Density Functional Approach Toward the Adsorption of Molecular

Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Density Functional Approach Toward the Adsorption of Molecular Hydrogen as Well as the Formation of Metal Hydride on Bare and Activated Carbon-Supported Rhodium Clusters Abhijit Dutta and Paritosh Mondal* Department of Chemistry, Assam University, Silchar 788011, Assam, India

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ABSTRACT: A systematic density functional theory (DFT) investigation has been performed to understand adsorption phenomenon as well as the mechanism of hydrogen molecule dissociation to form metal hydride, catalyzed by bare and activated carbon-supported small rhodium clusters. H−H bond length of hydrogen molecule adsorbed on activated carbon-supported rhodium cluster is found to be higher. Five- as well as six-member rings of the activated carbon act as the support for hydrogenadsorbed rhodium clusters. Rhodium cluster linked with fivemember ring of activated carbon has the enhanced ability to activate hydrogen molecule. DFT-evaluated transition states show lower activation energies in the dissociation of hydrogen molecule catalyzed by activated carbon-supported rhodium clusters, whereas dissociation of hydrogen molecule catalyzed by Rhn, supported on activated carbon, follows two pathways. First, hydrogen atoms stay on Rhn after dissociation, and in the second, hydrogen is dislodged from Rhn to carbon of the activated carbon, which is called spillover. The first pathway is observed to be more favorable in comparison to the second pathway. However, the supported Rh4 exhibits equal feasibility for both the pathways.

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polarization and multiple σ-bonding interactions between the hydrogen molecule and d orbitals of transition metals. Adsorption phenomenon of hydrogen molecule on small transition-metal clusters, such as Au, Pd, Cu, and Pt, has been extensively investigated.11−14 Chen et al.11 investigated adsorption and dissociation of hydrogen molecule on small neutral and charged Aun (n = 1−6) clusters by density functional theory (DFT) method. It is observed that H2 undergoes dissociation only at low temperature on both neutral and cationic Au4 and Au5. Kshirsagar et al.12 studied the adsorption of H2 molecule on small neutral and cationic Aun clusters (n = 1−8). This study reveals that hydrogen molecule forms weak binding with neutral Aun and strong binding with Aun+. All electron scalar relativistic calculation of adsorption of hydrogen molecule on small Cun (n = 1−13) suggests stronger Cu−Cu and weaker H−H bonds.13 Vertical ionization potentials, highest occupied molecular orbital (HOMO)−lowest unoccupied molecular orbital (LUMO) gaps, and vertical electron affinities of CunH2 show odd− even oscillation. Hydrogen molecule is found to be dissociatively adsorbed on Pdn, (n = 2−7), which is considered more stable than nondissociative adsorption. It has been observed that the binding energy of hydrogen on Pdn decreases

INTRODUCTION Growing awareness on the consequences of greenhouse gases released in nature has increased the efforts and demands for the environment friendly energy production as well as their storage. Hydrogen gas is considered one of the most important clean energy source and also as a raw material for chemical industries. In petroleum industries, all crude oils are allowed to be treated with hydrogen to remove impurities containing sulfur, nitrogen, and oxygen.1 Addition of hydrogen to unsaturated C−C bond is one of the elemental steps in the synthesis of various chemicals that plays a significant role in the production of fuels, construction materials, fabrics, edible products, etc.2 Hydrogen molecule has a very strong twoelectron H−H bond and is chemically useful only when H−H bond is catalytically broken in a controlled fashion.1,2 Transition metals supported on oxides or sulfides are very effective and widely used heterogeneous catalysts for the splitting of H2.1−8 It is very important to understand adsorption and splitting of hydrogen molecule catalyzed by transition metals. Transition metals are found to have wide application in the various hydrogenation−dehydrogenation reactions. Small rhodium clusters play a significant role in catalyzing various industrially important reactions. However, catalytic activity and selectivity of rhodium nanoclusters depend on their nuclearity.9 The mode of interaction between hydrogen molecule and transition-metal atom is known as Kubas bonding.10 This bonding is based on the molecular © XXXX American Chemical Society

Received: April 3, 2018 Revised: July 3, 2018 Published: July 5, 2018 A

DOI: 10.1021/acs.jpcc.8b03142 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C Table 1. DFT-Evaluated Rh−H, H−H, and Rh−Rh Bond Distances in the Case of RhnH2 cluster Rh3H2 Rh4H2 Rh5H2 Rh6H2 Rh7H2 Rh8H2

(doublet) (singlet) (doublet) (singlet) (doublet) (singlet)

Rh−H (Å)

H−H (Å)

Rh−Rh (Å)

adsorption energy (eV) (DFT method)

adsorption energy (eV) (DFT-D TS method)

