Recent Developments in the Modelling of Heterogeneous Catalysts for CO2 Conversion to Chemicals

Density functional theory (DFT) of the CO2 behavior on the catalyst surface provides valuable insights about the C=O bond activation, information about adsorption and dissociation of CO2, understanding the elementary steps involved in the mechanism of the CO2 hydrogenation reaction. Nowadays, DFT computational studies for the catalytic hydrogenation of CO2 are becoming very popular. Therefore, this article is focused on a comprehensive review of the DFT studies in thermocatalytic hydrogenation of CO2 at the gas‐surface interface and discusses three aspects: 1) processes taking place on the surfaces and facets of transition metal heterogeneous catalysts, 2) adsorption of CO2 on surfaces of different transition metals; 3) current understanding of reaction mechanisms taking place on the catalytic surface for the production of different compounds. A detailed schematic overview of the possible CO2 hydrogenation mechanisms and DFT simulations presented here will enhance the current understanding of the CO2 catalytic hydrogenation.


Introduction
The increasing average temperature of the Earth's atmosphere is a global environmental problem which continues to grow as a consequence of a constantly rising carbon dioxide (CO 2 ) concentration in the atmosphere. Upper scenarios for CO 2 emissions show the rise of CO 2 concentration up to 936-1200 ppm by 2100 with global temperature increase by 3-5.5°C. [1] Under the conservative scenarios atmospheric CO 2 levels are forecasted to remain below 450-550 ppm with mean global temperature 1.5°C and an increase of global mean sea level between 0.26 to 0.77 m. [1,2] Hence, it is imperative to reduce the emissions of CO 2 . Developing efficient methods to employ CO 2 as an abundant C1 building block to produce chemicals, materials, fuels or carbohydrates is a very attractive approach.
In the case of chemical CO 2 utilization, CO 2 is typically converted by thermochemical processes such as homogeneous [3,4] and heterogeneous hydrogenation; [5,6] and by biochemical, [7] electrochemical, [5,[8][9][10] photochemical [11] and photoelectrochemical reduction processes. [12,13] The use of specific catalysts is key to overcome high activation energy barriers, to extend the electrode life and stability or to capture solar radiations that generate excitons (e À + hole) for CO 2 reduction. [14,15] For the CO 2 conversion processes heterogeneous catalysts are preferred and widely used in the industries. They exhibit high catalytic activity, robustness, high efficiency in the recovery and recycling with the possibility of simple product separation, which can be economically advantageous in industrial CO 2 conversion. They also provide significant durability and stability in handling and reactor design.
The publication activity for catalytic CO 2 conversion by hydrogenation, electrochemical and photochemical reduction was examined by a bibliometric analysis which was performed using the SCI-expanded search platform and the search results are shown in Figure 1. Currently, the most examined area is electrochemical way of CO 2 conversion. Electrochemical CO 2 reduction has received a great deal of attention recently, but the low solubility of CO 2 in aqueous solution has been a major obstacle which leads to mass transport limitation. [16,17] The use of a gas diffusion electrode has enabled the direct use of gaseous CO 2 for electrochemical conversion because the electro-chemical conversion process does not require H 2 as a reactant. [17] The attention towards photochemical reduction started increasing from 2012. Because of its similarity to photosynthesis, the process typically suffers from low productivity and poor stability. [17] The most widely used method of CO 2 conversion is catalytic hydrogenation. Several articles about current experimental research of the CO 2 hydrogenation summarize the development of the most recent catalysts with proposed mechanisms. [5,[18][19][20][21] The majority of the literature is focused on methanol synthesis and mechanism of methanol formation on mainly used and most debated ZnO/Cu catalytic surface [22][23][24][25][26] which makes it more accessible to find information about reaction pathways for methanol production. Information about reaction intermediates and reaction pathways on various catalytic surfaces for preparation of other chemicals is not easily obtainable. Therefore, this review summarizes and systematizes mechanisms for CO 2 hydrogenation using catalysts based on different type of transition metals.
The use of quantum mechanics simulations for understanding the CO 2 hydrogenation process is effective in finding new intermediates, searching for new catalysts, and identifying reaction pathways. [27] The DFT simulation of CO 2 behavior on the surface of the catalysts can provide invaluable insights about the C=O bond activation, help to understand the evolution adsorbed species on the surface of the catalyst, information about rate-determining step, and overall insight into reaction mechanism which can speed up and diminish the system cost significantly and contribute to obtain a better understanding of the catalyst role. DFT is helpful to understand the nature of chemical reaction deeply from the molecular level, study the reaction including every primitive step, then find the pathway of chemical reaction, and eventually find out the key points affecting the reaction rate. [28] In the case of literature that is oriented towards DFT simulations of the CO 2 hydrogenation on catalytic surface there is one review [27] that solely summarizes theoretical results and one review that is more oriented towards mechanisms of solid-gas interface thermocatalytic CO 2 reduction. Since more and more studies use different DFT

