CO₂ hydrogenation to formic acid on Pd–Cu nanoclusters: a DFT study

Abstract

Carbon dioxide (CO₂) hydrogenation to formic acid is a promising method for the conversion of CO₂ to useful organic products. The interaction of CO₂ with hydrogen (H₂) on Pd_mCu_n (m + n = 4, 8 and 13) clusters to form formic acid (HCOOH) has been explored using density functional theoretical (DFT) calculations. Pd₂Cu₂, Pd₄Cu₄ and 13-atom Pd₁₂Cu clusters are found to be the most stable among all of the Pd_mCu_n (m + n = 4, 8 and 13) clusters with binding energies of −1.75, −2.16 and −2.40 eV per atom, respectively. CO₂ molecules get adsorbed on the Pd₂Cu₂, Pd₄Cu₄ and Pd₁₂Cu clusters in an inverted V-shaped way with adsorption energies of −0.91, −0.96 and −0.44 eV, respectively. The hydrogenation of CO₂ to form formate goes through a unidentate structure that rapidly transforms into the bidentate structure. To determine the transition state structures and minimum energy paths (MEPs) for CO₂ hydrogenation to formic acid, the climbing image nudge elastic band (CI-NEB) method has been adopted. The activation barriers for the formation of formic acid from formate on Pd₂Cu₂ and Pd₄Cu₄ are calculated to be 0.79 and 0.68 eV, respectively whereas that on the Pd₁₂Cu cluster is 1.77 eV. The enthalpy for the overall process of CO₂ hydrogenation to formic acid on the Pd₂Cu₂, Pd₄Cu₄ and Pd₁₂Cu clusters are found to be 0.83, 0.48 and 0.63 eV, respectively. Analysis of the density of states (DOS) spectra show that the 4d orbital of Pd, the 3d orbital of Cu, and the 2p orbitals of C and O atoms are involved in the bonding between CO₂ molecules and the Pd₂Cu₂ clusters. The CO₂ adsorption on the Pd_mCu_n (m + n = 4 and 8) clusters has also been explained in terms of the charge density distribution analysis.

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Introduction

In recent decades, increased consumption of fossil fuels has resulted in a significant increase in the concentration level of carbon-dioxide (CO₂) in the atmosphere. This has changed the global climate and caused ocean acidification.^1–4 CO₂ sequestration, carbon capture and storage have been suggested as different new ways to manage global CO₂ levels. However, the catalytic conversion of CO₂ into useful chemical products e.g. methane (CH₄), methanol (CH₃OH) and formic acid (HCOOH) has attracted considerable attention in recent years.^5–14 CO₂ is abundant in nature; it is an inexpensive feed stock for chemical processes and its removal from the atmosphere will reduce the greenhouse effect significantly. One very good example is CO₂ conversion to the useful liquid hydrocarbon formic acid (HCOOH) through hydrogenation. Formic acid is an important chemical used in making animal feed, in tannery and dying leather and textiles and as a food preservative.¹⁵ Currently, formic acid synthesis is mainly performed through a two-step process: (i) carbonylation of methanol to methyl formate (HCOOCH₃) using a high pressure of toxic CO as the feedstock and (2) hydrolysis of HCOOCH₃ to formic acid and methanol. Formic acid production by direct hydrogenation of CO₂ is a promising alternative way in terms of economy, ecology and safety. CO₂ is extremely stable both thermodynamically and kinetically, exhibiting negative reaction entropies and high Gibb's energies. Hence, an effective, cheap and recyclable catalyst for this conversion of CO₂ to formic acid and methanol is urgently required.

A number of reports on experimental and theoretical studies of CO₂ conversion to methanol and formic acid catalytically on metallic and bimetallic surfaces have been reported.^16,17 Several Cu based catalysts like Pd–Cu, Ga–Cu, Ni–Cu, Co–Cu, Cu/ZnO and Cu/ZrO have been developed experimentally for enhancing the conversion of CO₂ to CH₃OH and HCOOH.^18–21 Among these, a Pd–Cu catalyst is one of the most active bimetallic catalysts for CO₂ hydrogenation. Pd has been widely used as a promising catalyst to enhance CO/CO₂ hydrogenation. Melian-Cabrera et al. have found that the reduced state of Cu has been maintained via hydrogen spill over by Pd doped Cu-based catalysts.²² The reducibility of Cu sites is enhanced by Pd addition because of electron donation from Pd. The Pd–Cu catalysts exhibit a strong synergistic promotion of the methanol formation rate compared to that of pure Cu because of the combination of Cu and Pd. In the DFT study by Liu et al., a Cu(111) surface with a Pd monolayer substituted on the topmost layer has been employed as a Pd–Cu bimetallic system to explore the underlying mechanism of methanol synthesis from CO₂ hydrogenation.¹⁹ In formic acid formation, CO₂ hydrogenation is one of the most important steps. In this aspect, it is assumed that bimetallic Pd–Cu can act as a good catalyst for formic acid formation also. The experimental studies are not sufficient to elucidate a catalytic process over the catalytic surface and therefore, DFT calculations are essential to illustrate the reaction mechanism of CO₂ hydrogenation on bifunctional catalyst.

A large number of transition metal complexes, mostly Ir, Rh and Ru-based ones, have been used for CO₂ hydrogenation to formic acid. In recent times, the synthesis of formates and formic acid using homogeneous catalysis have been reviewed by several research groups.^{16,17,23–25} Sredojevic et al. have studied the formic acid synthesis by CO₂ hydrogenation over single-atom catalysts based on Ru and Cu embedded in graphene.²⁶ They made this synthesis possible with low activation energy by proceeding with the mechanism of H₂ dissociation over the metal atom prior to CO₂ adsorption. A Ni and Ni–Fe bimetallic system has also been found to be suitable for CO₂ reduction to formic acid and other valuable chemicals.^27,28 Most recently, Liu et al. have reported CO₂ hydrogenation to formate and formic acid by a bimetallic palladium-copper hydride cluster.²⁹ The reaction between PdCuH₄⁻ and CO₂ to produce formic acid and PdCuH₂⁻ has been analysed by mass spectrometric analysis. Different isomers of PdCuH₄⁻ and PdCuCO₂H₄⁻ are identified by anion photo electron spectroscopy (PES) and electronic structure calculations. Their mechanistic study confirms the metastable structure as the catalytic driving force.

