Beyond traditional TOF: unveiling the pitfalls in electrocatalytic active site determination

Arun Karmakar*^ab and Subrata Kundu*^ab
aAcademy of Scientific and Innovative Research (AcSIR), Ghaziabad-201002, India. E-mail: arunkarmakar020@gmail.com
^bElectrochemical Process Engineering (EPE) Division, CSIR-Central Electrochemical Research Institute (CECRI), Karaikudi-630003, Tamil Nadu, India. E-mail: skundu@cecri.res.in; kundu.subrata@gmail.com; Fax: +91 4565 241487; Tel: +91 4565 241487

First published on 29th July 2025

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1. Introduction

TOF has become an important parameter in electrocatalysis, providing a more inherent gauge of catalytic activity than standard performance descriptors such as current density or overpotential.¹ Significant effort has been made previously to understand the significance of the term ‘TOF’ (Fig. 1). For instance, the first comprehensive discussion was put forward by Martin and co-workers.² This viewpoint critically examined and clarified the often-confused definitions of TOF and turnover number (TON) in catalysis. A strict kinetic framework was proposed for unambiguously defining and calculating these parameters in catalytic cycles. This report offers insightful guidance for experimental and theoretical chemists to assess catalytic efficiency more meaningfully and reproducibly.

However, the given discussion is purely based on a normal chemical reaction and does not account for any electrochemical aspect of interest. The importance of TOF in electrocatalysis was first highlighted in an editorial that pointed out the need to consider TOF as a true descriptor of intrinsic electrocatalytic activity.³ It sets out clear best practices for normalization of catalytic performance using electrochemical surface area and TOF, facilitating reasonable and useful comparisons. Subsequently, two seminal reports by Anantharaj et al. and Gan et al. further emphasized the importance of accurately reporting TOF while also discussing potential methods of ECAS.^4,5 More recently, Kundu and co-workers gave insightful thoughts on the advantages and limitations of various reported methods of determining ECAS across various electrocatalysts.^6,7 However, none of the above studies consider the core fundamental understanding of TOF and its molecular significance.

A conventional mathematical formulation signifies the dependence of TOF on the current density and number of electroactive sites. The details of the electrochemical rate equation analysis and consideration of Faraday's law of electrolysis suggest that the current density obtained from the polarization information reflects information about the rate of an electrochemical reaction. The TOF signifies the corresponding rate constant, which (normalized rate of reaction with respect to the ECAS) directly relates the energy of activation according to the Arrhenius equation.⁸ Although current density reflects the overall rate of a reaction, it is extremely sensitive to the number and accessibility of active sites, so it is not easy to determine whether increased activity is due to improved catalytic performance or merely due to a greater density of reactive centers. TOF, in contrast, is the extent to which every active site accelerates the reaction and works towards revealing only how effective particular catalytic sites are in effectuating the electrochemical process. Furthermore, detailed kinetic analysis reveals that the TOF is strongly related to the RDS of the overall reaction. Therefore, consideration of the nature of the active sites in RDS is crucial for understanding the origin of the improved electrocatalytic activity. As a measure of the rate constant of an electrocatalyst, a small deviation in the TOF value directly introduces an exponential error in the energy activation, which is purely determined from the RDS. This signifies the importance of determining the exact TOF information for the catalytic cycle.

Nevertheless, the precise determination of TOF is still one of the most enduring problems in this field of research. This is largely due to the uncertainty involved in identifying and measuring active sites, particularly in complicated, heterogeneous, and dynamically changing materials. Conventional electrochemical techniques for the estimation of active sites based on double-layer capacitance, faradaic charge analysis, or redox peak integration depend on general electrochemical or physical assumptions that may distort the actual number of reactive centers and result in incorrectly reported TOF values.⁷ Quantitative analysis towards direct determination of the number of metal ions via Inductively Coupled Plasma (ICP) analysis could potentially offer an electrochemical assumption-free method to determine ECAS value.^9–11 However, without having exact knowledge of the nature of active sites and their participation in the RDS, it usually introduces an overestimation of the ECAS value. Moreover, for multi-metallic heterogeneous electrocatalysts, assuming that all the metal components are equally active, does not consider the importance of the RDS and the nature of the active sites participating in it.

Combining in situ and operando spectroscopic methods with kinetic modelling and density functional theory (DFT) can offer a more complete understanding of the active site topography and its evolution under applied potentials.¹² Ultimately, it will take a convergence of rational design of catalysts, quantitative active site determination, and mechanistic interpretation from experiment and theory to move our knowledge of TOF forward in electrocatalysis. It is only through this multifaceted effort that TOF can live up to its promise as an entirely intrinsic activity descriptor, thereby informing the design of next-generation materials for energy storage and conversion applications. Overall, this report presents a critical conceptual model emphasizing the molecular importance of TOF in electrocatalysis for distinguishing intrinsic activity from apparent performance. Addressing the pitfalls in ECAS determination and the significance of RDS enhances the knowledge of active site efficiency, leading to the rational design of high-performance electrocatalysts.

2. TOF in electrocatalysis: what is it and why does it matter?

In 1966, Boudart et al. put forward the following statement:

Indeed, the catalytic activity, for a valid comparison, must be referred to the number of exposed surface atoms of a specified kind. Thus, a convenient way to express catalytic activity is using a turnover number equal to the number of reactant molecules converted per minute per catalytic site for given reaction conditions.

With this statement, the first statement of TOF has arisen and crossed the threshold into the land of the heterogeneous catalytic field.¹³ Recently, TOF is a pervasive term that mainly focuses on catalytically active centres and is different from the classical ‘rate of the reaction’, which accentuates the formation of the product. Despite its universal utility, the perception of TOF is still unclear. According to the IUPAC, the more concise definition of TOF is as follows:²

Commonly called the turnover number (TON), N, and defined, in enzyme catalysis, as molecules reacting per active site in unit time.