Current understanding of CO 2 catalytic hydrogenation
In CO 2 , carbon is in its highest oxidation state which makes the compound thermodynamically very stable with C=O bond dissociation energy (750 kJ mol À 1 ) much higher than the CÀ C (336 kJ mol À 1 ), CÀ O (327 kJ mol À 1 ) or CÀ H (441 kJ mol À 1 ). [13] To break such a stable bond, higher temperatures during conversion processes are needed where an increase in temperature facilitates CO 2 activation. However, with a high temperature, the whole process of conversion is energetically very demanding and can result in higher selectivity towards undesirable products. By introducing another substance with higher Gibbs energy as co-reactant, such as hydrogen, the conversion will become thermodynamically easier. [29] To resolve these problems several processes of CO 2 conversion such as thermochemical, electrochemical and photochemical reduction with the use of catalysts have been developed. An appropriate catalyst will Dr. Victor Sans graduated in Chemical Engineering at the University Jaume I followed by a MSc and a PhD in Sustainable Chemistry. After he took a post-doctoral appointment at the University of Bath and later Warwick under the supervision of Prof. Alexei Lapkin. Since 2011 he worked in the Cronin group as a PDRA and since 2013 as a Research Fellow in the same group. In 2014 he was appointed Assistant Professor and promoted to Associate Professor in 2018 at the University of Nottingham. Currently, he is a CIDEGENT Fellow and group leader at the Institute of Advanced Materials (INAM) at the Universitat Jaume I. His research interest include reactor engineering, 3D-printing, advanced materials, sustainable chemical processing and process automation.
decrease the temperature of the process and improve the selectivity.
The CO 2 hydrogenation to hydrocarbons can be seen as a modified FTS with CO 2 as a reactant instead of carbon monoxide (CO). [30] Some of the main products of CO 2 hydrogenation are methanol (CH 3 OH), methane (CH 4 ), formic acid (HCOOH) and hydrocarbon fuels (represented by À CH 2 À ) depending on the type of the catalyst (Table 1) and reaction conditions. CO and water (H 2 O) are considered by-products. The endothermic RWGS is widely used as the intermediate step in combination with exothermic reactions that lead to the formation of methanol and hydrocarbon fuels. The production of methanol and hydrocarbon fuels by CO 2 hydrogenation is regarded as the most viable way of reducing CO 2 emissions in the atmosphere significantly. [31,32] Light olefins such as ethylene and propylene are produced worldwide in amounts exceeding 200 million tons per year and are very important building blocks in chemical industry. [33] Many catalysts have been explored to achieve selective control towards industrially widely demanded products. As shown in Table 1, each hydrogenation reaction prefers a different metal-based catalyst type which improves selectivity towards the specific compounds. For RWGS, the most commonly used catalysts are based on Cu-, Pt-, Rh-, Fe-, Ce-, while catalysts based on Cu-together with Cu/ZnO-based catalysts enhance the formation of methanol. For CO 2 methanation Ru-, Fe-, Ni-, Co-, Mo-based catalysts are the most effective and the formation of formic acid is reached with Ru-, Rh-, Ir-, Pd-based catalysts, although various studies have been reported employing Ni [34,35] or Cu [36,37] based catalysts.
Most of these catalysts are used and examined in combination with support where mostly metal-oxides, [43,44] -carbides, [44][45][46] -sulfides [47,48] and -nitrides [49] are used. Metal oxides are frequently used as supports for the dispersion of metals and reduced oxides have a strong tendency to react with CO 2 . [44] Metal-carbides due to their bonding between carbon atom and transition metal atom have unique properties such as high   [27,38] CO 2 + 4H 2 * * CH 4 + 2H 2 O(g) À 164.9 À 113.5 Ru-, Fe-, Ni-, Co-, Mo-based catalysts [39,40] CO 2 + 3H 2 * * CH 3 OH + H 2 O(l) À 131.0 À 9.0 Cu-and Cu/ZnO-based catalysts, Pd-, based catalysts [41,42] CO 2 + H 2 * * HCOOH(l) À 31.2 33.0 Ru-, Rh-, Ir-, Pd-based catalysts [40] nCO 2 + 3nH 2 * * C n H 2n + 2nH 2 O À 128 [19] melting temperature (> 3300 K), high hardness (> 2000 kg/ mm 2 ) and high tensile strength (> 300 GPa) and show catalytic activity similar to activity of noble metals. [45,46,50] Metal-nitrides are characterized by two different effects: ligand effect and ensemble effect. [51] Ligand effect results in changes in their electronic structure which strengthens adsorption of reactants and products similar to noble metals improving the selectivity of reaction. Ensemble effect decreases the number of available metal sites and results in creating of different adsorption sites. Several theoretical studies are devoted to examination of CO 2 behavior on these surfaces. [52][53][54][55] However, this is a difficult task. One of the example are transition metal oxides which are difficult to model using DFT with simple local and semi local functionals. [56] LDA and GGA approximations do not account properly for exchange and correlation effects in transition metal oxides and lead to self-interaction errors. [52] A better description of metal oxide surfaces is provided by self-interaction correction (SIC) and GW approximations (GWA) but these methods are computationally very demanding and not appropriate for the large systems that are required to surfaces and clusters simulations. The only method that takes account the on-site Coulombic repulsion among localized d-electrons by incorporating an extra energetic penalty for delocalization and is relatively computationally low costing is DFT + U method. Also, the results obtained by DFT studies greatly vary depending on the used method which leads to diverse conclusions. The use of the right functional is not trivial and is still highly discussed between researchers not only for complicated systems but also for transition metal surfaces. We think that metal-oxides, -carbides, -sulfides and -nitrides require separate review devoted to computational studies of these surfaces and therefore, this review is aimed mainly on the computational studies of transition metal surfaces and their impact on CO 2 hydrogenation.

Carbon monoxide formation
Carbon monoxide formed by RWGS reaction is a feedstock or key intermediate for the production of methanol, hydrocarbon fuels via FTS [57] and a building block for carbonylation reactions. [58,59] The RWGS reaction is endothermic (Table 2) and thermodynamically favored at high temperatures with pressureindependent chemical equilibrium [60] and direct gas-phase reaction which makes it one of the most promising hightemperature chemical reactions. [61]

Potential reaction mechanisms via RWGS
The literature classifies the reaction mechanism into two categories; the redox mechanism and associative mechanism. [62] In the redox mechanism the oxidation reduction cycle occurring on the catalyst surface is responsible for the reaction. [63] CO 2 is firstly adsorbed on the reduced metal sites or metal oxide sites, and then subsequently reacts with them to form CO. After that the oxidized catalyst is reduced by H 2 and the reduced sites are formed again. [64,65] The associative mechanism, also known as dissociative [66,67] or formate [6,27,68] mechanism is an adsorption-desorption model where the adsorbed species interact to form an adsorbed intermediate (carbonate, formate, carbonyl, etc.) as a critical step in the RWGS process which then decomposes to form H 2 and a mono-dentate carbonate. [64,69] Prevailingly a bidentate formate reaction intermediate is produced through the CO 2 * reaction with dissociated H* by the adsorption of preferably oxygen atoms to the metal surface. Additional hydrogenation leads to the formation of HCOOH which splits into HCO* and O* and subsequently into CO* and H*. For the hydroxyl pathway CO 2 is adsorbed onto the surface with carbon and oxygen atoms followed by hydrogenation. COOH* intermediate is then hydrogenated to form COH* and O* that leads to formation of CO* and H* or may be directly dissociated into CO*and O*. Additional O* and H* intermediates lead to H 2 O formation. The associative mechanism is depicted in Figure 2.

RWGS catalysts and challenges
The RWGS studies of supported metal catalysts consist primarily of Cu, [70,71] Pt, [72,73] and Rh [74] immobilized on a variety supports. [38] Catalysts that are active in the WGS reaction are also active in the RWGS reaction according to the principle of microscopic reversibility. [27] Cu has been shown to perform RWGS at low temperatures, [75,76] and little or no methane is formed as a side product. But without hydrogen, CO 2 dissociation is highly unfavorable on clean Cu surfaces, which directly translates to the need for high H 2 /CO 2 feed ratios to achieve high CO 2 conversions. [38] Therefore, Cu demands a support and is combined with other metals. From the recent studies Zou et al. [77] investigated CeCu composite catalysts with different Ce/Cu mole ratios due to high capability to form oxygen vacancies and reversible reducibility of CeO 2 as support. The Ce 1.1 Cu 1 catalyst demonstrated high stability and the highest CO 2 conversion rate in the RWGS reaction with 100 % selectivity towards CO, reaching 1.38 mmol.g cat À 1 min À 1 at 400°C. Efficient and stable Cu-based catalyst was also prepared and examined by Zhang et al. [78] They studied effect of β-Mo 2 C transition metal carbide on dispersion, stabilization of copper nanoparticles and subsequently their activity in RWGS reaction. The strong interaction between Cu and β-Mo 2 C effectively promoted the dispersion of supported copper and prevented the aggregation of Cu particles which led to extraordinary activity and stability for RWGS reaction. Noble metal catalysts, mainly Pt and Rh based supported catalysts, have high activity towards hydrogen dissociation, relatively moderate strength with the adsorption of reaction intermediates and the incompletely filled D-orbital electrons make them easier for the adsorption of reactants with moderate strength, which is further benefiting to form the intermediate "active compound" in RWGS reaction. [62] Besides mentioned catalysts other metal catalysts as active components or as supports are Pd, [79] Ni, [80,81] Co, [82,83] Fe, [84] Fe supported on CNTs [85] and carbide (Mo 2 C) catalyst. [86,87] As a support for different metal catalysts Al 2 O 3 , CeO 2 , TiO 2 and SiO 2 are primarily examined. NiÀ Al 2 O 3 catalyst was investigated by Wolf et al. [88] They achieved the CO 2 equilibrium conversion of 80 % at 900°C and proved the catalyst's stability at 900°C. TIO 2 was investigated in combination with Pt at 200-500°C by Chen et al. [89] PtÀ O v À Ti 3 + species formed at the interface between Pt and reducible TiO 2 support was identified as the active sites for the formation of CO, while large Pt particles facilitated the hydrogenation of CO to CH 4 . Dai et al. [88] studied the RWGS reaction on mesoporous MÀ CeO 2 catalysts. According to their results, CO 2 RWGS reaction catalytic activities decrease in the order NiÀ CeO 2 > CuÀ CeO 2 > CoÀ CeO 2 > FeÀ CeO 2 � MnÀ CeO 2 . Besides, CuÀ CeO 2 , FeÀ CeO 2 , and MnÀ CeO 2 catalysts maintained 100 % CO selectivity at the temperature 400°C. Pt was investigated in combination with TiO 2 or SiO 2 as a support by different researchers [90,91] where the supports promoted the overall CO 2 conversion, although the impact on the selectivity was rather small. To improve the Pt/TiO 2 catalytic impact on RWGS reaction Lee et al. [92] investigated the effect of CeO 2 addition to a Pt/TiO 2 at temperature range 300-600°C. CeO 2 affected the lattice and pore structure through substitution with TiO 2 and optimized the catalyst activity.
Despite the comprehensive studies conducted to develop high-performance catalysts for the RWGS reaction, a fundamen-tal understanding of the roles of the metal catalysts and their mechanisms during the spontaneous, dynamic, and hightemperature RWGS reaction is lacking. [93] Since the thermodynamics of the RWGS reaction requires high temperatures to reach satisfactory levels of conversion, hence an additional challenge is to improve catalytic activity for the RWGS reaction at lower temperatures maintaining an acceptable CO selectivity. [94]

