1 Introduction

Hydrogen adsorption involves molecular hydrogen activation and dissociation that are important for storing hydrogen as vehicle fuel [1, 2] and also for fuel cell applications. Hydrogen storage requires high volumetric and gravimetric densities, low molecular hydrogen sorption temperature, fast reaction kinetics and effective reversibility [1]. Several methods to store energy require low temperatures, high pressures, or chemical compounds to release hydrogen on demand. Correspondingly, molecular dynamic simulations were used to study the effect of pressure and temperature on adsorption energy and gravimetric density [3,4,5].

The nature of the support and catalyst has important influence on catalytic performance, in terms of hydrogen adsorption, dissociation and desorption [6]. Molecular hydrogen can be dissociated by any metal adsorbed on any surface to form dihydride systems. Transition metal nanoparticles represent the most promising catalysts for hydrogen activation, dissociation and consequently for adsorption. For example, Pt and Pd catalysts can be used for a wide range of reactions such as hydrogenation, dehydrogenation and dehalogenation. The dissociative chemisorption of hydrogen on Pt and Pd clusters is easy and involves strong bonds between the Pt and Pd clusters and the hydrogen [6]. Binding energy between Pt clusters and H atoms is 56 kcal/mol and 74 kcal/mol, at full and zero hydrogen coverage respectively [7]. Significantly, dissociative chemisorption of molecular hydrogen is barrierless for carbon supported and Pt\(_4\) clusters [8, 9]. In the case of Pd dissociative chemisorption, barriers of molecular hydrogen are dependent on cluster size [6]: For example barriers of molecular hydrogen of \(\sim 0\), \(\sim 0\), 10.6, 6.0, 6.9, 2.9, and 0.7 kcal/mol can be observed in Pd\(_2\), Pd\(_3\), Pd\(_4\), Pd\(_5\), Pd\(_6\), Pd\(_9\) and Pd\(_{13}\) clusters, respectively [2, 10,11,12].

In addition to catalysts, the support is important because it conditions the active site in reactivity [6]. Supports are critical for the efficiency and stability of catalytic systems and supports may even function as catalysts themselves [6]. The support has influence on catalytic properties because of charge transfer, structure of the metal nanoparticle and the specific active sites at the metal-support boundary [6]. Consequently, different effects can be considered, i. e. electronic, geometric, spillover and confinement [6]. The support can be based on carbon or it can be doped with for example nitrogen, to alter its properties. Nitrogen doped carbon support has claimed attention due to the fact that nitrogen doping is able to modify the properties of carbon support systems for various applications of interest. Some examples include super capacitor applications and electro-catalysts for the Oxygen Reduction Reaction. The pyridinic nitrogen system in particular exhibits experimentally higher chemical reactivity than pyrrolic or graphitic and traps better atoms, such as Mg, Al, Ca, Ti, Mn, and Fe.

Furthermore, when doping of the support with nitrogen or boron is undertaken, this also affects the Pd–H bonding energy [13,14,15,16,17,18]. An energy barrier of 60 kcal/mol [10] was found to migrate atomic hydrogen from the a Pd\(_{13}\) cluster to the clean graphene support. The former value diminishes to 48 kcal/mol, if the cluster is saturated with 10 hydrides. Pd clusters adsorbed on graphene with vacancies have been studied for hydrogen storage. Pristine graphene with vacancies alters the electronic structure of the catalysts (transition metal clusters), as a result of charge transfer. In the same way vacancies affect binding energy [19]. Charge transfer from the metal to the support (graphene) is induced, when vacancies or nitrogen atoms are present and control for example, O\(_2\) or CO adsorption [6]. Charge transfer may be very important for photo, electro and thermal catalysis [6]. Charge transfer, typical of a covalent chemical bond with partial ionic character was observed to occur as a consequence of the interaction between pyridine N and Pd [20]. The influence of charge transfer on dihydride dissociation requires investigation. For example, spontaneous dissociation of H\(_2\) was reported for small Pt clusters [21].

Another important phenomenon involved in hydrogen adsorption and dissociation is hydrogen spillover, defined as the transport of species to another surface, which does not adsorb or form these species under the same conditions [6, 22]. Hydrogen spillover consists of several steps: (1) molecular hydrogen is activated and dissociated on a catalyst in contact with the support, (2) subsequently, migration from the catalyst to the support of H species is expected [6]. Furthermore, spillover involves transport phenomena of atoms other than hydrogen, such as O, CO [23] or S [24]. Spillover is not favorable for a defect-free surface of a carbon support [8, 25], but it is possible if the carbon support presents defects or when it is doped [1]. Theoretical studies [25, 26], focused on calculating energy barriers (2.7 eV = 62.26 kcal/mol [26] and 2.6 eV = 59.96 kcal/mol [25]) for hydrogen migration from the Pt\(_4\) cluster to the carbon surface were proposed. In the case of Pd\(_6\) and Pd\(_{13}\) clusters supported on graphene barriers of 2.7 eV were calculated [10]. These results suggest that hydrogen migration is very difficult and that under normal conditions, spill-over would not occur [1]. In the case of Pd\(_{13}\) and Pd\(_{6}\) clusters anchored on pristine graphene [10], molecular dynamics were used and not a single dissociation was present in the hydrogen saturated clusters. Furthermore, to date, there is no general consensus that satisfactorily explains spill-over.

