A density functional study on the electronic structure ...

NJC PAPER

Cite this: New J. Chem., 2018, 42, 1121

A density functional study on the electronic structure, nature of bonding and reactivity (n = 2–8) clusters of NO adsorbing Rh0/ n Abhijit Dutta and Paritosh Mondal

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Systematic investigations on lowest energy NO adsorbing neutral and ionic Rhn (n = 2–8) clusters in the gas phase are executed with an all electron relativistic method using density functional theory (DFT) within the generalized gradient approximation. Geometrical parameters like bond length, adsorption energy, and vibrational stretching frequency and reactivity parameters such as electron density, density of states (DOS), LUMO (lowest unoccupied molecular orbital), HOMO (highest occupied molecular orbital), etc. are evaluated to understand the bonding nature as well as the binding interaction of NO (n = 2–8) clusters. RhnNO with stable Rh0/ n

clusters are found to be more stable on the basis of

adsorption energy when compared to RhnNO0/+. Synergic bond formation is noticed between the rhodium atom and the NO molecule due to back-donation of electrons from the metal d-orbitals to the p* orbital of NO in the case of RhnNO0/ . Deformed electron density also suggests a stronger bond between the rhodium and N atoms of the NO molecule in the anionic adducts. HOMO and LUMO Received 27th October 2017, Accepted 5th December 2017 DOI: 10.1039/c7nj04166g

isosurface diagrams reveal that electrons are delocalized from the d-orbitals of rhodium (HOMO) to the p* orbital of NO (LUMO). Mu ¨ lliken charge analysis along with electron density distribution shows the higher stability of RhnNO clusters than that of RhnNO0/+. Energy profile diagrams for the conversion of NO to NO2 catalysed by neutral and ionic Rhn clusters reveal a lower activation barrier for the anionic except for Rh7. Anionic Rh4 and Rh6 clusters are seen to be rhodium clusters in comparison to Rh0/+ n

rsc.li/njc

catalytically more active for the conversion of NO to NO2.

Introduction Growth in scientific and technological regimes in the current era has amplified the demand to investigate the miscellaneous properties of atomic clusters. Exceptional and size dependent chemical, electronic, optical and magnetic properties are the important features of small sized transition metal nanoclusters.1 For instance, a single size cluster shows amazing properties viz. multiple reaction rates2–4 or multiple ionization potentials5 which suggests that each geometrical isomer represents some individual features. Combined experimental and computational studies are required to establish these properties of transition metal clusters.6–8 Assessment of an appropriate geometry of transition metal clusters is a vital footstep for recognizing their structural, electronic, catalytic and magnetic properties. Smaller clusters have been extensively studied in the past few years for making high-density recording materials9 and sensors10 in biomedical applications,11 and also making catalytic devices.12 The reactivity of nanoclusters can be easily tuned by varying Department of Chemistry, Assam University, Silchar 788011, Assam, India. E-mail: [email protected]

their size, geometry, charge and chemical composition. For instance, Hanmura and co-workers13 have established that a hydrogen doped small cobalt cluster exhibits higher reactivity for NO adsorption. Swart and his co-workers14 confirmed that a CO molecule adsorbs on hydrogen doped vanadium clusters without being damaged, while CO gets dissociated upon adsorption onto bare vanadium clusters. Noble metals have the supremacy in controlling the route of chemical reactions through catalysis.15 Rhodium, platinum and palladium play a vital role in catalysis viz. reduction of nitric oxide, oxidation of CO and unburned hydrocarbons in automotive converters.16–18 Rhodium metal is always preferred over platinum and palladium due to its higher catalytic activity for the reduction of NO to N2 by overlooking its cost.19,20 Nowadays, nitrogen oxides discharged from thermal industrial processes, power stations and from automobile exhausts are prime environmental concerns because of the formation of acid rain along with the origin of various health hazards. Investigation on the adsorption of small molecules on metal surfaces is important for exploring and understanding the surface phenomenon and catalytic activities. The chemical nature of NO adsorbed on a metal cluster is fairly different from that of adsorbed CO.