Methane synthesis
Due to the increasing demand for mitigating global warming and storing surplus renewable power, the CO 2 methanation or Sabatier reaction is an advantageous way to store renewable energy such as wind and solar power, to transfer biogas effectively to biomethane, and to convert CO 2 to chemical feedstocks and fuels. [19] The CO 2 methanation is exothermic, pressure dependent and is thermodynamically favorable at low temperatures (ΔG 298K = À 130.8 kJ/mol). However, the reduction of the fully oxidized carbon to methane is an eight-electron process (Equation 1 and 2) with significant kinetic limitations, which requires a catalyst to achieve acceptable rates and selectivity and makes the process kinetically favorable. [60,95]

Associative and dissociative CO 2 methanation mechanism
The reaction mechanism proposed for CO 2 methanation (Figure 3) is divided into two main categories, associative and dissociative mechanism. The first one involves the direct hydrogenation of CO 2 to methane without the formation of CO as an intermediate. [95] The associative adsorption of CO 2 and H 2 adatom H ad is followed by the hydrogenation of the associated species to form methane. [96,97] The other one involves the conversion of CO 2 to CO prior to methanation, and the subsequent reaction follows the same mechanism as CO methanation. [98] CO methanation over supported metal catalysts proceeds via the dissociation of CO on the metal and the hydrogenation of the resultant surface carbonaceous species. [96,99]

Challenges in catalytic CO 2 methanation
CO 2 methanation can reach 99 % CH 4 selectivity through the use of appropriate catalysts, avoiding the subsequent product separation and overcoming the difficulty of dispersed product distribution. [19] The most studied noble and nonnoble metalbased catalysts for CO 2 methanation are Ni, [100][101][102] Ru, [103][104][105] Rh, [106,107] Pd, [108,109] Co, [110,111] Fe, [112,113] Cu, [114,115] Pt, [116] Ag [39] and Au [39] catalysts from which the most important role to methanation process has Ru, Fe, Ni, and Co. [39,117] According to the various studies the activity performance and selectivity of different metal-based catalysts decreases in the following order: [118] Ni and Ru are reported to have maximum activity and stability. [119] Ni based catalysts are very effective due to the presence of easily transferable electrons in the frontier d orbitals and therefore are the most efficient and active catalytic system together with alumina as a support that may be applied on industrial scale. [120,121] Ru catalysts at 300°C results in a 96 % methane yield while Ni catalysts shows a maximum yield of 80 % at 400°C. [40] Ru is about 120 times more expensive than Ni and Ni catalysts have a short lifetime, because of carbon deposition which blocks pores and con-sequently deactivates the catalyst. [39,122] A rational design of Nibased methanation catalysts with high activity at low temperatures, good redox properties, and better stability at reaction temperatures are still required for industrial applications. [121] Gnanakumar et al. [123] prepared nickelÀ niobia catalyst 40NiÀ Nb 2 O 5 -700 with CO 2 conversion of 92 % and CH 4 selectivity of 99 % and catalyst showed stable activity during a continuous test of 50 h. According to their results the strong acid sites seemed to be more favorable for the CO2 hydrogenation, however they could not find the direct reason for this. Several studies observed promotional role of transition metals on catalytic performance and stability of NiÀ Al 2 O 3 . Daroughegi et al. [124] studied incorporation of Cr, Fe, Mn, Cu and Co into NiÀ Al 2 O 3 . The 25NiÀ 3MnÀ Al 2 O 3 catalyst with the highest BET surface area and the lowest crystalline size improved the low temperature activity and selectivity toward methane and passed a stable activity at 350°C for 10 h in CO 2 methanation reaction. Garbarino et al. [125] observed the effect of Ni/LaÀ Al 2 O 3 catalysts on CO 2 methanation. The introduction of lanthanum at low loadings strongly increased the catalytic activity in the 500-630 K temperature region, with increase in methane selectivity to~100 %. The addition of lanthanum resulted in the formation of basic sites which adsorbed CO 2 more strongly.
From other transition metal catalysts, pure Fe has low activity and selectivity towards methanation and consequently is not active metal in CO 2 methanation. [126] However with the use of a support [127] or in combination with other metals such as Ni [128,129] or Co [130] the activity may increase. Even though Co catalysts are more expensive, they show a similar activity to Ni in CO and CO 2 methanation and also do not require an induction period [39] that is observed with Ni catalysts and necessary to an increase of the Ni particle size. [131]

Methanol synthesis
Methanol as one of the most valuable chemicals obtainable by CO 2 hydrogenation is not only considered as easily-transport liquid energy storage medium with high energy density, but also served as an essential chemical feedstock with a wide range of utilization ways [132] to produce different chemicals such as formaldehyde, acetic acid, methyl methacrylate, dimethyl terephthalate, methylamines, dimethyl ether, methyl tertÀ butyl ether, chloromethanes or light olefins. [133] From a thermodynamic point of view, lower reaction temperature or a higher reaction pressure favors the synthesis of methanol. Indeed, enhanced reaction temperature (e. g., higher than 513 K) facilitates CO 2 activation and subsequent methanol formation. Furthermore, other by-products are formed during the hydrogenation of CO 2 , such as CO, hydrocarbons, and higher alcohols. Therefore, a highly selective catalyst is required to avoid the formation of undesired byproducts for methanol synthesis.