Hydrogen adsorption, dissociation and diffusion on the PdCu surface has been shown in our earlier study.³⁰ If CO₂ gets adsorbed on the PdCu surface, the CO₂ reduction to formic acid and methanol is possible. Aiming for this, using DFT, we have investigated CO₂ adsorption on the PdCu surface with all possible orientations. But, it has been found that the PdCu surface does not adsorb CO₂ in ambient conditions. In our next attempt, we have partially substituted the Pd atoms with Pt, and the Cu atoms with Ag, and Au on the PdCu surface to see whether the CO₂ molecule gets adsorbed or not. It is observed that the CO₂ molecule does not get adsorbed in any of these compositions of the PdCu surface. As, CO₂ does not get adsorbed on the PdCu surface, the target of CO₂ reduction to formic acid has been eliminated. Further, we have focused on the finite size of the PdCu clusters which have a large surface area, a high number of dangling bonds and large number of active sites. CO₂ adsorption on the Pd_mCu_n (m + n = 4, 8 and 13) clusters has been studied using DFT based computational methodology. It is found that CO₂ gets adsorbed on the Pd_mCu_n (m + n = 4, 8 and 13) clusters. As, the PdCu clusters also take a H₂ molecule, the CO₂ reduction to formic acid has been studied here on the Pd_mCu_n (m + n = 4, 8 and 13) clusters.

Although many researchers have focussed on CO₂ hydrogenation for formic acid and methanol synthesis, to the best of our knowledge, formic acid formation from CO₂ on nanoclusters, especially, Pd–Cu nanoclusters is rare. Nanoparticles have a high surface to volume ratio and better reactivity compared to their surface and bulk counterparts, so they can act as a better catalyst compared with those forms. Any real-life catalytic system would require the use of a support system. Here, small PdCu clusters are considered to study the basic reaction mechanism of formic acid formation by CO₂ hydrogenation. By considering reactions on free clusters, which have higher degrees of freedom, it is possible to underscore the reaction mechanism at the smallest scale length. The results of these calculations are useful to study the reaction mechanism on supported clusters. Here, in this computational study, formic acid formation by CO₂ hydrogenation on Pd–Cu nanoclusters has been investigated using a DFT formalism.

The geometry, energetics and reaction mechanism are of prime importance for the synthesis of formic acid on the bimetallic clusters. Here, CO₂ hydrogenation with H adsorbed on the Pd_mCu_n (m + n = 4, 8 and 13) clusters is systematically studied using a state of the art first principles method for the generation of formic acid. The reaction pathways for the conversion of CO₂ to formic acid have been revealed by a nudge elastic band (NEB) method. The calculated properties for the formic acid formation provide comprehensive data which will be useful for experimental understanding.

Results and discussion

Structural optimization of Pd_mCu_n (m + n = 2, 4, 8 and 13) clusters

Dimer (m + n = 2). The binding energy, bond length and spin moment of the PdCu dimer along with its constituent element dimers Pd₂ and Cu₂ have been calculated with and without a spin–orbit coupling scheme and are given in Table 1.^31–34 From Table 1, it is found that the spin–orbit coupling effect has no significant contribution in the binding energies and bond lengths of the clusters. Hence, the entire calculation has been performed without including the spin–orbit coupling effect. The above mentioned properties of the dimers are calculated to test the accuracy of the theoretical method employed for the total energy calculation and the reliability of the potential used here. The calculated values with PBE are given in Table 1 and are compared with the reported experimental values. The calculated bond length and binding energy heteroatomic PdCu dimer is found to be comparable with other reported theoretical data.³⁵

Table 1 Calculated and experimental binding energies and bond lengths of the Pd₂, Cu₂ and PdCu dimers

Cluster (s)	Binding energy (eV per atom)			Bond length (Å)
	Calc. (NSO)	Calc. (SO)	Expt	Calc. (NSO)	Calc. (SO)	Expt
NSO = non spin–orbit, SO = spin–orbit.
Pd2	−0.64	−0.65	−0.51^43	2.48	2.49	2.48^44
Cu2	−1.12	−1.12	−1.04^45	2.22	2.22	2.21^46
PdCu	−0.91	−0.92	—	2.32	2.33	—

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After establishing the properties of the PdCu dimer, the total energy and binding energy of different Pd_mCu_n (m + n = 4, 8 and 13) clusters are calculated. A large number of geometrical isomers of each composition of the Pd_mCu_n (m + n = 4, 8 and 13) clusters are shown in Tables S3–S5 (ESI†). The specific coordinates of the clusters are given in Table S9 (ESI†). The results reveal that the small PdCu clusters favor a 1 : 1 composition (e.g. Pd₂Cu₂, Pd₄Cu₄) and for the 13-atom cluster it is Pd₁₂Cu where the Cu atom is at the centre of the icosahedron. The ground state geometric configurations for each composition of the Pd_mCu_n (m + n = 2, 4, 8 and 13) clusters are shown in Fig. 1.

Fig. 1 Stable isomers of thePd_mCu_n (m + n = 2, 4, 8 and 13) clusters (a) dimer (b) tetramer (c) octamer (d) 13-atom cluster (atomic colours: green = Pd, brown = Cu).

Tetramer (m + n = 4). The tetramer is an important model for investigating several catalytic processes.^36–40 The structure of the tetramer also plays a significant role in cluster growth as this is the smallest size where clusters can possess either a planar or non-planar geometry. This provides an initial clue for understanding the structural pattern of larger size clusters i.e, pentamer onward. For tetramer (m + n = 4) heteroatomic clusters, three compositions (1 : 3, 2 : 2 and 3 : 1), apart from the homoatomic clusters, are considered for calculation. Accordingly, the various possible isomeric structures of Pd₄, Cu₄, Pd₃Cu, Pd₂Cu₂ and PdCu₃ clusters are optimized. The average binding energy, average bond length and spin moments of these clusters are summarized in Table 2.

Table 2 Average binding energy (B.E), average bond length (Pd–Cu) and spin moments of the Pd_mCu_n (m + n = 4, 8 and 13) clusters

Number of atom (n)	System	Average B.E. (eV per atom)	Average Pd–Cu B.L. (Å)	Spin moment (μB)
n = 4	Pd4	−1.67	2.60 (Pd–Pd)	0
	Pd3Cu	−1.74	2.50	1
	Pd2Cu2	−1.75	2.47	0
	PdCu3	−1.62	2.46	1
	Cu4	−1.59	2.25 (Cu–Cu)	0
n = 8	Pd8	−2.07	2.67 (Pd–Pd)	2
	Pd7Cu	−2.10	2.54	3
	Pd6Cu2	−2.09	2.51	2
	Pd5Cu3	−2.15	2.50	1
	Pd4Cu4	−2.16	2.56	0
	Pd3Cu5	−2.09	2.50	1
	Pd2Cu6	−2.14	2.55	2
	PdCu7	−2.13	2.56	1
	Cu8	−2.14	2.28 (Cu–Cu)	0
n = 13	Pd13	−2.32	2.73 (Pd–Pd)	8
	Pd12Cu	−2.40	2.60	7
	PdCu12	−2.28	2.62	4
	Cu13	−2.24	2.53 (Cu–Cu)	5