This journal is © The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2018

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An adsorption study of NO on rhodium clusters leads to an understanding of the decomposition of NO catalysed by rhodium nanoclusters. Supported metal clusters are found to be catalytically more active than bare clusters. Pd supported on ZSM-5 or HZSM-5 shows marvellous catalytic activity in methane combustion, NO reduction etc.21 Hao and co-workers have shown the effect of NO on CO oxidation reactions catalysed by Pt, Pd, and Pd–Au with the help of a pulse technique within the temperature range of 50 1C to 200 1C.22 It is observed that NO inhibits the oxidation of CO on both Pt and Pd, but appreciably enhances CO oxidation activity on Pd–Au catalysts. Rhodium is one of the dynamic constituents for three-way catalysis utilized in automotive catalytic converters due to its vital role in catalyzing NOx reduction.23,24 NO can adsorb either molecularly or in a dissociative manner on Rh surfaces at different temperature scales. At room temperature, NO adsorption is dissociative at low exposure on all low index planes while NO adsorbs molecularly on Rh at low temperature.25–30 The binding nature of molecular NO on the (111),25,27 (100),28 and (110)31,32 planes of rhodium nanoclusters has been investigated in detail. Adsorption and dissociation of NO on a rhodium single-crystal to form atomic nitrogen and oxygen have been the focal point of several research groups.33 Decomposition of NOx species on extended Rh surfaces has been widely analyzed. Recognizing the nature of Rh–NO bonds is the first step in understanding the mechanism of the reactions. High-resolution electron energy loss spectroscopy (HREELS) helps obtain the structural information of NO chemisorbed on metal surfaces. The vibrational mode obtained from HREELS studies is usually matched up with the infrared reflection absorption spectra (IRAS) of metal–nitrosyl to obtain the proper site of the nitrosyl and configuration of the complex.34,35 Dynamical LEED analysis has also been employed to resolve the bonding geometry.27 Higher catalytic activities of rhodium in comparison to palladium and platinum clusters for the reduction of NO are still unclear. However, functions of the surface structure,36 alloying effects37 and the power of oxygen preoccupation38 in nitrogen oxide decomposition are well understood. Numerous studies dealing with the adsorption properties and catalytic activities of bare and alloys of Rh-based nanoparticles are available in the literature.39–43 Nolte et al.39 reported a work which confirms the change of the global shape of rhodium nanoparticles prompted by the oxidation of the nanosurface. Grass and co-workers40 also studied the catalytic activity of rhodium-oxide obtained by the oxidation of surfaces towards CO oxidation reactions. Park et al.41 reported that the CO oxidation rate is altered by a change in the composition of atoms in Rh–Pt bimetallic nanoparticles. The catalytic activities of Rh–Pt bimetallic nanoparticles are observed to be higher than those of bare rhodium or platinum clusters. Anderson et al.42 and Ford and co-workers43 investigated ionic RhnNO using Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry and found that cationic clusters reacted appreciably faster than the anionic clusters. Due to their low symmetry, the presence of various structural isomers, the possible existence of complex atomic relaxation and the finite size effect of small clusters are very challenging to study. First principles theoretical

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studies are vital in understanding the adsorption properties and catalytic activities of these types of materials at the molecular level. Harding et al.44 investigated the structure, energetics and reactivity of Rh6 and Rh6+ clusters using DFT and observed different types of reactivity exhibited by the Rh6 clusters toward NO molecules. Reaction kinetics of rhodium clusters has also been depicted nicely by Ford et al.43 based on an experimental study. It is quite possible to study the reaction pathways and transition states of systems using the nudged elastic band (NEB) method.45 The role of structural relaxation effects on adsorption properties and catalytic activity can be analyzed by performing constrained and fully unconstrained structural optimizations. Adsorption of small molecules such as CO or NO on transition metal surfaces has been widely studied in order to understand the surface reactivity and hence, to find the mechanistic path in catalytic reactions.46,47 Special attention has been paid to the adsorption of CO and NO molecules on rhodium surfaces because of its excellent catalytic activity towards the oxidation of CO48–51 and decomposition of NO.52,53 The experimental54,55 and theoretical56–60 investigations on CO and NO adsorption lead to a sizeable number of research publications. Deka et al.61 also reported a theoretical observation on catalytic oxidation of nitric oxide by Pd2 and mixed bimetallic PdM clusters (M = Cu, Rh, Ag, Au, Pt). It is observed from the study that an Eley–Rideal type of mechanism is followed by these clusters for conversion of NO to NO2 and also found that a PdCu cluster is a more dominating system towards oxidation of NO than the other clusters. In spite of these theoretical and experimental reports, a systematic investigation on the bonding interaction of NO on neutral and ionic small rhodium clusters is still very demanding. In this work, we have systematically reported an evaluation of the lowest energy geometry of NO adsorbing neutral and ionic Rhn (n = 2–8) clusters. The contribution of electron density by a metal surface to the adsorption of NO is also presented. The reaction mechanism for the reduction of NO catalysed by RhnNO has also been presented in detail in this work.

Computational details In order to study the adsorption behaviour of NO on rhodium nanoclusters, ground state geometries of neutral and ionic Rhn (n = 2–8) clusters are taken from our recent publication.62 The low-lying isomers are considered to be the stable geometry of rhodium clusters for adsorption of NO at various possible adsorption sites, including atop, bridge and higher coordination sites. NO adsorbing rhodium clusters are optimized without imposing any symmetry constraints. All calculations including transition states are performed using DFT with the DMOL3 package.63,64 DFT calculations are performed under the generalized gradient approximation (GGA) with the BLYP exchange correlation functional.65,66 BLYP incorporates the exchange functional of Becke and the gradient corrected functional of Lee–Yang–Parr. A DNP67 basis set is chosen for geometry optimization. The DNP basis set is equivalent to the Gaussian split-valence 6-31G** basis set. Relativistic calculations are very important for heavy metal atoms.


