrodes at a scan rate of 1 mV s^-1, comparing with that of commercially available Pt/C, a benchmark HER catalyst, immobilized on NP Cu current collector. By virtue of the presence of Cu₅Zr clusters, the NP Cu/Cu₅Zr electrode exhibits remarkably enhanced HER catalytic activity, with an onset overpotential (~30 mV) much lower than the values of NP Cu (~140 mV) and Zr (~260 mV), which have either too low or too high HBE. The superior HER catalysis of NP Cu/Cu₅Zr is also demonstrated by the ultralow Tafel slope of ~68 mV dec^-1, compared with the values of bare NP Cu (~172 mV dec^-1) and NP Zr (~249 mV dec^-1) (Figure 3(b)). With the low onset overpotential and small Tafel slope due to high-density and high-activity Cu₅Zr clusters, the NP Cu/Cu₅Zr rapidly reaches the geometric area-normalized current density of 100 mA cm^-2 at the potential of -155 mV versus RHE, which is higher than that of NP Cu-supported Pt/C electrode (-199 mV) although the former exhibits slightly lower activity than the latter at low overpotential range from 0 to -86 mV (Figure 3(a)). The fast kinetics of NP Cu/Cu₅Zr electrode is further justified by electrochemical impedance spectroscopy (EIS) measurements in the frequency range of 100 kHz to 10 mHz. As shown in the Nyquist plots (Figure 3(c)), the EIS spectra of all nanoporous catalysts display characteristic semicircles in the high- and middle-frequency range, of which the diameters represent their charge transfer resistances (R_{\text{CT}}). Based on the equivalent circuit (inset of supplementary Figure S14), the NP Cu/Cu₅Zr is demonstrated to have the lowest R_{\text{CT}} value (~12  Ω) at the overpotential of 0.1 V among these catalysts with nanoporous architecture including the NP Cu-supported Pt/C (~41  Ω) (inset of Figure 3(c)), in agreement with their observations in Tafel plots (Figure 3(b)). The impressive HER catalysis results from the Cu₅Zr clusters, on which the hydroxygenated Zr surface atoms not only adsorb strongly HO{}^{\ast } but adjust the H{}^{\ast } adsorption at the Cu-Cu bridge sites, essentially boosting the HER kinetics as a result of the balance between the water dissociation and the H{}^{\ast } adsorption/desorption [52]. The unique behavior differs from the NP Cu/ZrO₂ hybrid electrode, on which the constituent ZrO₂ nanoparticles serve as strong HO{}^{\ast } adsorption sites but the Cu skeleton is too weak to adsorb the H{}^{\ast }, as well as the fully electrooxidized NP Cu/Cu₅Zr (NP Cu/Cu₅Zr-EO), on which there are only strong HO{}^{\ast } adsorption sites. This leads to the distinct HER activity of the pristine NP Cu/Cu₅Zr, with the overpotential at 100 mA cm^-2 being ~100 and ~250 mV lower than those of the NP Cu/ZrO₂ and NP Cu/Cu₅Zr-EO (Figure 3(d)) in addition to the exceptional Tafel slope (Figure 3(e)).