However, with significant advancements in electrochemical water splitting research, the commonly accepted definition of TOF is as follows: the number of products formed in an electrochemical reaction per active site of the catalyst per unit time interval. In some cases, it is expressed in terms of moles of products, i.e., the number of moles of products formed or reactants consumed per mole of active site per unit time. Mathematically, it can be expressed as follows:

	(1)

The definition of TOF is straightforward in typical chemical reactions, where the quantity or moles of consumed reactants can be easily measured using standard analytical techniques. This proves to be more complicated in electrochemical systems. In highly alkaline conditions, for example, the variation in the concentration of the reactant (e.g., OH⁻ or H₂O) tends to be zero. In addition, when dealing with water splitting, the reaction is not chemical but electrochemical, and it includes charge transfer across the electrode/electrolyte interface. Thus, connecting TOF with electron transfer kinetics is essential for properly assessing catalyst performance in these systems.

Consider an electrochemical reaction defined as follows:

A + ne− → B	(2)

From basic electrochemistry, it is known that the term ‘current’ in an electrochemical system is defined as follows:

	(3)

where Q represents the accumulated charge. The corresponding quantification of the molecules of the reactants electrolyzed (N) can be expressed as follows:

	(4)

Therefore, the rate of the reaction can be expressed as follows:

	(5)

It is often more complicated to interpret the rate of an electrode reaction than to interpret the rate of a reaction occurring in the solution or gas phase. The latter is referred to as a homogeneous reaction, as it occurs throughout the medium at a consistent rate. In contrast, an electrode process is a heterogeneous reaction that takes place solely at the interface between the electrode and electrolyte. In addition to the usual kinetic variables, its rate depends on mass transfer to the electrode and various surface effects. Since electrode reactions are heterogeneous, their reaction rates are usually described in units of mol s⁻¹ per unit area (A); that is,

	(6)

Now, considering the rate of the reaction in terms of the catalyst's concentration, we define the rate as follows:

	(7)

where is the number of active metal sites present for a particular electrochemical reaction. Notably, considering the number of a particular active site is much more justified than considering the moles of the catalyst based on the molecular weight of the catalyst under heterogeneous conditions. Now, from eqn (6) and (7), we have the following equation:

	(8)

Therefore,

	(9)

Considering Faraday's law, the number of faradaic products obtained by electrolysis is given as follows:

	(10)

Or

	(11)

Replacing J in eqn (11) in eqn (9) and considering t = 1 s, we have

	(12)

Thus, the rate constant of an electrochemical reaction is simply the amount of product molecules produced per active site per unit time, and this defines the TOF. According to this definition, TOF is a representation of the rate constant of an electrochemical reaction in terms of the active sites of the catalyst and hence represents a key and intrinsic property of a specific catalyst.

3. Turnover frequency as an intrinsic activity parameter

A catalyst's intrinsic activity demonstrates site-specific or per-site activity information and, therefore, relates it to the chemical and physical properties of the catalytic site. It is essential to advance a fundamental clarification of the origins of high catalytic performance by establishing an appropriate intrinsic activity measurement. However, the absence of proper experimental techniques makes the task of determining intrinsic activity challenging. Depending on the application and mechanical outcomes of the electrochemical reaction, most of the catalysts possess different types of surface sites, with each of the active sites having its inherent activity.

The most common approach to derive the intrinsic activity, per-site activity is first to quantify the total number of active sites, followed by the determination of the TOF value as a function of overpotential. Regrettably, most recent studies do not consist of TOF data and report only the apparent extrinsic parameter, as mentioned in an earlier report.¹⁴ A more appropriate explanation of why the TOF information is an essential parameter to scrutinize the intrinsic activity of an electrocatalyst can be elucidated through the LSV polarization information of two catalysts, ECat-1 and ECat-2 (Fig. 2a). Although the overpotential outcomes are identical, when examining the activity below and above the cross point, a distinct trend in activity arises. ECat-1 outperforms in low-current devices operating below 30 mA cm⁻², while ECat-2 excels in high-current density devices, i.e., >30 mA cm⁻². Consequently, the correlation between current and overpotential cannot offer a precise and comprehensive assessment of an electrocatalyst's efficiency in facilitating OER or any electrocatalytic reaction. Moreover, while analysing the nature of charge transfer kinetics through Tafel slope analysis, despite the identical chemical nature, the two catalysts show different potential-dependent kinetics at the interface (Fig. 2b). This, in turn, validates the use of TOF information as the most important electrochemical parameter in this field of research. However, it is crucial to examine the experimental details to ensure that its fundamental significance is preserved.

4. Insight into the active site: a catalytic perspective

As highlighted in the earlier section, the TOF value for an electrocatalyst is mainly a function of the obtained current density at a specified overpotential value and ECAS over the working electrode. There might be two main viewpoints when evaluating catalytic efficiency: (a) based on the amount of product formed and (b) considering the catalytic cycle's turnover (Fig. 3). The first approach deals with the number of products (say O₂) formed over a specific period, measured using various techniques, such as gas chromatography (GC), relative to the moles of the catalyst used. Usually, for a homogeneous electrocatalytic reaction involving a molecular catalyst (with a well-defined molecular configuration and a single active metal site), this measurement is straightforward and relatively free from obstacles in determining the number of active sites. However, in the second approach, which is often more appropriate for characterizing the efficiency of an electrocatalyst, consideration of the nature of catalytic cycles is more appropriate. From the given TOF equation:

	(13)

With three constant parameters, the TOF value primarily varies with overpotential-dependent current density (J) and the number of active sites ‘τ’, which remains independent of applied overpotential. Since TOF is linearly proportional to the current density for a particular catalyst, it follows an exponential variation according to the Butler–Volmer equation. However, being independent of applied overpotential, the variation of TOF with ‘τ’ is not the same as with the current density. Therefore, the terms ‘J’ and ‘τ’ vary independently in the TOF formulation.

