1 Introduction

\(\hbox {CO}_2\) hydrogenation to methanol is an important reaction towards a closed carbon cycle [1,2,3]. \(\hbox {In}_2\hbox {O}_3\)-based catalysts have shown promising properties for \(\hbox {CO}_2\) hydrogenation with high selectivity and catalyst stability [4,5,6,7]. Moreover, the performance has been measured to be further enhanced by promoting \(\hbox {In}_2\hbox {O}_3\) with Pd [5,6,7,8,9]. However, it is not clear what the state of the Pd/\(\hbox {In}_2\hbox {O}_3\) catalyst is and one suggestion is that a PdIn intermetallic compound is formed during reducing conditions [6, 8]. Intermetallic compounds of palladium and indium in the absence of the \(\hbox {In}_2\hbox {O}_3\) oxide have proven to be promising materials for \(\hbox {CO}_2\) hydrogenation to methanol [8], as well as its reverse reaction being methanol steam reforming [10]. The formation of Pd–In intermetallic phases is energetically favourable with respect to the parent metals across the entire composition range, and can be achieved at mild temperatures via reactive metal support interaction (RMSI) by reducing Pd/PdO particles supported on \(\hbox {In}_2\hbox {O}_3\) with hydrogen [6, 10,11,12].

Alloy formation leads to changes in the geometric and electronic structure of the metal, which has consequences for adsorbate binding and reactivity [13, 14]. In particular, changes in the position of the d-band center [15,16,17,18] of transition metals upon alloying with another metal can modify the adsorption properties of atoms and molecules. However, adsorption on metal/alloy surfaces does not always follow the simple d-band model, and additional descriptors such as d-band shape and site coordination have been included to accurately describe adsorption energies [19,20,21]. A previous computational study shows that the shift in calculated adsorption energies of propane dehydrogenation intermediates correlates with a negative shift in the d-band center of Pd-M intermetallic surfaces, with respect to pure Pd [22]. In addition to electronic effects, alloying changes the site assembly at the metal surface. Changes in the site assembly could be important as isolation of the active metal sites could enhance the selectivity of hydrogenation/dehydrogenation reactions [22,23,24].

In our previous density functional theory (DFT) and microkinetic modelling studies on methanol synthesis over PdIn and \(\hbox {In}_2\hbox {O}_3\), we found that increasing hydrogen stability while keeping other parameters unchanged leads to considerable enhancement of the methanol synthesis rate [25, 26]. Due to the high vapour pressure of In and the complex phase-diagram of Pd–In, controlling and predicting the composition of Pd–In intermetallic compounds is generally challenging [24]. Thus, it is important to consider multiple compositions when investigating the effects of alloying on the catalytic properties.

Herein, we have investigated the effect of alloying on the electronic structure and the consequences for hydrogen adsorption properties of Pd–In. Atomic ratios of 1:1, 2:1, and 2:3 (Pd:In) were considered and compared to the single metallic Pd, In, and Cu by employing DFT calculations. The results for PdIn are compared to Cu as Pd–In has been referred to as having a “Cu-like” electronic structure [27,28,29]. Our results show that alloying Pd with In narrows the d-band and shifts the d-band center of Pd to a lower energy. The shift to lower energies results in weaker bonding of hydrogen to the surface Pd atoms due to presence of occupied anti-bonding states. The hydrogen adsorption energy is found to correlate with the position of the d-band center, providing a convenient descriptor for hydrogen adsorption on Pd–In systems.

2 Computational Methods

The Vienna Ab initio Simulation Package (VASP; version 5.4.4)) was used for the electronic structure calculations [30,31,32,33,34]. The BEEF-vdW [35] functional was used to include dispersion forces. The metal bulk structures were optimised using a 600 eV energy cut-off and a \(16\times 16\times 16\)/\(16\times 16\times 12\)/\(12\times 12\times 12\) Monkorst–Pack mesh for (Cu, In, Pd, PdIn)/\(\hbox {Pd}_2\)In/\(\hbox {Pd}_2\hbox {In}_3\). Hydrogen, palladium, indium, and copper were treated with 1, 10, 13, and 11 valence electrons, respectively. Table 1 contains a summary of the used bulk structures, as well as the optimised lattice constants with a comparison to experimental data. Our computed lattice constants are slightly elongated compared to the experimental values, in line with previous results for fcc-transition metals using BEEF-vdW [36], however the general agreement is good.