To further attest that intermetallic Cu₅Zr clusters are indeed active sites for the HER, we investigate the NP Cu/Cu₅Zr electrode after removing the exposed Cu₅Zr clusters in H₂SO₄ solution. Supplementary Figure S15a shows a typical SEM image of the H₂SO₄-treated Cu/Cu₅Zr electrode, displaying almost the same nanoporous architecture as the pristine one. Nevertheless, the XRD characterization demonstrates that most of the Cu₅Zr are removed except for a few clusters imbedded in the Cu ligaments (supplementary Figure S15b), as confirmed by the Cu/Zr/Al component change of 98.9/0.4/0.7 (supplementary Figure S15c) as well as the Zr 3d and Cu 2p XPS spectra with little amount of Cu^δ- and Zr²⁺ (supplementary Figures S15d and e). Figure 3(f) compares the HER polarization curve of the H₂SO₄-treated NP Cu/Cu₅Zr with that of the pristine one. Owing to the absence of Cu₅Zr clusters at the surface, the H₂SO₄-treated NP Cu/Cu₅Zr exhibits remarkably degraded HER activity, with the overpotential at the current density of 100 mA cm^-2 increasing to ~350 mV, which implies the indispensable role of Cu₅Zr clusters in achieving superior HER performance of NP Cu/Cu₅Zr electrodes. This is also reflected by the linear dependence of the overpotentials at 100 mA cm^-2 on the surface areas, which are adjusted by controlling the dealloying time (supplementary Figures S16a–c) or precursor alloy components (supplementary Figure S17). Although there is always residual Al component in the ligaments, it is not expected to significantly influence the HER catalytic activity of NP Cu/Cu₅Zr. As shown in supplementary Figure S16d, the NP Cu/Cu₅Zr electrodes with different residual amount of Al exhibit almost the same specific activities at the overpotential of 100 mV. To evaluate quantitatively the HER activity of Cu₅Zr clusters, here we approximately estimate the specific current density (j_{\text{s},\text{C}{\text{u}}_5\text{Zr}}) of the electroactive Cu₅Zr clusters according to the equation [53] j_{\text{s},\text{C}{\text{u}}_5\text{Zr}}=\left(j_{\text{Cu}/{\text{Cu}}_5\text{Zr}}{A}_{\text{Cu}/{\text{Cu}}_5\text{Zr}}-j_{\text{s},\text{Cu}}{A}_{\text{s},\text{Cu}}\right)/A_{\text{s},\text{C}{\text{u}}_5\text{Zr}}, where j_{\text{Cu}/{\text{Cu}}_5\text{Zr}} and j_{\text{s},\text{Cu}} are the specific current densities of NP Cu/Cu₅Zr and the constituent Cu surface, A_{\text{Cu}/{\text{Cu}}_5\text{Zr}}=A_{\text{s},\text{Cu}}+A_{\text{s},\text{C}{\text{u}}_5\text{Zr}} with A_{\text{s},\text{Cu}} and A_{\text{s},\text{C}{\text{u}}_5\text{Zr}} being the specific surface areas of Cu and Cu₅Zr components in the NP Cu/Cu₅Zr, respectively. Considering that the NP Cu/Cu₅Zr and bare NP Cu electrodes have almost the same nanoporous architectures with primary (111) surface (Figure 2(e) and supplementary Figure S5), the value of j_{\text{s},\text{Cu}} refers to that of NP Cu while the A_{\text{s},\text{Cu}} is calculated through the broad anodic peak between 0.5 and 0.71 V corresponding to the formation of Cu₂O with a charge density of 360  μC cm^-2 (supplementary Figure S18) [25]. With an assumption that the Zr²⁺ corresponds to the surface Zr atom, A_{\text{s},\text{C}{\text{u}}_5\text{Zr}} is evaluated according to A_{\text{s},\text{C}{\text{u}}_5\text{Zr}}={cA}_{\text{s},\text{Cu}} with c being the surface Zr²⁺/Cu component ratio. At the potential of -200 mV versus RHE, j_{\text{s},\text{C}{\text{u}}_5\text{Zr}} reaches ~3.1 mA cm^-2_SSA, ~300-fold enhancement relative to Cu. This enlists NP Cu/Cu₅Zr to outstand among the best nonprecious metal-based HER catalysts, including alloys and compounds, as shown in Figure 3(g) and supplementary Table S3 for the overpotential comparisons at various current densities in 1 M KOH electrolyte.