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The binding energies of the Pd_mCu_n clusters are shown in Table 2. It is seen that Pd₂Cu₂ is the most stable structure among all of the Pd_mCu_n (m + n = 4) clusters with the average binding energy of −1.75 eV per atom. Table S3 (ESI†) shows that Pd₄ forms a triangular pyramid (Tpy) structure as the lowest energy with an average Pd–Pd bond length of 2.60 Å. The substitution of a single Pd atom by a Cu atom in Pd₄ resulting in Pd₃Cu does not change the Tpy geometry and the average Pd–Cu bond length for that is found to be 2.50 Å. Further substitution of a Pd atom in Pd₃Cu forming Pd₂Cu₂ does not allow a change of its Tpy geometry and here the average Pd–Cu bond length is found to be 2.47 Å. The further substitutions of the Pd atoms in Pd₂Cu₂ resulting in PdCu₃ and Cu₄ changes the geometry to planar rhombus. The Pd₂Cu₂ cluster can be visualized as a combination of a maximum of two PdCu dimer moieties which gives stability to Pd₂Cu₂ whereas in Pd₃Cu and PdCu₃ only one PdCu dimer moiety is present. The spin moment of both Pd₄ and Cu₄ clusters are calculated to be 0 μ_B. The substitution of Pd atoms in the Pd₄ cluster and Cu atoms in the Cu₄ cluster increases the spin moment except for Pd₂Cu₂ which is paramagnetic in nature.

Octamer (m + n = 8). The atomic and electronic structure of Pd_mCu_n (m + n = 8) has been investigated through all composition ranges. We have considered several initial structures and those have been optimized to find out the most stable one among them. Based on the comparison of the relative energies, the homoatomic Pd₈ and Cu₈ clusters are found to favour bicapped octahedron structures as shown in Table S4 (ESI†). The average bond length of Pd–Pd and Cu–Cu are 2.67 Å and 2.28 Å, respectively. The geometry of other low-lying isomers, close to the lowest energy isomer, along with the bond length and spin moment are listed in Table S4 (ESI†). In alloy clusters, the equiatomic Pd₄Cu₄ moiety also forms a bicapped octahedron geometry, like Pd₈ and Cu₈, with a particular type of arrangement of the Pd and Cu atoms as shown in Fig. 1. All of the possible isomers of Pd₄Cu₄ are shown in Table S4 (ESI†) along with corresponding energy values. There are two close energy isomers of Pd₄Cu₄. In the most stable one, the two capped positions outside the main octahedron unit are constituted by two Pd atoms and an edge of the octahedron is also made up by two Pd atoms. The remaining atoms of the bicapped octahedron or dodecahedron are four Cu atoms. The close energy structure of the dodecahedron Pd₄Cu₄ moiety is a Cu-capped pentagonal bi-pyramid. The difference in energy between these two structures is 0.16 eV.

13 Atom cluster (m + n = 13). The 13 atom cluster, also called a magic cluster, has a unique identity as it bears interesting properties because of its higher relative structural and energetic stability.^41–44 It generally possesses an icosahedron structure with the central atom having the coordination number 12. This coordination resembles the FCC bulk structure. Thus, it is obvious; the difference between a 13 atom cluster and the bulk is mainly due to size and shape effects. This present study is focused on formic acid formation by CO₂ hydrogenation on different size PdCu clusters including a 13 atom moiety. As a requirement, the most stable structure of PdCu₁₂ and Pd₁₂Cu has been established along with the icosahedron Pd₁₃ and Cu₁₃ clusters. In order to obtain the lowest energy isomer of the Pd₁₂Cu cluster, one Pd atom was replaced by Cu at different positions of the Pd₁₃ icosahedron i.e., Cu at the apex and Cu at the centre. On the basis of the total energy considerations, the icosahedron with the Cu atom at the centre position forms the lowest energy isomer of the Pd₁₂Cu cluster (see Fig. 1(d)). The close energy structures of Pd₁₂Cu are given in Table S5 (ESI†). The binding energy and average bond lengths (Pd–Cu and Pd–Pd) are shown in Table 2. The total spin moment of this cluster is 7.0 μ_B. But, the PdCu₁₂ icosahedron with the Pd atom at the apex position forms the lowest energy isomer of that cluster. The total spin moment of that PdCu₁₂ cluster is calculated to be 4.0 μ_B.

Formic acid formation on Pd_mCu_n (m + n = 4, 8 and 13) clusters

CO₂ hydrogenation to formic acid on Pd₂Cu₂ tetramer. First, the adsorption behaviour of H₂ molecules on the Pd₂Cu₂ cluster has been studied (see Fig. 2). For optimization, the H₂ molecule is placed on top of the Pd as well as the Cu atoms. The distance of the H atoms from the Pd/Cu atoms is kept 3 Å and the H–H bond length as 0.75 Å. The results show that the H attached to the top of Pd forms the lowest energy isomer as shown in Fig. 2(a). The energy released during the H₂ adsorption on Pd is estimated to be −5.05 eV. After optimization, the Pd–H and H–H bond lengths become 1.75 Å and 0.86 Å, respectively. The increase in the H–H bond length from equilibrium separation suggests activation of the bond. Other than molecular adsorption, the adsorption of the H-atom on the top, bridge and hollow sites of Pd₂Cu₂ cluster is also investigated. The results show that the H atom favours the on-top Cu location as shown in Fig. 2(b). The energy released is found to be −2.05 eV and the average Cu–H distance is 1.51 Å. The stability of two H atoms on the Pd₂Cu₂ cluster has also been investigated. It is found that both the H atoms prefer to bind with the Cu–Pd bridge sites as shown in Fig. 2(c). The binding energy for these two H atoms is calculated to be −5.19 eV with Cu–H and Pd–H bond lengths of 1.75 and 1.80 Å, respectively.

Fig. 2 Lowest energy structure of the Pd₂Cu₂ clusters along with their (a) H₂ (b) H (c) 2H (d) CO₂ (e) CO₂ + H (f) carboxyl (g) bidentate (h) HCOO + H and (i) HCOOH adsorbed species.

We have first studied the CO₂ adsorption on the Pd₂Cu₂ cluster which is the primary step for HCOOH formation. The most stable configuration of CO₂ on the Pd₂Cu₂ shows that one of the C–O bonds is attached in such a way so that C and O atoms are attached to the Pd and Cu atoms, respectively as shown in Fig. 2(d). The binding energy of CO₂ is −0.91 eV. The optimum lengths of the Cu–O and Pd–C bonds are 2.00 and 1.99 Å, respectively. As a consequence, the C–O bond is elongated from 1.16 Å (free CO₂) to 1.26 Å. The O–C–O bond angle of the adsorbed CO₂ is optimized to 139.8°. Another possibility of CO₂ adsorption on the Pd₂Cu₂ cluster could be where the C and O atoms could be attached to the Cu and Pd atoms. However, this configuration is unstable. The reason behind this is the extent of electron transfer between Cu–O and Pd–C in the CO₂ adsorbed Pd₂Cu₂ cluster. The details have been discussed in DOS analysis in the Electronic structure section.