We recently studied the interplay between N-graphene defects and small Pd (Pd\(_n\), \(n = 1-4\)) clusters for enhanced hydrogen storage, via a spill-over mechanism [1]. We found migration energy barriers of 0.5–0.8 eV (11.53–18.45 kcal/mol), suggesting that migration from the Pd-clusters to the N-graphene support may occur spontaneously at room temperature [1].

The main objective of this article is to study hydrogen adsorption on graphene-based surfaces with core–shell type catalysts. Besides, the objetive is to study charge transfer and how charge transfer relates to structural properties, hydrogen adsorption energies, magnetic behavior and electronic properties of a particular nitrogen-doped graphene surface. Notably, the surface will be coupled to various catalysts, initially composed of Pd\(_{13}\), Pt\(_{13}\), PdPt\(_{12}\) and PtPd\(_{12}\) core–shell structures.

The paper is organized as follows. In Sect. 2 a brief description of the methodology is given. In Sect. 3, structural parameters, charge transfer, adsorption energies, magnetic and electronic properties are discussed. Finally, the results are summarized in Sect. 4.

2 Computational methods

In this work, Density Functional Theory (DFT) was implemented with the Vienna Ab-initio Simulation Package (VASP) [27, 28]. In the same way, the Projector Augmented Wave (PAW) method [29, 30] and the GGA functionals were also utilized. Additionally the exchange correlation form according to the Perdew–Burke–Ernzerhof (PBE) [31] exchange correlation was also considered.

DFT together with GGA and PBE was also considered to study hydrogen storage using small Pd-clusters and N-graphene defects in our previous work [1]. In reference [1] GGA and PBE functionals were used to calculate barrier energies and other physical properties. The former functionals were compared with the HSE06 hybrid functional to verify the accuracy of the GGA and PBE functionals. It was found for example a difference \(<0.2\) eV in barrier energies between GGA and HSE06 functionals [1].

In this work chemically bound hydrogen molecules is of interest and is the reason why van der Waals interactions were not considered. Furthermore, Monkhorst-Pack sampling and a value of 500 eV for the energy cutoff were used. In all our calculations the 1s\(^{1}\), 2s\(^{2}\)2p\(^{2}\), 2s\(^{2}\)2p\(^{3}\), 5s\(^{1}\)4d\(^{9}\) and 6s\(^{1}\)5d\(^{9}\) configurations were considered as valence electrons for H, C, N, Pd and Pt atoms respectively. Finally, an exhausted analysis was carefully performed to ensure energy convergence of \(\Delta E < 0.001\) eV/atom. The former energy convergence was achieved using (\(3\times 3\times 1\)) k-points and an energy cutoff of 500 eV. Electronic charge density difference (\(<1\times 10^{-4}\)) and an ionic force convergence criterion (\(<2\times 10^{-2}\) eV/Å) were used. In this paper a slab model composed of a periodic hexagonal unit cell (\(a = b = 12.20\) Å and \(c = 16.00\) Å) of C\(_{50}\) carbon ions was considered. The magnitude of c was used as the vacuum space to prevent interactions between slabs. Two vacancies (V) were introduced in the unit cell and 4 N ions replaced 4 C ones in a pyridinic way to change the properties of graphene. The unit cell is composed of a pyridinic C\(_{44}\)N\(_4\)V\(_2\) \(\equiv \) N\(_4\)V\(_2\) system. The slab model proposed and the nitrogen content is comparable with experimental results as it will be discussed in Sect. 3. Several clusters Pd(Pt)-based and hydrogen ions were also introduced in the former model to study hydrogen adsorption.

3 Results and discussions

The system studied in this paper initially entails a N\(_4\)V\(_2\) pyridinic substrate (nitrogen content of 8.3%) and an ensemble of Pd-Pd\(_{12}\), Pt-Pt\(_{12}\), Pd-Pt\(_{12}\) and Pt-Pd\(_{12}\) core–shells as catalysts. Notably, the nitrogen content in our model is comparable to experimental results. For example, the experimental nitrogen content for a pyridinic and graphitic substrate synthesized using the deposition-precipitation method [32] was 5.7%, 8.6%, and 11.3%. Likewise, the nitrogen content for pyridinic, pyrrolic and graphitic defects was 7% in a N-doped graphene via nitrogen plasma treatment of hydrogen exfoliated graphene [33]. Formation energies for different nitrogen-doped graphene defects were calculated previously [34]. Consequently, it was suggested that N\(_4\)V\(_2\) pyridinic defect will predominate in experimental conditions, over other N\(_x\)V\(_y\) ones. This is the main reason for considering the N\(_4\)V\(_2\) (nitrogen content of 8.3%) as the substrate.