Table 1 Bulk structures and the corresponding calculated and experimental lattice constants in Å
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Surface slabs of Pd(111), In(101), Cu(111), PdIn(100),PdIn(110), PdIn(111), PdIn(211), PdIn(310),\(\hbox {Pd}_2\)In(100), \(\hbox {Pd}_2\)In(110), \(\hbox {Pd}_2\hbox {In}_3\)(100), and \(\hbox {Pd}_2\hbox {In}_3\)(110) were cut from the bulk structures to represent the most stable single metal surfaces, and multiple Pd–In intermetallic surfaces. The dimensions of the slabs were chosen to achieve approximately the same low hydrogen coverage for all surfaces, and to have a thickness of at least four stoichiometric layers. An energy cutoff of 450 eV and a \(3\times 3\times 1\) Monkorst–Pack mesh was used for all surface calculations. A 12 Å vacuum was kept between the periodic images of the slabs in the direction perpendicular to the surface. Atoms in the first two stoichiometric layers of the slabs were allowed to relax whereas the rest were fixed at their ideal bulk positions.

Surface formation energies \(\gamma\) of the slabs were calculated as

$$\begin{aligned} \gamma = \frac{\mathrm 1}{\mathrm 2A}(E_{slab} - NE_{bulk}) \end{aligned}$$
(1)

where A, \(E_{slab}\), and N are the surface area, total energy, and number of atoms of the slab, respectively. \(E_{bulk}\) is the bulk energy per atom. PdIn(100) and PdIn(111) can have either Pd or In terminating the surface. To determine surface energy with respect to the PdIn bulk, the ratio of In and Pd atoms must be the same as in the bulk, but for the PdIn(100) and PdIn(111) surfaces this is only possible if one side of the slab is In terminated, and the other is Pd terminated. Therefore, the surface energy calculated according to Eq. 1 represents the average surface formation energy of both terminations. Furthermore, the In and Pd terminated surfaces can undergo different degrees of relaxation upon surface formation. To account for this, we have used thicker 10/8 stoichiometric layer slabs with the 6/4 middle layers kept fixed to allow the relaxation of both terminations of the (111)/(100) surface slabs.

The hydrogen adsorption energy, \(\Delta E_{ads}\), was calculated as

$$\begin{aligned} \Delta E_{ads} =E_{slab+H} - E_{slab} - 0.5E_{H_2} \end{aligned}$$
(2)

where \(E_{slab}\) and \(E_{slab+H}\) are the total energies of the clean slab and a slab with one adsorbed hydrogen atom, respectively. \(E_{H_2}\) is the energy of a hydrogen molecule in the gas-phase. \(\Delta E_{ads}\) is calculated with one H in the surface cell, which is appropriate as the systems are metallic, and the H-H interactions are weak [43]. The hydrogen binding energy, \(E_b\), was calculated as

$$\begin{aligned} E_{b} =E_{slab+H} - E_{slab} - E_H \end{aligned}$$
(3)

where \(E_H\) is the energy of a hydrogen atom in the gas-phase. For both the adsorption and binding energy, a negative value indicates exothermic adsorption. The geometric relaxation of the hydrogen molecule and single-point calculation of the hydrogen atom were performed in \(15\times 15\times 15\) Å computational cells.

3 Results and Discussion

3.1 Effect of Alloying Pd with In on the Electronic Structure

The computed density of states (DOS) for the optimised bulk structures (Fig. 1) clearly demonstrate the dramatic effect on the electronic structure of Pd when alloying with In. Upon alloying with In, the Pd d-band shifts away from the Fermi energy, appearing more similar to the d-band of copper. Furthermore, the magnitude of the d-band center shift increases with increasing In content. Although the DOS at Fermi level is drastically reduced, there is no band-gap formation, showing that the Pd–In intermetallic compounds retain metallic character.