1.730 1.741 1.761 1.799 1.746 1.786

0.867 0.865 0.858 0.849 0.848 0.838

2.479 2.521 2.412 2.506 2.548 2.467

1.76 2.36 2.07 1.97 1.69 2.38

1.77 2.37 2.08 1.97 1.69 2.39

Figure 1. Ground-state optimized geometries of hydrogen-adsorbed Rhn.

with size and is found to be almost constant when n ≥ 4. However, experimental and computational studies suggest that hydrogen molecule dissociates very easily on Pd surface even though subsurface binding interaction is energetically less favorable.15−18 Adsorption and dissociation of H2 catalyzed by bimetallic clusters have also been investigated theoretically.19−23 V site of AlnV (n = 1−13)19 is found to be more favorable for the adsorption of H2. On the other hand, platinum impurity enhances the reactivity of AunPt (n = 1−12) toward adsorption of hydrogen.20 Hydrogen molecule is found to be easily adsorbed on the top Au atom of AlnAu (n = 2−5, 7, 12, 13) with end-on orientation rather than side-on orientation because of the greater feasibility of orbital overlapping.21 A detailed splitting mechanism of H−H bond at the molecular level for forming metal hydride-like compounds is still not clearly understood.10 However, dissociation of H2 molecule on the surface of the transition metal is one of the simplest surface reactions. Hence, dissociation of hydrogen on metal surface has been studied widely by experimental24 and theoretical methods.25,26 Among transition metals, rhodium exhibits excellent catalytic activity27 for the conversion of various toxic gases like CO and NO, emitted from automobile exhaust into their nontoxic or less toxic form such as CO2, NO2, etc. Basically, rhodium exhibits higher catalytic activity in its thinfilm form or in the form of small clusters. Self-consistent

scattering theory suggests that single hydrogen atom unites in a 4-fold hollow Rh(001) layer at a height of 2.46 Å,28 whereas each atom of hydrogen molecule interacted with a 2-fold bridge site of Rh(001) surface.28 Chemisorptions of atomic hydrogen and oxygen on Rh(111) show29 a 3-fold adsorption phenomenon. Very few reports are available on hydride production as well as spillover reaction catalyzed by bare and activated carbon (AC)-supported transition-metal clusters. Activated carbons are used on a massive scale for purification of water and gases, extraction of metals, in the field of medicines, etc.30 Activated carbon consists of curved fragments, including pentagons and other nonhexagonal rings in addition to the six-member ring.31−33 In this article, a detailed theoretical investigation has been presented probably for the first time on adsorption and dissociation of hydrogen molecule catalyzed by bare and activated carbon-supported small rhodium clusters. Further, splitting of hydrogen molecule and formation of metal hydride has also been reported.

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COMPUTATIONAL DETAILS

To study adsorption phenomenon of hydrogen molecule on bare and activated carbon-supported small rhodium clusters, ground-state geometries of neutral Rhn (n = 3−8) clusters have been taken from our recent publication.34 Stable geometry of B


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The Journal of Physical Chemistry C rhodium clusters is considered as low-lying isomer for adsorption of H2 at various possible adsorption sites, such as atop, at the bridge, and for higher coordination. Hydrogenadsorbed bare and supported rhodium clusters are optimized without imposing any symmetry constraints. Optimization of geometries including transition states (TS) is performed by DFT method using DMol3 package.35,36 DFT calculations are performed under generalized gradient approximation with Perdew−Burke−Ernzerhof (PBE) functional.37,38 DNP39 basis set is chosen for geometry optimization, which is equivalent to Gaussian split-valence 6-31G** basis set. All electron relativistic corrections to valence orbitals using a local pseudopotential are utilized for direct inversion in a subspace method. In this study, self-consistent field procedures having convergence criteria of energy 1 × 10−5 Ha, maximum force gradient 2 × 10−3 Ha Å−1, and displacement convergence 5 × 10−3 Å on the total energy as well as 10−6 a.u. on electron density are chosen as boundary conditions. Zero-point vibrational energy correction is incorporated to all energy calculations. Local minima and transition states are confirmed by evaluating the frequencies at the same level of theory with the geometry optimization. Adsorption energy of hydrogen on bare rhodium clusters is computed by using the following equation. adsorption energy = E(Rh n) + E(H 2) − E(Rh nH 2)

Figure 2. Variation of Rh−H, H−H, and Rh−Rh bond lengths with cluster size.

