Combining experimental and theoretical insights for reduction of CO2 to multi-carbon compounds

The electrochemical reduction of carbon dioxide is a promising method for both recycling of atmospheric CO2 and storing renewably produced electrical energy in stable chemical bonds. In this paper, we review the current challenges within this promising area of research. Here we provide an overview of key findings from the perspective of improving the selectivity of reduction products, to serve as a contextual foundation from which a firmer understanding of the field can be built. Additionally, we discuss recent innovations in the development of catalytic materials selective toward C3 and liquid products. Through this, we form a basis from which key mechanisms into C3 products may be further examined. Carbon–carbon (C–C) bond formation provides a key step in the reduction of CO2 to energy dense and high value fuels. Here we demonstrate how variations in catalytic surface morphology and reaction kinetics influence the formation of multi-carbon products through their impact on the formation of C–C bonds. Finally, we discuss recent developments in the techniques used to characterise and model novel electrocatalysts. Through these insights, we hope to provide the reader with a perspective of both the rapid progress of the field of electrocatalysis, as well as offering a concise overview of the challenges faced by researchers within this rapidly developing field of research.


Introduction
Fossil fuels form the cornerstone of industrial and economic growth globally, accounting for over 87% of the world's total energy consumption [1,2]. Dwindling fuel reserves and mounting environmental damage as a result of burning fossil fuels demonstrate the need to move beyond our global dependence on non-renewable sources of energy. As of 2015, the remaining oil and natural gas reserves were estimated at 1697.6 billion barrels and 186.9 trillion cubic meters respectively. Based on global consumption levels as of 2015 and the remaining supply of fossil fuels at that time, it was estimated that around 50 years of oil and gas remain [2].
The burning of such large quantities of fossil fuels, particularly in the transport sector, has resulted in the uncontrolled release of CO 2 into the atmosphere, significantly contributing toward climate change [3][4][5]. This realisation has led to considerable efforts being made to transition from fossil fuels toward low carbon and renewable alternatives such as biofuels, hydroelectric power, solar, wind, geothermal, and nuclear energy [1]. Whilst some low carbon energy sources such as nuclear and hydroelectric energy are being implemented on a large scale [1], most alternatives to fossil fuels, such as solar and wind, have been unable to achieve this due to intermittent operating times and are incapable of consistently meeting global energy demands in their current state [6]. A key method in tackling this inherent intermittancy is through the conversion of otherwise surplus energy into a medium which is both portable and storable so that it may be implemented wherever and whenever it is needed, much like fossil fuels are used today [3,[7][8][9][10][11]. CO 2 reduction poses an attractive method of converting said energy. By using the abundant greenhouse gas CO 2 to produce carbonaceous fuels compatible with existing infrastructure it effectively forms a carbon neutral cycle for the production of hydrocarbons [12][13][14]. An example of such a cycle as this can be observed in Fig. 1.
By implementing carbon capture technology to siphon waste CO 2 from the atmosphere, as well as natural and industrial processes. CO 2 reduction aims to mimic the natural process of photosynthesis (i.e. "artificial photosynthesis") [3,6], effectively managing atmospheric levels of CO 2 whilst providing a carbon neutral source of fuels. An added bonus of recycling CO 2 via electrochemical reduction is that the fuels produced are highly compatible with existing technology which would otherwise be powered by fossil fuels, with most only requiring minor modifications [7,15,16].
It is for these reasons that the electrochemical reduction of CO 2 has begun to see notable interest within the field of electrochemistry [15,[17][18][19][20]. The electrochemical reduction of CO 2 however is still an emerging technology. There are significant challenges to current electrocatalyst performance, including: issues regarding energy efficiency, reaction selectivity both between CO 2 reduction (CO 2 RR) products and with the competing hydrogen evolution reaction (HER), as well as overall conversion rate. Before carbonaceous fuels produced via the reduction of CO 2 can be considered as a viable method of energy storage, each of these challenges must first be addressed [20].
A 2008 review by Hori [21] examined many elemental metal catalysts in terms of their overall catalytic performance and product selectivity. Since then, considerable work has been conducted into improving the activity and selectivity of reduction products. A overview of some of the most active electrocatalysts selective towards specific products can be observed in Table 1. Despite the stability of the CO 2 molecule [22], it can be reduced to simple products requiring only a 2-electron transfer process such as CO and HCOOH with low overpotential and high Faradaic efficiency. For larger products requiring higher numbers of electron transfers however, such as ethylene or alcohols, markedly higher overpotentials and lower selectivities among CO 2 RR products are observed [20].
The aim of this review is to examine and discuss some of the history of electrochemical CO 2 reduction, as well as its more recent advances, to provide the reader with an overview of the field itself. Through this, this review aims to provide a sense of where the field has come from, as well as how it maybe further develop in the future [17,18,[17][18]. Among the topics discussed within this paper are: the CO 2 reaction processes; including initial activation, catalyst design; both past and present, and finally the use of computational methods to improve our fundamental understanding of the CO 2 reduction reaction (CO 2 RR).