Additionally, transition metal nanoparticles like Pt or Pd are the most promising catalysts for hydrogen adsorption and they will be considered as the main components in our catalysts. In this work, the hydrogen molecule was initially placed at different orientations and on top of the catalysts. The results of certain structures, selected according to their lowest energies are presented in Fig. 1. Part of our figures were made using the XCrySDen software [35]. The physical properties vary depending on the position of the hydrogens around the catalyst, as apparent in the Supporting Information (SI) (Figure \(\mathcal {S}\)1 in SI). System number 20 was used for the former case, where the hydrogen molecule was placed very close to the surface. From a qualitative point of view, the results in terms of charge transfer and its correlation with other properties remain. Depending on the position of the hydrogen molecule on the cluster, two states were to be expected; one activated and the other dissociated; the dissociated state manifests higher hydrogen adsorption energies, large hydrogen-hydrogen distances and low magnetic moments [1, 13, 17, 36]. An exhaustive study concerning the influence incurred by the position of hydrogens around the catalysts will be the subject of another study.

Hydrogen adsorption energies (\(\Delta E\)) on optimized structures (OS) were calculated as \(\Delta E=E_{\mathrm{OS+2H}}-E_{\mathrm{OS}}-E_{\mathrm{H}_{2}}\) [1, 37]. \(E_{\mathrm{OS+2H}}\) is the total energy of the optimized structure following hydrogen adsorption. \(E_{\mathrm{OS}}\) and \(E_{\mathrm{H}_{2}}\) represent total energies of the optimized structures and molecular hydrogen, respectively. In this case \(\Delta E<0\) implies hydrogen adsorption. This energy may also imply activation and dissociation hydrogen energy.

Structural parameters that could include a hydrogen-hydrogen distance, a substrate vertical mean absolute deviation as used in reference [38] and a core shell-type structure indicator are presented in Tables 1 and 2, for selected structures, characterized by a system number (SN). Additional structural parameters can be found in Tables \(\mathcal {S}\)1 and \(\mathcal {S}\)2 in supporting information. A structure, not of the core shell-type, is the one where the core is not observed within the shell and a cluster is simply formed, see for example Fig. 1h. All these structures are discussed after optimization. Tables 3 and 4 present a Bader analysis to study charge transfer. Likewise, adsorption energies and magnetic moments are presented in Tables 5 and 6.

3.1 Structural parameters

Structural characterization is presented in this section. Initially N\(_4\)V\(_2\) pyridinic substrate, together with some Pd-Pd\(_{12}\), Pt-Pt\(_{12}\), Pd-Pt\(_{12}\) and Pt-Pd\(_{12}\) core shell-type structures were considered. After structural optimization several structures in the gas phase are presented in Table 1. Furthermore, in Table 2, some structures will be discussed, after interaction with N\(_4\)V\(_2\) pyridinic substrate and after hydrogen adsorption. Structural representations of selected systems are presented in Fig. 1.

Fig. 1
figure 1

Selected structural representations. System numbers (SN) in accord with Tables 1 and 2 are also indicated. a PdPd\(_{12}\) SN = 3, b Pt\(_{13}\)(1) SN = 4, c PtPd\(_{12}\) SN = 6, d PdPt\(_{12}\)(1) SN = 7, e PdN\(_{4}\)V\(_{2}\)-PdPd\(_{11}\)-2H SN = 18, f PtN\(_{4}\)V\(_{2}\)-Pt\(_{12}\)(1)-2H SN = 19, g PdN\(_{4}\)V\(_{2}\)-PtPd\(_{11}\)-2H SN = 20 and h PtN\(_{4}\)V\(_{2}\)-PdPt\(_{11}\)(1)-2H SN = 21. Yellow, blue, brown, red and green colors are asigned to carbon, nitrogen, palladium, platinum and hydrogen ions respectively

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Specific parameters such as H–H distance d\(_{\mathrm{H-H}}\) are presented in Tables 1 and 2 (other typical A-B ion distances d\(_{A-B}\) can be observed in Tables \(\mathcal {S}\)1 and \(\mathcal {S}\)2 in SI).

Table 1 Hydrogen-hydrogen d\(_{\mathrm{H-H}}\) distance in Å and a core–shell type are presented in this table
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Specific H–H distance is important, when describing molecular hydrogen dissociation. A molecular hydrogen dissociation may be considered when the hydrogen inter-nuclear distance exceeds 1.6 Å [10]. In Tables 1 and 2, hydrogen dissociation is indicated by the \((*)\) symbol. The greatest dissociation correlates directly with a non-core shell-type structure, see for example Table 1 and 2. The former hydrogen dissociation condition (1.6Å) is almost twice the hydrogen-hydrogen distance for the hydrogen molecule in the gas phase of 0.75Å, see Table 1. This distance is similar to previously reported results for 0.75 Å [37, 39, 40]. Our results can be compared to those obtained for hydrogen adsorption in reference [37]. A hydrogen-hydrogen distance of d\(_{\mathrm{H-H}}=0.81-0.84\) Å was observed in a typical Kubas configuration of a system formed out of SiC substrate with one Pd-atom as catalyst. This result can be compared to the distance of our system number 18 of 0.88 Å, see Table 2. In our selected system, a PdN\(_{4}\)V\(_{2}\)-PdPd\(_{11}\) structure interacts with a molecular hydrogen. The distance in our system is a little bit longer than that found in reference [37], due to the effect of our substrate.