(1)

where E(Rhn) is the energy of rhodium clusters, E(H2) is the energy of H2, and E(RhnH2) is the energy of H2 adsorbed rhodium clusters. Similarly, adsorption energy of hydrogen on Rhn, supported on activated carbon (AC) is computed by using the following equation. adsorption energy = E(AC) + E(Rh n) + E(H 2) − E(AC@Rh nH 2)

(2)

where E(AC) is the energy of activated carbon, E(Rhn) is the energy of rhodium clusters, E(H2) is the energy of H2, and E(AC@RhnH2) represents energy of H2-adsorbed rhodium clusters supported on activated carbon. E signifies the electronic energy with zero-point correction. Understanding the adsorption behavior of gases on metal surfaces, it is also necessary to study van der Waals interactions. To investigate the van der Waals interactions, DFT-D (TS)40 method has been used for hydrogen adsorption on bare and supported finite rhodium clusters. This hybrid semiempirical dispersioncorrection approach of Tkatchenko and Scheffler (DFT-D TS)40 has been utilized in geometry optimization.

Figure 3. Variation of adsorption energies with cluster size.

Table 2. DFT-Evaluated Ionization Potential and HOMO Energies of Clusters cluster Rh3H2 Rh4H2 Rh5H2 Rh6H2 Rh7H2 Rh8H2

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RESULTS AND DISCUSSION Molecular Hydrogen Adsorption on Rhn (n = 3−8) Clusters. Adsorption phenomenon of hydrogen molecule on Rhn (n = 3−8) clusters has been investigated by DFT method at PBE/DNP level. To study the adsorption of H2 on supported Rhn, it is essential to analyze the interaction of bare Rhn with free H2. Rh−H, H−H, and Rh−Rh bond length values of H2-adsorbed Rhn are summarized in Table 1, and stable ground-state structures are given in Figure 1. Adsorbed H2 on Rh3 cluster shows bridged type geometry at doublet multiplicity and C1 symmetry in the ground state. Rh−H, H− H, and Rh−Rh bond distances are found to be 1.680, 0.896, and 2.479 Å, respectively, in the case of Rh3H2. Adsorption energy of hydrogen on Rh3 is found to be 1.76 eV. Again,

ionization energy (eV) clusters 7.11 8.52 6.01 5.50 5.94 7.26

Rh3 Rh4 Rh5 Rh6 Rh7 Rh8

HOMO energy (eV)

ionization energy (eV)34

−3.12 −3.92 −2.68 −2.93 −3.22 −3.81

7.03 6.48 5.90 5.45 5.76 5.68

bridge-type hydrogen-adsorbed Rh4 geometry is the ground state at singlet multiplicity, with C1 symmetry having adsorption energy of 2.36 eV. Rh−H, H−H, and Rh−Rh distances are observed to be 1.741, 0.865, and 2.521 Å, respectively, in the case of Rh4H2. Similar bridge-type adsorption of H2 molecule is also noticed on Rh5, Rh6, Rh7, and Rh8. Table 1 shows that H−H bond lengths of H2, adsorbed on Rh5, Rh6, Rh7, and Rh8 clusters are 0.858, 0.849, 0.898, and 0.848 Å, respectively, whereas Rh−H and average Rh−Rh bond distances are seen to be 1.761, 1.799, 1.701, and 1.786 Å and 2.412, 2.506, 2.548, and 2.467 Å for hydrogenC


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The Journal of Physical Chemistry C

Figure 4. DFT-evaluated H2-adsorbed activated carbon-supported Rhn clusters (top monolayer).

Figure 5. DFT-optimized structure of activated carbon.

adsorbed Rh5, Rh6, Rh7, and Rh8, respectively. Ground-state geometries of Rh5H2 and Rh7H2 are obtained at doublet multiplicities, whereas Rh6H2 and Rh8H2 are obtained at singlet multiplicities. Calculated H−H distance of adsorbed hydrogen is found to be longer than the experimentally determined free H−H bond distance (0.741 Å),41 which leads to an inference that hydrogen molecule gets activated on adsorption to Rhn. This activation occurs due to the interaction of rhodium d-electrons with the antibonding molecular orbital of hydrogen molecule, which enhances the strength of Rh−H and lengthens H−H bond distances. Adsorption energies of hydrogen on Rhn evaluated by using DFT and DFT-D (TS) methods are found to be comparable. Therefore, results obtained only by DFT calculation are reported in this manuscript. Variation of bond lengths and adsorption energies with cluster size are mentioned in Figures 2 and 3. Calculated H−H bond lengths in the case of smaller RhnH2 is found be higher in comparison to those of larger RhnH2, which reveals that smaller clusters activate hydrogen molecule more effectively. It is noticed that Rh−H bond distance is larger, whereas H−H bond length is smaller in the case of larger RhnH2, which suggests that hydrogen molecule is not easily activated by larger clusters. Higher back donation of electrons from