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Thus, all electron relativistic correction to valence orbitals using a local pseudopotential are used for direct inversion in the subspace method (DIIS). In this study, self-consistent field (SCF) 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 and 10 6 a.u. on the electron density are chosen to be the boundary conditions. All the ground state neutral and charged isomers of the rhodium clusters are optimized corresponding to the low spin configuration. In order to compare the energy values of the ground state geometries with their higher multiplicities, symmetry restricted calculations are executed at higher spin multiplicities. NO adsorbing even atomic neutral and odd atomic ionic rhodium clusters are optimized with multiplicities M = 2, 4 and 6, while odd atomic neutral and even atomic ionic rhodium clusters are optimized with multiplicities M = 1, 3 and 5 to evaluate the stable geometrical isomers. Zero point vibrational energy corrections are incorporated into all the energy calculations. Local minima and transition states are confirmed by the evaluation of frequency at the same level of theory with the geometry optimization. The adsorption energies of NO on bare neutral and ionic rhodium clusters are computed by using the following equation. Adsorption energy = EBare cluster + ENO

EBare cluster–NO adduct

Results and discussion Structural details The accuracy of the existing computational methods is weighed up by the calculation of Rh2 clusters and NO molecules. The calculated bond length (1.16 Å), binding energy (7.33 eV) and vibrational frequency (1840 cm 1) of a free NO molecule are found to be comparable with the corresponding experimental values (1.15 Å, 6.50 eV and 1876 cm 1).68,69 Similar values of bond length and stretching frequency of N–O are obtained by Grybos et al.70 (dN–O = 1.16 Å and anharmonic frequency of NO = 1888 cm 1). A convergence test for Rh2 at the same level of theory has been reported in our recent publication.62 No imaginary frequency is observed in the low as well as in the high spin state optimized geometry of RhnNO which corresponds to local minima in the potential energy surfaces. The lowest energy structure of neutral RhNO is found to be singlet with a bent geometry and CS symmetry. The ground state cationic RhNO cluster attains a linear geometry with doublet multiplicity and CNv point group, while the anionic cluster gives a bent geometry having doublet multiplicity and CS point group. The Rh–N and N–O bond distances evaluated for the neutral, cationic and anionic RhNO adducts using DFT are 1.75, 1.80; 1.78, 1.18 and 1.14, 1.24 Å, respectively. Lin and his co-workers71 reported the Rh–N and N–O bond distances for a neutral RhNO to be 1.75 and 1.15 Å, respectively. Optimized geometries of the neutral and ionic RhnNO (n = 2–8) clusters evaluated at the BLYP/DNP level are presented in Fig. 1. Bridge type bi-coordinated adsorption of NO is observed on neutral (doublet) and ionic (singlet) Rh2 at the ground state with C2V symmetry. The adsorption energies of NO

Fig. 1 Stable geometries of neutral, cationic and anionic RhnNO (n = 2–8) clusters derived at the BLYP/DNP level.

on the neutral and ionic Rhn clusters and their important geometrical parameters are summarised in Tables 1–3. The NO adsorption energies in stable neutral, cationic and anionic Rh2NO are found to be 2.96, 3.08 and 2.93 eV, respectively. The Rh–N and N–O bond distances in the Rh2NO cluster are found to be 1.88 and 1.213 Å, respectively. It is also noticed that the Rh–N bond length in Rh2NO+ is slightly larger (1.93 Å) and that in Rh2NO is slightly smaller (1.86 Å) in comparison to the corresponding neutral cluster. On the other hand, 1.18 and 1.24 Å are the N–O bond distances in the case of cationic and anionic Rh2NO. M. H. Lin and his co-workers71 reported the Rh–N and N–O bond separations and NO adsorption energy in Rh2NO to be 1.89 and 1.17 Å and 3.41 eV, respectively. The Rh–Rh bond length is 2.57 Å in the case of Rh2NO while the same distance is noticed to be smaller (2.52 Å) in cationic and larger (2.68 Å) in anionic Rh2NO. Atop geometries (Fig. 1) are found to be the lowest energy state for the neutral (M = 1) and


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Paper Table 1

NJC Bond length, adsorption energy and stretching frequency values of neutral RhnNO (n = 2–8) clusters

Adduct

Rh–Rh average bond length (Å)

Rh–N bond length (Å)

N–O bond length (Å)

N–O frequency (cm 1)