A clear consequence of this independent variation is reflected in the following facts:

❖ For a particular electrocatalyst with a defined active site, the calculated TOF value varies exponentially as a function of the overpotential value.

❖ Nevertheless, in a comparison between various catalysts, particularly state-of-the-art catalysts where τ may vary significantly, an increase in J does not always indicate a higher TOF. While considering the electrochemical performance of two NiFe-LDH (characterized with XRD analysis, Fig. 4a) with Ni to Fe ratio of 1:1 (ICP-MS ratio: 1:0.92) and 2:1(ICP-MS ratio: 2:0.95), the higher Ni-loaded LDH [NiFe-LDH (2:1)] drives a higher current density of 46.40 mA cm⁻² (at 1.55 V vs. RHE) compared to the low Ni-loaded LDH [NiFe-LDH (1:1)] of 32.76 mA cm⁻² (Fig. 4b).¹⁵ Additionally, the higher current density [NiFe-LDH (2:1)] possesses a) higher Ni³⁺→Ni²⁺ redox area, indicating increase in active site density (Fig. 4c and b) high surface accumulated charge density, indicating enriched electron transfer over the electrode surface (Fig. 4d and c) higher ECAS, reflecting enriched electro active sites compared to [NiFe-LDH (1:1)] (Fig. 4e). However, when measuring the TOF value, [NiFe-LDH (1:1)] possesses 3.3 times higher intrinsic activity compared to [NiFe-LDH (2:1)] (Fig. 4f). The possible rationalization of the given fact is that an increase in Ni loading and subsequent oxidation leads to an increase in surface charge density, which strengthens Ni–O bonds. This makes the desorption of O₂ molecules from the catalysts energetically unfavorable. Consequently, although a portion of the added Ni²⁺ ions favors the O₂ formation, contributing to an increase in the ‘J’ value in the numerator of eqn (9), this increase is insufficient to outweigh the significant rise in the denominator.¹⁶

5. Kinetic insights into the independent roles of current density and active site density in electrocatalyst efficiency

The rate of an electrochemical reaction provides information about how quickly the reaction occurs in the overall geometric area of the electrode, i.e., overall reaction speed across the entire electrode surface. However, the rate constant tells the activity per active site or the number of catalytic cycles that each active site undergoes per unit time.

A detailed insight into eqn (9) and an understanding of the significance of various terms indicate that the current density multiplied by a certain constant reflects the rate of the corresponding electrochemical reaction (Fig. 5). Therefore, the high current density for a particular electrocatalyst, say [NiFe-LDH (2:1)], reflects an increase reaction rate towards OER compared to [NiFe-LDH (1:1)]. However, while considering the intrinsic activity or the rate constant that deals with site-specific performance, [NiFe-LDH (1:1)] was superior to [NiFe-LDH (2:1)] despite having fewer active sites. This is possibly because NiFe-LDH with a 1:1 Ni to Fe distribution possesses fewer but highly efficient active sites with optimized as a result of the uniform distribution of Fe³⁺ ions. This uniform distribution enhances synergistic electronic interaction between Ni and Fe centers and therefore promotes faster charge transfer kinetics at the interface.

6. Does a higher rate of reaction always reflect a higher rate constant in OER catalysis?

An increase in catalytically active sites (τ), e.g., in the NiFe-LDH system with a 2:1 Ni:Fe ratio over a 1:1 ratio, can give rise to higher OER rates; this does not necessarily equate to an increase in the intrinsic activity per site, as reflected in the TOF value. Here, a higher loading of Ni drives a larger current density, reflecting the more active sites involved in the reaction. However, this is accompanied by a significant decrease in the observed rate constant (TOF), indicating that after a point, the greater active site density adds more to the numerator of eqn (9) (‘J’) than it offsets the accompanying increase in the effective τ in the denominator. This finding emphasizes two significant conclusions: (1) enhancing the catalytic activity solely based on the increase in the number of active sites can enhance the catalytic performance by improving the overall rate of an electrochemical reaction but may simultaneously lead to a decrease in the rate constant of TOF; and (2) an imbalance between current density and intermediate reaction lifetime can obscure the true kinetic advantages of such approaches.

7. Quality or quantity: what truly drives intrinsic electrocatalytic activity?

From the above discussion of having efficient electrocatalysts for electrocatalytic applications, such as OER, a common question often arises: should we focus on increasing the number of active sites or enhancing their intrinsic reactivity by modulating the activation energy barrier for the rate-determining step?. Usually, an immense effort has been made to improve catalytic performance by various surface engineering techniques, such as doping, nano-structuring, and heterostructure formation, to improve reaction kinetics and active site density as well. This would greatly enhance the overall current density, i.e., the rate of the reaction. However, this does not guarantee intrinsic activity performance, as observed previously. This leads to an important consideration: is it possible to increase catalytic efficiency by modulating the active sites rather than merely increasing their number?

For instance, Yousef Haik and his group developed amorphous gold-supported electrodeposited CoB as a new benchmark electrocatalyst for OER.¹⁷ The intrinsic activity of the given CoB was improved by doping Gd³⁺ ions in the lattice, which subsequently reduced the lower charge transfer resistance at the interface. Gd-CoB@Au possesses the highest TOF value (1570 s⁻¹) compared to reported cobalt-based electrocatalysts. This particular doping strategy increases the current density value by about 19 times compared to CoB@Au, whereas the increase in active sites was about 2 times higher (Table 1). The effect of Gd doping on OER was further evaluated over CoO@Au to determine the importance of the synergism between Co, Gd, and B ions to improve intrinsic activity. An enhancement in both the current density and number of active sites was observed compared to CoB@Au. This leads to the conclusion that the synergism of the active Co center in the presence of Gd and B ions is most important for improving the rate of the reaction and the rate constant. It is noteworthy that Gd-CoB@Au possesses a relatively lower number of the active sites compared to Gd-CoO@Au; however, the former displays a higher current density, indicating an enhanced reaction rate. In addition to the increased reaction rate, Gd-CoB@Au portrays a high TOF value, i.e., a higher rate constant compared to Gd-CoO@Au. This suggests that an increase in cooperative interaction between Gd³⁺ and Co ions in the presence of boron significantly accelerates charge transfer kinetics. Therefore, the presence of boron improves the quality of the active sites, which proves to be more beneficial than merely increasing their quantity.