Reaction mechanisms of methanol synthesis
According to the different studies, [5,32,134] methanol synthesis over Cu-based catalysts may proceed via three different reversible reaction pathways ( Figure 4). 1) Formate mechanism: CO 2 reaction with surface atomic H yields formate as an intermediate, 2) RWGS mechanism with carboxyl intermediate and 3) CO 2 hydrocarboxyl mechanism with *C(OH) 2 as intermediate. All three mechanisms lead to the formation of formyl (H 2 CO*) which is hydrogenated to methoxy (H 3 CO*) and methanol (CH 3 OH). During the formate pathway, chemisorbed formate can be formed from CO 2 reaction with dissociated surface hydrogen. Then, surface-bound formate is hydrogenated, which is the rate-determining step, to produce dioxomethylene that can lose oxygen with the formation of formaldehyde or lose hydroxyl and form H 2 CO*. H 2 CO* can be further hydrogenated to methoxy and methanol. The RWGS mechanism involves the formation of CO* through the loss of hydroxyl from hydrocarboxyl. HCO intermediate is then hydrogenated to formyl that leads to methanol. The hydrocarboxyl pathway assumes that hydrocarboxyl can be hydrogenated to form COOH* which may subsequently lose hydrogen to form *COH. *COH is then hydrogenated to hydroxymethylene.
Several studies suggest that formate mechanism leads to a dead end since formaldehyde has not been detected as a side product from methanol synthesis. [134] Some studies present that formate has not been converted to methanol via direct hydrogenation and is rather a spectator species. [5,134,136,137] The kinetics of formate hydrogenation also did not correlate with those of the formation of methanol. [134,138] According to the Wu et al. [134] the RWGS route is questionable as well and methanol formation seems to proceed via hydrocarboxyl route. Based on prior tracer and isotopic labelling studies in conjunction with extensive DFT calculations now available, the CO produced from the fast RWGS reaction was proven not to undergo subsequent H insertions/hydrogenations, on account of the poor stability of the surface HCO that is extremely reactive surface species, with infinitesimally small surface coverages, under integral conditions. [24] Figure 4. Possible mechanism and intermediates of methanol synthesis via CO 2 hydrogenation according to different studies [18,134,135] a) formate mechanism, b) RWGS mechanism, c) hydrocarboxyl mechanism.

Catalysts used in methanol synthesis
Most used catalyst remains Cu together with different promoters (Zn, Zr, Ce, Al, Si, V, Ti, Ga, B, Cr, etc.). [32] A proper support not only affects the stabilization and formation of the catalysts active phase, but it is also able to control the interaction between the promoter and major component. Additionally, acidity and basicity characteristics of the catalyst are also determined by the selected support. [23] Low-pressure methanol synthesis relies almost on catalysts based on copper, zinc oxide, and alumina, which acts as a promoter in this catalyst rather than as a classical support. [139] However, Cu/ZnO/Al 2 O 3 catalysts suffer from the limited selectivity (< 70 %) for methanol and stringent reaction conditions (50-100 bar, 200-300°C). [140] Allam et al. [141] evaluated the improvement of Cu-and Zn-based binary (CuOÀ CeO 2 , ZnOÀ CeO 2 ) and ternary (CuOÀ ZnOÀ CeO 2 , CuOÀ ZnOÀ Al 2 O 3 ) catalysts for CO 2 hydrogenation to methanol in terms of metal oxide dispersion and morphology. Ternary catalysts prepared by polyol method exhibited a higher activity (about 20 %) and selectivity (< 65 %). Many studies investigate the use of different promoter than ZnO in Cu-based catalysts. According to the Bhanage et al. [125] the CeO 2 has stronger basic sites than ZnO and may be a promising promoter. Wang et al. [125] studied the effect of Cu-based catalysts supported on CeO 2 and ZrO 2 between 200 and 300°C. The CO 2 conversion improved with increasing temperature and selectivity towards methanol was generally higher with Cu/CeO 2 catalyst with highest values at 220°C (> 80 %). Also Li et al. [142] synthesized mesostructured Cu/ AlCeO catalysts with CO 2 conversion up to 22.5 % at 553 K and 94 % selectivity at 473 K. The studies show that CeO 2 exhibits great performance not only in RWGS reaction but also in methanol synthesis.
Although the most used catalyst is Cu, there are still open questions rising about the active sites. One have suggested that metallic copper is the active site and addition of oxides would sustain the large copper surface and reduce CuO to metallic copper. [36,143] Other suggested the effect of "CuÀ Zn" synergy for being essential for the active site [144,145] where methanol is synthesized over Cu + at the Cu/ZnO interface, or over Cu cations that dissolve in the ZnO matrix and metallic copper only promotes the dissociation of H 2 . According to the Behrens' et al. [146] results where they combined experimentally obtained data with DFT calculations for studying the active sites of methanol synthesis over Cu/ZnO/Al 2 O 3 industrial catalyst, the most active surface was found to be a Cu step with Zn alloyed into it. The reason for this discussion is the difficulty of obtaining data for the industrial Cu/ZnO/Al 2 O 3 catalysts under realistic working conditions and the variety of different Cubased catalysts showing contradicting behavior. [147] Other most examined catalysts for CO 2 hydrogenation to methanol are Pd-based catalysts. Pd possesses the ability to activate hydrogen gas into H-adatoms that can spillover unto metallic oxide supports and in the presence of CO (originated from dissociative adsorption of CO 2 ) form a formate ion which can be further hydrogenated to methanol or methane. [42] The simplest example is Pd supported on ZnO and reduced with temperature >~300°C which results in the formation of the 1 : 1 PdZn alloy that shows very good selectivity to methanol. [148] From the computational point of view this shows that DFT calculations are very necessary in studies of transition metals and bimetallic systems.

Synthesis of formic acid
The direct synthesis of formic acid from CO 2 potentially represents a vector for hydrogen storage with promising energy storing capacity (53 g l À 1 ), which exceeds pressurized H 2 tanks (39.4 g l À 1 at 700 bar). [149][150][151][152] However, the CO 2 reduction reaction is energetically hampered and a serious practical difficulty lies in the low thermodynamic stability of formic acid and fast decomposition kinetics. [152]

Reaction pathways in formic acid synthesis
Recent studies [34,36,153,154] show that CO 2 hydrogenation to formic acid may undergo two different pathways which include formate as an intermediate and depend on the adsorption of the CO 2 molecule. The first pathway is depicted in Figure 5 and displays the formation and reaction of monodentate formate with dissociated hydrogen. In the second pathway the bidentate formate is generated and then hydrogenated to produce formic acid.

Modelling Catalyst Surfaces
Understanding the nature of the active sites, for example, on which and what type of catalysts does the reaction of CO 2 and hydrogen take place, and the reasons for such mechanistic differences among the metals is crucial in the effort to gain a mechanistic interpretation of CO 2 activation, and detailed analysis by the theory are required to link the different prevalent mechanisms on the metals to specific properties at the atomic scale. [167,168] Many DFT studies are aimed on the CO 2 adsorption and H 2 dissociation on the specific pure metal surfaces and their comparison with the previous studies with the intention of finding the mechanism of CO 2 conversion. However, results of quantum calculations are scattered among various papers with the use of different approaches, often mentioned between experimental results without an effort to establish a systematic approach which would make orientation more readable.
Consequently, the aim of this chapter is to summarize and systematize the results of the DFT investigations for the individual transition metal surfaces used in the synthesis of different chemicals from CO 2 hydrogenation.