Adsorption energy at the BLYP level (eV)

Adsorption energy with multiplicities in bracket at the B3LYP level (eV)

RhNO Rh2NO Rh3NO Rh4NO Rh5NO Rh6NO Rh7NO Rh8NO

— 2.57 2.49 2.62 2.54 2.49 2.52 2.47

1.75 1.88 1.81 1.92 1.82 1.82 1.77 1.80

1.18 1.21 1.18 1.23 1.19 1.19 1.19 1.19

1704 1550 1663 1431 1640 1647 1688 1803

3.17 2.96 2.41 2.11 2.15 2.08 2.81 2.09

3.11 2.67 2.32 2.41 2.16 2.52 2.31

Table 2

(2) (1) (2) (1) (4) (7) (10)

Bond length, adsorption energy and stretching frequency values of cationic RhnNO (n = 2–8) complexes

Adduct





Adsorption energy (eV)

Rh1+–NO Rh2+–NO Rh3+–NO Rh4+–NO Rh5+–NO Rh6+–NO Rh7+–NO Rh8+–NO

— 2.52 2.49 2.66 2.57 2.49 2.51 2.47

1.81 1.93 1.83 1.90 1.84 1.84 1.79 1.81

1.14 1.18 1.16 1.20 1.16 1.17 1.17 1.17

1941 1695 1792 1535 1765 2506 1781 1742

2.84 3.08 2.05 2.47 1.67 1.80 2.42 1.78

Table 3

Bond length, adsorption energy and stretching frequency values of anionic RhnNO (n = 2–8) clusters

Adduct Rh1 Rh2 Rh3 Rh4 Rh5 Rh6 Rh7 Rh8

–NO –NO –NO –NO –NO –NO –NO –NO





Adsorption energy (eV)

— 2.68 2.47 2.62 2.65 2.48 2.54 2.47

1.78 1.86 1.80 1.96 1.80 1.80 1.77 1.79

1.24 1.24 1.22 1.26 1.22 1.22 1.21 1.21

1400 1384 1504 1265 1539 2338 1594 1585

3.25 2.93 3.08 2.80 2.91 2.71 3.14 2.44

ionic (M = 2) Rh3NO clusters with C1 symmetry point group. The adsorption energy of NO on neutral, cationic and anionic Rh3 is observed to be 2.41, 2.05 and 3.08 eV, respectively. The Rh–N bond (1.813 Å) distance decreases and the N–O bond length (1.18 Å) increases in the case of Rh3NO in comparison to Rh2NO. DFT optimized cationic Rh3NO has the Rh–N and N–O distances of 1.83 and 1.162 Å, while anionic Rh3NO possesses the Rh–N and N–O distances of 1.80 Å and 1.22 Å. Comparable Rh–N (1.78 Å) and N–O (1.15 Å) distances and a slightly higher NO adsorption energy (2.59 eV) are reported by M. H. Lin et al.71 for a neutral Rh3NO cluster. Guirado-Lopez72 determined Rh–N bond length to be 1.89, 1.88 and 1.92 Å for neutral, cationic and anionic Rh3NO, whereas N–O distances for the corresponding clusters were 1.89, 1.88 and 1.92 Å, respectively. It is seen from Tables 1–3 that the calculated Rh–Rh bond distances in the neutral, cationic and anionic Rh3NO clusters are found to be slightly lower than those in the Rh2NO0/+/ clusters. The NO molecule prefers bridge type adsorption in the case of neutral and ionic Rh4NO clusters. The optimized geometries of neutral (doublet) and anionic (singlet) Rh4NO show a CS symmetry point group, while the

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cationic (singlet) cluster exhibits a C2V symmetry at the lowest energy states. The calculated NO adsorption energy values on neutral, cationic and anionic Rh4 are 2.11, 2.47 and 2.80 eV, respectively. The Rh–N bond distances in the neutral, cationic and anionic Rh4NO clusters are 1.92, 1.90 and 1.96 Å, while the N–O distances in the corresponding Rh4NO clusters are 1.23, 1.20 and 1.26 Å, respectively. These values are in good agreement with the corresponding values evaluated by GuiradoLopez.72 However, M. H. Lin et al.71 reported slightly lower Rh–N (1.84 Å) and N–O (1.20 Å) bond distances and a marginally higher NO adsorption energy (2.84 eV) in the case of Rh4NO. Atop adsorption mode of NO is found on the neutral (M = 1) and ionic (M = 2) Rh5NO clusters with the symmetric point group C1 in the ground state. The average Rh–Rh bond distances in the neutral, cationic and anionic Rh5NO clusters are found to be 2.62, 2.66 and 2.62 Å, respectively. 1.82, 1.84 and 1.80 Å and 1.19, 1.16 and 1.22 Å are the calculated Rh–N and N–O bond distances for the neutral, cationic and anionic Rh5NO clusters. The DFT evaluated NO adsorption energy on the neutral Rh5 cluster is found to be 2.16 eV. The adsorption energy of NO on cationic Rh5 is noticed to be lower (1.67 eV), while the anionic