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Another interesting finding was reported by Kundu et al., where a surface engineering strategy was developed to enhance OER kinetics on the CoFe-LDH surface by anchoring Ru nanoparticles (NPs).¹⁸ Anchoring of Ru NPs greatly reduces the charge transfer resistance (R_ct) at the electrode–electrolyte interface. In this work, an interesting Ru³⁺ (which subsequently reduced to metallic Ru NPs under reducing conditions) loading-dependent OER activity was observed. With an increase in Ru³⁺ loading from 1% (with respect to Co²⁺ ion concentration) to 3% over the CoFe-LDH surface, an increase in OER activity was observed. This was identified with the observed current density at 1.55 V vs. RHE of 8.53, 35.68, and 80.05 mA cm⁻² for pristine CoFe-LDH, Ru@CoFe-LDH (1%), and Ru@CoFe-LDH (3%), respectively. Further increase in Ru loading subsequently reduces the current density value to 63.80 mA cm⁻² in the case of Ru@CoFe-LDH(5%). Electrochemical analysis towards the determination of the number of the active sites exhibits the fact that there is a gradual increase in the value as a result of increased Ru loading over the surface. However, with a specific loading of Ru NPs, i.e., Ru@CoFe-LDH (3%), the catalyst possesses the highest rate of reaction and rate constant as well. A volcano-type relationship is observed between surface charge accumulation and thermoneutral current density across various Ru-loaded CoFe-LDHs, with Ru@CoFe-LDH (3%) showing peak performance. This indicates that 3% Ru loading achieves an optimal surface charge density, aligning with the Sabatier principle by balancing OH⁻ adsorption and O₂ desorption for efficient catalysis. Beyond this, Ru loading the enhanced positive charge led to strengthening of the M–O bonds, hence creating an extra barrier for O₂ detachment for OER.

These findings highlight that although increased active site quantity improves overall catalytic activity, it does not inherently ensure improved intrinsic activity per site. Rather, purposeful active site environment tuning by applying methods such as heteroatom doping or electronic structure manipulation is more effective in enhancing turnover frequency (Fig. 6a). For instance, Clemens et al. executed an interesting study to enhance electrocatalytic OER activity in NiFe-LDH via Zr⁴⁺ ion doping.¹⁹ Electrochemical results indicate that NiFeZr-LDH achieves an excellent TOF value of 0.06 s⁻¹, with an applied overpotential value of 216 mV. However, NiFe-LDH and NiZr-LDH (Ni as the active site) drive the same TOF values at 298 and 420 mV overpotential, respectively. The high intrinsic activity of strong synergism (Fig. 6b) among Ni, Fe, and Zr ions in the hydroxide lattice subsequently reduces the charge transfer resistance and the Tafel slope value (faster charge transfer) compared to pristine NiFe-LDH. The free energy assessment of OH* adsorption over the active site via DFT calculation suggested that with Zr⁴⁺ ions as dopants, was neither too low nor too high and subsequently possessed balanced adsorption and desorption. The authors calculated the number of active Ni via ICP-MS analysis. The observed respective amounts of Ni were 10.17 and 9.97 μmol mL⁻¹ before and after the Zr⁴⁺ ion doping, respectively. Moreover, the observed Ni in NiZr-LDH was 19.12 μmol mL⁻¹. Therefore, Ni ions with a relatively lower amount possess a high rate constant or TOF value towards OER, which is possibly attributed to facile mass transfer at the interface as a result of strong synergism between the three metal ions. Similarly, approaches for the enhancement of charge transfer kinetics over NiFe-LDH-modified electrodes were conducted by Chen et al. via Ce³⁺ ion doping.²⁰ The Ce³⁺ ions with a singly occupied 4f orbital enhance the charge transfer rate at the interface as a result of strong electron coupling between Ni and Fe in the LDH lattice (Fig. 6c). The ratios of Ni:Fe and Ni: (Fe + Ce) were 2.74 and 1.77 in pristine Ni₂Fe₁-LDH and Ni₂Fe_0.7Ce_0.3-LDH, respectively, from the EDS analysis. Although the report does not encounter any TOF value, other electrochemical outcomes, such as Tafel slope and charge transfer resistance (R_ct) values, indicate improvement of the efficiency of charge transfer and therefore increase its intrinsic activity in Ce-doped NiFe-LDH despite lower active Ni content. Therefore, from the overall analysis, it is notable that active site quality, not its quantity, is the determining factor in promoting intrinsic electrocatalytic activity.

8. TOF as a function of RDS: active site ambiguity in multi-center catalysts

Consider the following three-step electrochemical reaction:

A → B (Rate constant = k1)	(14)

B C (Rate constant = k2)	(15)

C D (Rate constant = k3)	(16)

Assuming the first step is RDS, the free energy change of activation is larger than the second step . Being the slowest step other than the first step, all subsequent steps are at quasi-equilibrium. Therefore, at equilibrium, applying the law of mass action, we have

	(17)

	(18)

Therefore, although product D formation is fast (owing to quasi-equilibrium), its rate depends indirectly on how fast B and from which catalytic site it is formed, and that is tied to the RDS, i.e., A → B. Therefore, the overall rate expression can be written as follows:

rate = k1[B]	(19)

When considering the catalytic system, the rate of formation of B intrinsically depends on the efficiency and number of corresponding catalytic sites. Hence,

rate = k1[cat]	(20)

The determination of TOF depends highly on the nature of the active sites utilized in the RDS. Therefore, the proper identification of the active site and the rate-determining step (RDS) nature, as identified from the above kinetic analysis, is highly important. This led to a more subtle strategy when dealing with catalytic performance beyond monometallic systems.