Fig. 1
figure 1

Density of states for metals and alloy bulk structures. The Fermi energy is shifted to 0 eV and indicated with a dashed vertical line. The d-band center is indicated with a solid black line

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To further investigate the electronic structure of the Pd–In compounds, a Bader charge analysis (as implemented by the Henkelman group [44,45,46,47]) was conducted. The computed Bader charges (Table 2) clearly show charge transfer from the less electronegative In to the more electronegative Pd. As the fraction of In atoms in the bulk increases, more charge is transferred to the Pd atoms on average, yet the positive charge per In atom is smaller for the In richer compounds. The Bader charge of \(\pm 0.53\) obtained for PdIn is in agreement with a previously reported value [24]. The charge transfer to Pd is consistent with the filling of the Pd(d) states as shown in the DOS analysis.

Table 2 Average bader charges (b.c.) on the Pd and In atoms in Pd–In intermetallic bulks expressed as a change in number of Bader electrons compared to the neutral metal atoms
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The calculated shift of the Pd(d) DOS away from the Fermi level is in agreement with previous experimental observations of the valence band spectra of PdIn [8, 27], and DFT calculated DOS of the PdIn bulk [24, 28], and the PdIn(110) surface [28]. Gradually more negative shift upon increased In content is consistent with a previous experimental study, where the shifts were observed in the valence band spectra of Pd–In nanoparticles [8]. A similar decrease in the DOS near the Fermi level has also been previously reported for PdCd and PdZn [48], and Pd-Ga intermetallic compounds [23].

3.2 Surface Energies

Computed surface formation energies \(\gamma\) (Table 3) of the pure metals Pd, In, and Cu are underestimated with respect to experiment, which is a known issue with the BEEF-vdW functional [36]. However, the surface energy of the metals obeys the correct trend that In has the lowest surface energy, and Pd the highest [49]. For PdIn, the surfaces with a higher density of surface atoms and more Pd–In bonds in the first surface layer are more stable than surfaces with lower atom density and more bonds between like atoms. The (100) and (111) facets of PdIn can have a In or Pd surface termination, and for both facets the Pd terminated surface compresses more upon relaxation than the In terminated counterpart. The distance between the top most layer and the first subsurface layer is 1.41/0.36 Å for Pd terminated (100)/(111) surface, whereas the corresponding value on the In terminated (100)/(111) surface is 1.86/1.18 Å. Similar trends with substantial relaxations of Pd atoms have been reported for the PdIn(110) surface, and can be rationalised as Pd has a higher surface energy than In [28].

Table 3 Surface formation energies \(\gamma\) (in meV/Å\(^2\)), hydrogen adsorption and binding energies (per atom in eV), and Bader charges on In,Pd,\(\hbox {Pd}_x\hbox {In}_y\) alloy, and Cu surfaces
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3.3 Hydrogen Adsorption

Hydrogen adsorption sites were screened by placing a hydrogen atom in each unique bridge, hollow, or top site on all surfaces and optimising the geometry of each obtained structure. The most favourable hydrogen adsorption geometries on the studied metal and alloy surfaces are presented in Fig. 2, and the corresponding adsorption and binding energies are reported in Table 3. In all cases where hydrogen was placed initially at a Pd top site, the hydrogen atom migrates during the structure relaxation to a nearby bridge or hollow position, i.e. hydrogen adsorbed atop Pd appears not to be a local minima. Hydrogen has the highest binding energy on the un-alloyed Pd(111) surface, where it binds to the fcc hollow site with a binding energy of \(-2.80\) eV. The calculated binding energies for the fcc hollow sites on Pd(111) and Cu(111) agree well with previously computed values [50, 51].

Fig. 2
figure 2

Most stable hydrogen adsorption structures on Pd, In, and Pd–In alloy surfaces. Pd, In, and H atoms are coloured blue,brown, and white, respectively

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The Pd-Pd bridge site is the preferred adsorption site on all intermetallic surfaces, provided that such a site is present. On the pure In(101) hydrogen binds preferably at the atop site, and the resulting adsorption energy is strongly endothermic. PdIn(310), \(\hbox {Pd}_2\)In(100), and \(\hbox {Pd}_2\)In(100) have the highest binding energies of the intermetallic surfaces. Interestingly, the weakest adsorption for Pd–In intermetallics is found on the Pd terminated PdIn(111), even though the hydrogen is adsorbed on a Pd-Pd bridge site. The reason for this behaviour could be that one of the Pd atoms involved in the bonding is in the subsurface, which means that it is highly coordinated. The effective coordination of the subsurface Pd atom is higher on Pd terminated PdIn(111) than on the \(\hbox {Pd}_2\hbox {In}_3\)(100), where hydrogen also binds to a subsurface Pd atom.