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cluster has a higher adsorption energy in comparison to neutral Rh5. A comparable NO adsorption energy (2.28 eV) on neutral Rh5 along with slightly smaller Rh–N (1.79 Å) and N–O (1.16 Å) bond distances is obtained by M. H. Lin et al.71 Guirado-Lopez72 reported the Rh–N bond distances to be 2.00, 2.01, 1.99 Å and the N–O distances to be 1.22, 1.20, 1.23 Å for neutral, cationic and anionic Rh5NO clusters. Mono-coordinated NO adsorption mode on neutral (M = 2), cationic (M = 7) and anionic (M = 1) prismatic Rh6 clusters is found to be the lowest energy state with C1 symmetry. The NO adsorption energy in neutral Rh6 is calculated to be 2.08 eV, while cationic and anionic Rh6 have 1.80 and 2.71 eV, respectively. The DFT evaluated Rh–N bond distances for the neutral, cationic and anionic Rh6NO clusters are noticed to be 1.82, 1.84 and 1.80 Å, whereas the N–O bond lengths in the corresponding clusters are 1.19, 1.17 and 1.22 Å, respectively. The average Rh–Rh bond lengths in the case of neutral and ionic Rh6NO clusters are calculated to be in the range of 2.48–2.49 Å. Atop adsorption of NO molecules on neutral (M = 9, C2V), cationic (M = 8, C1) and anionic (M = 2, CS) Rh7 clusters is found to be the lowest energy states. The ground state geometry of neutral, cationic and anionic Rh7NO has the Rh–N bond distances of 1.779, 1.794 and 1.775 Å, respectively, while 1.192, 1.171 and 1.214 Å are the N–O bond lengths in the case of neutral, cationic and anionic Rh7NO. The adsorption of NO molecules on the neutral, cationic and anionic Rh7 clusters is found to be exothermic by 2.80, 2.42 and 3.14 eV, respectively. Both cubic and bi-capped octahedral geometries are found to possess a comparable relative energy in the case of Rh8NO having a relative energy difference of 0.007 eV. Harding et al.73 and Mackenzie et al.74 observed a bi-capped octahedral structure to be stable for cationic Rh8 and N2O adsorbed Rh8 clusters. Relative energies of these two isomers of Rh8NO are also comparable at the hybrid B3LYP/DNP level with a relative energy difference of 0.002 eV. In this work, two different geometries are taken to study some of the geometrical properties. Monocoordinated NO adsorption mode on the neutral (M = 10, C1), cationic (M = 7, C3v) and anionic (M = 3, C3v) cubic Rh8 clusters is observed to be the lowest energy state. Moderately lower NO adsorption energy values are obtained in the case of the neutral (2.09 eV), cationic (1.78 eV) and anionic (2.44 eV) Rh8 clusters in comparison to neutral and ionic Rh8. The N–O bond distances in neutral, cationic and anionic Rh8NO are calculated to be 1.19, 1.17 and 1.21 Å, respectively. The mono coordinated NO geometry is also noticed for the bi-capped octahedral structure of Rh8 with adsorption energies of 2.09 eV for the neutral (M = 12), 1.80 eV for the cationic (M = 9) and 2.39 eV (M = 5) for the anionic systems. Neutral Rh8–NO has the same adsorption energies for both types of geometries. Cationic Rh8–NO possesses a higher adsorption energy for the bi-capped octahedral system than for the cubic one, whereas the anionic structure of the bi-capped octahedral system possesses a lower adsorption energy than the cubic Rh8–NO system. The N–O bond distances in neutral, cationic and anionic Rh8NO are calculated to be 1.19, 1.18 and 1.20 Å, respectively for the bi-capped octahedral system. As the two geometries of Rh8–NO possesses comparable relative energies and almost the

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Fig. 2

DFT optimized Rh–N bond length in RhnNO (n = 2–8) clusters.