On the basis of previous literature, it is seen that formic acid formation by hydrogenation of CO₂ can take place either through formate (HCOO˙) or carboxyl (COOH) radical formation. For the Pd₂Cu₂ cluster, the formate route is found to be more favorable than the carboxyl route. This fact is also established here by calculating the activation energy of the corresponding processes which are discussed in later sections. Two configurations are possible for the HCOO species, carboxyl (mono-HOCO) and bidentate (bi-HCOO), distinguished by the number of O atoms that are adsorbed on the Pd₂Cu₂ cluster. For carboxyl, one of the two O atoms of HOCO gets attached to the Pd atom of the Pd₂Cu₂ cluster, respectively as shown in Fig. 2(f). The Pd–O and Cu–H bond distances are found to be 1.14 Å and 2.33 Å, respectively. The adsorption energy for carboxyl (mono-HOCO) is found to be −1.21 eV. Another possibility of carboxyl radical (mono-HOCO) adsorption on Pd₂Cu₂ happens where the O and H atoms of HOCO are attached to Cu and Pd atoms, respectively. However, this route is found to be not stable.

For bidentate-complex (HCOO-Pd₂Cu₂) formation, two O atoms are connected to the Pd–Cu edge of the Pd₂Cu₂ cluster as shown in Fig. 2(g) with an adsorption energy of −3.39 eV. The optimized Pd–O and Cu–O bond lengths are 2.14 and 1.94 Å, respectively. The O–C–O bond angle is 128.6° and the C–H bond length is 1.10 Å for the HCOO adsorbed on the Pd₂Cu₂ cluster. In this context it should be noted that here CO₂ gets adsorbed on the Pd₂Cu₂ cluster in a V-shaped orientation, but addition of an H atom to the C of CO₂ makes it possible to adsorb bidentate HCOO in an inverted V-fashion. This is because of depletion of electronic charge on the O atom which gets attached to the Pd and Cu atoms. The DOS analysis in the Electronic structure section supports this statement.

The final step is formic acid formation from bidentate formate by adding an H-atom. The adsorption of formic acid on the Pd₂Cu₂ cluster has two possibilities; the H atom is either attached to a Cu or a Pd atom of the cluster. It is seen that the H atom of the COOH attached to a Pd atom of Pd₂Cu₂ has relatively lower energy compared to that of the H attached to a Cu atom. The Pd–H configuration (Fig. 2(i)) is found to be 0.29 eV lower in energy than Cu–H configuration. The adsorption energy of the Pd–H configuration is calculated to be −1.37 eV. The Pd–H and Cu–O distances in the lower configuration are 1.96 Å and 1.95 Å, respectively. The binding energies and related bond lengths of H₂, H, 2H, CO₂, HCOO and HCOOH adsorbed on the Pd₂Cu₂ nanocluster are given in Table 3.

Table 3 Binding energy (E_b) and related bond lengths of H₂, H, 2H, CO₂, HCOO and HCOOH on the Pd₂Cu₂ nanoclusters

Adsorbate species	Site	Bond lengths (Å)	E b (eV)
H2	Top-Pd	Pd–H = 1.75, 1.72, H–H = 0.86	−5.05
H	Top-Cu	Cu–H = 1.51	−2.05
2H	Cu–Pd bridge	Cu–H= 1.80, Pd–H = 1.75	−5.19
CO2	Cu–Pd bridge	C–O = 1.26	−0.91
HCOO	Carboxyl	Cu–H = 2.33, Pd–O = 1.14, C–O = 1.23, 1.32, O–H = 1.03	−1.21
	Bidentate	Pd–O = 2.14, Cu–O = 1.94, C–O = 1.28, C–H = 1.11	−3.39
HCOOH	Pd–H	Pd–H = 1.96, O–H = 1.10, C–O = 1.31, C–O = 1.25, C–H = 1.10, Cu–O = 1.95	−1.37
	Cu–H	Cu–H = 2.61, O–H = 1.05, C–O = 1.32, C–O = 1.24, C–H = 1.10, Pd–O = 2.21	−1.08

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The reaction between H and CO₂ on Pd_mCu_n (m + n = 4, 8 and 13) leads to the formation of bidentate formate whereas that between H and formate forms formic acid. For that, co-adsorption of H and CO₂ as well as H and formate HCOO on the Pd_mCu_n (m + n = 4, 8 and 13) clusters has been investigated. In the first case, H has been placed in different adsorption sites (top, bridge and hollow) of the model cluster keeping CO₂ adsorbed at a fixed site. The results show that H on the Pd–Cu edge opposite to the CO₂ adsorbed edge has the most stable geometry as shown in Fig. 2(e). The H adsorption energy in the pre-adsorbed Pd₂Cu₂–CO₂ cluster is −2.36 eV as per eqn (7). On the other hand, H is found to be stable on the Pd–Pd edge of the pre-adsorbed bidentate formate (Pd₂Cu₂–HCOO) complex (Fig. 2(h)) with an adsorption energy of −3.13 eV as per eqn (2).

The formation of formic acid by the reaction of CO₂ and H occurs through a bidentate formate route. These reaction pathways have been investigated using DFT and CI-NEB methods. The overall reaction pathway has been divided into two parts: (i) CO₂ to bidentate formation and (ii) bidentate to formic acid formation on the Pd_mCu_n (m + n = 4, 8,13) clusters. The initial and final images of the reaction pathways obtained from the stable geometrics are shown in Fig. 2 and Fig. S1 and S2 (ESI†). The intermediate geometrics are obtained by NEB calculations. Formic acid formation from CO₂ on the Pd_mCu_n (m + n = 4, 8, 13) clusters is discussed in the proceeding subsections.

NEB for CO₂ to formic acid conversion on Pd₂Cu₂ cluster

Based on the adsorption results, the reaction pathways for CO₂ to formic acid formation on the Pd₂Cu₂ tetramer cluster has been studied (see Fig. 3). The reaction between CO₂ and H to form formate on the Pd₂Cu₂ cluster is shown in Fig. 3(a). From the figure, it is seen that H is stable in the bridge of the Pd–Cu edge along with a co-adsorbed CO₂ molecule. The Pd–H and Cu–H bond lengths are found to be 1.71 and 1.62 Å, respectively. This H moves from its stable site to a C-atom of CO₂ to form formate which gets attached to the Pd₂Cu₂ cluster with its two O-atoms. The intermediate images are shown in Fig. 3(a). The activation barrier for this reaction of formate formation from CO₂ is found to be 0.81 eV.

Fig. 3 The potential energy profile for the formation of (a) bidentate formate by the reaction of H-atoms and CO₂ (b) formic acid by the reaction of H-atoms and formate on the Pd₂Cu₂ cluster.