Fig. 1
The "carbon neutral cycle". Here atmospheric CO 2 is captured and reduced to form synthetic hydrocarbons in the order of C 1 to C 3 chains (adapted from [3])

The activation of CO 2
Formed through the combustion of organic matter, CO 2 is a particularly stable molecule [22,58]. Due to this, it is kinetically challenging to convert CO 2 to products due to the high activation energy required for the reduction process [12,59]. The single electron reduction of CO 2 to CO − 2 has been shown to have a high thermodynamic potential of E o = −1.90V versus the standard hydrogen electrode (SHE) in aqueous media (pH = 7) [29,[60][61][62]. This initial activation step is critical as it forms the rate limiting step of the CO 2 RR [18]. The coordination of this intermediate additionally determines the whether the CO 2 molecule will be reduced to CO or formate following the transfer of 2 electrons [63]. For example, post-transition metals selective toward the formation of formic acid, such as Pb [64], Sn [65], Bi [66,67] and In [68] prefer to bind CO 2 via oxygen. Transition metals such as Cu [69] and Ag [70] however prefer to bind via carbon, resulting in the production of CO. Bagger et al. [71] however, suggests an alternative. For Cu surfaces they demonstrate how oxygen bonded HCOO* is stabilised more effectively than carbon bonded COOH*, suggesting a possible oxygen-bound pathway. In addition to this, they suggest the formation of formic acid to be related to the relative standing of the binding energies of H and COOH*. This was supported by the lack of experimental evidence showing a lack of HCOO* surface saturation prior to the onset of HER, despite adsorption energy values suggesting an earlier onset of HCOO* production [72][73][74][75].
Selectivity of the reaction pathway towards products such as this can be further improved using the appropriate catalyst [25,27]. It should be noted however, that the choice of material alone does not solely dictate product selectivity. One clear example of this was shown in a recent work by Scholten et al. [76] which demonstrated how highly ordered single-crystal Cu surfaces produced mainly hydrogen. By contrast, it was found that only through the introduction of surface defects such as with etching and plasma pre-treatment methods that significant amounts of hydrocarbons were produced. When considering the activation of CO 2 , the following 4 equations govern the reactions taking place where * denotes a binding site on the catalyst surface. Here *COOH is considered to likely be the be intermediate for CO formation and *OCHO the likely intermediate in the formation of formic acid for transition and post-transition metals [77].
A 2017 work by Adrien et al. [78], postulates that the reaction takes place in agreement with previous literature, however with subtle changes. Rather than following only the concerted proton-electron transfer (CPET) reactions as shown in Eqs. (1) and (2), the CO 2 RR could instead follow a combination of both a CPET reaction and sequential proton-electron transfer (SPET). For the SPET reaction, the single reaction step depicted in Eq. (1) instead takes place as a 2-step process consisting of the initial activation of CO 2 as shown in Eq. (3), followed by It was suggested in the same work by Adrien et al. that the conditions affecting the ratio of CPET to SPET reactions were tied to the local pH in the vicinity of the catalyst surface. In the vicinity of pH 3 for example, it was found that the SPET pathway became competitive with CPET, in agreement with experimental results, which saw a dramatic increase in the faradaic efficiency toward CO production. This pH dependence of CO 2 reduction pathways, and possibly differing pH dependence compared to the competing hydrogen evolution reaction (HER) was used to explain the strong pH dependence of product selectivity for graphite-immobilized CO-protoporphyrin, where H 2 was observed as the main reduction product at pH 1, and CO as the main product at pH 3 [79,80]. This pH dependence of reaction products is further agreed upon by Koper [81], who suggested that due to the nature of this pH dependence, an optimal pH for desired reaction products must be attainable, with a suitable catalyst. The pH dependent, decoupled proton-electron reaction pathways however, Koper explained, are more prevalent if the interaction between the catalyst and intermediates is weak, as CPET

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reactions dominate where catalyst-intermediate interactions are strong, resulting in a low pH dependence of reaction products. Not only have reaction conditions been shown to be sensitive toward electrolyte pH, but also to the nature of the electrolyte used. Monteiro et al. [82] for example, demonstrated how a lack of metal ions prevents the formation of CO on Cu surfaces. Their work highlighted the crucial importance of short-range electrostatic interactions between the electrolyte and catalytic surface in promoting CO 2 RR. For the formation of formate and formic acid, a similar situation is observed, particularly for molecular catalysts such as Rh, In and Sn metalloprotoporphyrins which were reported to produce formic acid selectively in aqueous electrolyte [83]. It should be noted however that the formation of formate using an Rh protoporphyrin is only capable at elevated pressures [84], with Rh ordinarily producing H 2 as the main product under ambient conditions [85]. Density functional theory (DFT) studies into molecular catalysts such as those mentioned previously showed a strong pH dependence on the formation of formic acid [86]. Here it was found that within a strongly acidic electrolyte the HER is favourable, following the same reaction path as outlined in Eq. (4). This result was in strong agreement with the literature [87,88]. From the production of an anionic hydride as shown in Eq. (4), the anion binds to the carbon atom of CO 2 like so The subsequent stability of the HCOO − intermediate can then dictate the formation of either CO or HCOOH. Discussion of this hydride dependent reaction pathway has been further examined for a range of catalysts observed to produce formic acid among their reaction products. Such catalysts include copper-hydride nanostructures [89], palladium electrodes [26], and in solution [90].
When considering Eqs. (3) and (4), as opposed to Eqs. (1) and (2), the pH sensitivities resulting from the charge of key intermediates suggests the another challenge when designing and implementing an electrochemical cell. For CO 2 reduction, this challenge is ensuring an optimal local and system-wide pH for the production of desired products. This is true in particular for reduction products formed following a 2-electron transfer such as CO and HCOOH. The formation of larger and more energy dense products from the CO 2 RR is however another desired result within the field of electrochemistry. As such, the following section shall cover some works published in this regard.