Fig. 3

DFT optimized N–O bond length in RhnNO (n = 2–8) clusters.

same adsorption energies (for neutral system), only the cubic arrangement is taken by us to study the different binding properties. Further, all the NO adsorbing rhodium clusters are optimized at the hybrid B3LYP/DNP level. The same types of geometries are noticed for both B3LYP/DNP and BLYP/DNP levels. All energy values with multiplicities are mentioned in Table 1. The variation of the Rh–N and N–O bond distances of neutral and ionic RhnNO clusters is shown in Fig. 2. Fig. 2 reveals smaller Rh–N bond lengths in anionic RhnNO in comparison to the neutral and cationic clusters (except for Rh4NO), while anionic RhnNO clusters have slightly larger N–O distances. Smaller Rh–N and bigger N–O bond distances are observed because of the synergic bond formation due to the back donation of electrons from the filled d-orbitals of rhodium to the vacant p* orbital of NO (Fig. 3). Therefore, higher adsorption energies of NO on anionic Rhn (n = 2–8) are observed because of the increased metal - NO back-donation (Fig. 4). This result is very much similar to the result from our recently published work on CO adsorption on neutral and ionic Rhn (n = 2–8), in which case also the anionic cluster adsorbs CO more strongly than others.75 Vibrational frequency analysis IR spectroscopy has been widely used to study the mode of vibration of free and adsorbed NO molecules. DFT evaluated vibrational frequencies have been found to be very helpful in understanding the experimentally evaluated corresponding data. The IR stretching frequencies of the N–O molecule adsorbed on the neutral, cationic and anionic rhodium clusters


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Fig. 4 DFT evaluated adsorption energy of NO on Rhn (n = 2–8) clusters.

Fig. 5

DFT optimized Rh–Rh bond length in RhnNO (n = 2–8) clusters.

are shown in Tables 1, 2 and 3, respectively and their graphical representation is presented in Fig. 6. Anionic RhnNO clusters show smaller N–O stretching frequencies in comparison to the neutral and cationic clusters except for Rh6NO. In general, a higher stretching frequency corresponds to a stronger chemical bond. In the case of RhnNO clusters, more electrons are transferred from the metal d-orbitals to the antibonding p* orbitals of the NO molecule suggesting a stronger Rh–NO bond and hence weakening of the N–O bond which leads to a decreased N–O stretching frequency. In the cationic clusters (RhnNO+), the N–O stretching frequency is found to be

Fig. 7 Electron density distribution of NO adsorbing Rhn (n = 2–8) clusters.

higher due to the low possibility of back donation. The bridge type NO adsorbing cluster has a lower N–O stretching frequency than the atop adsorbed NO. The N–O stretching frequency trend is found to be similar in the case of neutral and ionic Rh2NO, Rh3NO, Rh4NO and Rh5NO clusters. For the ionic cluster, the NO frequency trends are similar from Rh6 to Rh8 whereas the trend is different for the neutral cluster i.e. a sudden increase in the frequency of the NO–Rh6 complex is not observed in the neutral one. The stretching frequencies of N–O in the case of Rh2NO, Rh3NO, Rh4NO and Rh5NO are reported to be 1747, 1889, 1553 and 1820 cm 1, respectively by M. H. Lin et al.71 Electron density analysis

Fig. 6 DFT evaluated stretching frequencies of the N–O bond in RhnNO (n = 2–8).

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The deformed electron densities of the stable RhnNO (n = 2–8) clusters evaluated using DFT method are presented in Fig. 7. Highly deformed electron density along a bond reveals a stronger ionic character. The iso-surface diagram of electron density (Fig. 8) is seen to be more deformed along the Rh–N bonds in the anionic RhnNO clusters which makes the Rh–N bond stronger in comparison to the RhnNO+ clusters. Highly deformed electron densities are observed along the Rh–Rh and


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Fig. 9 LUMO isosurface diagrams of the neutral and ionic RhnNO (n = 2–8) clusters.

Fig. 8 HOMO isosurface diagrams of the neutral and ionic RhnNO (n = 2–8) clusters.

Rh–N bonds in the case of Rh7NO and Rh8NO compared to their neutral and cationic clusters i.e. the delocalized electrons are uniformly deformed along the Rh–Rh and Rh–N bonds. However, the electron density in most of the RhnNO+ clusters is found to be deformed on the metal atoms rather than along the bonds, while in the case of RhnNO , uniform deformation of electron density is noticed on the metal as well as along the Rh–N and Rh–Rh bonds that strengthens the Rh–N bonds and weakens the N–O bonds. Molecular orbital analysis The HOMO and LUMO iso-surface diagrams of the RhnNO0/ clusters are given in Fig. 8 and 9, respectively. It is observed from Fig. 8 and 9 that in most of the RhnNO adducts, the Rh–Rh bonds are formed by the overlapping of the d-orbitals whereas the p-electrons are involved in N–O bond formation. It is also noticed that the electrons are delocalized from the d-orbitals of the rhodium atom (HOMO) to the p* orbital of NO (LUMO). In some of the RhnNO clusters, a strong overlapping is noticed in between the orbitals of Rh and NO, but sidewise overlapping is observed among the d orbitals of the rhodium atoms in Rhn.