In the next NEB calculations i.e. the formic acid formation by the reaction of formate and a H-atom is depicted and shown in Fig. 3(b). In this graph, image 1 is the initial state where H is stable on the Pd–Pd edge of Pd₂Cu₂ along with the adsorbed bidentate formate. From the figure, it is seen that H gets transferred to the Pd–Cu edge of Pd₂Cu₂ where formate is already adsorbed with its two O-atoms, which is shown in image 3. This H is further transferred to one of the O-atoms of formate closer to the Pd atom to form formic acid as shown image 6 of Fig. 3(b). The activation barrier for this reaction of formate and H to formic acid is found to be 0.79 eV which is more or less similar to the previous step of formate formation.

CO₂ hydrogenation to formic acid on Pd₄Cu₄ octamer

In line with the study for CO₂ hydrogenation on the Pd₂Cu₂ cluster, we have started investigating the adsorption behaviour of H₂ on the Pd₄Cu₄ cluster. The optimization has been performed by placing the H₂ molecule in on-top positions of the Pd and Cu sites along with the other bridge and hollow sites available on the cluster. The distance of the Pd/Cu to H is kept at ∼3 Å. The results suggest that H₂ favours the on-top Cu site (Fig. S1(a), ESI†) with an adsorption energy of −4.91 eV. The two Cu–H bond distances are 1.68 Å and the H–H bond is elongated up to 0.83 Å. The adsorption of the H-atom on the top, bridge and hollow sites of the Pd₄Cu₄ cluster is also investigated. Among different configurations, the H atoms prefer the hollow site of a triangle formed by two Pd and one Cu atom (Fig. S1(b), ESI†). The adsorption energy for this is −2.87 eV with an average Pd–H distance of 1.75 Å. The stability of two H atoms on the Pd₄Cu₄ cluster has also been investigated. It is found that both of the H atoms prefer to bind with the Cu–Pd and Pd–Pd bridge sites as shown in (Fig. S1(c), ESI†). The binding energy for these two H atoms is calculated to be −5.87 eV with Cu–H and Pd–H bond lengths of 1.76 and 1.82 Å, respectively.

Like Pd₂Cu₂, CO₂ adsorption on this Pd₄Cu₄ cluster is also studied by placing the molecule at different well-defined sites. It is found that the CO₂ molecule gets adsorbed in a V-shaped fashion on the Pd₄Cu₄ cluster as shown in Fig. S1(d) (ESI†). The adsorption energy for this configuration is −0.96 eV. The Cu–O and Pd–C bonds are 1.93 and 1.98 Å, respectively. One of the C–O bonds attached to Cu–Pd edge of the Pd₄Cu₄ octamer is elongated from 1.16 to 1.26 Å. The adsorption nature of the CO₂ molecule in the Pd₄Cu₄ cluster is same as that on the Pd₂Cu₂ moiety and the reason lies within the nature of bonding. Like Pd₂Cu₂, here formic acid formation on the Pd₄Cu₄ cluster takes place through the formate route. The HCOO species can be adsorbed in two forms, carboxyl (mono HOCO) and bidentate (bi-HCOO) depending on the number of oxygen atoms that get attached to the Pd₄Cu₄ cluster. In case of carboxyl binding, O and C-atoms are attached to Pd and C atoms, respectively as shown in Fig. S1(f) (ESI†). The Pd–O and Cu–C bond distances are 1.99 Å each and the adsorption energy for monodentate carboxyl HOCO is −2.44 eV.

Like, for the Pd₂Cu₂ cluster, the co-adsorption of H and CO₂ has been compared with H and HCOO on the Pd₄Cu₄ cluster.

In the case of bidentate HCOO, it binds to the Pd–Cu edge of the Pd₄Cu₄ cluster where Cu is in the octahedron frame and Pd atom is out of the frame (Pd–Pd edge) as shown in Fig. S1(g) (ESI†). The Pd–O and Cu–O bond distances are 2.09 and 1.91 Å, respectively. The adsorption energy is found to be −3.67 eV. The C–H bond distance and O–C–O bond angle are 1.11 Å and 104°, respectively. It is interesting to report that CO₂ gets adsorbed to a Cu–Pd edge of Pd₄Cu₄ through a C bond and in a V-shape fashion (Fig. S1(d), ESI†) but addition of a H atom to a C-atom in CO₂, resulting in bidentate formate HCOO, favors the inverted V-shaped form for the adsorption of bidentate formate (bi-HCOO). The reason is depicted in the electronic structure analysis in the Electronic structure section.

The final step is formic acid formation from bidentate formate by addition of an H-atom. Adsorption of formic acid on the Pd₄Cu₄ cluster has two possibilities; the H atom is either attached to a Cu or a Pd atom of the cluster. It has been found that the protonic H atom of the HCOOH is attached to the Pd atom of the Pd₄Cu₄ with an adsorption energy of −1.17 eV (Fig. S1(i), ESI†). However, the adsorption of H with Cu is not stable. The adsorption energy of this adsorbed formic acid configuration is −1.37 eV. The Pd–H and Cu–O distances of this adsorbed formic acid configuration are 1.94 Å and 1.93 Å, respectively.

Like, Pd₂Cu₂, the co-adsorption of H atoms and CO₂ as well as H atoms and formate HCOO have been studied on the Pd₄Cu₄ cluster. Among different isomeric geometries, the H atom favors the hollow site (a triangle composed of two Pd and Cu atoms) as shown in Fig. S1(e) (ESI†). The position of the CO₂ is fixed and it is attached to the Pd–Cu edge adjacent to the H atom adsorption site. The H-adsorption energy for this Pd₂Cu₂–CO₂ moiety is found to be −2.60 eV as per equation (2). Similarly, a H atom in the same position i.e. in the mid of the triangle composed of two Pd and Cu atoms, adjacent to the adsorbed bidentate formate site, has the lowest energy structure as shown in Fig. S1(h) (ESI†). The H-adsorption energy for this Pd₂Cu₂–HCOO moiety is found to be −2.79 eV. The binding energies and related bond lengths of H₂, H, 2H, CO₂, HCOO and HCOOH adsorbed on the Pd₄Cu₄ nanocluster are given in Table S1 (ESI†).

NEB for CO₂ to formic acid conversion on Pd₄Cu₄ cluster

After investigating the formic acid formation on the Pd₂Cu₂ cluster, we have studied the same process on the higher order cluster Pd₄Cu₄. Here also, the process of formic acid formation has been divided into two parts i.e. CO₂ to formate and formate to formic acid formation. Fig. S3(a) (ESI†) shows the bidentate formate formation pathway by the reaction of CO₂ and H-atoms on a dodecahedron Pd₄Cu₄ cluster. The initial image of this NEB calculation is that H is stable on the Pd–Cu edge with CO₂ adsorbed on the adjacent Pd–Cu edge. The overall reaction pathway as shown in Fig. S3(a) (ESI†) shows the H atom movement from its stable position to the C atom of CO₂ to form formate. The activation barrier for this reaction is found to be 0.79 eV.