Formation of multi-carbon compounds
In order to form larger and more energy rich products such as hydrocarbons and alcohols, CO 2 reaction intermediates must undergo additional reaction steps requiring the transfer of multiple electrons. Due to the added complexity of the reaction, a clear drop in selectivity can be observed for C 2 and greater products when compared with the production of simpler products such as CO and formate which require fewer reaction steps. As well as this, notably higher overpotentials can also be observed [17]. Figure 2 illustrates some of the proposed reaction pathways to larger and more complex products following the formation of CO.
It should be noted that following the initial activation of the CO 2 molecule, the standard reduction potentials for sequential reaction steps under ambient conditions are relatively low. Even for the formation of large molecules such as ethanol and propanol, reduction potentials are of the order of ≈ −0.5V [93,94]. Whilst this would suggest the formation of hydrocarbons and alcohols would not be much more energetically demanding than the formation of formate or CO, the formation of larger hydrocarbons have been shown to be kinetically challenging [94,95]. This is due to the reaction kinetics involved in transferring large numbers of electrons, as well as the large structures of multiple carbon products involved in the reaction.
The formation of C 2+ and greater products such as propane and butane from the CO 2 RR is of particular interest due to the greater energy density provided by these products. Copper, and copper-based catalysts have been shown as being almost exclusively capable of providing the necessary conditions to form Carbon-carbon bonds at significant current densities [21,69]. Copper demonstrates an intermediate adsorption energy for CO, providing more ideal conditions for the formation of C-C bonds. Metals with higher binding energies, such as Pt, Ni, Fe and Ti, for example, show a greater selectivity toward hydrogen due to tighter CO binding on the catalyst surface [21,96,97]. By contrast, metals such as Au, Ag and Zn, which exhibit a lower adsorption energy, produce mainly CO as the intermediate desorbs from the catalyst surface before further reactions can take place [25,[98][99][100]. A more complete picture of the binding energies for Cu with various reaction intermediates can be observed in Fig. 3.
A small number of other catalyst designs have been proposed including NiGa, PdAu, NiP and N-doped carbon catalysts which have been capable of producing C 2 and greater products, however none have been able to do this as efficiently
Another point of interest in the formation of C 2 and greater products is the possibility of liquid products. Liquid fuels provide both a higher energy density and greater economic value, as well as a simpler method of storage [109]. Due to this, the study of the reaction pathway from CO 2 to the most typically produced liquid fuels from the CO 2 RR such as ethylene and ethanol have been subject to a plethora of theoretical [110][111][112][113][114] and experimental studies [32,52,[115][116][117][118].
From prior experimental studies, two pathways for ethylene production have been observed. The first takes place mainly on Cu(111) at high overpotential using a shared intermediate with methane, and the second on Cu(100) at lower overpotential which does not yield methane as a product [117]. The second method also differs from the first in that it is pH independent. It forms Carbon-carbon bonds through the formation of a CO dimer from adsorbed surface materials, as opposed to individual transfers of protons and electrons [69,84,91,119]. As a consequence of this, the production of ethylene is favoured on the face-centred cubic (fcc) (100) facet as local pH can be optimised toward CO formation over the HER with no impact on the selectivity of C 2 products. The formation of ethylene using the fcc(100) facet is in stark contrast with the formation of methane from copper electrodes which has been observed to be most actively produced on the fcc(211) facet [25,120]. Numerous experimental [52,115] and theoretical works [110][111][112] however confirm the different reaction pathways taken when producing either ethylene or methane. Such works demonstrate drastic differences in the reaction conditions required to form larger hydrocarbons over smaller products. Based on results from DFT calculations, it is believed that at more negative potentials the dimerisation of CO is replaced by a more favourable reaction based on the coupling of *CO and *CHO. The reaction between these intermediates is believed to be due to the lower activation energy of the latter reaction [112,121]. DFT calculations additionally confirm the tendency for CO dimerisation to be favoured on Cu(100) facets. Furthermore, DFT calculations provide additional insights into C-C bond formation in this case, such that the CO dimer is energetically favoured in the presence of a water layer, a local electric field and in the presence of alkali cations [111,113]. This pH sensitivity has been attributed to the rate-determining step in the formation of C-C bonds involving a decoupled proton-electron transfer. This hypothesis is based on a combination of both DFT calculations and experimental data [110].
A recent report by Perez-Gallent et al. [122] observed the formation of a hydrogenated CO-dimer (OCCOH) intermediate during CO reduction using Fourier transform infrared spectroscopy at low overpotentials in LiOH solutions. All results for this work were supported with DFT calculations. In agreement with previous literature, the formation of CO dimers was structurally sensitive; only being observed on the fcc(100) facet. Thus it was concluded, in agreement with prior works, that the formation of the dimer was favoured both thermodynamically and kinetically on Cu(100) compared to Cu (111) [111,117].
Whilst the effect of adding certain organic layers to copper catalysts such as pyridium [106] or triazole [107] is yet to be fully understood, studies have suggested the modification of copper with such layers results in an enhanced selectivity toward the production of C 2 products. Currently however, this effect is believed to possibly be due to local pH effects caused by the presence of such organic materials. One recent study by Hoang et al. [107] for example, reported faradaic efficiencies for the production of C 2 H 4 and C 2 H 5 OH reaching approximately 60 and 25% respectively for a cathode potential of − 0.7 V vs. RHE. The same study also reported a total current density of ∼ − 300 mA∕cm 2 , one of the highest catalytic activities at low potential reported to date.
Despite the volume of research published into possible reaction pathways towards the formation of C-C bonds however, current faradaic efficiencies for the formation of C 3 products such as propane and propanol remain relatively low [64,123]. Previous studies have suggested that by promoting a high selectivity toward the formation of C 2 , the right conditions to produce C 3 or larger products could be achieved. The current understanding of the reaction mechanisms towards the formation of propane and larger hydrocarbons however, is still unclear. Due to the large number of electron transfers involved, developing a clear picture of a reaction pathway would be a time-consuming and difficult process. An alternative method of examining C 3 however, as shown by Bagger et al. [124] could use descriptors for product distribution on specific facets to categorise reaction products by comparing coordination number distribution and the binding energies of intermediates. Currently however, researchers propose either the further use of CO as a reaction intermediate, or the formation of C-C bonds between C 1 and C 2 intermediates [31,125,126]. Current research also seems to suggest a likely intermediate toward C 3 being formed through the coupling of CO and C 2 H 4 precursors [127,128]. A 2019 study by Wang et al. [123] reported the highest Faradaic efficiency to date for the formation of propanol of 33 ± 1% with a cathodic energy conversion efficiency of 21% for metal-doped copper catalysts. Due to the increased energy density and