Overlapping between the dz2 orbital of rhodium and the p orbital of NO is noticed in the case of the LUMO of Rh3NO and Rh5NO. For many RhnNO complexes bond formation overlapping among bare Rhn clusters occurs mainly with the dz2 and dyz/zx orbitals of Rh. A strong overlapping is noticed among dz2 orbitals of Rh–Rh bonds in the case of HOMO isosurface of Rh2NO+ and LUMO isosurface of Rh7NO . Density of states The DFT evaluated partial density of states (DOS) of the neutral and ionic RhnNO clusters is given in Fig. 10. It is seen from Fig. 10 that the width of the d-electron band near the bonding region i.e., below the Fermi level is found to be higher which suggests that the d-electrons are more involved in the bonding rather than the s- and p-electrons while, in the antibonding region, the p-electron density is higher. However, mixing of d-electrons with s- and p-electrons is also noticed in the bonding region. Electron transfer from the d-orbitals to p-orbitals of the metal-NO adducts is noticed. The width of the d-electron density increases from smaller to larger clusters. In some of the larger clusters, the width of the d electron density is also observed to be in the antibonding region along with the s- and p-electron density. ¨lliken charge analysis Mu ¨lliken population Charge transfer values calculated based on the Mu analysis of NO adsorbing rhodium clusters are listed in Table 4.


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Fig. 10 DFT derived DOS diagrams of NO adsorbing Rhn (n = 2–8) clusters.

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Table 4 Mu ¨ lliken charge distribution (Q) on the N and O atoms and on the Rh atom connected to NO in the case of neutral and ionic RhnNO

Complex Rh2NO Rh2NO+ Rh2NO Rh3NO Rh3NO+ Rh3NO Rh4NO Rh4NO+ Rh4NO Rh5NO Rh5NO+ Rh5NO Rh6NO Rh6NO+ Rh6NO Rh7NO Rh7NO+ Rh7NO Rh8NO Rh8NO+ Rh8NO

QRh/e 0.172 0.551 0.234 0.179 0.326 0.052 0.193 0.378 0.018 0.170 0.232 0.110 0.170 0.232 0.131 0.048 0.104 0.010 0.164 0.188 0.146

QN/e 0.161 0.099 0.199 0.058 0.037 0.157 0.151 0.119 0.190 0.086 0.006 0.149 0.087 0.012 0.152 0.090 0.035 0.139 0.093 0.044 0.136

QO/e 0.184 0.003 0.333 0.122 0.022 0.270 0.219 0.099 0.344 0.142 0.010 0.263 0.143 0.025 0.257 0.141 0.033 0.243 0.141 0.048 0.234

The higher the charge transfer between the atoms in a molecule, the higher the ionic character of a bond. Due to the electronic charge redistribution between the rhodium atoms and the NO molecule in RhnNO, there is a decrease in the Rh–N (stronger) bond distances and an increase in the N–O (weaker) bond separations. Basically the N–O bond distance increases in RhnNO due to the p back donation of electrons from rhodium to NO. Higher charge transfer is noticed in the case of RhnNO clusters in comparison to neutral and cationic clusters. For example, charge transfer values of QN/e and QO/e of NO are seen to be higher in the case of anionic clusters with respect to their respective neutral and cationic ones. Higher charge transfer suggests that electronic charge distribution occurs from Rh to NO. Again, in the RhnNO+ clusters, the NO adsorbing rhodium atom develops more positive charge which allows less charge transfer from the rhodium to the nitrogen atom. Therefore, more covalency is noticed in the Rh–N bond in cationic clusters than in neutral and anionic clusters, whereas the larger charge transfer of electrons from Rh to NO strengthens the Rh–N bond in anionic clusters. Catalytic activity of neutral and ionic Rh4, Rh5, Rh6, Rh7 and Rh8 clusters The mechanism for the conversion of NO to NO2 catalyzed by neutral and ionic Rh4, Rh5, Rh6, Rh7 and Rh8 clusters is also investigated in the present study. For this purpose stable neutral and ionic RhnNO clusters are chosen. In the present study an O2 molecule is allowed to adsorb on the Rh atom in the vicinity of a NO molecule to study the mechanism of NO oxidation. The reaction scheme is Rha–NO1 + RhbO2* = Rha–NO1O* + RhbO*. The transition state corresponding to the O–O bond dissociation of the oxygen molecule catalyzed by rhodium clusters