In the next step, the reaction pathway for formate to formic acid formation on the Pd₄Cu₄ octahedron is shown in Fig. S3(b) (ESI†). Here the H-atom on the Pd–Cu edge of Pd₄Cu₄ has a stable position along with the formate adsorbed on the adjacent Pd–Cu edge. The NEB calculation shows the H movement from its stable position to the O-atom which was attached to the Pd atom in the formate. The activation energy for this reaction is calculated to be 0.68 eV which is lower compared to the first step of formate formation on this Pd₄Cu₄ cluster.

CO₂ hydrogenation to formic acid on Pd₁₂Cu cluster

At first, the adsorption properties of H₂ molecules on the Pd₁₂Cu icosahedron cluster have been studied. For that, a H₂ molecule was placed on the top of the Pd atom at a distance of ∼3 Å, setting the H–H bond length equal to the value of the free H₂ molecule, 0.75 Å. The H₂ at the top of the Pd-atom has the lowest energy structure as shown in Fig. S2(a) (ESI†). The adsorption energy of the H₂ molecule adsorbed on this top Pd atom is found to be −5.06 eV. The two Pd–H bond distances are optimized to 1.70 Å, whereas the H–H bond distance is 0.88 Å.

Now the adsorption of the H-atom on different sites (top, bridge and hollow) of the Pd₁₂Cu icosahedron cluster is also investigated. Among the different structures, it has been found that the H at the mid of the triangle constituted by three Pd atoms has the stable structure as shown in Fig. S2(b) (ESI†). The adsorption energy and average Pd–H distance are −2.85 eV and 1.83 Å, respectively. The stability of two H atoms on the Pd₁₂Cu cluster has also been investigated. It is found that both the H atoms prefer to bind with the three Pd atom hollow sites (fcc and hcp) as shown in (Fig. S2(c), ESI†). The binding energy for these two H atoms is calculated to be −5.13 eV with an average Pd–H bond length of 1.83 Å, respectively.

After studying the adsorption of H₂ molecules and H-atoms, the adsorption of CO₂ gas molecules on the Pd₁₂Cu icosahedron cluster and the energetics associated with that have been investigated. It has been observed that one C–O bond, of bond length 1.27 Å, of the CO₂ molecules is parallelly attached to the Pd–Pd bond of the CuPd₁₂ cluster as shows in Fig. S2(d) (ESI†). The other O-atom of that CO₂ molecule is not bonded to any atom of that cluster. Initially a linear CO₂ molecule is placed parallelly to the Pd–Pd edge of the Pd₁₂Cu cluster. In the most stable geometry the shape of the CO₂ molecule became V-shaped with an O–C–O bond angle of 105°. The adsorption geometry together with the calculated binding energy of −0.44 eV implies that the CO₂ molecule is bonded to the cluster.

Both by experiment and theoretical studies, it is established that HCOO is a key intermediate for CO₂ hydrogenation to formic acid and methanol.^45,46 There are two configurations of HCOO species, carboxyl (mono-HOCO) and bidentate (bi-HCOO), distinguished by the number of O atoms that are adsorbed on the Pd₁₂Cu cluster. For carboxyl (mono-HOCO), the C–O bond of HOCO binds to the Pd–Pd edge of the Pd₁₂Cu cluster as shown in Fig. S2(f) (ESI†). The O–H bond of HOCO does not attach to the cluster, it remains attached to the C-atom. The Pd–C, Pd–O and C–O bond lengths of mono-HOCO adsorbed on the Pd₁₂Cu cluster are found to be 1.96, 2.26 and 1.25 Å, respectively. The adsorption energy for this mono-HOCO moiety is −2.50 eV. For, bidentate-HCOO, it binds to the Pd–Pd edge of the Pd₁₂Cu cluster through two O-atoms (see Fig. S2(g), ESI†) with an adsorption energy of −3.22 eV. The two Pd–O bond lengths are identical at 2.10 Å.

The co-adsorptions of H atoms and CO₂ as well as H atoms and formate HCOO on the icosahedron Pd₁₂Cu cluster are similar to those on the Pd_mCu_n (m + n = 4, 8) clusters. Among the different isomeric geometries, the H atom is found to be most stable in the mid of the triangle composed of three Pd atoms as shown in Fig. S2(b) (ESI†). The position of the CO₂ is fixed and it is attached to the Pd–Pd edge adjacent to the H atom adsorption site (Fig. S2(e), ESI†). The H-adsorption energy for this Pd₁₂Cu-CO₂ moiety is found to be −2.87 eV. Similarly, the H atom in the same position i.e. in the mid of the triangle composed of three Pd atoms, adjacent to the adsorbed bidentate formate site, has the lowest energy structure as shown in Fig. S2(h) (ESI†). The H-adsorption energy for this Pd₁₂Cu–HCOO moiety is found to be −2.84 eV.

After formate adsorption, we turned our attention to adding an H atom to formate to produce a formic acid molecule on the Pd₁₂Cu cluster. For the adsorption of the final product formic acid on the Pd₁₂Cu cluster, there are two possibilities of HCOOH adsorption, where the two H-atoms are in cis and trans positions. The trans configuration (shown in Fig. S2(i), ESI†) is found to be 0.43 eV more stable than the cis one. The Pd–H and Pd–O bond distances in the trans configuration are 2.16 and 2.19 Å, respectively. The adsorption energy for that trans species is −0.90 eV. The binding energies and related bond lengths of H₂, H, 2H, CO₂, HCOO and HCOOH adsorbed on the Pd₁₂Cu nanocluster are given in Table S2 (ESI†).

NEB for CO₂ to formic acid conversion on Pd₁₂Cu cluster

In this case, the process of formic acid formation from CO₂ has also been divided into two parts like the previous two clusters (i) CO₂ to bidentate formate (ii) formate to formic acid. The first step is the reaction of CO₂ and H to form bidentate formate, which is shown in Fig. S4(a) (ESI†). Here, all of the adsorbed species i.e. CO₂ and H-atoms are on the Pd–Pd edge as the outer shell of the Pd₁₂Cu cluster is made up with Pd atoms. The H-atom moves from the Pd–Pd edge to the adjacent CO₂. At first, it goes to one of the O-atoms of CO₂ and is then transferred to the C atom of that CO₂ to form formate. The activation barrier for the reaction is found to be 1.92 eV which is higher than the same process on the Pd₂Cu₂ and Pd₄Cu₄ clusters.