3.4 Electronic Structure Analysis

The antibonding metal-hydrogen states are occupied for hydrogen adsorbed on noble metals, which results in lower hydrogen binding energies. As discussed in the previous section, alloying of Pd with In shifts DOS away from the Fermi level, which results in the antibonding adsorbate states to be occupied, unlike for pure Pd. This is illustrated in the projected density of states (PDOS) on the adsorbed hydrogen and the surface metal atoms (Fig. 3). Another prominent feature in the PDOS, are the H(s) and metal d resonant states below − 5 eV (w.r.t Fermi level), and Pd–In surfaces which bind hydrogen the strongest also exhibit more localised resonance peaks.

Fig. 3
figure 3

Projected density of states (PDOS) for hydrogen (black line) adsorbed on Pd–In, Pd, and Cu surfaces. The surface PDOS includes atoms in direct contact with the adsorbed hydrogen atom. H(s), In(s), and In(p) states are scaled up by a factor of 5 compared to the Pd(d) and Cu(d) states to improve visibility. The In and Pd terminated surfaces are labelled with ’In’ and ’Pd’ after the surface indeces, respectively. The Fermi energy is shifted to 0 eV and indicated with a dashed vertical line

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The analysis of the hydrogen binding energy as a function of the d-band center shows a linear trend with a small mean absolute error of 0.06 eV and a maximum error of 0.15 eV, i.e. hydrogen binding on Pd–In intermetallic surfaces can be adequately described by the d-band model (Fig. 4).

Fig. 4
figure 4

Hydrogen binding energy (\(E_b\)) on the Pd, Cu, and Pd–In surfaces as a function of the d-band center (\(\epsilon _d\)) of surface metal atoms. d-band center is calculated for the atoms on the clean metal surfaces that form the site which hydrogen adsorbs at

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Bader charges on the H atoms and Pd atoms participating in bonding on the Pd and Pd–In surfaces (Table 3) show that hydrogen adsorbs as a negatively charged hydride species. In general, the Pd atoms directly bonded to the adsorbed hydrogen have lower Bader charges compared to the bulk Pd–In values. On the PdIn(211) and In terminated PdIn(111) surfaces where hydrogen adsorbs on a In-Pd bridge site, the hydrogen atoms have the most negative Bader charges. The changes in the PDOS and Bader charges of Pd atoms in the Pd–In intermetallics together indicate that the electronic configuration is changing from \(\hbox {d}^9\hbox {s}^1\) of elemental (condensed) Pd closer to \(\hbox {d}^{10}\hbox {s}^1\), i.e. more similar to the configuration of Cu.

4 Conclusions

Our DFT calculations show that alloying Pd with In causes changes in the electronic structure, shifting the d-band center to lower energies further away from Fermi level, making the intermetallic appear more “noble” or “Cu-like”. Furthermore, the Bader charge and PDOS analysis together show that the electronic configuration of Pd changes from \(\hbox {d}^9\hbox {s}^1\) to the direction of \(\hbox {d}^{10}\hbox {s}^1\) upon alloying with In. Forming the intermetallic compound is also accompanied by charge separation so that the Pd(In) atoms have slightly negative(positive) Pd(In) Bader charges. The systems are, however, still metallic without a band gap. Hydrogen adsorbs as a slightly negatively charged hydride species, and prefers to bind to Pd-Pd bridge sites on all Pd–In intermetallic surfaces, provided that such sites are available, followed by In-Pd sites, and finally least favourably on In atop sites. The binding energy of hydrogen scales linearly with the projected d-band center of surface Pd atoms directly involved in bonding i.e. the closer the d-band center is positioned to the Fermi level, the stronger the binding energy. \(\hbox {CO}_2\) hydrogenation is known to depend critically on the adsorption energy of hydrogen. The present work outlines how the composition and structure affect the hydrogen adsorption energy and can potentially be used to enhance the performance of PdIn-based \(\hbox {CO}_2\) hydrogenation catalysts.