Review
Discover Chemical Engineering (2022) 2:2 | https://doi.org/10.1007/s43938-022-00009-y ease of storage of liquid fuels, a greater understanding of the reaction mechanisms required to form C-C bonds in order to produce larger hydrocarbon and alcohol products could prove revolutionary in improving the commercial viability of the electrochemical reduction of CO 2 .

Optimising catalyst structure for the formation of fuels
Following Hori's review in 2008 [84], the development of catalysts has seen drastic improvement. From his results it was found, as previously stated, that copper most effectively produces fuels from the electrochemical reduction of CO 2 (see Table 2). Among the metals tested, it was found consistently that the formation of CO from the CO 2 RR occurred on face centred cubic (fcc) transition metal lattices [84,129,130], suggesting a strong dependence on the surface morphology on overall product selectivity. Due to this, considerable work has been conducted aimed toward optimising catalyst surface structure to produce an electrocatalyst highly selective toward a given CO 2 RR product, whilst minimising the effect of the competing HER. Studies have included the alloying of surface materials [24,[131][132][133][134], production of nanoparticles [12,65,135] as well as an Ag "nano-coral" structure prepared by an oxide-reduction method in the presence of chloride anions in an aqueous medium [136].

Bimetallic alloy catalysts
With regards to alloy catalysts, the introduction of heteroatoms to form bimetallic alloys allows for both the structural and electronic properties of the catalyst to be altered due to the interaction between the two elements involved. For example, one study using Ru-Pd catalysts saw in increase in the selectivity of formic acid production from 70% at −0.7V for pure Pd catalysts to 90% at −1.1V vs. NHE [137]. Similarly, a 2015 work by Rasul et al. [132] saw a dramatic improvement in the selectivity of CO production through the introduction of In hetero-atoms into an oxide-derived copper catalyst structure. Here a total Faradaic efficiency of 95% at −0.7V vs. RHE was observed, higher than values observed for either Cu or In separately. It was suggested in this study that the enhanced Faradaic efficiency toward the production of CO was due to the suppression of the HER through structure changes. These changes were believed to have been caused by the preferential binding sites of In within the Cu lattice, based on the high overpotentials observed for HER for In in comparison with copper. Figure 4 demonstrates the preferential binding sites of In within the Cu lattice based on calculations in a follow-up paper by Jedidi et al. [131] demonstrating the preference for In atoms to replace Cu atoms in positions of low coordination such as defects and the fcc(211) facet step-site.

Nanoparticles
An alternative approach to optimising catalyst selectivity through morphological changes is the fabrication of nanostructures such as nanoparticle and nano-coral structures. The size of metal nanoparticles has been reported to have a strong influence on both the activity and selectivity of CO 2 reduction catalysts [138][139][140]. For example, a 2014 study by Reske et al. [140] on Cu nanoparticles 2-15 nm in diameter found that for nanoparticles below 5nm the formation of hydrocarbons such as methane and ethylene were suppressed, resulting in an enhanced selectivity toward CO and H 2 formation. Such changes in selectivity were attributed to higher concentrations of low-coordinated surface sites, resulting in stronger chemisorption, as well as boosted catalytic activity. A similar study on the size dependency of Au nanoparticles on catalytic activity in the range ∼ 1-8 nm observed a similar trend [141]. On the other hand, for Ag, Pd and Sn nanoparticles, a volcano effect can be observed [139,142,143]. For Ag nanoparticles for example, CO 2 reduction current first increased as particle size decreased to 5 nm, below which the reduction current then began to decrease [142]. This volcano effect was suggested to have been related to the binding energy of key intermediates in relation to particle size, however convolution effects may have been at play due to the experiments taking place in ionic liquid electrolyte as opposed to aqueous media.