Considering the overall water splitting activity of LDH as a new alternative to noble metal-based electrocatalysts, with a general chemical formula of M²⁺_1−x M³⁺_x(OH)₂ (A)ⁿ⁻_x/n yH₂O, where M²⁺ and M³⁺ are the bivalent and trivalent metallic cations, respectively, and Aⁿ⁻ is the intercalated anion. When considering M²⁺, metal ions with a low positive charge possess a higher d-band center and therefore act as preferential OH* adsorption sites under anodic conditions, where the valence state is taken up further towards the Fermi level.^21–23 The metal ions with a higher valence state (M³⁺) support the electron transfer process by stabilizing the high-valent metal ions formed by the oxidation of M²⁺. However, under cathodic HER conditions, the M³⁺ metal ions support the activation of water molecules by forming a strong M–O bond, followed by the abstraction of a proton by M²⁺ in the reduced state to form an M–H bond. For example, while considering the electrocatalytic activity of NiFe-LDH in total water splitting applications, the variation in active sites in OER and HER has been noticed (Fig. 7a–c).

In the case of OER, it is quite straightforward that the low valent Ni²⁺ ions majorly act as the OH* adsorption site and simple ICP-MS analysis or redox peak integration could be useful for determining the amount of Ni present. However, in cathodic HER under alkaline conditions, detailed insight into the kinetics reveals that a cooperative interaction between Ni²⁺ and Fe³⁺ ions is necessary. The presence of Fe³⁺ ions activates the water molecules (chemical step) to release free H* to be adsorbed over active Ni²⁺ ions, as experimentally identified by Edvinsson et al.²⁴ Now, as an active site for H-adsorption, one might consider evaluating the Ni concentration by ICP-MS analysis (electrochemical step) (Fig. 8).²⁷ However, as highlighted earlier, the TOF as a rate constant of a particular reaction varies depending on the nature of RDS. When considering the overall HER kinetics, there is a finite possibility of a water activation step being the RDS one; therefore, considering Ni²⁺ sites as the active site instead of the Fe³⁺ site might be misleading.

It is important to have an exact understanding of the nature of the active site as it was highlighted by Chan et al., being equivalent to rate constant of an electrochemical reaction the variation in TOF by 1-2 orders of magnitude reflect in the change of activation energy by 0.1–0.15 eV at 300 K using Arrhenius equation (eqn (20)).⁸

	(21)

where A is the pre-exponential factor, ΔG^# is the activation energy barrier, R is the universal gas constant, and T is the temperature in Kelvin. This diversification can be demonstrated based on the example of NiFe-LDH. There is sufficient evidence that variously composed NiFe-LDHs have been deeply investigated through adjustments in the ratio of Ni to Fe.

Systematic research of NiFe-LDH with various ratios of Ni:Fe, such as 1:1, 2:1, and 3:1, was performed by Kundu et al. Their electrochemical study reported that the most active catalyst was the NiFe-LDH with a 2:1 ratio of Ni:Fe.²⁵ Conversely, Shviro et al. conducted interesting research on hydrothermally synthesized NiFe-LDHs with various Ni:Fe ratios and established that the optimal ratio was 3:1, providing higher electrocatalytic activity.²⁶ Now, considering the variation in the active site with varying Ni:Fe ratios, it may vary from 1 to 3 or even more, and thus have the corresponding variations in the activation energy barrier (ΔG^#). What if Fe³⁺ is used as the active site for the activation of water in HER, such that this step becomes the rate-determining step (RDS) of the process?. If we calculate the turnover frequency (TOF) based on Ni in terms of its being the active site for the adsorption of hydrogen in the RDS, it is nearly three times smaller compared to using Fe as the active site for the activation of water in the RDS. Consequently, the ΔG^# is larger in the first case compared to the second one. One specific example of such a scenario was previously identified by Feng et al., where theoretical analysis revealed the importance of H₂O activation as RDS in NiFe-LDH. Subsequent surface modification Ru³⁺ ion doping lead to accelerate the HER kinetics.²⁷ Therefore, without exact knowledge of the nature of RDS and the corresponding active site, the determination of the active site from ICP-MS analysis or structural analysis introduces substantial error in the TOF information, and as a measure of the rate constant, this error could introduce a substantial change in the free energy of the reaction.

9. Determining the number of active sites in electrocatalysts: methods and common pitfalls

9.1. Determination of ECAS using the electrochemical method

The previous section dealt with the molecular significance of TOF and the importance of characterizing the nature of active sites and their quantification. Being equivalent to the rate constant of an electrochemical reaction, TOF represents the most important molecular character of an active site for a particular catalyst. Furthermore, detailed electrochemical rate analysis has revealed that the TOF corresponding to a specific catalytic cycle is highly sensitive to RDS. Therefore, the electrochemical active sites (ECAS) involved in the RDS play a particularly significant role in determining the overall catalytic activity. The common methodology of obtaining ECAS information is the integration of redox CV curves, followed by normalization by scan rate to obtain accumulated charge information corresponding to single electron transfer from the active sites, as highlighted by Machada et al.²⁸ Apart from the redox CV integration method, the ECAS information is usually determined by other electrochemical methods, such as hydrogen underpotential deposition (HUPD),²⁹ Cu underpotential deposition (Cu-UPD),³⁰ CO-stripping,³¹ and double layer capacitance (C_dl) method.³²

