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Accepted Manuscript Structural, electronic and catalytic properties of single magnesium atom doped small neutral Rhn (n=2-8) clusters: Density functional study Abhijit Dutta, Paritosh Mondal PII: DOI: Reference:

S2210-271X(17)30322-5 http://dx.doi.org/10.1016/j.comptc.2017.07.003 COMPTC 2565

To appear in:

Computational & Theoretical Chemistry

Received Date: Revised Date: Accepted Date:

4 October 2016 16 June 2017 3 July 2017

Please cite this article as: A. Dutta, P. Mondal, Structural, electronic and catalytic properties of single magnesium atom doped small neutral Rhn (n=2-8) clusters: Density functional study, Computational & Theoretical Chemistry (2017), doi: http://dx.doi.org/10.1016/j.comptc.2017.07.003

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Structural, electronic and catalytic properties of single magnesium atom doped small neutral Rhn (n=2-8) clusters: Density functional study Abhijit Dutta, Paritosh Mondal* Department of Chemistry, Assam University, Silchar 788011, Assam, India *Corresponding author: Email: [email protected] Abstract Rhodium nano clusters exhibit unique electronic, magnetic and catalytic properties. Physical and chemical properties of rhodium cluster can be tuned by incorporating different metal and non metal atoms. In this study magnesium doped rhodium clusters are investigated to evaluate their structure, stability, electronic and magnetic properties using density functional theory (DFT). Stability function, fragmentation energy and LUMO-HOMO gap reveals that Rh5Mg, Rh6Mg and Rh8Mg clusters are more stable than the other magnesium doped rhodium clusters. Chemical reactivity of rhodium cluster increases on doping with magnesium atom. Deformation density, density of electronic state, force vector analysis suggest that electronic redistribution are occurred to attain the higher stability in Rh5Mg as well as in Rh8Mg. Negative electrostatic potential is generally generated on rhodium atoms opposite to magnesium atom while, electrons are transferred from magnesium to rhodium atoms in magnesium doped rhodium clusters. Calculated structural, electronic and orbital parameters suggest higher stability of Rh5Mg, Rh6Mg and Rh8Mg clusters. Magnesium doped rhodium clusters are found to be more reactive than pure rhodium clusters on the basis of evaluated Fukui function values. Rh5Mg cluster is seen to be better catalyst for the dissociation of CH3OH in comparison to pure Rh5. Activation of O−H bond is observed to be more favourable in comparison to methyl C−H bond in the dissociation of CH3OH. Key words: Rhodium, Magnesium, DFT, stability, force vector, CH3OH.

Introduction Exploration of diverse assets of atomic cluster has developed for both scientific as well as technological improvement in the society. Metal nano clusters enjoyed great attention due to their exceptional properties as weigh against individual atoms, molecules, or bulk solids [14]. These small clusters are extensively utilized in numerous applications such as electronics, magnetic, nanotechnology and heterogeneous catalysis [5–9]. To investigate the properties of metal clusters, it is very important to obtain the exact size and structure of these clusters. Comprehensive information regarding the electronic structure of atomic clusters is obligatory to realize the progression of their properties with size towards the macroscopic scale. This feature is usually significant for systems where novel non-bulk like properties come into existence at the nano-scale [10]. Multiple ionization energies [11] or rate of reactions [12, 13] exhibited by the particular isomer of metal clusters has been featured by the existence of multiple isomeric clusters, each of which demonstrate distinct physicochemical properties. Among all the d block transition metal clusters, rhodium clusters are found to be the most important as they are used as heterogeneous catalyst for reduction of NO, oxidation of CO and unburned hydrocarbons, which are toxic pollutants to environment [14]. Another fascinating characteristic exhibited by the rhodium clusters is its magnetism. Rhodium clusters possess super paramagnetic properties at very low temperature and their magnetic moment per atom is found to be 0.35–1.06 µ [15]. Most of the recent investigations related to rhodium clusters are motivated by the theoretical studies of Galicia [16] and Reddy et al. [17] and experimental works of Cox et al. [18, 19]. Large number of experimental as well as theoretical studies has been performed to understand the stability, structural and catalytic properties of rhodium based binary clusters [20-22]. These binary clusters are observed to be exhibited by improved electronic, magnetic, and catalytic properties. Higher catalytic activity for the hydrogenation CO is shown by the presence of a second metal atom such as Mn or W to rhodium clusters in comparison to pure rhodium clusters [21]. Ghatak et. al. [23] observed that Rh4Ru2 cluster has been found to be better catalyst for the activation of methanol over Rh6. It is also noticed that methanol activation is leading to the dissociation of O−H bond rather than C−H bond. Similar trend of higher catalytic activity is also observed in the partial hydrogenation of 1, 3-cyclooctadiene by Pd-doped rhodium clusters [24]. Additionally, reactivity of these bimetallic clusters strappingly depends on the Rh/Pd ratio and found to be maximum at Rh/Pd ratio equal to 2. Very few theoretical investigations are known in regard to the determination of equilibrium geometries, stabilities,