Oxide-derived electrocatalysts
Another method of surface morphology engineering has been observed through the oxidation and subsequent reduction of bulk metal catalysts in order to improve catalytic activity [29,73,120,[144][145][146]. Studies on oxide-derived metal catalysts such as Cu, Au and Sn have demonstrated an enhanced density of active sites through the modification of surface structures, leading to improved overpotentials observed for CO 2 RR [29,73,144]. In a 2012 work by Li et al. [120] conducted on oxide-derived copper ( Cu 2 O ) electrodes observed a coarse surface structure consisting of nanowires, with the reduction activity being strongly dependent on the initial thickness of the Cu 2 O layer. The primary products observed from the examined Cu 2 O catalysts were formate and CO, produced at both enhanced selectivity and activity. Based on the observed Tafel slope for Cu 2 O catalysts, a similar reaction mechanism could be suggested as bulk Cu for the formation of products based on the formation of an activated CO 2 molecule, as observed in Eq. (3), as the rate-determining step. Due to the study focusing on the comparison of geometrical surface area, it would be difficult to conclude as to whether or not the activity of individual catalytic sites was improved without further characterisation with regards to the electrochemically active surface area. Conversely, for oxide-derived Au, it was found that, as opposed to the nanowire morphology observed for Cu, oxidederived Au formed a thick layer ( ∼ 1 μm ) of nanoparticles [29]. Similarly to oxide-derived Cu, an enhanced faradaic efficiency was, at lower potential, observed for oxide-derived Au when compared with the performance of the bulk metal. This increase in both selectivity and activity was attributed to a higher stability of the reaction intermediate (see Fig. 5). For Au nanoparticles, the enhanced activity has been directly correlated to the density of grain boundaries resulting from the oxidation-reduction step [147,148].
Oxygen plasma activation has been found to be another form of pre-treatment which results in drastically enhanced CO 2 RR activity [33,149]. Following plasma treatment, the surfaces of oxide-derived metal catalysts were suggested to be defect rich. For plasma treated Cu, both the enhanced reactivity and selectivity have been attributed to the presence of Cu + ions and subsurface oxygen. A 2016 work by Eilert et al. [150] suggested that the involvement of subsurface oxygen lead to increased CO binding energies, primarily in the vicinity of grain boundaries. It was believed this was due to its influence on the electronic structure of the catalyst, reducing -repulsion. An alternative explanation is that the presence of subsurface oxygen enhances CO 2 RR activity by facilitating neutral and charged Cu sites, resulting in in chemisorbed CO 2 in the presence of water [151]. Studies using DFT calculations agree that interstitial oxygen is stable on the Cu fcc(111) surface, unlike the fcc(211) facet, and are capable of improving surface binding of CO 2 [152]. Cavalca  (211)  . It was further suggested that the presence of subsurface oxygen withdrew charge from the copper sp-and d-bands, selectively enhancing the binding energy of CO. Recent DFT-based work however disputes this, suggesting it unlikely for subsurface oxygen to remain stable at the negative potentials at which CO 2 RR takes place due to their low diffusion barriers [154]. A 2018 work by Lum and Ager [155] conducted using 18 O labelling similarly concluded that subsurface oxides should indeed be unstable under CO 2 RR conditions. Additionally, theoretical work has shown that subsurface oxygen is not a prerequisite for CO 2 adsorption [156] and coordinatively unsaturated Cu atoms promote C-C bond formation [54,113,157,158]. Furthermore, a 2018 work by Fields et al. [154] demonstrated how, from thermodynamic and kinetic perspective, subsurface oxygen should have a negligible effect on the activity of crystalline Cu under reducing potentials. In short, the role of subsurface oxygen within OD electrocatalysts remains a controversial topic with, as yet, no single agreed solution. Reliable methods capable of measuring, with a certain degree of accuracy, the electrochemically active surface area of metal electrodes [159,160] will be of paramount importance in once and for all, resolving this ongoing debate of effective surface area effects.

Computational methods
Whilst the implementation of Density functional theory (DFT) calculations on the electrode surface can be a complicated affair, a considerable amount of effort has been put into improving models. A recent comprehensive review of such works was produced by Rendòn-Calle et al. [161]. Here we provide a brief review of some of the more fundamental approaches and issues regarding current computational models, in addition to advances in calculating the kinetics of electrochemical steps, structure-sensitive screening, ion effects, and machine learning.

Kinetic and thermodynamic models
Estimations of catalytic activities based on theoretical calculations have, in recent years, provided fast and increasingly accurate results [24]. By employing DFT and the computational hydrogen electrode model (CHE), calculations can be performed on an atomic scale. This opens up the possibility of screening many novel electrochemical materials and active sites from a thermochemical perspective [162]. The CHE model can be seen discussed in greater detail in Sect. 4.2 however the model has seen widespread use since its creation [163][164][165].
Through the use of such methods, it has been made feasible to examine possible lowest-overpotential pathways from CO to various C 1 and C 2 products including ethylene, acetaldehyde and ethanol. For any given reaction pathway, the limiting potential U L is the electrode potential at which all steps are exergonic, i.e. the change in Gibbs energy ΔG is always negative. U L can be found as the inverse of the largest reaction energy (ΔG L ) [101].