A detailed discussion on various ECAS determination methods has recently been provided by Ananthraj et al.⁵ However, after a detailed understanding of the importance and molecular significance of active sites, it is crucial to understand whether the existing methodology truly defines the TOF accurately. In this section, we highlight various available ECAS determination methods and their common pitfalls. Considering eqn (9), we calculate the TOF value of three commercial NiO-modified electrodes subjected to the OER study in 1 M KOH solution (Fig. S1a–d). The ECAS value for all the modified working electrodes is determined with the knowledge of the redox peak area corresponding to the Ni²⁺ → Ni³⁺ the oxidation process (Fig. S3a–d). A detailed calculation procedure is provided in the SI. The ‘J’ value (eqn (9)), which signifies the current density, can be of geometrical current density, i.e., normalized with respect to the geometrical surface of the electrode or electrochemical active surface area (ECSA) determined from the C_dl curve (Fig. S2a–d) or mass-activity normalized result. Fig. 9a–c depict the calculated TOF values of NiO materials with 0.1, 0.2, and 0.3 mg cm⁻² mass loadings, respectively. However, it is surprising that the TOF values vary with changes in the catalyst loading value. The calculated TOF values for NiO-1, NiO-2, and NiO-3 are 0.264, 0.144, and 0.086 s⁻¹, respectively (Fig. 2a). Therefore, despite the similarity in chemical aspects with changes in catalyst loading from 0.1 mg cm⁻² to 0.3 mg cm⁻², the TOF value decreased three times.

A similar trend can be observed from the ECSA and mass-normalized results shown in Fig. 2b and c, respectively.³³ Therefore, the expected characteristics of a descriptor are ‘intrinsic’ in nature, i.e., invariability towards any physical parameter; the given TOF equation does not hold (Fig. 2d). This variation could be ascribed to the different surface roughness behaviour and effective surface area of the three electrodes with different mass loadings. In addition to the geometric or exposed surface area, the TOF value of the catalyst varies with other physical parameters: (1) the nature of the current collector and (2) potential dynamics employed for polarization. The electrochemical behavior of the current collector employed for electrochemical analysis strongly influences the overall TOF outcomes. With an increase in the development of designing electrocatalysts, an in situ growth of catalyst material over various metallic foams, such as Ni or Cu foam (NF or CF), has been noticed. The enriched electrocatalytic activity of metal atoms of the metallic foam during LSV polarization led to an overestimated number of active sites available for OER compared to the same material loaded over a non-reactive carbon cloth (CC) or glassy carbon (GC) electrode. Fig. 10 illustrates the TOF and the number of the electrochemical active site (ECAS) information (Fig. 10a) of NiFe-LDH coated over CC and NF (with the same catalyst loading).⁷

Despite the same catalyst loading, the NiFe-LDH/CC possesses 1000 times lower ECAS value than NiFe-LDH/NF. This results in variations in the TOF value (Fig. 10b) for the same materials and the same loading for a particular scan rate value employed. Comparing the activity trend in terms of the obtained current density, the NiFe-LDH/NF possesses ∼35 times higher electrocatalytic activity. However, NiFe-LDH/NF depicts 25 times lower TOF value compared to NiFe-LDH/CC. Therefore, an increased current density value does not necessarily ensure an improved intrinsic activity for an electrocatalyst.⁷

When an electrode has a high current density, which provides information about the amount of product, a high TOF value is typical. Therefore, even though TOF is proportional to the current density value, why does NiFe-LDH/NF with a high current density value not exhibit a high TOF value?. Let us investigate what led to this outcome. During anodic polarization, there is a finite chance of the self-oxidation of metallic Ni to Ni²⁺ ions. This occurs along with the oxidation of metal ions in the catalyst to a high valence state, thereby contributing to overall activation. Therefore, adding a cation from the substrate increases the active sites, or ECAS value, in addition to the parent metal ions in the catalyst (Fig. 11). Although this effectively enhances the quantity of active sites, the accumulation of positive charge density on the working electrode surface may inhibit the desorption of oxygen intermediates. Consequently, this can compromise the quality of the active sites and negatively impact overall catalytic performance. Besides, for an identical electrocatalyst, depending on the scan rate employed for electrochemical analysis, the ECAS value and TOF value of the same materials vary. In addition to this substrate influence, another common pitfall has been observed recently by Anantharaj et al.; the TOF outcomes of an electrocatalyst calculated using eqn (9) depend on the TOF value over potential dynamics or scan rate employed for the electrochemical analysis.³⁴ A detailed experimental outlook of this phenomenon can be found in Fig. 12a and b, where Ni(OH)₂ is employed. With the change in the scan rate value employed for redox peak analysis from 10 to 50 mV s⁻¹, the TOF value could vary by about 9 times. This could be attributed to a change in the interfacial structure due to the influence of the employed potential dynamics; therefore, the current voltage pattern comes up with a different redox CV area, which was analyzed in depth in our previous work.

From the general discussion above, the true intrinsic activity of an electrocatalyst can be far from what is revealed with conventional TOF evaluations. The dependence of TOF on mass loading, scan rate, and the nature of the working electrode substrate undermines the objective of this determination. According to eqn (9), TOF is directly proportional to the current density obtained at a certain overpotential and is inversely proportional to the ECAS. This relationship may indicate that an increase in both current density and ECAS with higher mass loading could balance the numerator and denominator, thus resulting in a constant value of TOF. However, although mass loading may be increased by a factor of x with a proportionate increase in ECAS, this does not apply to the case of current density. Additionally, variations in scan rate significantly affect the ECAS value but only have a marginal effect on current density. Consequently, the TOF value significantly varies, indicating that the traditional evaluation method cannot truly reflect the intrinsic activity of the electrocatalyst.