involves the breaking of the O–O bond and subsequent transfer of the oxygen atom to the nearby NO molecule attached to rhodium (Fig. 11). The energy barrier (relative energy) for O–O bond dissociation is given in Fig. 11. Only one imaginary frequency is obtained for each transition state which corresponds to the movement of the oxygen atom to the nearby N atom of NO. The product NO2 is formed after complete rupture of the O–O bond and shifting of one oxygen atom to the adjacent NO molecule. Some of the selected geometrical parameters of the DFT evaluated transition states are given in Table 5. It is noticed from Table 5 that Rh–N and N–O1 (O1 is that oxygen atom which is connected with N before the reaction) bond lengths are evaluated to be higher at the transition state in comparison to reactants (reactant bond lengths are mentioned in Tables 1–3). When one oxygen atom of O2 dissociates and forms a bond with NO there is a change in the hybridization of the original NO molecule. The change in hybridization of NO on interaction with the oxygen atom of O2 reinforces the formation of NO2. The activation barrier for the formation of NO2 from NO catalyzed by Rh4 is calculated to be 0.39 eV, while the activation free energies for the same reaction catalyzed by cationic and anionic Rh4 clusters are 0.49 and 0.33 eV, respectively. In all cases product NO2 and the oxygen atom formed from the oxygen molecule are found to be adsorbed on the rhodium atoms as shown in Fig. 11. The formation of NO2 from NO catalyzed by small rhodium clusters is seen to be exothermic. The dissociated oxygen atom in the product is seen to be bridge coordinated with two rhodium atoms of the small rhodium cluster except for cationic Rh5 (Fig. 5). The activation free energies for the said reaction catalyzed by neutral, cationic and anionic Rh5 clusters are 0.47, 0.55 and 0.41 eV, respectively. One of the oxygen atoms is observed to be linked with two rhodium atoms for neutral and anionic Rh5 while for Rh5+, the oxygen atom is singly coordinated in the product. The activation free energy barrier for the neutral Rh6 catalyzed reaction is 0.38 eV, whereas for cationic and anionic Rh6, the activation energy barrier values are 0.48 and 0.35 eV, respectively. In the product, the oxygen atom is bridge coordinated to two Rh atoms for all neutral and ionic clusters of Rh6. This reaction by Rh6 is exothermic for neutral and ionic clusters. The activation energies of the reaction calculated at the BLYP/DNP level on neutral, cationic and anionic Rh7 clusters are 0.52, 0.48, and 0.41 eV, respectively. In this case, the cationic Rh7 cluster is noticed to be a better catalyst than neutral and anionic Rh7. The activation energy for anionic Rh8 is calculated to be 0.46 eV which is lower than those for the neutral and cationic clusters. NO to NO2 conversion catalyzed by anionic Rh4, Rh5, Rh6, and Rh8 clusters shows a lower activation free energy barrier in comparison to the corresponding neutral and cationic clusters. In contrast, only cationic Rh7 is evaluated to be more favorable than neutral and anionic Rh7 nanoparticles. This is explained on the basis that the NO hybridization is changed to a greater extent for the cationic cluster compared with the neutral and anionic ones, which enhances the acceptance of another oxygen atom by NO.


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Fig. 11 DFT evaluated transition state picture of neutral and ionic Rhn (n = 4–8) clusters for the conversion of NO to NO2.

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Table 5 Calculated Rh–N and N–O1 bond lengths at the transition states for the conversion of NO to NO2

Transition states Clusters


N–O1 bond length (Å)

Rh4 Rh4+ Rh4 Rh5 Rh5+ Rh5 Rh6 Rh6+ Rh6 Rh7 Rh7+ Rh7 Rh8 Rh8+ Rh8

1.97 1.97 1.99 1.90 1.84 2.00 1.82 1.83 1.84 1.80 2.01 1.80 1.91 1.90 1.89

1.23 1.22 1.23 1.21 1.19 1.22 1.20 1.19 1.24 1.21 1.22 1.23 1.20 1.98 1.22

Conclusions We have systematically investigated the structure, bonding and reactivity of neutral and ionic NO adsorbing Rhn (n = 2–8) clusters with different multiplicities. These studies reveal that the anionic RhnNO clusters are more stable than their corresponding neutral and cationic clusters with shorter Rh–N and longer N–O bond lengths. Deformed electron density and ¨lliken charge analysis suggest higher electronic delocalizaMu tion along the Rh–N bond in the anionic clusters in comparison to the neutral and cationic clusters which leads to an increase in the ionic character of the bond. The partial double bond character of Rh–N bonds in the case of anionic clusters weakens the N–O bond. DOS shows that the d-electrons are found to be more involved in bonding rather than the s- and p-electrons of Rh atoms in the case of rhodium clusters. Iso-surface diagrams (HOMO and LUMO) reveal that electrons are transferred from the d-orbitals of rhodium (HOMO) to the p* orbital of NO (LUMO). A sidewise overlapping is observed among dz2 and dyz/zx orbitals of rhodium atoms in the formation of rhodium nanoclusters. The studied reaction mechanism for the conversion of NO to NO2 suggests that anionic Rh4 and Rh6 as well as cationic Rh7+ are catalytically more active.

Conflicts of interest There are no conflicts to declare.

Acknowledgements The authors thank the Department of Science and Technology (DST), New Delhi, India, for financial support (SB/EMEQ-214/2013).

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