For the bidentate formate to formic acid conversion the H-atom moves from the Pd–Pd edge to the apex Pd-atom with which one of the O-atoms of formate (HCOO) is attached as shown in image 3 of Fig. S4(b) (ESI†). This H-atom further gets attached to that O-atom and forms formic acid where two H-atoms are in the trans position with respect to each other. The activation barrier for the reaction is found to be 1.77 eV.

From the six NEB calculations (Fig. 3 and Fig. S3, S4, ESI†), it is seen that, formate and formic acid formation require more energy in the Pd₁₂Cu cluster compare to that in the Pd_mCu_n (m + n = 4, 8) clusters. The reason may be the Pd–Cu and Pd–Pd edge of the clusters where CO₂ and formate HCOO got adsorbed. Also, the activation energy for CO₂ to formate and formate to formic acid formation decreases as the PdCu cluster size increases except for the stable Pd₁₂Cu magic cluster.

Thermochemistry of CO₂ hydrogenation to formic acid

Depending on the stability of the H₂ molecule and the two H atoms on the Pd_mCu_n (m + n = 4, 8 and 13) clusters, we have extended our study to the hydrogenation of CO₂ to formic acid via the formate route on these clusters. The overall reaction can be given as follows:

H₂ + PdCu → H₂–PdCu* (1)

H₂–PdCu* → 2H–PdCu* (2)

2H–PdCu* + CO₂ → H–PdCu–HCOO* (3)

H–PdCu–HCOO* → PdCu–HCOOH* (4)

PdCu–HCOOH* → PdCu + HCOOH (5)

Here the PdCu = Pd_mCu_n (m + n = 4, 8 and 13) clusters and the (*) mark denotes the species in their adsorbed state. The reaction energies of each elementary reaction have been calculated. The potential energy diagram for the hydrogenation of CO₂ on the Pd_mCu_n (m + n = 4, 8 and 13) clusters is shown in Fig. 4. The most stable adsorption configurations of these clusters have been chosen as the initial states. In the first step (reaction (1)), a H₂ molecule gets adsorbed firstly at the top site with the formation of either Pd–H (for Pd₂Cu₂ and Pd₁₂Cu) or Cu–H (Pd₄Cu₄) bonds. The reaction energies for this adsorption reaction are found to be −5.05, −4.91, −5.06 eV for the Pd₂Cu₂, Pd₄Cu₄ and Pd₁₂Cu clusters, respectively. In the second step (reaction (2)), the adsorbed H₂ molecule gets dissociated into two H atoms. These two H atoms are found to be stable at the three atom hollow site or bridge site for these three clusters as shown in Fig. 1. This reaction is found to be exothermic and the reaction energies are calculated to be −0.17, −0.95 and −0.07 eV for the Pd₂Cu₂, Pd₄Cu₄ and Pd₁₂Cu clusters, respectively. In the third step (reaction (3)), which is one of the most important steps, CO₂ interacts with the 2H–PdCu species and forms formate as the stable adsorbed group with one H atom located at the nearby bridge or three atom hollow sites. The reaction is also found to be exothermic with reaction energies of −1.02, −0.52 and −0.84 eV for the Pd₂Cu₂, Pd₄Cu₄ and Pd₁₂Cu clusters, respectively. In the next step (reaction (4)), the H atom, located at a nearby site, diffuses to the formate group and forms formic acid which remains adsorbed to the cluster with its O atom centre. This reaction is found to be endothermic for all of the clusters under study. The reaction energy for this reaction on the Pd₂Cu₂, Pd₄Cu₄ and Pd₁₂Cu clusters are found to be 0.65, 0.79 and 0.62 eV, respectively. The final step of the process (reaction (5)) is desorption of the formic acid molecule from the cluster. The reaction is also found to be endothermic with reaction energies of 1.37, 1.17 and 0.92 eV for the Pd₂Cu₂, Pd₄Cu₄ and Pd₁₂Cu clusters, respectively. For all of the clusters, as the reaction energy for this last step is higher compared to the other steps, it is regarded as the rate determining step of the overall process of hydrogenation of CO₂ to formic acid. The enthalpies for the overall process on the Pd₂Cu₂, Pd₄Cu₄ and Pd₁₂Cu clusters are found to be 0.83, 0.48 and 0.63 eV, respectively.

Fig. 4 Potential energy diagram of CO₂ hydrogenation to formic acid on the Pd_mCu_n (m + n = 4, 8 and 13) clusters.

Electronic structure

Adsorption of CO₂ on the Pd_mCu_n (m + n = 4, 8 and 12) clusters is the crucial step for the formation of formic acid and methanol either through the formate or carboxyl route. The reason behind the adsorption of CO₂ on these clusters in a particular fashion needs to be explored. From the Fig. 2(d) and Fig. S1(d) and S2(d) (ESI†), it is seen that CO₂ gets adsorbed either on the Pd–Cu edge (for Pd₂Cu₂ and Pd₄Cu₄ clusters) or on the Pd–Pd edge of the Pd₁₂Cu icosahedron cluster. In the Pd_mCu_n (m + n = 4, 8 and 12) clusters, a linear CO₂ molecule has been placed in various positions like on top of Pd, on top of Cu, on the Pd–Pd edge, on the Cu–Cu edge, at the mid of the Pd–Cu–Cu triangle, at the mid of the Pd–Pd–Cu triangle etc. Among those, CO₂ gets adsorbed on the Pd–Cu edge in an inverted V-shaped fashion with the C-centre attached to the Pd-atom and one O-centre attached to the Cu atom of the clusters. The other O-atom of the CO₂ remains unattached to any Pd or Cu atom of these clusters. A similar configuration for CO₂ adsorption has been seen in the case of the Pd₄Cu₄ and Pd₁₂Cu clusters also.

To understand the nature of the chemical bonding present in the CO₂ adsorbed Pd₂Cu₂ cluster, the total and orbital projected density of states for Pd₂Cu₂ and Pd₂Cu₂–CO₂ have been calculated and shown in Fig. S5 and S6 (ESI†). From the Fig. S5(b) (ESI†), it is seen that the Pd-4d and Cu-3d orbitals are mainly contributing to the Fermi energy in the Pd₂Cu₂ cluster, whereas in the Pd₂Cu₂–CO₂ moiety, the 2p orbital of the C and O atoms are contributing along with the Pd-4d and Cu-3d orbitals (Fig. S6(b), ESI†). The presence of finite DOS at the Fermi level indicates the metallic nature and the electron conduction behaviour of the Pd₂Cu₂ and Pd₂Cu₂–CO₂clusters. In Fig. S6(b) (ESI†), the DOS peaks of the C-atom which range from 0–5 eV are overlapping with DOS of the Pd atom to which it is attached. Whereas, the DOS spectra of one of the O-atoms (¹O atom) of the CO₂ is overlapping with those of Cu atom to which it is attached. The DOS spectra (p-orbital DOS) of the other O-atom (²O atom) which is not attached to any Pd or Cu atoms has its position much below the Fermi level mainly ranging from −12.5 eV to −5 eV. From the charge density distribution table given in Table S6 (ESI†), it is seen that the C-atom takes charges from two O-atoms and donates that to one Pd atom of the Pd–Cu edge of the Pd₂Cu₂ cluster. Whereas, the Cu atom of that Pd–Cu edge donates charges to one of the O-atoms of the CO₂ (¹O atom) to which it is attached and becomes an electron deficient centre. This charge transfer facilitates the bond formation between the Pd–Cu edge and the CO₂ molecule and helps the CO₂ molecule to get adsorbed on that edge in an inverted V-shaped fashion. A similar type of bonding and charge transfer has been seen in the case of the Pd₄Cu₄ cluster and its CO₂ adsorbed counterpart. The supporting information of the charge density distribution is given in Table S7 (ESI†).