Surface energy of transition metal facets
Different facets of catalysts possess unique geometric, electronic structure and thermal stability which may prolong the catalyst durability and increase the product selectivity. The surface energy has an influence on physico-chemical properties, such as the surface tension, strain, etc. It is well-known that these properties are crucial in the catalytic performance of the materials. [169,170] For example, using DFT with RPBE functional Li et al. [171] found that surface tension affects the reactivity of metal nanoparticles. They studied adsorption energies of oxygen on Au and Pt clusters with 3 nm diameter and found that surface tension of the clusters induces a compression, which weakens the bonding of adsorbates compared with the bonding on extended surfaces. The effect is largest for closepacked surfaces and almost nonexistent on the more reactive steps and edges. The effect is also largest at low coverage and decreases at higher coverages where the strain changes from compressive to tensile. According to them this has direct quantitative relevance to understanding reactions on small particles.
There are many different values of surface energies calculated using different functionals (Table 3) although, the values generally are similar for individual metal. Many studies use PBE functional to calculate surface energies are calculated by PBE functional, however Waele et al. [172] stated that GGA-PBE significantly underestimates the surface energy for materials with a large correlation energy while LDA provides satisfactory results. The surface energy of different metal facets typically decrease in the order of γ{111} < γ{100} < γ{110} and surface with the lowest surface energy is the most thermodynamically stable surface. From the 3d metals the lowest surface energy has Cu surface, from 4d metals it is Ag and from 5d metals the lowest surface energy has Au. The highest surface energy from 3d, 4d and 5d metals has Fe, Rh and Ir, respectively. For Fe surface with bcc structure the surface energy decrease in opposite order as the surface energy of fcc structures.
The most favorable facets are the (110) facet for a bodycentered cubic (bcc) metal and the (001) facet for a hexagonal close-packed (hcp) metal. However, the low index surfaces are frequently studied due to the fact, that the majority of facets have low surface energy and transition metal nanoparticles are mostly bounded by low-index facets. [173] Also, small nanoparticles, especially clusters, may differ from larger ones, as they expose a higher fraction of coordinatively unsaturated surface atoms in the form of corner and edge atoms. The lower coordinative unsaturation may lead to narrowing of the d-band, which results in an upward shift of the band's energy and, consequently, in stronger adsorption of reaction intermediates. [174] Therefore, DFT studying of CO 2 molecule activation, adsorption and dissociation together with hydrogenation on different low index surfaces is very important for understanding the catalytic activity and reaction mechanism and for development of new nano-catalysts.

CO 2 adsorption behavior on solid surfaces
The first step of CO 2 activation and dissociation is its adsorption on the catalyst metal surface. In CO 2 hydrogenation, the interaction between hydrogen and the metal surfaces is a crucial part. An appropriate H 2 and CO 2 co-adsorption equilibrium will strongly affect the reaction. [182] Different computational studies investigated the most stable adsorption structures of CO 2 on metal surfaces. Burghaus [183] summarized possible adsorption structures of physisorbed CO 2 conformations, where CO 2 is adsorbed linearly, parallelly or upright on the surface and weakly chemisorbed CO 2 where CO 2 can be adsorbed in a carbon-atom-down, carbon-atom-up and mixed position (Figure 6). Various sites may be populated simultaneously with a population distribution depending on the surface temperature.
The effect of the surface can be also examined with DFT calculations. The adsorption may occur on different sites of fcc, The adsorption energies calculated computationally with the use of different functionals is shown in Table 4. The adsorption energies were mostly calculated with PBE functional. The presented values do not show adsorption free energies which values depend on the temperature and are > 1 eV higher than adsorption energy. It can be observed that Fe surfaces have the lowest adsorption energy and it seems that the adsorption of CO 2 is strongest from selected transition metal surfaces. At the present, only few articles show DFT calculated values of adsorption energy for transition metals. Besides, for various surfaces the adsorption energy values are not consistent between different articles and show negative and positive values. Liu et al. [173] used GGA and PAW potentials which resulted in negative values of adsorption energies. However, the values calculated by Wang [184] and Muttaqien et al. [185] using PBE functional with Vanderbilts ultrasoft pseudopotentials and vdW-DF functional respectively, are positive. This indicates that the interaction with the surface is repulsive and positive numbers are due to artefacts of the DFT calculations as they are a local minimum that has no meaning. Hence, more calculations are essential to prove the adsorption energy values calculated by DFT since the use of different functionals and potentials  [175] 2.10 [175] , 2.58 [176] ---2.73 [177] -100 -2.5 [178] 2.13 [175] 2.15 [175] , 2.47 [176] ---2.22 [177] -110 -2.45 [178] 2.25 [175] 2.27 [175] , 2.37 [176] ---2.43 [177] -211 ---2.5 [176] ---2.59 [177] -Ni 111 -1.92 [178] -----2.01 [177] 1.17 [179] 100 -2.22 [178] -----2.43 [177] 1.31 [179] 110 -------2.37 [177] 1.42 [179]

211
---1,29 [181] ----0.76 [179]  leads to incoherent adsorption energy values which report completely different results and therefore show various processes taking place on transition metal surfaces. The adsorption energy calculated for Ni surfaces by Czelej et al. [186] decrease in order Ni(111) > Ni(100) > Ni(110) and for Cu surfaces adsorption energy calculated by Wang et al. [184] increases from Cu(111) < Cu (100) < Cu (110). For 4d and 5d metals, the adsorption energy is weaker across the different planes analyzed. It is important to note that for these metals more computational studies of adsorption energies would be also desired to be able to draw meaningful conclusions.

The accuracy of the DFT using various functionals
When comparing the simulations to experiments there is additionally the uncertainty of whether one picked the correct experimental structure to simulate, for example the structures of the metal surfaces, the adsorption sites, and the adsorbate coverage ratio. There is also uncertainty in the measurement of the adsorption energies due to the possible surface defects.

Performance of DFAs for gas phase reaction energetics
Several scientists worked on the compilations of experimental data of adsorption reactions to compare them with values obtained by using different functionals. Every functional is used for different purposes and provides different values. The only specifically designed functionals to treat adsorption energies are RPBE and BEEF-vdW, [187] although there are many other functionals that have general-purpose and may provide good values.
There is no well-defined way to know what contribution to the adsorption energy really comes from van der Waals interactions and therefore it is not exactly know how to classify surface reactions into the two classes provided by Wellendorff et al. [187,190] Different division of the experimental database was proposed by Duanmu et al. [187] They divided experimental database to open-shell radical adsorption processes (adsorption of H atoms on metal surface) and closed-shell molecular adsorption processes (adsorption of CO molecule on metal surface). The adsorption energies were recalculated with PBE and previously untested M06-L, GAM and MN15-L functionals were applied for same transition metal surfaces. The results shown in Table 5 were compared with the values calculated by Wellendorff et al. [190] They found that BEEF-vdW, GAM, RPBE, and M06-L are best performing functionals for open shell radical adsorption processes while MN15-L, followed by BEEF-vdW, M06-L, and GAM are the best for closed-shell molecular adsorption processes (Table 6).
Overall, literature shows that relatively good performance can be provided by BEEF-vdW, M06-L, GAM, MN15-L and RPBE functional which makes them good candidates for application to heterogeneous catalysts.
A different type of benchmark database was provided by Schmidt et al. [191] from many-body perturbation theory. They used RPA to construct and calculate 200 different full coverage adsorption reactions including OH, CH, NO, CO, N 2 , N, O, and H adsorbed on transition metals. The high coverage was used due to the large computational cost of the calculations. They also calculated 5 adsorption energies for CO and 2 adsorption energies for H 2 at experimentally relevant coverage listed in Table 5 and surface energies. The RPA was compared to LDA, PBE, RPBE, vdW-DF2, mBEEF, BEEF-vdW and MBEEF-vdW. RPA was found to perform as well as the GGA and van der Waals density functionals RPBE and BEEF-vdW for adsorption and it outperformed all DFT functionals for surface energies. The problem of RPA is high computational cost since the method is computationally much more demanding. With high coverage the problem can be overcome, and RPA results can be compared with experimental data of reactions taking place at high gas pressure conditions.