As a consequence of the unique monolithic and steady architecture, all NP Cu/Cu₅Zr electrodes with different Cu/Zr/Al compositions can reach the current density of as high as 500 mA cm^-2 at low overpotentials in 1 M KOH aqueous solution (supplementary Figure S17a). It takes the NP Cu₉₂Zr₅Al₃ electrode only an overpotential of -280 mV, lower than the values of NP Cu₉₇Zr₁Al₂ and Cu₈₀Zr₁₆Al₄ that have either less electroactive Cu₅Zr clusters or smaller specific surface areas (supplementary Figure S17b). To our knowledge, this is the lowest overpotential reported in literature (supplementary Table S3). Furthermore, the NP Cu/Cu₅Zr electrodes exhibit exceptional structural and electrochemical durability in the accelerated stability tests, which are carried out by the continuous potential cycling between -0.2 and 0.1 V versus RHE at a scan rate of 100 mV s^-1 in 1 M KOH solution. As shown in supplementary Figure S19, the NP Cu/Cu₅Zr electrode not only maintains the nanoporous architecture but keeps the constitutes of Cu ligaments and Cu₅Zr clusters with almost the same chemical states. Although Al thermodynamically tends to dissolve in basic solution (the standard dissolution potential of -1.66 V versus RHE for Al to Al³⁺), ICP measurement indicates that there is no evident change of Al component because of the protection of Cu surface layer. As a consequence, the HER polarization curve after 10,000 cycles only shifts negatively by 4 mV relative to the initial one, which leads to ~2% decay of current density at the overpotential of ~280 mV (Figure 4(a)) probably due to a slight increase in charge transfer resistance (Figure 4(b)). To simulate the industrial product of H₂ at large current density, we perform a galvanostatic stability test at various current densities from 10 to 500 mA cm^-2 in 1 M KOH electrolyte (Figure 4(c)). When performing at each current density for 8 h, the NP Cu/Cu₅Zr electrode exhibits stable potentials, indicating the outstanding durability. Even at the current density of as high as 500 mA cm^-2, the NP Cu/Cu₅Zr electrode can withstand the violent H₂ gas evolution to maintain the original nanoporous structure in the long-term durability measurement (inset of Figure 4(c)). The impressive catalytic stability can be attributed to the electrochemical stability of Cu₅Zr clusters and the robustness of nanoporous Cu structure for hydrogen bubble release. Moreover, the practical hydrogen production rate in Figure 4(d) agrees well with the theoretical value, revealing that the Faradaic efficiency reaches approximately 100%.

Catalyst electrodes with a nanoporous structure were fabricated by a facile alloying/dealloying procedure. Precursor Cu_20-xZr_xAl₈₀ (x=0, 1, 3, 5, and 20 at%) alloys were produced by arc melting pure Cu, Zr, and Al under an argon atmosphere. After cutting into thin sheets with thickness of ~400  μm and further polishing by sandpapers (600, 1200, and 2000 Cw), nanoporous catalyst electrodes were prepared by chemical dealloying in a N₂-purged 6 M KOH aqueous electrolyte at 70°C until there is no gas to be produced. To identify the electroactive sites that enhanced the Zr atoms, the nanoporous Cu/Cu₅Zr catalyst electrode was further treated in a N₂-purged 0.5 M H₂SO₄ aqueous electrolyte at 70°C to remove surface Zr atoms. All these catalysts were rinsed in ultrapure water (18 MΩ) for multiple times to remove substance in nanoporous structure. Commercially available Pt/C catalyst with weight of 1.5 mg (20 wt%, Johnson Matthey) was mixed into a Nafion (0.05 wt%, Sigma-Aldrich) solution containing isopropanol (20%) and water (80%) to form Pt/C ink under rigorous sonication. 100  μL Pt/C ink was drop-cast onto NP Cu electrode (2\text{mm}\times 5\text{mm}\times 0.4\text{mm}) to prepare the Pt/C catalyst electrode for electrochemical measurements.

Field-emission scanning electron microscope (JSM-6700F, JEOL, 15 keV) equipped with X-ray energy-dispersive spectroscopy (EDS) was employed to characterize microstructure and chemical composition of nanoporous catalysts. High-resolution transmission electron microscopy (HRTEM) and scanning transmission electron microscopy (STEM) characterizations were performed on a field-emission transmission electron microscope (JEM-2100F, JEOL, 200 keV) and a field-emission transition electron microscope (JEM-ARM200CF, JEOL) operated at 200 keV and equipped with double spherical-aberration correctors for both condenser and objective lens, respectively. X-ray diffraction patterns of all nanoporous catalyst electrodes were collected from a D/max2500pc diffractometer with a monochromated Cu K_α radiation. X-ray photoelectron spectroscopy (XPS) analysis was conducted on a Thermo ECSALAB 250 with an Al anode. Charging effects were compensated by shifting binding energies based on the adventitious C 1s peak (284.8 eV). Atomic ratio of elements was analyzed using ICP-MS (Thermo electron). N₂ adsorption/desorption isotherms were collected at 77 K by a Micromeritics (ASAP 2020 Plus) system.