After exploring the nature of the bonding in the Pd₂Cu₂ and Pd₄Cu₄ clusters and their CO₂ adsorbed counter parts, the same has been investigated for the Pd₁₂Cu clusters and its CO₂ adsorbed species in terms charge density distributions. From the charge density distribution table given in Table S8 (ESI†), it is seen that one of the two Pd atoms of the Pd–Pd edge (¹Pd atom) to which the C atom of CO₂ is attached acts as an electron depletion centre as it receives electronic charges from two O atoms via a C-atom centre. Another Pd atom of that Pd–Pd edge (²Pd atom) donates electronic charges to the O-atom of the CO₂ to which it is attached and it becomes an electron deficient centre. This promotes the CO₂ to get adsorbed in an inverted V-shaped way like the previous cases for the Pd₂Cu₂ and Pd₄Cu₄ clusters.

Computational details

All calculations are performed within the spin-polarized density functional theory using the plane wave-pseudopotential approach as implemented in the Vienna ab initio simulation package (VASP).^47–49 The electron-ion interaction and the exchange correlation energy are described under the projector-augmented wave (PAW) method and the generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE), respectively.^50–52 The energy cut off for the plane wave basis set has been fixed at 500 eV for assuming a good energy convergence. Finding the ground state structure of a cluster is a challenging task. For this, several methods like, Generic Algorithm, basin-hoppins, evolutionary algorithm are used to generate a large number of geometries. However, for small clusters one can use chemical intuition, which in other words is called an educated guess structure and one can then relax these structures to the possible nearest minima. Following this, we have generated a large number of initial geometries and found out the lowest energy structure for each composition.^53–55 A large number of spin states have also been considered for all these structures. The ionic optimization has been carried out using the conjugate gradient scheme and the forces on each ion are minimized up to 5 meV Å⁻¹.^56,57 A suitable simulation box of size 15 × 15 × 15 Å has been considered for all of the calculations. The k-point sampling in the Brillouin zone (BZ) are treated with the Monkhorst–Pack scheme, using the gamma point.⁵⁸ The total energies of each relaxed structure using the linear tetrahedron method with Blochl corrections have been subsequently calculated in order to eliminate any broadening-related uncertainty in the energies.⁵⁹ In all of the DFT based calculations, the electrons are described by the scalar-relativistic approximation, in which spin–orbit coupling (SOC) is taken into account for the core states but is neglected for the valence states.^60,61 However, few studies have showed that SOC plays a crucial role for heavy element systems.^62–64 Due to the presence of Pd atoms, here in this work, DFT-PBE calculations with and without SOC for the valence states have been performed for the dimers. The binding energies (E_b) of the Pd_mCu_n (m + n = 2, 4, 8, and 13) clusters have been estimated from the total energy calculations using eqn (6)where, E_PdmCun = total energy of the Pd_mCu_n cluster, E_Pd-atom = total energy of the Pd atom, E_cu-atom = total energy of the Cu atom, m = total number of the Pd atom(s) and n = total number of the Cu atom(s).

The adsorption energies of adsorbate on the Pd_mCu_n (m + n = 4, 8 and 13) clusters, E_ads have been calculated by eqn (7)

E_ads = E_{adsorbate+cluster} − (E_adsorbate + E_cluster) (7)

E_{adsorbate+cluster} = total energy of the adsorbate and cluster, E_adsorbate = total energy of the adsorbate and E_cluster = total energy of the cluster.

Conclusion

In summary, CO₂ adsorption and hydrogenation on Pd_mCu_n (m + n = 4, 8 and 13) clusters have been studied using DFT calculations. The stable adsorbed structures of the possible intermediates like adsorbed H₂ molecules, one H atom, two H atoms, CO₂ molecule, CO₂ molecules with one H atom etc. have been evaluated and the energetics associated with those have been calculated. It has been found that CO₂ got adsorbed on these clusters in an inverted V-shaped fashion and CO₂ hydrogenation occurs through a formate intermediate. The first hydrogenation to formate goes through a unidentate structure which later transforms to a more stable bidentate structure easily. The second hydrogenation from formate to formic acid is energetically less difficult. An investigation of the possible pathways of forming formic acid on Pd_mCu_n (m + n = 4, 8 and 13) clusters is reported. The reaction energies for the CO₂ hydrogenation to formic acid on all of the clusters have also been calculated. The nature of chemical bonding present between the adsorbate and adsorbent was investigated by electronic structure analysis. The calculated results provide a potential candidate for formic acid synthesis and the present study can be useful for CO₂ conversion and utilization with Pd–Cu bimetallic catalysts.

Data availability

The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to ethical restrictions.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors are thankful to Dr S. Kannan, Director, Radiochemistry and Isotope Group, Bhabha Atomic Research Centre (BARC) and Dr S. C. Parida, Head, Product Development Division, BARC for their interest and encouragement during progress of this work. The authors are also thankful to the members of the Computer Division, BARC for their kind cooperation during the work.

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Footnote

† Electronic supplementary information (ESI) available: See supplementary Tables S1 and S2 (ESI†) for binding energies and bond lengths of different adsorbates adsorbed on Pd₄Cu₄ and Pd₁₂Cu clusters, respectively; Tables S3–S5 for the different geometric isomers of Pd_mCu_n (m + n = 4, 8 and 13) clusters and Tables S6–S8 for the charge density distribution of Pd_mCu_n (m + n = 4, 8 and 13) clusters. See supplementary Fig. S1 and S2 for the lowest energy structure of Pd₄Cu₄ and Pd₁₂Cu clusters along with different adsorbates on those clusters, respectively; S3 and S4 for the potential energy profile of CO₂ hydrogenation to formic acid on Pd₄Cu₄ and Pd₁₂Cu clusters, respectively; S5 and S6 for the density of states of Pd₄Cu₄ and Pd₁₂Cu clusters along with their CO₂ adsorbed counterparts, respectively. See DOI: https://doi.org/10.1039/d2cp03805f

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