Dispersion forces
BEEF-vdW functional in presented papers with best values of adsorption energy showed that van der Waals correction advance theoretical data towards experimental values of adsorption energy and therefore displays that dispersion forces may play an important role. This may be also the reason for the high errors in benchmark database for LDA functional. Dispersion forces are the result of correlation between zeropoint fluctuations of the dipole moments of atoms, molecules, etc. long distanced from each other. The conventional semilocal XC functionals, such as LDA, are very local and cannot capture long-range correlations.
Another study that examines the results of CO 2 hydrogenation using functionals including van der Waals forces was done by Studt et al. [192] They performed DFT calculations for CO and CO 2 hydrogenation on Cu(211) using RPBE and BEEF-vdW functional. BEEF-vdW functional resulted in quite different results where intermediates and transition-states involved in CO 2 hydrogenation interacted considerably stronger with Cu (211) surface in comparison with RPBE functional. Therefore Studt et al. suggested that a functional explicitly including van der Waals interaction is needed to get the details of selectivity in CO 2 hydrogenation correctly.
Tameh et al. [143] examined the accuracy of DFT for prediction of kinetics in CO 2 hydrogenation to methanol using microkinetic modelling. They compared RPA method to different functionals including RPBE and BEEF-vdW functionals. BEEF-vdW functional predicted that hydrogenation of CO 2 is thermodynamically favorable which they explained by their errors treating the OCO backbone. However, RPA also provides a description of the vdW interaction. Tameh et al. also found different results in the case of including dispersion forces. Their PBE results suggested that metallic copper is not the active site for CO 2 hydrogenation in industrial methanol synthesis while RPA predicted that metallic copper is still a possible active site for catalyzing CO 2 hydrogenation.

DFAs reliability for activation barriers on transition metal surfaces
While the DFT functionals have been extensively studied in calculations of adsorption and surface energies, their reliability for activation barriers on surfaces is not well understood. Sharada et al. [193] proposed an experimental database consisting of accurate barriers for dissociation reactions of molecules on transition metals. The BEEF-vdW GGA outperformed the MS2 meta-GGA and HSE06 hybrid, in direct contradiction to the gas phase barrier accuracies of these functionals. Therefore, the key Table 5. Comparison of experimental and theoretical energy values of chemisorption reactions upon gas adsorption, in kJ/mol according to different studies. Type

Recent DFT calculations of the most commonly used metal surfaces
A systematic review of the literature regarding the mechanism of CO 2 hydrogenation on various metal surfaces is presented in this section. The critical discussion is based on data about adsorption and surface energies. Furthermore, it is focused on the different metal crystallographic sites and their surface interactions with CO 2 that leads to various intermediates. The section also discusses the role of microkinetic modelling in obtaining information about reaction mechanism of CO 2 hydrogenation.

Fe catalytic surfaces
DFT calculations were carried out for CO 2 adsorption on Fe (100), (110), (111) and (211) surfaces. Also, several studies examined H 2 adsorption and dissociation on Fe surfaces to determine the most effective H 2 : CO 2 ratio for the activation of the reagents. In RWGS reaction: Wang et al. [194] investigated the adsorption dissociation and hydrogenation of CO 2 on fcc Fe(100), (110), (111) and (211) facets with the use of GGA with the PBE functional and with the use of PAW pseudo-potentials. They suggested that the Fe facet plays an important role in impacting the formation of key intermediates and thus altering the preferred pathways for CO 2 conversion. The results indicated that an appropriate H 2 À CO 2 co-adsorption equilibrium is important for effective activation of the reactants. Energetically most favorable for CO 2 adsorption was Fe (111) and (211) facet (Figure 8). During the dissociation and hydrogenation of CO 2 , the Fe(111) favored associative pathway with the HCOO* formation due to a relatively lower kinetic barrier while the (100) and (110) facets were more selective to redox pathway with CO* formation. The Fe(211) exhibited a competitive preference for the formation of CO* and HCOO*. All these Fe surfaces did not favor the formation of COOH* intermediate. Liu et al. [195] examined the adsorption and decomposition of CO 2 on transition metal fcc and bcc (100) surface atoms of Fe, Co, Ni and Cu using PW-DFT. From the cases studied, Fe surfaces were found to be the most favorable for CO 2 adsorption. However, Co and Ni showed favorable thermodynamics and low decomposition barriers for CO 2 reduction. Furthermore, their results showed that different Fe structure (fcc, bcc) affects thermodynamics. Accordingly, Wang el al. [182] investigated the adsorption and activation of CO 2 and H 2 over bcc Fe(100) with PAW pseudo-potentials and GGA approximation with PBE functional. The energetically most favorable adsorption of CO 2 occurred on the 4-fold hollow site with the C atom sitting in the middle of the 4-fold unit and right above the second layer Fe atom, and the two O atoms bound at the center of two FeÀ Fe bridge bonds. The adsorption energy of this configuration was 0.92 eV. Their calculation results suggest that a moderate H 2 versus CO 2 ratio is likely more suitable to achieve better adsorption and effective activation of the reactants which would facilitate CO 2 hydrogenation.
To understand the abilities of the waterÀ gas shift reaction catalysed by metallic Fe Li et al. [196]  In methanol synthesis: Since CO 2 hydrogenation on Fe surfaces seem to proceed via an associative pathway in RWGS, the formate intermediate may also lead to the production of methanol. Chen et al. [197] studied Fe(111) surface for decomposition of CO 2 with PW-DFT method. Their data show that isomers FeCO 2 (S-μ 3 À C,O,O'), FeCO(S-η1À C) and FeX(T,S-μ 2 À X) or FeX(B-μ 3 À X), for X = C and O atoms, are energetically favored among calculated structures of Fe(111)/CO 2 , Fe(111)/CO and Fe (111)/X. Their simulations of CO 2 dissociation on Fe (111) surface showed that the catalytic process is likely to proceed via a three-step mechanism. Li et al. [198] with the use of PAW method in conjunction with the rPBE functional studied microkinetic modelling of CO 2 hydrogenation on Fe (111) surface. They found out that the most probable path for the hydrogenation of CO 2 on Fe(111) surface is the formation of a formate-vertical structure.
Even though these studies show interesting results, they report different structures or do not mention whether the studied Fe surfaces were fcc or bcc structures. Moreover, while there are many DFT studies discussing the effect of Fe on CO 2 conversion the microkinetic calculations were not performed for Fe surfaces. Table 6. Comparison of the mean signed errors and mean unsigned errors for each functional according to the Duanmu et al. [187] Open-shell reactions