Generally, other structures with lower energies than the corresponding Pt-Pt and Pd-Pt core–shell structures were found. For example the system number 4 (Pt\(_{13}\)(1)) in Table 1 that can be observed in Fig. 1b. For system number 19, see Fig 1f and system number 21 can be observed in Fig 1h.

After optimization, the initial Pt-core ion and the Pd-core were found outside the cluster in the Pt-shell, forming a straight forward cluster, see Fig 1b, f, h. The former phenomenon is comparable with the inversion process found in reference [41]. Notably, there was an apparent structural transformation of the SN = 7 core–shell structure (Fig 1d) to a non-core, shell-type structure (SN = 17 or 21 see Table 2) that was surface-mediated.

In the gas phase, for the core–shell structures (SN = 3,6 and 7), the average distance between the core ion and the ions forming the shell is \(\sim \) 2.61–2.64 Å. Additionally, average distance between first neighboring ions that form the shell is \(\sim \) 2.74–2.78 Å. Apparently, when our selected gas phase structures (SN = 3,4,6 and 7 in Table 1) interact with the N\(_{4}\)V\(_{2}\) surface, see Figure 1e–h in main text and Figure \(\mathcal {S}\)2 in SI, one transition metal ion of the catalyst typically becomes detached from the cluster forming the substrate. The results from magnetic and electronic properties confirm this premise. This behavior is similar to that proposed by Cardozo-Mata et al. [34]. The transition metal adsorbed on the N\(_{4}\)V\(_{2}\) surface changes the electronic and magnetic properties of the N\(_{4}\)V\(_{2}\) substrate, as initially considered. In this case, a better nomenclature for the substrate can be proposed as Pd(Pt)N\(_{4}\)V\(_{2}\) see Table 2, being Pd(Pt) the transition metal ion adsorbed on the N\(_4\)V\(_2\) substrate that was initially considered.

Generally it seems that the effect of the presence of the substrate on core–shell systems is to increase the average distance between the core ion and the ions that form the shell and likewise to decrease the first neighbor’s average distance between the ions that form the shell.

Table 2 Substrate vertical mean absolute deviation Z\(_{\mathrm{MAD}}\) in Å, hydrogen-hydrogen d\(_{\mathrm{H-H}}\) distance in Å and a core–shell type are presented in this table
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A vertical mean absolute deviation Z\(_{\mathrm{MAD}}= \frac{1}{N}\) \(\sum _{i=1}^{N} |z_{i}-\langle z \rangle |\) [38] was also calculated on (Pd,Pt)N\(_4\)V\(_2\) substrate, see Table 2. As reference, the graphene is perfectly flat, meaning that the corresponding vertical deformation is Z\(_{\mathrm{MAD}}=0\). Vertical deformation increases to Z\(_{\mathrm{MAD}}=0.13\) Å for N\(_4\)V\(_2\) system. The characteristic graphene sp\(^{2}\) symmetry is distorted because of the vacancies and a little contribution from sp\(^{3}\) is the reason for the increase of Z\(_{\mathrm{MAD}}\). The former vertical deformation relaxes somewhat when molecular hydrogen is introduced, even if there is a physical interaction (adsorption energy of 30 meV) between the substrate and the molecular hydrogen. In this case Z\(_{\mathrm{MAD}}=0.12\) Å.

Vertical deformation increases when catalytic clusters are introduced to the system, see Table 2, for example Z\(_{\mathrm{MAD}}=0.21-0.22\) Å, when the catalysts mainly consist of Pd ions and 0.23–0.25 Å for Pt ions, see Table 2. Vertical deformation directly correlates with the greatest dissociation.

3.2 Charge transfer

Bader analysis was used to study charge transfer. Charge transfer was calculated as valence electrons (described in the computational methods) minus Bader electrons. The representation of charge transfer for example for the carbon ion will be C\(^{\pm x}\) or ±xe\(^{-}\), being ± x charge transfer. In the case of 2 hydrogens, (2H)\(^{\pm y}\) will be the hydrogen charge transfer presented in Tables 3 and 4. Bader analysis of this section can be observed in Tables 3 and 4. A positive value for charge transfer indicates oxidation and a negative one indicates reduction of the system. It is generally apparent that there is a correlation between non-hydrogen dissociation and a very low hydrogen charge transfer Table 3. In this case, we have the SN = 8 ((2H)\(^{0.00}\)), SN = 9 ((2H)\(^{+0.01}\)) , SN = 12 ((2H)\(^{+0.00}\)), SN = 18 ((2H)\(^{+0.00}\)) and SN = 20 ((2H)\(^{-0.00}\)) of Table 3. Contrarily, the highest values for hydrogen dissociation were obtained when the hydrogens (2H) were reduced, as in SN = 13-v ((2H)\(^{-0.03}\) ), system number 19 ((2H)\(^{-0.05}\)) and 21 ((2H)\(^{-0.09}\)) of Table 4.