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The first DFT-based studies detailing mechanisms to C 1 species were proposed by Nørskov et al. [166]. By analysing adsorption energies for Cu(100) surfaces, they concluded the lowest energy pathway to be Using this mechanism, Durand et al. [167] calculated the Gibbs free energies of each reaction intermediate on various Cu facets. Their work found that adsorbates were more easily stabilised on the (211) facet, followed by (100) and (111), in line with simple coordination rules [113,[168][169][170]. Further studies have since expanded upon this work by examining further Cu facets [171], as well as other transition metals and alloys [172][173][174]. CO 2 RR screening techniques based on scaling relations assuming a single mechanism for all facets and materials however can be further improved [161,175,176]. Further information on this can be found in Sect. 4.3. Nie et al. [114,177], for example, examined the activation barriers for every possible transition state from CO 2 to methane. Based upon their findings, it was discovered that for the Cu(111) facet, *CO is more favourably hydrogenated to *COH rather than *CHO, supporting work performed by Hussain et al. [178]. The pathway continues from here as * COH → * CH → * CH 2 → * CH 3 → CH 4 . A later work by Luo et al. [179] further supports this, demonstrating how unlike the (111) facet, Cu(100) kinetically favours the *CHO pathway over *COH, suggesting a structure-sensitive mechanism dictated by elementary-step kinetics.
Beyond methane formation, thermodynamic studies into the formation of C 2 products such as ethylene ( C 2 H 4 ) and ethanol ( C 2 H 6 O ) have been explored thermodynamically by Calle-Vallejo and Koper [110]. In their work, the electrochemical reduction of CO (CORR) was studied on Cu(100), considering *CO dimerization as the believed first step toward ethylene, acetaldehyde and ethanol [180]. The electroreduction of CO is contained within CO 2 RR, forming a rate limiting step in most CO 2 RR reduction processes. The square sites of the Cu(100) facet exhibit strong stabilisation of *CO dimers, helping to explain the Cu(100) facet's preference for ethylene production, whereas step sites tune the product selectivity towards ethanol production [180]. Cheng et al. [157], supports this hypothesis, suggesting in their work that Cu structures with stepped square sites show enhanced selectivity and catalytic activity toward C 2 reaction products. Garza et al. [121] further expanded upon these studies, proposing reaction pathways for all reported C 2 products from CORR (ethylene, ethanol, acetaldehyde, ethylene glycol, glycolaldehyde, glyoxal, and acetate) on both Cu(100) and Cu(111) facets.
The activation energies for C-C bond formation on Cu in vacuum were determined by Montoya et al. [181]. From their work it was found that kinetic barriers depend on the degree of hydrogenation of adsorbates. It was concluded that *CO dimerization is kinetically unfavourable in a vacuum. An initial protonation step of *CO followed by the dimerization of *CHO molecules however, was agreed to be more favourable by comparison. In subsequent work however demonstrated that water-solvated cations stabilize *CO dimers, thus making * CO ← * CO coupling feasible under CORR conditions, particularly on Cu(100) facets [111].
A key challenge currently facing researchers within catalysis is the formation of multiple C-C bonds, forming C 3 and greater products such as n-propanol. Due to the increasing kinetic barriers faced due to the increased complexity of the n-propanol molecule, faradaic efficiencies for C 3 products currently remain at consistently low values around 10-13% [127,182] for n-propanol. Small quantities of other C 3 products such as allyl alcohol, acetone, propylene and propane have additionally been observed at low Faradaic efficiencies of < 3% [31,182]. Rui et al. suggests that the coupling mechanism for multi-carbon products follows a "polymerisation" scheme of adsorbed CO that obeys the Flory-Schulz distribution [183].
Initial works by Hori performed under strictly galvanostatic conditions ( −5 mA cm −2 , E = −1.1 V vs. NHE) gave a faradaic efficiency of 4.2% [72,184]. Under such extreme conditions, Rahaman et al. explains how poor selectivity is a direct result of high overpotentials lowering the required kinetic activation barriers for a variety of competing hydrogenation and C-C coupling processes, particularly those involving *CO [72,182]. Since then, many strategies aiming to improve product selectivity of CO 2 RR have often followed the path of reducing required overpotentials. In his 2017 work Rahaman demonstrates how the addition of a thin oxide "skin" on catalytic surfaces which can be later reduced under CO 2 RR conditions [171,185] can reduce the required overpotentials for C-C bond formation [182]. Such reductions are achieved through the formation of low-coordinated sites from the precursor species, resulting in improved stabilisation of chemisorbed * CO .− 2 radical anions, as well as *CO [23]. Such methods were applied to form Cu meshes using annealing and electrodeposition methods to produce catalysts capable of producing n-propanol at 13.1% FE at − 1.0V vs. RHE.
Ebaid et al. [186] supports this hypothesis, suggesting surface roughness to be a strong indicator of catalyst performance, as higher surface roughness was attributed to high population of under-coordinated sites. Among the various methods used to roughen catalyst surfaces, the reduction of Cu 2 O [54,187,188] and Cu 3 N [189] have been shown to be the most effective methods of achieving high selectivity toward C 2+ products. C 3 product selectivity however, remains a issue in virtually all Cu-based catalysts [186,[189][190][191][192]. Whilst surface roughening methods have shown a drastic improvement in C 3 production, the lack of a controlled or regimented method of surface roughening limits the extent to which structure and activity relationships can be investigated for CO 2 RR performance.