Ni catalytic surfaces
In methanation: Ren et al. [199] studied the mechanism of CO 2 methanation on the fcc Ni (111) [200] Their calculations using the PWSCF code within the GGA and PBE functional shown that the CO 2 hydrogenation passes via various stable intermediates, namely, carbon monoxide, methoxy, formate and yield the product methane. All three stable (formate, CO 2 or CO) intermediates can be hydrogenated to produce methane. The adsorption and decomposition processes of CO 2 on Ni (110) surface were also examined by Czelej et al. [201] using SP-DFT method and performing CI-NEB calculations. The CO 2 adsorption conformations and adsorption, desorption on Ni (110) surface are displayed in Figure 9a and 9b. They gave insight into the CO 2 /Ni(110)!CO/Ni(110) + O/Ni(110) reaction mechanism and distinguished two decomposition steps: 1) surface diffusion of CO 2 to the H-2 conformation with (depending on the starting geometry) 1-2 transition states; and 2) breaking of the coordinated CÀ O bond with total reaction barrier of 0.44 eV. In methanol synthesis: Maulana et al. [202] recently investigated the CO 2 hydrogenation to methanol on clean Ni (111) and Ni(111)À M (M = Cu, Pd, Pt, Rh) surfaces using DFT and microkinetics. The DFT calculations with PBE functional showed that formate-mediated and carboxyl-mediated pathways depicted in Figure 10 seem to be the main routes for production of methanol. The microkinetic modelling determined that formate route prefers mechanism via HCOOH* intermediate with much higher TOF value than carboxyl route and carboxyl pathway prefers HCO* intermediate. The kinetic performance was increased by Ni catalysts doped with Cu, Pd and Pt for formate mechanism and with Cu, Pt and Rh for carboxyl route at 573 K.
In formic acid synthesis: Ni metal surface was also investigated by DFT calculations to see if the formation of formic acid is also possible on this surface. Peng et al. [34] using DFT-PW91 and CI-NEB calculated activation energy barriers and  (111), Fe (110) and Fe (211) surfaces [reprinted from [194] with permission from Elsevier]. detailed reaction coordinates for CO 2 hydrogenation to formate, carboxyl and formic acid on Ni(110) surface. They provided insights into the possible role of subsurface H and suggested that transiently energetic subsurface H emerging onto the Ni (110) surface can lead to hydrogenation of formate to formic acid.
Recent studies show that there is still enough space for further computational studies. Microkinetic modelling is lightly used for comprehension of CO 2 conversion of Ni surfaces. Additional DFT calculations in conjunction with microkinetic modelling would bring more information about the Ni(100) and Ni (110) surface elementary steps of CO 2 hydrogenation which are still not clear.

Cu catalytic surfaces
The mechanism of CO 2 hydrogenation to methanol over Cu (111) surface was proposed by many researchers through DFT calculations [22,174,204,205] however, if the active site is metallic Cu or CuZn alloy is still an open question.
In RWGS reaction: Choi et al. [93] studied catalytic behavior of metal catalysts (Pd, Ni, Cu, Ag) with different facets (100), (110), (111) in high-temperature RWGS reaction. They observed that Cu, Pd and Ni catalysts have higher H adsorption energies and easily produce H-adsorbed species and Ag surface is unfavorable for H adsorption. For all highly activated catalysts, the formate group was an intermediate adsorbed species and Cu, Ni and Pd catalysts can be used to promote RWGS reaction.
In methanol synthesis: Grabow et al. [22] performed DFT and very detailed microkinetic calculations to determine the energetics of 22 surface species and the activation energy barriers and pre-exponential factors for description of 49 elementary surface reactions on Cu (111) [147] also performed DFT with BEEF-vdW and microkinetic calculations which showed reasonable reaction barriers for the formate-mediated route which promoted the results of Grabow et al. [22] In combination with their catalytic tests of reduced Cu/  (100), (110) and (111) surfaces [reprinted from [186] with permission from Elsevier], b) CO 2 adsorption and desorption structures on Ni(110) surfaces and c) CO 2 methanation mechanism on Ni(111) surface [reprinted from [203] with permission from Elsevier].
MgO and Cu/ZnO/Al 2 O 3 catalysts at 523 K performed in fixedbed flow reactor at 30 bar and 503 K they concluded that the catalyst mixture optimizes the reaction kinetics and the feed gas optimizes the equilibrium thermodynamics of the system. In contrast, Zhao et al. [204] by using PAW DFT calculations with PW91 functional and dimer method for examination of various reaction and diffusion pathways stated that CO 2 conversion to methanol on Cu(111) surface does not lead through direct hydrogenation of formate intermediate. Their reason for that are high reaction barriers of HCOO and H 2 COO. Models using dimer method showed that hydroxycarbonyl mechanism may be possible, but the H 2 O plays a crucial role in hydrocarboxyl mechanism enhancement. Accordingly, the methanol may be produced by CO 2 + 6H + (H 2 O)!trans-COOH + 5H!t,t-COHOH + 4H!t,c-COHOH + 4H!c,c-COHOH + 4H!COH + OH + 4H! HCOH + 3H + OH!H 2 -COH + 2H + OH!H 3 COH + H + OH! H 3 COH + H 2 O. They also suggest that both RWGS and methanol synthesis from dry CO 2 + H 2 mixtures on the clean Cu (111) surface at low temperatures are unlikely because the dominant HCOO surface species is a mechanistic ''dead end''. The hydrocarboxyl mechanism was suggested also by Yang et al. [205] performing the DFT calculations with the use of PW-GGA approximation in combination with experimental kinetic tests of clean Cu (111) and Cu/ZnO(0001) surfaces carried out in an ultrahigh-vacuum. Their calculations performed on Cu (111) and Cu nanoparticles unsupported and deposited on ZnO(0001) indicated that methanol production via the RWGS pathway is hindered by the first hydrogenation of CO to HCO. The latter is not stable on Cu and prefers to dissociate into CO and H. Therefore, the faster RWGS only leads to the accumulation of CO, rather the methanol formation.
Results obtained by microkinetic modelling, dimer method and combination of theoretical and experimental studies show that the use of different methods for examination of reaction pathways can lead to completely opposite conclusions. Similarly, Zhang et al. [174] studied optimum Cu nanoparticles for CO 2 hydrogenation towards methanol synthesis with DFT and PBE functional and microkinetic modelling following the elementary reaction steps depicted in Figure 11b. This mechanism involves direct CO 2 dissociation to CO and O and generation of HCO intermediate. The comparison of CO 2 adsorption was made between different types of Cu clusters (Cu13, Cu15, Cu19, Cu55, Cu99) and Cu (111) and Cu(211) surfaces shown in Figure 11a. They reported that intermediate sized Cu19 clusters are optimal for CO 2 hydrogenation and the Cu particle size effect originates from changes in the adsorption energies of the reaction   (111) and Cu(211) surfaces c) CO 2 hydrogenation to methanol on Cu extended surfaces. [174] intermediates which can be correlated to the location of the dband of the Cu clusters that strengthens the bonding interaction between metal and intermediates and therefore influencing CO 2 reduction activity. However, their results are in stark contrast with experimental results of Berg et al. [206] where they studied the catalytic activity of reduced Cu(Zn)/C catalysts obtained from Cu(Zn)/SiO 2 and Cu/ZnO(/Al 2 O 3 ) samples using synthesis gas composed of 10 % Ar, 7 % CO 2 , 23 % CO and 60 % H 2 . It was shown that particles smaller than~8 nm are less active than larger particles per surface area of copper. The difference between theoretical and experimental data may be the result of the conditions that are more industrially correct for experimental studies. While simulations consider only the CO 2 molecule the experiment works with a synthesis gas which has certain ratio of various gases that can affect the results of nanocatalyst activity.
Some researchers included Zn into the Cu surface to study the effect of CuZn catalysts on CO 2 hydrogenation. Behrens et al. [207] performed DFT calculations of CO 2 hydrogenation to methanol on Cu(111), Cu(211) surfaces and CuZn (211) where Cu in the step was partially substituted by Zn. According to their results hydrogenation of CO 2 proceeded via formate mechanism (formation of HCOO, HCOOH and H 2 COOH), although the formate intermediate was identified as spectator species by previously mentioned articles. Cu (111) surface bounded the intermediates more weakly than Cu(211) and alloying of Zn into the Cu step increased the adsorption strength of intermediates and decreased barriers. If more Zn atoms are considered in the CuZn(211) surface, the binding to these species is further strengthened. Therefore, the presence of steps and Zn is required for higher activity towards methanol.
In summary, theoretical studies show different results and are not uniform in identifying the reaction pathway for methanol synthesis on copper surface.