3.2.1 Systems without hydrogen dissociation

System number 8 in Table 3 does not present dissociation of hydrogen, Table 3. The hydrogen-hydrogen distance (0.75Å) is characteristic of molecular hydrogen in the gas phase. The former agrees with physical adsorption (\(-0.03\) eV) and correspondingly, this agrees with very low hydrogen charge transfer (0.00e\(^{-}\)). SN = 8 results from molecular hydrogen and graphene substrate doped with nitrogen (GNS\(\equiv \)N\(_{4}\)V\(_{2}\)) denoted as system number 2. SN = 2 presents charge transfer from the carbon ions to the nitrogen ions: \(\sim \)4.5e\(^{-}\) (C\(_{44}\))\(^{4.5}\)(N\(_{4}\))\(^{-4.5}\), Table 3. This is to be expected because the electronegativity of nitrogen exceeds the electronegativity of carbon.

System number 9 in Table 3 does not present hydrogen dissociation and is made up of the Pd-Pd\(_{12}\) core–shell system (system number 3) and two hydrogens. The SN = 9 presents charge transfer from the Pd-core (0.13e\(^{-}\)) and the hydrogen ions (0.01e\(^{-}\)) to the Pd\(_{12}\)-shell (-0.14e\(^{-}\)), Table 3. This implies a reduction in the Pd\(_{12}\)-shell. At the moment when the core–shell of system number 3 is incorporated into GNS, system number 14 of Table 3 is obtained. Charge transfer of 0.11e\(^{-}\) from the Pd-core to the Pd\(_{11}\)-shell (\(-0.02\)e\(^{-}\)) and charge transfer to the substrate (\(-0.09\)e\(^{-}\)) is calculated, Table 3. The same qualitative behavior is observed when the former system adsorbs hydrogen (system number 18 in Table 3), in this case the charge transfer from the Pd-core decreases slightly to 0.08e\(^{-}\) and the charge transfer to the Pd\(_{11}\)-shell remains at − 0.02e\(^{-}\), Table 3. No charge transfer to hydrogens is apparent, Table 3. The effect of hydrogen adsorption on charge transfer properties in the former case acts to lower the charge transfer value from the core to the substrate, meaning that the hydrogens indirectly decrease the reduction at the surface.

Table 3 Bader analysis, (2H)\(^{\pm y}\) (± y) hydrogen charge transfer and hydrogen dissociation is presented in this table
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Another system that does not present hydrogen dissociation is system number 12 in Table 3. This system consists of the Pt-Pd\(_{12}\) core–shell system (SN = 6) and two hydrogens. The SN = 12 presents qualitatively similar charge transfer behavior to that presented by system number 9. This implies charge transfer from the Pt-core (0.03e\(^{-}\)) to the Pd\(_{12}\)-shell (-0.03e\(^{-}\)). Charge transfer of the hydrogen ions has a very low value of +0.00e\(^{-}\), Table 3. The result of changing the palladium core for platinum results in a less reduced Pd\(_{12}\)-shell. This may occur because the electronegativity of platinum exceeds that of palladium.

In contrast, if the core–shell (Pt-Pd\(_{12}\)) of system number 6 is incorporated into to GNS, system number 16 is obtained. Similarly, when SN = 16 adsorbs hydrogen system number 20 is obtained.

In the first case, (SN = 16) charge transfer from the Pd\(_{11}\)-shell (0.13e\(^{-}\)) to the Pt-core (− 0.02e\(^{-}\)) and charge transfer to the substrate (− 0.11e\(^{-}\)) is obtained, Table 3. This implies a reduction of the substrate. Similar behavior occurs after hydrogen adsorption (SN = 20), Table 3. In the former case, no charge transfer to hydrogens is apparent and the oxidized state of Pd\(_{11}\)-shell (0.13e\(^{-}\)) remains after hydrogen adsorption, Table 3. In this case, the effect of hydrogen adsorption is to decrease the reduction of PdN\(_{4}\)V\(_{2}\) at the surface from − 0.11e\(^{-}\) to − 0.08e\(^{-}\). In very general terms, the non-dissociation of hydrogen is related to core–shell structure, very low charge transfer of hydrogens and to the reduction of the PdN\(_{4}\)V\(_{2}\) surface. Likewise, a very different qualitative behavior for charge transfer is observed, when the core of the core–shell structure is changed from Pd to Pt; in the second case, the electronegativity of Pt causes charge transfer to occur from the Pd\(_{11}\)-shell to the surface and to the Pt-core, Table 3.