Table 3. Calculated C−C Bond Lengths of Activated Carbon on Adsorption of RhnH2 supported clusters

average C−C bond length of five-member ring

average C−C bond length of six-member ring

activated carbon (AC) AC@Rh3 AC@Rh4 AC@Rh5 AC@Rh6 AC@Rh7 AC@Rh8

1.425

1.430

1.432 1.439 1.442 1.440 1.438 1.443

1.433 1.435 1.440 1.441 1.437 1.438

rhodium cluster to hydrogen molecule makes Rh4H2 and Rh8H2 more stable; that is, adsorption energies of hydrogen on Rh4 and Rh8 are seen to be higher. Stronger interaction between two molecules is observed when HOMO energy of one molecule is closer to the energy of LUMO of another molecule.42 HOMO and LUMO energies of Rhn clusters and hydrogen molecule, respectively, are evaluated at PBE/DNP level. DFT-evaluated HOMO energies of Rhn are given in Table 2. LUMO energy of H2 is −3.87 eV. Table 2 shows that D


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Figure 6. Adsorption of H2 on activated carbon-supported Rhn clusters (top layer).

Figure 7. Adsorption of H2 on activated carbon-supported Rhn clusters (interfacial layer).

HOMO energy of Rh4 and Rh8 is closer to LUMO energy of hydrogen molecule, which leads to the stronger reactivity of Rh4 and Rh8 toward hydrogen molecule. Higher adsorption

energy is noticed in the case of Rh4H2 due to smaller HOMO and LUMO energy difference between Rh4 and H2 molecule. Similar energy variation is also noticed in the case of Rh8H2. E


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Table 4. Adsorption Energy and Rh−H, H−H, and Rh−Rh Bond Distances in Hydrogen-Adsorbed Activated CarbonSupported Rhn (on Five-Member Ring) supported cluster on five-member ring

Rh−H (Å)

H−H (Å)

Rh−Rh (Å)

Rh−C (Å)

adsorption energy (eV) top monolayer

adsorption energy (eV) (DFT-D TS method) top monolayer

AC@Rh1H2 AC@Rh2H2 AC@Rh3H2 AC@Rh4H2 AC@Rh5H2 AC@Rh6H2 AC@Rh7H2 AC@Rh8H2

1.703 1.712 1.718 1.712 1.678 1.715 1.717 1.741

0.899 0.891 0.901 0.897 0.916 0.907 0.884 0.895

2.598 2.616 2.695 2.614 2.567 2.581 2.486

2.161 2.182 2.197 2.212 2.189 2.294 2.387 2.478

0.87 0.86 1.08 1.31 0.88 0.99 1.21 1.46

0.88 0.86 1.09 1.31 0.88 0.99 1.21 1.47

Table 5. Adsorption Energy and Rh−H, H−H, and Rh−Rh Bond Distances in Hydrogen-Adsorbed Activated CarbonSupported Rhn (on Six-Member Ring) supported cluster on six-member ring

Rh−H (Å)

H−H (Å)

Rh−Rh (Å)

Rh−C (Å)

adsorption energy (eV)

AC@Rh3H2 AC@Rh4H2 AC@Rh5H2 AC@Rh6H2 AC@Rh7H2 AC@Rh8H2

1.721 1.699 1.681 1.723 1.734 1.779

0.891 0.885 0.816 0.867 0.878 0.865

2.586 2.579 2.601 2.558 2.389 2.412

2.221 2.225 2.192 2.267 2.357 2.499

0.86 0.91 0.87 0.80 0.97 1.06

On the other hand, ionization potential of hydrogen-adsorbed rhodium clusters calculated by DFT method also attested the phenomenon of higher adsorption energies for Rh4H2 and Rh8H2.43 Rh4H2 and Rh8H2 exhibit higher ionization potential (Table 2) in comparison to that of bare Rh4 and Rh8. All complexes actually possess higher ionization potential than bare ones, but for Rh4 and Rh8, this value is much higher than that of the bare ones. Much higher ionization potentials of Rh4H2 and Rh8H2 signify stronger interaction as well as higher adsorption energies. Molecular Hydrogen Adsorption on Activated Carbon-Supported Rhn (n = 3−8) Clusters. Adsorption behavior of hydrogen molecule on activated carbon-supported small rhodium clusters has also been investigated in detail at PBE/DNP level. Geometry of the activated carbon has been adopted from the report of Harris et al.44 In this investigation, a number of only carbon chains have been manipulated. The most stable DFT-evaluated geometries (AC@RhnH2) are given in Figure 4. Figure 4 represents the top monolayer type of adsorption phenomenon, i.e., both the hydrogens adsorb on one rhodium atom (Figure 5). Interfacial and top-layer adsorptions of hydrogen on AC@Rhn are mentioned in Figures 6 and 7, respectively. The interfacial sites indicate the hydrogen atoms on the interface of Rhn and AC, and the top-layer sites indicate that the adsorption occur on two Rh atoms. Binding energy of Rhn on activated carbon has been evaluated before obtaining the adsorption energy of H2 on activated carbon-supported Rhn. Binding energies of Rhn on activated carbon have been calculated on the basis of eq 3. Binding energies of Rh1, Rh2, Rh3, Rh4, Rh5, Rh6, Rh7, and Rh8 on activated carbon are noticed to be 1.09, 0.85, 0.75, 0.82, 0.98, 0.80, 0.83, and 0.73 eV, respectively. Rh1 and Rh4 clusters supported on activated carbon are found to be more stable. binding energy = E(AC) + E(Rh n) − E(AC@Rh n)