Rh catalytic surfaces
In methanol synthesis: Rh metal surfaces are poorly examined by computational studies and there is no DFT study on pure Rh surfaces. Recently, Liu et al. [208] explored the effect of Rh doped Cu(111) surfaces (Cu(111), Rh 3 Cu 6 (111), Rh 6 Cu 3 (111) and Rh ML surfaces) on CO 2 hydrogenation via RWGS pathway using GGA with PW91 functional together with DNP function. The calculated results shown both kinetic and thermodynamic facilitation of methanol synthesis, especially on Rh 3 Cu 6 (111) surface. The most intermediates adsorbing through C atom preferred to bind at the Rh site and were strengthened by the doped Rh. The rate-limiting steps were CO 2 hydrogenation to trans-COOH* on Cu (111) and Rh 3 Cu 6 (111) surfaces, and the formation of HCO* from CO* hydrogenation on Rh 6 Cu 3 (111) and Rh ML surfaces. Furthermore, the by-product of CO was inhibited due to the dissociative adsorption of H 2 .

Pd catalytic surfaces
Similarly, as with Rh surfaces the Pd metal surfaces are not well investigated by DFT methods. Only few studies deal with computational calculations and describe the mechanism of CO 2 hydrogenation on Pd surfaces.
In methanol synthesis: Zhang et al. [209] proposed a mechanism of methanol synthesis from CO 2 hydrogenation on Pd (111) surface using GGA approximation with PBE functional. They suggested that CO 2 can be chemically adsorbed as a bidentate configuration on Pd(111) hollow site consisting of three Pd atoms and the H 2 can dissociate to H atoms spontaneously. The lower adsorption energy À 0.70 eV indicated that the CO 2 can be activated by Pd, however the adsorption is weak. This shows that Pd catalyst would be a better catalyst in combination with other metal or chemical compound. The adsorption configuration of CO 2 and H atoms is presented in Figure 12a). The HCOO and COOH intermediates are both possible to form via the reaction between the CO 2 and the surface H atom which is displayed on Figure 12b). By further hydrogenation of HCOO or HCOOH intermediate HCOOH is generated. In the next step HCOOH dissociates to HCO, which then hydrogenates consecutively to H 2 CO, H 3 CO and H 3 COH ultimately. In their study, the formation of H 2 CO is the rate-limiting step with an activation barrier of 0.91 eV and CO is the by-product, formed mainly from the dissociation of COOH. Two reaction pathways are depicted in Figure 12.
Liu et al. [210] using GGA with PW91 functional together with DNP function found out that the addition of Pd atoms on the Cu (111) surface not only affect the adsorption configuration but also alter the interactions between the adsorbed species and the metal surfaces. The rate-limiting step was the formation of trans-COOH* from CO 2 hydrogenation on Pd 3 Cu 6 (111) and Pd 6 Cu 3 (111) surfaces which is the same as on pure Cu (111) surface, however, it changed to cis-COOH* decomposition to CO* and OH* on Pd ML surface. The change of the rate-limiting step was mainly due to the strengthened adsorption of COOH*, while the adsorption of OH* was greatly weakened by the added monolayer of Pd atoms.
Pd (111) surface was examined in combination with Cu(111) by Jiang et al. [212] using PAW potentials and spin-polarized GGA with PBE functional and catalytic tests of PdÀ Cu bimetallic catalysts in fixed-bed reactor. PdÀ Cu bimetallic combination enhanced the adsorption of H 2 and CO 2 , although, the adsorption strength was still weak. DFT results shown formation of HCOO* intermediate. In the transition state configuration for HCOO* formation, the two O atoms of bent CO 2 are stabilized by two Pd atoms on the surface; the H* atom bonds to the remaining Pd atom in the triangle site and attacks the C atom of CO 2 for hydrogenation.
These studies have shown that the adsorption of CO 2 on the Pd surfaces is weak. However, the microkinetic studies could bring more light to the mechanism of CO 2 hydrogenation on Pd surfaces. Therefore, finding a right combination of Pd catalyst with different type of catalyst is needed to increase the CO 2 adsorption and more DFT calculations in this direction are needed.

Conclusions
The DFT simulations of CO 2 on transition metal surfaces provide information about the intricate mechanisms of CO 2 hydrogenation. Understanding of elementary processes on atomic scale is important to design novel catalysts with outstanding activity and selectivity towards specific compounds. Here, a review of the current understanding of CO 2 catalytic hydrogenation to fuels and chemicals including CO, CH 4 , CH 3 OH and HCOOH and mechanisms with different reaction pathways and elementary steps is presented.
Our review shows that surface and adsorption energies values are highly affected using different functional. Several studies displayed that the best results of adsorption energies for transition metals can be currently provided by BEEF-vdW, M06-L, GAM functionals and RPA method. Recent DFT calculations provides interesting insights into the adsorption, dissociation of CO 2 and overall reaction mechanism of CO 2 hydrogenation on different transition metal surfaces, however many studies do not include the microkinetic modelling which could provide more information about the mechanisms and intermediates. Moreover, as it was mentioned with Cu-based catalysts, several DFT studies in combination with microkinetic modelling present opposite results not only in comparison to experimental data but also in comparison with each other.
Current research should be focused not only on the comparison of various facets of transition metals but also on the different type of metal structures which can change a catalytic effect and help to better control the whole CO 2 hydrogenation process. Seeing that metals such as Rh, Pt, Au, Ag are expensive for experimental research, more computational simulations of these surface would be financially advantageous. DFT simulations would also be very useful in CO 2 conversion to formic acid since the synthesis of catalysts is complicated and very energy consuming. There are not many studies that deal with catalyst development for formic acid synthesis which has after methane the second largest storing capacity for hydrogen.  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57