3.2.2 Systems that manifest hydrogen dissociation

Unlike systems that do not present hydrogen dissociation, hydrogen dissociation is closely correlated with the oxidation of the PtN\(_{4}\)V\(_{2}\) surface, and with a non-core shell-type structure of the systems, Table 4. Reduction at the surface is very important for hydrogen storage by means of the spillover mechanism. For non-reducible supports, it is not clear whether hydrogen spillover takes place [42]. In our systems, non-reduction at the surface is related to hydrogen dissociation.

Table 4 Bader analysis, (2H)\(^{\pm y}\) (± y) hydrogen charge transfer and hydrogen dissociation is presented in this table
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The first system that presents hydrogen dissociation is system number 10 in Table 4. This system consists of the Pt\(_{13}\)(1) cluster (SN = 4) and two hydrogens. The former system presents charge transfer from the hydrogens (0.04e\(^{-}\)) to the cluster, Table 4. In this case, the hydrogens collectively acquire an oxidized state. The former system can be compared to SN = 11 in Table 4. The SN = 11 is a Pt-Pt\(_{12}\)(2) core shell-type structure and similar qualitative charge transfer behavior was found to that of the previous case, Table 4. In this case, charge transfer from the hydrogens (+0.05e\(^{-}\)) to the core–shell was obtained, Table 4. The interaction of the SN = 4 with GNS (SN = 15 in Table 4) produces oxidation of the (PtN\(_{4}\)V\(_{2}\))\(^{+0.10}\) surface and reduction (− 0.10e\(^{-}\)) of the Pt\(_{12}\)(1) cluster, Table 4. The interaction of the former system with hydrogen (system number 19) diminishes both surface (+0.08e\(^{-}\)) and Pt\(_{12}\)(1) cluster (− 0.03e\(^{-}\)) charge transfer values, in addition to reducing the hydrogens (− 0.05e\(^{-}\)), Table 4. The effect of hydrogens in the former system is to decrease oxidation of the surface, as well as to decrease the reduction of the Pt\(_{12}\)(1) cluster.

Two other systems that exhibit hydrogen dissociation are those of SN = 13 and SN = 13-v, Table 4. These systems consist of 2 hydrogens and SN = 7 and SN = 7-v, respectively. Two different charge transfer behaviors were obtained in the SN = 13 (PdPt\(_{12}\)(1) core–shell system + 2H) and in the system number 13-v (PdPt\(_{12}\)(2) non-core shell-type +2H). In the first one of these, charge transfer of the Pd-core (+0.28e\(^{-}\)) and charge transfer of the hydrogens (+0.05e\(^{-}\)) to the Pt\(_{12}\)(1)-shell (− 0.33e\(^{-}\)) was observed. This indicates that there is a charge transfer from the hydrogens to the core–shell structure. In the second case (SN = 13-v), charge transfer from the PdPt\(_{12}\)(2) cluster (+0.03e\(^{-}\)) to the hydrogens (− 0.03e\(^{-}\)) was obtained. In the former systems, it should be emphasized that the structure of the systems is very important in terms of the charge transfer process, given a reduction in hydrogens, when considering the cluster type system.

In the case of the interaction between SN = 7 and GNS (SN = 17 in Table 4), there was charge transfer from the surface (+0.1e\(^{-}\)) to the PdPt\(_{11}\)(1) cluster. Following interaction with hydrogens (system number 21), charge transfer from the (PtN\(_{4}\)V\(_{2}\)) surface (0.03e\(^{-}\)) and the PdPt\(_{11}\)(1) cluster (0.06e\(^{-}\)), to the hydrogens (− 0.09e\(^{-}\)) was calculated. Notably, this system presents the most hydrogen dissociation of any of the systems (2.28 Å).

3.3 Adsorption energies

As apparent in Table 5, there is hydrogen adsorption in all our systems \(\Delta E< 0\). There is a correlation between non-dissociation and low hydrogen adsorption energies (\(\mid \Delta (E) \mid =0.63-0.87\) eV Table 5. SN = 8 is not considered), which may also relate to a very low hydrogen charge transfer (± 0.00–0.01e\(^{-}\) Table 5).

Table 5 Hydrogen adsorption energies \(\Delta E\) in eV/Kcal mol\(^{-1}\), magnetic moment m in \(\mu _B\), hydrogen dissociation and (± y) hydrogen charge transfer, are presented in this table
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Systems involved are SN = 9,12,18 and 20 in Table 5. At the time when charge transfer increases (± 0.03–0.09e\(^{-}\) Table 5) with respect to systems without dissociation, hydrogen dissociation is observed and the hydrogen adsorption energies are higher with respect to non-dissociated systems \(\mid \Delta (E) \mid =1.25-1.74\) eV. Systems involved in hydrogen dissociation and high adsorption energies are SN = 10,11,13, 13-v, 19 and 21 in Table 5.