Table 6. DFT-Evaluated Adsorption Energy Values of Different Types of Adsorption supported cluster on five-member ring

adsorption energy (eV) top monolayer

adsorption energy (eV) top layer

adsorption energy (eV) Interfacial layer

AC@Rh1H2 AC@Rh2H2 AC@Rh3H2 AC@Rh4H2 AC@Rh5H2 AC@Rh6H2 AC@Rh7H2 AC@Rh8H2

1.96 1.71 1.83 2.13 1.86 1.79 2.04 2.19

1.62 1.51 1.48 2.09 1.85 1.41 1.68 1.73

1.22 1.11 1.15 1.24 1.18 1.13 1.19 1.11

where E(AC) represents energy of activated carbon, E(Rhn) represents energy of free Rhn, and E(AC@Rhn) signifies energy of activated carbon-supported rhodium clusters. Two types of interactions have been proposed between RhnH2 and activated carbon. RhnH2 interacts either on a hollow five-member ring (type 1) or on a hollow six-member ring (type 2) (Figure 5). However, adsorption energy in the latter case is found to be lower. Interaction of RhnH2 with activated carbon surface modifies the hybridization (sp2) of carbon atoms, which leads to the elongation of C−C bonds of activated carbon. Calculated C− C bond distances of activated carbon of AC@RhnH2 are given in Table 3. Table 3 reveals that the interaction of the fivemember ring of the activated carbon with RhnH2 is more distorted in comparison to that of the six-member ring with RhnH2. The five-member ring of activated carbon is surrounded by six-member rings, which favors the adsorption of small rhodium clusters on the five-member ring because it may release the strain to attain stability. Release of strain leads to smooth delocalization of electrons. Because of modification of hybridization, planarity of activated carbon is disturbed on

(3) F


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Figure 8. Deformed electron density diagrams of some selected systems.

Figure 9. Density of states (DOS) of supported rhodium clusters.

carbon-supported Rhn is found to be larger in comparison to that of bare Rhn-adsorbed H2 (Table 1). Longer H−H bond distances of H2 in the case of RhnH2 interacting with the hollow site of the five-member ring reveal that it can activate an adsorbed hydrogen molecule more effectively than RhnH2 interacting on a six-member ring (hollow). Therefore, Rhn interacting with the five-member ring of the activated carbon has been chosen to investigate adsorption and dissociation behavior of a hydrogen molecule because of the possibility of stronger interaction between activated carbon and d orbitals of Rhn. It is also noticed that supported Rhn clusters have larger average Rh−Rh bond lengths in comparison to those of bare Rhn, which suggests that electrons are more delocalized in the

interaction with RhnH2, which leads to the change in conformation of activated carbon. It is also noticed that even atomic rhodium clusters interacted strongly with activated carbon; that is, even atomic Rhn can effectively distort the support because of its symmetry, which has the ability to fit on the surface cavity of activated carbon lattice. Adsorption energy values along with significant geometrical parameters of RhnH2 interacting with five- and six-member rings of the activated carbon are summarized in Tables 4 and 5, respectively. It is noticed that interfacial and top-layer types of adsorption are less favorable than the top monolayer adsorption (Figure 4). It is observed from Tables 4 and 5 that H−H bond distance of H2 molecule adsorbed on activated G


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Figure 10. Optimized stationary points, such as reactants, transition states, and products, for H2 dissociation catalyzed by bare Rhn.