The computational hydrogen electrode (CHE) model
The CHE model is commonly used in the simulation of electrocatalytic systems [162]. It involves the posteriori correction of standard constant charge, allowing for the electrode potential to be taken into account [193]. When utilised in combination with DFT calculations, CHE can provide a picture of the possible reaction pathways and the potentials at which the redox reactions take place [101,110,194]. By approximating the equilibrium between protons and electrons with hydrogen, CHE avoids the explicit treatment of the solvated particles like so The chemical potential of a proton-electron pair can therefore be written where x is the chemical potential of species x. For a reductive process, the Gibbs free energy G can be related to the electrode potential U as thus providing a consistent evaluation of Gibbs energy for all species involved. It should be noted here that e is the positive (+) electron charge. The hydrogenation of CO, * CO + H + + e − → * CHO for example, can, for a given potential U, be written Additionally, through the combination of CHE and DFT calculations, one can gain insight into the coverage of surface species at specific pH using a Pourbaix diagram [195]. Works using a combination of both Pourbaix diagrams and CHE can also be found throughout electrochemistry literature [196,197].
Typically, CHE methods incorporate only CPET steps, however a recent study by Göttle and Koper [78] introduced a method, based on first-principles calculations of acid-base equilibrium constants, which incorporates decoupled proton-electron transfer pathways. Through this, the sequential proton-electron transfer (SPET) pathways can be estimated and provide a computational understanding of pH effects observed experimentally for molecular, metal and oxidederived catalyst 2 s [23,198,199]. This method has seen use, for example, in rationalising the experimentally determined pH dependence of CO reduction on immobilized cobalt protoporphyrins [79].

Scaling relations
Scaling relations, i.e. linear correlations between adsorption energies of adsorbates [200], are effective in simplifying DFT-based catalytic models. Through their implementation, scaling relations may impose additional constraints toward further optimising current electrocatalysts. Due to this, scaling relations have been studied extensively [201][202][203]. Recent works have examined the possibility of breaking scaling relations [113,204,205], however breaking such relations has proven to be difficult to achieve experimentally. In order to effectively break scaling relations, one must first stabilise one intermediate with respect to the others. For example, Li et al. [113] explained in their 2014 work how the preference for the producing C 2 products over methane on Cu(100) facets was due to the breaking of scaling relations. They suggest the scaling relations between bound CO and * C 2 O 2 on the facet are broken due strong ensemble effects observed during the dimerization step. For CO 2 RR, a number of methods have been discussed within the literature with regards to breaking scaling relations. Alloying, addition of promoters, tethering, the introduction of p-block dopants and creation of low-coordination sites are among some of the strategies which have been suggested throughout the literature [101,206]. As well as this, some other methods of note are; the alteration of adsorbate solvation via modification of the electrolyte composition/dielectric constant [101,206], strain effects [207], the study of transition-metal-free catalysts [197] and the anchoring of active ligands on active sites [208].
Conversely, recent studies have shown, based on scaling-relation-based volcano plots, that whilst a single mechanism is operative on all materials and facets [101,206], the CO 2 RR itself is highly sensitive to both structure and material, as previously discussed.