To compare our results, we take the Pd\(_{13}\) + 2H system with number 9 in Table 5. A binding energy of 0.63eV was observed. This energy is lower than the Kubas state of 0.88eV reported in reference [37]. In the former case, the interaction of molecular hydrogen and one Pd atom in a Kubas state was considered [37]. In the former case, hydrogen adsorption energy is affected by the size of the catalyst.

3.4 Magnetic properties

General ferromagnetic behavior is found in our systems, induced by the d-orbital contribution of the palladium and platinum ions in the core–shell and cluster structures (non-core shell-type structures). Non-dissociation and very low value of charge transfer appear to correlate generally with high magnetic moments (m) (\(m=4.78-7.91\)) \(\mu _B\), Table 5. The systems involved are SN = 9,12,18 and 20 in Table 5. Charge transfer produces dissociation and low magnetic states (\(m=0.19-5.62\)) \(\mu _B\) compared to systems that lack dissociation. The transition metal ions (Pd,Pt) adsorbed on the N\(_{4}\)V\(_{2}\) substrate do not present a large contribution to the magnetic moment compared to the ions in the catalysts. The nitrogen doped pyridinic systems N\(_{4}\)V\(_{2}\) and N\(_{4}\)V\(_{2}\)+H\(_{2}\) and molecular hydrogen H\(_{2}\), present no magnetic moment, Tables 5 and 6. The first one of these has already been studied in reference [1].

Table 6 Magnetic moment m in \(\mu _B\) is presented in this table
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However, it has been reported that other nitrogen doped (pyrrolic and pyridinic) systems with one vacancy are spin-polarised [1]. Our magnetic behavior can be compared to the results in references [2, 10], where the magnetic behavior of free Pd\(_{13}\) cluster is 6 \(\mu _B\) and is reduced to 4 \(\mu _B\), when it is deposed on the pristine graphene layer, after adsorption of one hydrogen molecule quenches the moment of the cluster to 2 \(\mu _B\) [2, 10]. The magnetic behavior of references [2, 10] can be compared to the Pd-Pd\(_{12}\) core–shell system (SN = 3) with a magnetic moment of 8.17 \(\mu _B\) Table 6. It is clear that our magnetic moment exceeds that described in references [2, 10]. After deposition of SN = 3 on GNS (SN = 14 Table 6), the magnetic moment diminishes to 4.31 \(\mu _B\). After hydrogen adsorption (SN = 18), the magnetic moment increases to 4.78 \(\mu _B\) Table 5. As apparent, a different qualitative magnetic behavior was found because of the nature of the substrate. Another different qualitative magnetic behavior was evident in system number 4 in Table 6. SN = 4 presents a magnetic moment of 3.40 \(\mu _B\). After deposition of the former system on GNS (SN = 15), the magnetic moment increases to \(m=3.70\) \(\mu _B\). Hydrogen adsorption of SN = 15 leads to system number 19 and the magnetic moment decreases to \(m=2.27\) \(\mu _B\). However we found results similar to those given in references [2, 10] in our SN = 6 with \(m=8.07\) \(\mu _B\) and SN = 7 with a magnetic moment of \(m=3.81\) \(\mu _B\) . After deposition of the former systems on GNS, the following magnetic moments were obtained \(m=5.30\) \(\mu _B\) (SN = 16) and \(m=3.63\) \(\mu _B\) (SN = 17), respectively. Finally, hydrogen adsorption of SN = 16 and SN = 17 diminishes the magnetic moment to \(m=5.06\) \(\mu _B\) (SN = 20) and 0.19 \(\mu _B\) (SN = 21), respectively Tables 5 and 6.