and 0.901 Å, respectively. H−H bond length of adsorbed hydrogen molecule on supported Rh3 is found to be longer than that on bare Rh3. This observation suggests that supported Rh3 activates H−H bond more effectively. On the other hand, adsorption energy of hydrogen on Rh3 interacted with the six-member ring of the support is 0.86 eV, where Rh− H and H−H bond lengths are 1.721 and 0.891 Å, respectively. It is noticed that hydrogen activation is easier with Rh3 interacting with either the five- or six-member ring of the support. However, activation of hydrogen is more feasible for the five-member-ring-connected Rh3. Similar results are also noticed in the cases of Rh4, Rh5, Rh6, Rh7, and Rh8. These observations show that decorated or supported small rhodium clusters are more promising toward hydrogen activation. On the other hand, it can be mentioned that rhodium clusters decorated on activated carbon are found to be more useful for

case of bare Rhn. Hydrogen molecule gets activated due to stronger interaction with supported Rhn. Therefore, it can be concluded that activated carbon-supported Rhn can easily split a hydrogen molecule to hydride, i.e, atomic hydrogen can be stored on supported rhodium clusters. Adsorption energy of hydrogen on pure activated carbon is 0.64 eV, having H−H bond length 0.769 Å, whereas adsorption energy of hydrogen on AC@Rhn is found to be lower in comparison to that on bare Rhn. Adsorption energies of activated carbon-supported Rh1H2 and Rh2H2 (top monolayer) are obtained to be 0.87 and 0.86 eV, respectively, using eq 2 (Table 4). Supported Rh1 and Rh2 are also found to activate H−H bond, i.e., H−H bond length increases on adsorption. Adsorption energy of hydrogen on Rh3 interacted with five-member ring of activated carbon is evaluated to be 1.08 eV, with Rh−H and H−H bond distances being 1.718 H


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Figure 11. DFT-evaluated activation free-energy diagram for the hydrogen dissociation catalyzed by bare Rhn.

storage of hydrogen as well as production of metal hydride. In all cases, differences in the adsorption energies evaluated by DFT and DFT-D (TS) methods are seen to be comparable. Verdinelli et al.45 and Jasen et al.46 obtain adsorption energies of rhodium and ruthenium on single-walled carbon nanotube on the basis of eq 4. In our study, adsorption energies of H2 on activated carbon-supported Rhn clusters have been also evaluated by using the same eq 4 along with eq 2. Adsorption energies of H2 on activated carbon-supported rhodium clusters are mentioned in Table 6. Calculated adsorption energies obtained by eq 4 are seen to be higher than those from eq 2. It is noticed from Table 6 that top monolayer adsorption of hydrogen possesses higher adsorption energies than that of top and interfacial layer adsorption.

Dissociation of only top monolayer-adsorbed hydrogen molecule has been investigated. Among top layers, only AC@Rh4H2 and AC@Rh5H2 are considered for investigation of the mechanism of hydrogen dissociation (adsorption energy close to the top monolayer). On the other hand, interfacial adsorption is found to be less favorable compared with top monolayer and top-layer adsorption. The difference between eqs 4 and 2 gives the binding energy of Rhn supported on activated carbon. It is noticed that interfacial and top-layer types of adsorption are less favorable than the top monolayer adsorption. Deformed Electron Density and Density of States (DOS). Deformed electron densities of the selected hydrogenadsorbed bare and supported rhodium clusters are shown in Figure 8. Deformed electron density is observed to be more or less uniform around rhodium, hydrogen, and carbon atoms in the case of AC@RhnH2 (Figure 8). Uniform deformed electron density among bonds in the case of AC@RhnH2 suggests higher delocalization of electrons, making the bonds stronger.

adsorption energy = E(AC@Rh n) + E(H 2) − E(AC@Rh nH 2)