Effect of structure and pH
pH, structural sensitivity and ion effects are all interconnected during CO 2 RR, the interplay of their effects altering reaction mechanisms. Observed onset potentials, faradaic efficiencies and product distributions have been shown to be not only dependant on the chosen catalyst material [23,209,210], but also on its surface structure [32,117]. Typically however, studies based on scaling relation screenings only consider a single reaction mechanism [101,174,206]. A work by Calle-Vallejo and Koper [176] however showed that metal-and structure-sensitive bifurcating pathways can be incorporated into screening routines using scaling relations. It should be noted however that breaking scaling relations between *CO and *CHO may lead to enhanced CO 2 RR electrocatalysis [101,206].
In addition to this, it has been observed that both electrolyte pH and local pH effects play an important role in the CO 2 RR mechanism. When modelling a system, successive proton-coupled electron transfers are often assumed to take place at every step of the reaction process, so as to enable the use of the CHE model [194]. It should be noted however that the CHE model cannot capture pH effects as the adsorption energies of all intermediates shift proportionally. This problem becomes most apparent when analyzing the CORR due to the strong pH and structure dependent features of the CO intermediate. For example, for pristine Cu, whilst ethene is produced most commonly on the fcc(100) terrace site, CO and methane are more preferentially produced on the fcc(111) facet, both with a strong dependence on pH [209,211]. A report by Hori [91] suggests the disparity between pH responses indicate that the rate-limiting step of CORR to CH 4 involves proton-coupled electron transfers, making the study of CO 2 RR and CORR to CH 4 suitable for CHE models. The formation of C 2 H 4 however does not include such reactions, and should be analyzed cautiously.
In a 1991 work by Murata et al. [212], it was shown that the production of multi-carbon species could be enhanced through the use of alkaline cations. The selectivity toward C 2 H 4 , for example, can be increased by the inclusion of larger cations as their smaller hydration spheres better favour adsorption on cathodic surfaces, yielding more positive potential values. Singh et al. [213] explained cation effects based on the pk a values for their hydrolysis. The larger CO 2 concentrations near the cathode and lower local pH observed with increasing cation size both being satisfactorily explaining cation effects for the CO 2 RR but not those observed for the CORR.
When factoring-in cation effects into computational models, cation effects may be included implicitly or explicitly. For example, one study by Chen et al. [214] used an implicit method of modelling cation effects, applying a general electric field as opposed to individual point charges. The electric field then interacts with adsorbates, modifying the adsorption energies depending on the on the dipole moment of a given species [215]. Conversely, Akhade et al. [216], used an explicit model of cation effects in combination with DFT calculations to account for the impact of adsorbed and co-adsorbed I − and K + ion, on *CO protonation. Through this work it was found that K * improves *CO and *CHO binding over *COH, improving the selectivity toward the *CHO pathway. By contrast, I * weakens the binding energy of *CO, *COH and *CHO, resulting in an improved selectivity toward the formation CO as the primary reduction product. In later works, it was suggested that specific halide adsorption on Cu may occur at negative electrode potentials [179]. As a consequence of this, it was found that the specific adsorption of Cl − , Br − , and I − affect the CO 2 RR. A 2016 work by Vaela et al. [217] supports these results. Their experimental observations showing a 3.5 times higher selectivity toward CO production using Br − as opposed to Cl − , as well as I − favouring the reduction of CO to methane over CO desorption. Perez-Gallent et al. [122] presented a joint computational-experimental study on the impact of cation effects on CORR. Using an explicit model, it was observed that hydrogenation of monomers was particularly more difficult than that of dimers. This was attributed to the fact that cations stabilize C 2 adsorbates but not C 1 intermediates. This discovery could explain why C 2 H 4 exhibits earlier onset potentials than CH 4 [122].

Machine learning
Computational works fully based upon DFT calculations for CO 2 RR providing a comprehensive amount of detail for the catalytic activity of materials. such works however are often computationally expensive. In addition to the study of scaling relations, machine learning algorithms offer an alternative approach toward electrocatalyst selection and design. By using an extensive library of preexisting data from previous research, trends within previously documented results are detected and examined during an initial "training phase". Following this, provided suitable descriptors have been selected, a process of statistical analyses can be used to predict, within a degree of accuracy, new materials selective toward a desired product without performing new DFT calculations [218,219]. One such machine learning framework, for example, was presented by Ulissi et al. [220]. Through this framework, they examined numerous configurations and active sites on intermetallic compounds. The results of their method explained the activity of certain NiGa sites and suggested the need for a composition-, configuration-and structure-sensitive methods to speed up the discovery of new catalytic materials. Research conducted by Jiang et al. used genetic algorithms to find stable solid-liquid interfaces on Cu to account for solvation effects when modelling CORR [221]. Similarly, Xin et al. used a neural network-based chemisorption model in tandem with scaling relations to predict CO 2 RR to C 2 reaction products on (100−) terminated catalysts [222]. One such work by Zhong et al. [223], developed a machine learning accelerated, high-throughput DFT framework allowing for new materials to be screened ab-initio. Through this particular work, Zhong et al. discovered a promising bi-metallic CuAl compound with near optimal CO adsorption energy ( −0.67 eV) with an observed faradaic efficiency of ∼ 80% with a partial current density of 600 mA cm −2 .
Despite the tremendous potential of machine-learning algorithms, their predictive capabilities depend largely on the size and quality of the training dataset, as well as the descriptor of choice. For example, assuming a single mechanism for all materials, datasets made of unrelaxed calculations and similar simplifications can lead to incorrect predictions [219].
To summarise, significant progress has been made in the development of computational models, however a number of challenges must be overcome in order to develop more accurate screening routines for the design of CO 2 and CO reduction materials [175].

Conclusion
The reduction of CO 2 to multi-carbon products such as hydrocarbons consists of multiple complex reaction steps involving many shared intermediates depending on the desired reaction product. In recent decades, a significant amount of progress has been made regarding the design of highly active or selective electrocatalysts, particularly for the formation of CO and formate. For the formation of larger products involving multiple carbon atoms such as ethylene however, a greater understanding of the reaction mechanisms is required. In particular, improving understanding of key areas such as the effect of the electrode surface morphology on product selectivity, sub-surface structure as well as the effect of local pH. Now, due to a lack of effective probes able to examine quantities outside macroscopic equilibria, a combination of both experimental and computational methods could provide the key to developing a greater understanding of the reaction phenomena taking place. In terms of computational modelling of electrocatalysts, one possible method of improving the understanding of a system could be through combining numerous theoretical models to develop beyond the specific cases which certain models are tuned toward. This would require both a more standardised approach toward future experimental setups, as well as a conscious effort to develop future computational models beyond merely the surface characteristics of potential catalyst designs. Even after 35 years of research, there is still much work to be done, particularly in the development of catalysts more selective toward the production of liquid fuels. The "one-pot" synthesis of chemicals from waste CO 2 however, particularly fuels, represents a useful and potentially game-changing method of moving toward a carbon neutral future with minimal impact on existing infrastructure.