9.2. Determination of ECAS from other methods

The number of metal ions or ECAS present over the working electrode substrate could also be determined by a non-electrochemical quantitative analysis, such as ICP-MS analysis. This commonly raises an important question: does 100% of metal ions participate in electrochemical reactions?. The answer is no: not all metals are catalytically active or involved in the catalytic process. Therefore, in real cases, there will be a site-specific distribution of metal activity; hence, the true active site will be different (depending on the active surface area). Therefore, to correlate this, Dutta et al. normalized the active site information for the ECSA value for a particular catalyst.³⁵ Interestingly, the same group and other groups have highlighted a fascinating approach to calculate the molecular active site density from the lattice parameter (from the X-ray diffraction information) and the number of metal ions in the unit cell of the lattice as follows:³⁶

	(22)

It is worth mentioning that the determination of ECAS using eqn (21) has no deal with scan rate information or substrate specificity. Moreover, this ECAS value is completely based on the molecular-level information of any catalyst and therefore should not vary with mass loading, scan rate, and working electrode substrate. Normalization of total oxygen turnover at a specified current density by active site density truly implies a ‘per-site’ TOF value for an electrocatalyst. However, the preceding methodology has a few shortcomings (not in terms of TOF outcomes) related to its material-specific applicability:

• For bi/multi-metallic electrocatalysts, it is not necessary for all the metals to be active sites for electrocatalytic applications. Therefore, determining the number of a particular atom is probably not easy.

• For amorphous electrocatalysts, owing to the absence of proper diffraction peaks, the calculation of cell parameters is difficult or impossible.

• For metal-free electrocatalysts, such as covalent organic frameworks (COFs), porous organic polymers (POPs), or graphene-based materials, owing to uncertainty in the exact active site, the assessment of the total number of active carbons is difficult despite having proper structural information. Neergat et al. made an effort to determine the active site density over nitrogen-doped carbon catalysts by monitoring the oxidation peak area characterization of adsorbed anthraquinone-2-sulfonate probe molecules.³⁷ The active site density measurement was performed using the following equation:

	(23)

It is worth noting that, according to eqn (22), the active site density varies as a function of the scan rate. A similar approach was recently executed by Banerjee and co-workers by employing an integrated CV area to evaluate the active site density.

• For an electrocatalyst with multiple co-ligand ligands, such as S, Se, and N, the proper assessment of the active site from the diffraction pattern is problematic. A thorough viewpoint on the determination of the active site density in these materials is given by Hoffmann et al., and from their report, it is worth pointing out that most of the available methods are scan rate dependent.³⁸

9.3. In situ spectroscopic and theoretical analysis of the active site in electrocatalysis

In the given circumstances, the quantitative analysis of metal ions via ICP-MS or OER, and related analysis for co-ligands, such as CHNS, could be an option, as it is devoid of any scan rate-dependent or substrate factor in the electrochemical system. Assuming 100% of metal ions to be active for electrocatalysis might be misleading, but normalization with respect to ECSA could bring the exact reactivity in the system. From the overall discussion, it is important to point out that whatever methods may be available, methods of deriving active site density give the relative information by keeping some restriction (constant mass loading, defined scan rate, specific substrate, consideration of 100% metal to be active, etc.). There is no available method that can determine the exact number of active molecules in terms of molecular basis. Therefore, the obtained TOF is nothing but a relative one, and for the very first time, we implemented this term in our previous works. One might argue that since TOF is determined under specific constraints, any error introduced by the multiplicative active site density for a bare and modified catalyst could be nullified when measuring the relative TOF. However, upon closer examination of the physical and molecular significance of TOF, it becomes evident that a variation of 1-2 orders of magnitude can significantly alter the activation energy profile of a system. Being equivalent to the rate constant of an electrochemical reaction, the exact TOF value for an electrocatalyst in its catalytic cycle can be determined. From the given kinetic analysis for a multi-step electrochemical reaction, the TOF is highly sensitive toward the nature of RDS and the active metal/active site present.

Therefore, through the characterization of RDS, the active site involved is crucial for specifying the rate constant of an electrochemical reaction. The nature of RDS in the field of electrocatalysis is commonly assessed through density functional theory (DFT) analysis. However, few experimental efforts by in situ spectroscopic analysis have recently been executed. For instance, Chen et al. studied a control system (Fe/WP-Tungsten phosphide) that was developed to study the role of the hetero-atomic Co–Fe pair.³⁹ Comparative studies with Fe–Co/WP showed enhanced OER activity when Fe occupied the distal site. In situ XAS revealed that Fe³⁺ promotes the formation of high-valent Co⁴⁺ species through electron withdrawal, boosting catalytic performance. However, Co at the distal site was not effective in showing OER performance, which suggests the existence of a Co site for RDS and therefore acts as the main active site for OER (Fig. 13a–e). Comprehensive in situ and operando studies have considerably advanced knowledge about active sites on NiFe-layered double hydroxides (LDHs) for the oxygen evolution reaction (OER). Bell's group initially employed in situ Raman spectroscopy to monitor the electrochemical conversion of Ni(OH)₂ into NiOOH at 0.47 V vs. Hg/HgO, suggesting Ni³⁺ in NiOOH as the active species.⁴⁰ This was complemented by Nocera's group using X-ray absorption spectroscopy (XAS) to identify the formation of Ni⁴⁺ as the central OER species, with Fe³⁺ being a Lewis acid that stabilizes Ni⁴⁺ and promotes catalytic activity.⁴¹ Subsequent in situ XAS studies by Bell and Friebel provided evidence of shortening Fe–O bonds during OER, which means that Fe actively contributes to the catalytic process and has a stronger interaction with lattice oxygen compared to Ni.⁴² This was corroborated by Cai et al., who doped Fe²⁺ into NiFe-LDHs and monitored the oxidation states through in situ XANES.⁴³ The analysis revealed the formation of a partially oxidized Fe³⁺/Fe⁴⁺ state under applied potential, further confirming Fe as an active center. Jin et al. proposed another twist to this by utilizing operando Mössbauer spectroscopy to track valence changes in Fe during OER. At greater potentials (1.62 and 1.76 V), they observed the development of Fe⁴⁺ species (up to 21%), which persisted even upon a decrease in potential, thus verifying the partial stabilization and catalytic significance of Fe⁴⁺.⁴⁴ Theoretical perspectives from Friebel et al. investigated Fe-doped NiOOH models, showing that surface Fe was extremely effective at lowering the overpotential (η = 0.43 V), with subsurface Fe being less effective.⁴⁵ An excess of Fe (55 at%) caused low activity, indicating that Fe atom location and coordination play an important role in performance. Markovic et al. experimentally confirmed the dynamic Fe dissolution–redeposition cycle at OER potentials using ⁵⁷Fe labelling and ICP-MS.⁴⁶ They showed that Fe continuously dissolves from MO_xH_y surfaces but redeposits when Fe³⁺ is present in the electrolyte, maintaining catalytic activity. Rapid exchange between ⁵⁶Fe and ⁵⁷Fe stabilized the surface Fe content. Activity and Fe incorporation are saturated above 0.1 ppm Fe³⁺, suggesting that Fe adsorption controls surface coverage and active site density during OER. An expression for the number of dynamically stabilized Fe active sites as a function of electrolyte Fe concentration (C⁰_Fe) was proposed by considering Fe(aq.) incorporation process as a surface adsorption reaction as follows:

	(24)

where R is the ideal gas constant, T is the temperature, r_depC⁰_Fe is the overall rate of Fe deposition, r_diss is the rate of Fe dissolution during the OER, and ΔG_Fe–M is the strength of the interaction between the Feⁿ⁺ species and the MO_xH_y surface. Eqn (23) suggests that to maintain a large at the interface, a high enough level of Fe(aq.) is needed to guarantee that the rate of Fe redeposition is not less than the rate of dissolution.r_diss≪r_depC⁰_Fe). As the identified active site for OER, with specific knowledge of various terms in eqn (23), one can easily find out and thereby could access the rate constant very precisely. Therefore, combining in situ-operando spectroscopy with theoretical modeling offers more profound insights into active-site electronic structure, local coordination shell, and dynamic reaction evolution. These effective strategies enable better quantification of intrinsic catalytic activity and lead to systematic TOF assessment protocols.

10. Conclusion

TOF is considered the most important evaluation parameter in the field of electrocatalysis, such as water splitting into hydrogen and oxygen. TOF is a physical activity marker originally introduced for normal chemical reactions by Boudart et al. in 1966, which measures the efficiency of a catalyst with respect to its concentration per unit time. Several highlighted reports have been showcased mainly based on the importance of TOF in electrocatalysis and potential methods of its determination based on previous definitions. However, defining TOF without understanding its fundamental origin—especially when evaluating the efficiency of the catalytic cycle—may lead to discrepancies or misinterpretations in the results. In the context of fundamental electrochemistry, the TOF performs a measure of the rate constant, the most important reaction parameter being related to the free energy of activation according to the Arrhenius equation. Therefore, even a small discrepancy in the TOF value can lead to a misrepresentation of the activation energy profile of an electrocatalyst, which is unlikely to reflect the true intrinsic properties of the material. As a function of the number of electrochemical active sites (ECAS), the present methodology faces certain challenges. Detailed electrochemical analysis demonstrates that the intrinsic ECAS information varies by various physical parameters, such as mass loading, scan rate, and nature of the working electrode substrate. This variation directly affects the TOF information, and it varies widely with the given physical parameters. This certainly raises a serious concern about the molecular meaning of the TOF. Considering the scan rate and substrate effect on the ECAS, followed by the TOF, we aimed to find out an alternative method for determining ECAS that does not depend on such physical parameters. A detailed literature survey reveals that the determination of ECAS information from molecular structural information, ICP-MS, and CHNS analysis could be an alternative to the conventional procedure. However, a certain limitation still exists in the above-mentioned method. Existing methodologies fail to determine the exact number of active sites in terms of molecular basis, and the TOF values obtained from the reported procedures are thus relative, especially when compared to pristine or state-of-the-art electrocatalysts. Most importantly, from this perspective, we revealed the importance of considering the nature of RDS in the case of various catalysts where there is a possibility of having multiple active centers, either for the chemical or electrochemical steps involved in the catalytic cycle. Depending on the nature of the RDS and the exact ECAS in various catalysts, errors in TOF information could lead to huge variations in the activation energy of the system. Recent advancements in using theoretical analysis, in situ spectroscopic techniques, and various electrochemical analyses have proven effective in identifying the nature of RDS and the active sites involved. Therefore, integrating such advanced measurements along with standard electro/non-electrochemical techniques can provide a more accurate picture of TOF, which would certainly help to develop effective electrocatalysts for sustainable hydrogen production in the future. In conclusion, standardizing ECAS determination methods that account for both physical parameter independence and RDS considerations is crucial for establishing meaningful TOF values that truly reflect catalytic efficiency on a molecular level, ultimately advancing the field of electrocatalysis toward more accurate performance evaluations and rational catalyst design.

Conflicts of interest

There are no conflicts to declare.

Data availability

The authors respectfully declare that all the data of the manuscript entitled “‘Beyond Traditional TOF: Unveiling the Pitfalls in Electrocatalytic Active Site Determination” are available from the authors upon request.

Supplementary information contains the details of the experimental procedure and various electrochemical results to support the findings. See DOI: https://doi.org/10.1039/d5ta04810a.

Acknowledgements

Arun Karmakar acknowledges CSIR-New Delhi for the award of a Senior Research Fellowship (SRF). S. K acknowledges the Department of Science and Technology (DST) for CRG (Core Research Grant) funding of number # CRG/2021/001089 dated November 20th, 2021. CSIR-CECRI manuscript number: CECRI/PESVC/Pubs/2025-022.

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