(4) I


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Therefore, it can be mentioned that orbitals of rhodium atoms are involved in bonding with hydrogen and carbon atoms in AC@RhnH2, whereas less deformed electron density is noticed among hydrogen and connected rhodium atoms in the case of bare RhnH2. Therefore, it can be concluded that well-deformed electron densities between hydrogen molecule and Rhn interacting with activated carbon exhibit stronger interaction. DFT-derived density-of-state (DOS) diagrams of some AC@Rhn and AC@RhnH2 are shown in Figure 9. It is seen from Figure 9 that the width of the p-electron band near the bonding region, i.e., below the Fermi level, is found to be higher, which suggests that the p-electrons are more involved in the bonding rather than the s- and d-electrons. Again, pelectron density is also seen to be higher in the antibonding region, which reveals that electrons are transferred from bonding p-orbitals to antibonding p-orbitals. Figure 9 also shows that electronic distributions remain unchanged on adsorption of hydrogen molecule on AC@Rhn; that is, selectrons are unable to change the overall electronic distribution in the cases of AC@Rhn and AC@RhnH2. Dissociation of Hydrogen Catalyzed by Bare Rhn. All stationary points, viz., reactants, products, and transition states, involved in the dissociation of hydrogen molecule catalyzed by bare Rhn to form rhodium metal hydride are shown in Figure 10, and their energy profile diagrams are given in Figure 11. Transition state (Rh3_TS) shows the dissociation of hydrogen molecule catalyzed by Rh3. It leads to the breaking of H−H bond and subsequent transfer of dissociated hydrogen atom to nearby rhodium atoms to form a bridge. Activation free energy for this reaction is found to be 0.93 eV. (Figure 11), whereas activation free energy for the dissociation of hydrogen molecule catalyzed by Rh4 is calculated to be 0.72 eV. Rh4_TS shows the lengthening of H−H bond distance leads to the transfer of one hydrogen atom to another rhodium atom of Rh4. However, geometry of Rh3_P and Rh4_P are found to be different. DFT-evaluated free energy of activation for the dissociation of hydrogen molecule catalyzed by Rh5, Rh6, Rh7, and Rh8 clusters is reported to be 0.67, 1.02, 0.87, and 1.15 eV, respectively. Only one imaginary frequency is observed in each of the transition states, which corresponds to the movement of a dissociated hydrogen atom to nearby rhodium atom, but the mode of attachment of hydrogen atoms in the products is seen to be different. DFT-evaluated imaginary frequencies of all transition states are listed in Figure 10 inside the bracket. Figure 11 shows that dissociation of hydrogen molecule catalyzed by small rhodium clusters follows an exothermic pathway. Calculated activation free energies suggest that Rh4 and Rh5 are better catalysts for H−H bond dissociation. Dissociation of Hydrogen Molecule Catalyzed by Activated Carbon-Supported Rhn Clusters. Mechanism of hydrogen molecule dissociation catalyzed by Rhn supported on activated carbon has also been investigated by quantum chemical method. Stationary points related to dissociation of hydrogen molecule catalyzed by activated carbon-supported rhodium clusters evaluated by DFT at PBE/DNP level are mentioned in Figure 12, and their energy profile diagrams are given in the Figure 13 (top monolayer adsorption). Activation barrier height for the dissociation of hydrogen molecule catalyzed by AC@Rh1 and AC@Rh2 is obtained to be 0.41 and 0.49 eV, respectively. These activation energy values are lower than the values of hydrogen dissociation by bare clusters. Activation barrier height for the dissociation of H−H bond catalyzed by AC@Rh3 is calculated to be 0.51 eV. This barrier

Figure 12. Optimized structures of reactants, transition states, and products for H2 dissociation on activated carbon-supported rhodium (in AC@Rhn_X, AC = activated carbon, Rhn = rhodium cluster, and X = reactant, transition state, or product). J


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Figure 13. DFT-evaluated activation free-energy diagram for the hydrogen dissociation catalyzed by activated carbon-supported Rhn.

is bridge coordinated with different rhodium atoms in the product (AC@Rh4_P). Similarly, activation energy values for dissociation of hydrogen molecule catalyzed by activated carbon-supported Rh5, Rh6, Rh7, and Rh8 are calculated to be 0.48, 0.36, 0.79, and 0.71 eV, respectively. Energy profile diagrams (Figure 13) suggest that activated carbon-supported Rh4 and Rh6 are more effective in the dissociation of hydrogen molecules. Similar to the bare rhodium clusters, activated carbon-supported rhodium clusters involved hydrogen molecule dissociation also follows exothermic pathway. Therefore,

height is lower in comparison with H2 dissociation catalyzed by bare Rh3. Transition-state AC@Rh3_TS leads to the breaking of the H−H bond and transfer of one of the hydrogen atoms to a nearby rhodium atom, whereas product AC@Rh3_P obtained after dissociation of H2 molecule has one bridge-type and other monocoordinated hydrogen atoms. Activation energy of H−H bond dissociation catalyzed by AC@Rh4 is 0.39 eV, which is lower than that of the same reaction catalyzed by bare Rh4. In this case, one of the dissociated hydrogen atoms is seen to be monocoordinated and the other K