All nanoporous catalyst electrodes were directly used as working electrodes for electrochemical measurements, which were performed in a classical three-electrode setup with a graphite rod as the counter electrode and a saturated calomel electrode (Hg/Hg₂Cl₂, SCE) as the reference electrode. The HER polarization curves of nanoporous catalyst electrodes were collected at a scan rate of 1 mV s^-1 in a N₂-saturated 1 M KOH aqueous solution at room temperature. The reference electrode was calibrated to the reversible hydrogen potential (RHE). Electrochemical impedance spectroscopy (EIS) analysis was performed at various overpotentials with frequency 0.01 to 100,000 Hz with 5 mV amplitude. To evaluate the electrochemical surface area (ECSA), cyclic voltammograms (CVs) were collected from 0.5 to 1.65 V (versus RHE) at a scan rate of 20 mV s^-1. The HER stability tests of nanoporous Cu/Cu₅Zr electrode were carried out at the current densities of 10, 100, 200, 300, 400, and 500 mA cm^-2 in 1 M KOH solution, respectively, for 8 h. In addition, a potential cycling in a window of -0.2 and 0.1 V was also performed for 30,000 cycles with a scan rate of 100 mV s^-1 in a N₂-saturated 1 M KOH solution. The hydrogen production via the HER experiments were further conducted at the current density of 20 mA cm^-2 for NP Cu/Cu₅Zr electrode (0.35 cm^-2) in a typical H-type cell separated by a proton exchange membrane, and the generated gas was analyzed by gas chromatography (GC-2014).

All spin-unrestricted DFT calculations were carried out using the Vienna Ab initio Simulation Package (VASP) with the Perdew, Burke, and Ernzerhof (PBE) functional. The projector augmented wave (PAW) method was adopted to describe the electron-ion interactions. According to our careful convergence tests, the cutoff of plane wave basis sets was set to 400 eV. A Monkhorst-Pack grid of 4\times 4\times 1 and 12\times 12\times 3 k-points were used for geometry optimization and electronic structure calculations, respectively. A first-order Methfessel-Paxton smearing of 0.2 eV was applied to accelerate electronic convergence for geometry optimization. The electronic structure and geometry optimization convergence tolerance were 10^-5 eV, 0.005 eV Å^-1, respectively. The transition states were obtained using the Climbing Image Nudged Elastic Band (CI-NEB) method. The convergence tolerance of NEB image was 0.05 eV Å^-1. The Cu(111), Cu₅Zr(111), and single-Zr-atom–doped Cu(111) and Zr(111) were modeled by using five layers, the bottom two layers were fixed while others were fully relaxed. A vacuum layer of 15 Å was used to avoid the unwanted interaction between the slab and its period images. The optimized structures and the charge density difference plots were illustrated with VESTA software.

The reaction free energy (\Delta G) was calculated according to \Delta G=\Delta E+\Delta E_{\text{ZPE}}-T\Delta S, where \Delta E is the reaction energy, \Delta E_{\text{ZPE}} is the zero-point energy, T is the absolute temperature, and \Delta S is the change of entropy. {\Delta E}_{\text{ZPE}}=1/2\int F\left(\omega \right)ħ\omega d\omega, where ħ is the Planck constant, F\left(\omega \right) is the phonon density of states. \Delta S_{\text{H}} is considered as -1/2{S^0}_{\text{H}2} due to the fact that the vibrational entropy in the adsorbed state is small meaning, where {S^0}_{\text{H}2} is the entropy of H₂ in the gas phase at standard conditions. In addition, the adsorption energy (E_{\text{M}‐\text{H}}, H denoting the corresponding species) was determined by the equation E_{\text{M}‐\text{H}}=E_{\text{T}}-E_{\text{M}}-E_{\text{H}}, where E_{\text{T}} is the total energy of the catalyst with species, E_{\text{M}} and E_{\text{H}} are the energies of the isolated catalyst and the species, respectively.