3.5 Electronic properties

Metallic behavior (see Density of States (DOS) and d orbital Projected Density of States (PDOS) in Figures \(\mathcal {S}\)3–6 in the SI) and 3 main regions were identified in all our systems. The first one of these corresponds approximately to the structural bonding denoted by the hybridization of p\(_{x}\), p\(_{y}\) and s orbitals of the C and N ions in the region \(-20\) eV\(\lesssim E \lesssim -10\) eV. The second one of these, − 10 eV\(\lesssim E \lesssim -4\) eV is indicated by the hybridization of p\(_{x}\), p\(_{y}\), p\(_{z}\) and s orbitals of C and N ions and all d and s orbitals of Pd and Pt ions. The third region − 4 eV\(\lesssim E \lesssim \varepsilon _{F}\) (\(\varepsilon _{F}\) being the energy of Fermi), is caused by the hybridization of p\(_{z}\) orbitals of C and N ions and all d and s orbitals of Pd and Pt. Generally, it is apparent that an s hydrogen orbital contribution occurs at around \(\varepsilon _{F}\), when a hydrogen molecule is adsorbed on all systems. For system number 14 in Table 6, two different spin-dependent d-orbital contributions were found around \(\varepsilon _{F} =-1.05\) eV. The first one consisted of d\(_{xz}\) and d\(_{xy}\) orbitals and the second one of d\(_{x^2-y^2}\) orbitals of Pd. In the former system, the Pd-core orbital main contribution around Fermi’s energy is caused by d\(_{xz}\) for both spins. In the case of SN = 16 in Table 6, two different spin-dependent d-orbital contributions were found at around \(\varepsilon _{F} =-1.03\) eV. The first one consisted of d\(_{xy}\) and d\(_{x^2-y^2}\) orbitals and the second one of d\(_{x^2-y^2}\), d\(_{z^2}\), d\(_{xy}\) and d\(_{xz}\). The main contribution of the Pt-core orbital in this system is produced by d\(_{xy}\) and d\(_{yz}\) for one spin contribution and d\(_{xz}\) for the other. For the SN = 15, d\(_{z^2}\) orbitals of the Pt ion mainly hybridize with p\(_{z}\) orbitals for both spin polarizations around \(\varepsilon _{F}=-1.17\) eV. In the case of SN = 17 in Table 6, two different spin-dependent d-orbital contributions were found around Fermi’s energy \(\varepsilon _{F} =-1.12\) eV for similar Pt and Pd ion contributions. The first of these basically consisted of entirely d-orbitals and the second of d\(_{x^2-y^2}\) ones. Additionally, PDOS showed that there is no important contribution concerning Fermi’s energy of the transition metal (Pd,Pt) ions adsorbed on the N\(_4\)V\(_2\) substrate. Conversely, the main electronic contribution of the former ions is found in the first and second regions, which are the main regions that form the electronic structure of the surface.

4 Conclusions

In this work, a hydrogen adsorption study concerning graphene-based surfaces with core–shell type catalysts, using density functional theory is presented. A correlation between charge transfer and structural properties, hydrogen adsorption energies, magnetic behavior and electronic properties was found. A slab model composed of a pyridinic N\(_{4}\)V\(_{2}\) system and an ensemble of hydrogen ions and initially Pd-Pd\(_{12}\), Pt-Pt\(_{12}\), Pd-Pt\(_{12}\) and Pt-Pd\(_{12}\) core–shells as catalysts was studied. In this work, Reduction of hydrogen, together with larger values of charge transfer for the highest values of hydrogen dissociation, compared to the case of non-dissociation was observed. Importantly in most cases, these values may be an order of magnitude greater, if compared to non-hydrogen dissociation behavior. For example, in this study, hydrogen charge transfer values for hydrogen dissociation ± (0.03–0.09) e\(^{-}\) are greater than the non-hydrogen dissociation case ± (0.00–0.01) e\(^{-}\). Hydrogen dissociation is also related to oxidation of the (PtN\(_{4}\)V\(_{2}\)) surface. Hydrogen dissociation correlates with a non-core, shell-type structure, high adsorption energies and generally, low magnetic moments. Contrarily, non-hydrogen dissociation is directly related to low values (compared to the hydrogen dissociation case) of hydrogen charge transfer and to a reduction of the (PdN\(_{4}\)V\(_{2}\)) surface. In the same way non-hydrogen dissociation correlates with a core, shell-type structure, low hydrogen adsorption energies and high magnetic moments. Structural characterization indicates that structures with lower energies than those corresponding to the Pt-Pt\(_{12}\) and Pd-Pt\(_{12}\) core–shell ones were found for the gas phase and on substrate. After optimization, the (Pd)Pt-core ions were found outside the cluster in the Pt-shell. It was also found that when the catalysts interact with initially N\(_{4}\)V\(_{2}\) substrate, one transition metal ion is detached from the cluster to the substrate, changing the physical properties of the substrate. As is generally noted, the effect of the substrate on Pd(Pt)-Pd core–shell system increases the core–shell distance and decreases the distance between first neighboring ions inside the shell. Charge transfer for the non-hydrogen dissociation case involves core shell-type structures and presents two different charge transfer behaviors, which depend on the nature of the core ion and its electronegativity. In presence of surface oxidation of the core, in the case that the core is palladium and reduction in the case that it is platinum, the effect of hydrogen adsorption is to decrease the reduction of the surface in the non-hydrogen dissociation case. Contrarily, the effect of hydrogen adsorption is to decrease oxidation of the surface in the hydrogen dissociation case. Ferromagnetic behavior is found in our systems given by d-orbital contribution of the palladium and platinum ions in the catalysts. As mentioned previously the magnetic moment of our systems relates to hydrogen dissociation and charge transfer behavior. Metallic behavior and 3 main PDOS regions were identified in all our systems, produced by varying orbital hybridization. In contrast, very different d-orbital contribution was found in all our systems around Fermi’s energy. In general, an s hydrogen orbital contribution is observed around Fermi’s energy when hydrogen molecule is adsorbed on all systems. The importance of charge transfer in hydrogen dissociation suggested in this work may lead to further theoretical and experimental work and could be important for storing hydrogen. Besides, this study may also represent the first step for a subsequent theoretical study that involves larger clusters, where the core–shell interface plays an important role, as shown experimentally in reference [43].