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activated carbon-supported Rhn-catalyzed hydrogen dissociation is found to be more feasible in comparison with bare Rhn. All transition states possess only one imaginary frequency, which leads to the dissociation of hydrogen molecule. Imaginary frequencies of transition states are listed in Figure 12 in brackets. On the other hand, dissociation of top-layeradsorbed hydrogen in Rh4H2 and Rh5H2 has also been performed. Optimized geometries of reactants, transition states, and products are mentioned in the Supporting Information Figure S1, and activation barrier for hydrogen dissociation is given in Figure S2. Dissociation of H2 catalyzed by activated carbon-supported Rh4 has the activation barrier height of 0.32 eV, whereas a higher activation barrier is noticed in the case of supported Rh5-catalyzed reaction (0.57 eV). Dissociation of top-layer-adsorbed hydrogen molecule in AC@ RhnH2 is found to be more favorable than that in bare RhnH2. AC@Rh4H2 is found to give the best result toward molecular hydrogen dissociation. Transfer of Hydrogen (Spillover) from Rhodium to Activated Carbon. Hydrogen spillover has been proposed to be a promising mechanism for understanding hydrogen storage.47 Carbon-based materials, such as carbon nanofibers, graphite, and carbon nanotubes are some of the potential hydrogen storage materials.47−50 Transfer of dissociated hydrogen atoms from Rhn to activated carbon has been investigated using DFT method at PBE/DNP level. This phenomenon is known as spillover. All important geometries obtained in the investigation of spillover reaction are incorporated in Figure 14, and energy profile diagrams are given in Figure 15. Dissociatively adsorbed hydrogen molecule on activated carbon-supported Rhn has been utilized to understand the spillover reaction. Activation free-energy barriers for hydrogen spillover catalyzed by AC@Rh1 and AC@Rh2 are obtained to be 0.52 and 0.67 eV, respectively. Transition-state-formed (AC_SO@Rh3_TS) shows the transfer of dissociated hydrogen atom from Rh3 to the carbon of the support. Activation free energy of this reaction is 0.98 eV. Higher activation energy of this spillover reaction suggests lesser feasibility of the process. Again, activation free-energy values calculated in cases of activated carbon-supported Rh5, Rh6, Rh7, and Rh8 catalyzed spillover reactions are found to be 0.61, 0.83, 1.44, and 1.30 eV, respectively. However, comparatively lower activation energy (0.42 eV) is obtained in the case of activated carbon-supported Rh4. Activation freeenergy values derived by DFT method suggest that spillover is less favorable in comparison to normal dissociation of hydrogen on supported clusters. Spillover reactions catalyzed by AC@Rh4, AC@Rh5, and AC@Rh6 are observed to be more favorable compared with the other spillover type dissociation of hydrogen molecule catalyzed by bare Rhn. However, AC@ Rh4 favors both normal dissociation as well as spillover of hydrogen. Spillover reactions have also been studied with toplayer-adsorbed hydrogen in AC@Rh4H2 and AC@Rh5H2. Optimized stationary points of hydrogen dissociation-catalyzed Rh4 and Rh5 supported on activated carbon are mentioned in the supplementary Figure S3, and activation barriers are given in Figure S4. It is noticed from Figure S4 that the activation barrier height of hydrogen spillover top-layer-adsorbed hydrogen on activated carbon-supported Rh4 and Rh5 is 0.91 and 1.02 eV, respectively, which is less favorable than that of top monolayer- and top-layer-adsorbed hydrogen.

Figure 14. DFT-evaluated optimized diagrams of spillover reaction catalyzed by activated carbon-supported Rhn. Imaginary frequencies of transition states are given inside the brackets.

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Figure 15. DFT-evaluated activation free-energy diagram for the reverse spillover reaction catalyzed by activated carbon-supported Rhn.

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CONCLUSIONS

clusters are more suitable for rhodium hydride formation. Top monolayer adsorption of hydrogen is more suitable than top-layer and interfacial adsorption. Well-deformed electron density enhances the interaction between hydrogen and supported rhodium atoms. Five-member ring of activated carbon-connected Rhn is found to be preferable for molecular hydrogen activation and production of hydride. The activation barrier height suggests that dissociation of hydrogen is more favorable than spillover on a supported system. However, supported Rh4 exhibits comparable feasibility of dissociation as well as spillover of hydrogen.

Detailed investigation has been performed to understand adsorption and dissociation phenomenon of hydrogen molecule catalyzed by bare and activated carbon-supported finite-sized rhodium clusters. Activated carbon-supported as well as bare rhodium clusters have the capability to activate hydrogen molecules. Basically, p-electrons are involved in the interaction of hydrogen-adsorbed rhodium clusters with activated carbon surface. Bare Rh4 and Rh5 clusters are found to be catalytically more active for the activation of hydrogen molecule. Activated carbon-supported rhodium M


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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.8b03142. Optimized geometries of reactants, transition states, and products in the case of H2 dissociation catalyzed by activated carbon-supported rhodium clusters (Figure S1); DFT-evaluated activation free-energy diagram for hydrogen dissociation catalyzed by top-layer adsorption of activated carbon-supported Rh4 and Rh5 (Figure S2); DFT-evaluated activation free-energy diagrams for the spillover reaction catalyzed by activated carbonsupported Rh4 and Rh5 (Figure S3) (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Paritosh Mondal: 0000-0003-1089-1620 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Authors are grateful to the Department of Science and Technology (DST), New Delhi, India for financial support (SB/EMEQ-214/2013).

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Density Functional Approach Toward the Adsorption of Molecular

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