electronic and magnetic properties of other element including transition metal doped rhodium clusters [25–28]. Electronic and magnetic properties of small Mn-doped rhodium clusters are studied by Srivastava et al. [25] which suggests that Rh2Mn2 cluster is more stable than its neighbouring clusters. It is also pointed out that electronic and magnetic properties of these bimetallic clusters are largely controlled by Rh/Mn ratio. Mokkath et al. [26] studied the electronic and magnetic properties of small FenRhm (n+m≤8) clusters and observed that dorbitals play a significant role in determining the magnetism of the most stable FenRhm clusters. Structures and magnetic properties of RhnCom (n+m≤4) clusters are also scrutinized by Dennler et al. [27] and they observed that Co doped Rhn clusters have higher local magnetic moment. Yang et al. [29] theoretically investigated the stability and electronic properties of AunRh (n=1–8) clusters and observed that the ground state geometries of AunRh clusters favour a planar geometry and Au5Rh has been found to be the magic cluster. Soltani et al. [30] performed DFT studies on electronic and magnetic properties of Ca doped Rh clusters and found that ground state structure of RhnCa always favours three dimensional geometries. Magnetic moment solely depends on rhodium atoms. Doped calcium atom hardly has any effect to the total magnetic moment of RhnCa. Therefore, it is very important to study the variation of structural, electronic and magnetic properties of pure rhodium clusters on incorporation of a single atom of other transition metals, as well as alkali and alkaline earth metals. Free magnesium atom is very reactive. Alloy of magnesium with certain 3d transition metals such as Fe, Ni, Cu and Co are corrosion resistant [31]. Structures and electronic properties of Mgn (n = 2–22) clusters are investigated by Jellinek and Acioli using DFT [32]. Mg4 and Mg10 are obtained to be the magic clusters based on the study of structure and bonding nature of Mgn (n = 2–13) clusters using local density approximation (LDA) method by Kumar and Car [33]. Kyasu et al. [34] also performed anion photo electronic study on AunMg- (n=2-7) clusters. Theoretical investigation on structure and bonding of Au5Mg cluster was performed by Majumdar et al. [35] and predicted that the propertied of planar structure of Au5Mg is similar to that of Au6. Li et al. [36] explored methodically the properties of anionic AunMg (n= 1–8) clusters and observed the different geometrical structures of doped one in comparison to pure Aun. Zhang et al. [37] studied the structural properties of MgnNim(n+m≤5) clusters and mentioned that the incorporation of Ni atoms considerably alter the structure and symmetries of magnesium clusters. Higher stability of MgnNim clusters are observed when large numbers of Ni atoms are incorporated. Jing et al. [38] investigated the

geometries of Mg nNi2 (n=1-6) and revealed higher binding energies with higher values of n while energy gap of these clusters follow a declining tendency. They also reported the odd– even oscillation of ionization energies of these binary clusters. Rhodium nano clusters are very important because of their unique catalytic as well as magnetic and electronic properties than their bulk counterparts. In this study we basically emphasized on the changes in the structural, electronic and magnetic properties of magnesium atom doped rhodium clusters and also investigated their catalytic activity towards methanol activation. To the best of our knowledge, no theoretical investigations on Mg doped Rh clusters are known. Therefore, a systematic investigation is necessary to evaluate the electronic, magnetic properties and stability as well as catalytic behaviour of magnesium doped small rhodium clusters. Magnesium atom is incorporated into the stable geometry of neutral pure rhodium clusters. DFT method is utilised to obtain the geometrical, electronic, orbital and magnetic properties as well as density of states (DOS) of magnesium doped rhodium binary clusters. Computational details To study the structural and electronic properties of magnesium doped rhodium clusters, ground state geometries of neutral Rhn (n=2–8) clusters are taken from our recent publication [39]. Stable geometries of rhodium clusters are considered as low-lying isomers for doping of Mg at various possible coordination sites, including atop, bridge, and tri coordinate etc. Mg doped rhodium clusters are optimized without imposing any symmetry constraints. All calculations were performed by DFT method using DMOL3 package [40, 41]. DFT calculations are performed under generalized gradient approximation (GGA) with BLYP exchange correlation functional [42, 43] which incorporates exchange functional of Becke’s with the gradient corrected functional of Lee–Yang–Parr. DNP [44] basis set is chosen for geometry optimization. DNP basis set is equivalent to Gaussian split-valence 6-31G** basis set. Incorporation of relativistic effect is very important for heavy metals like rhodium atom. Hence, all electron relativistic correction to valence orbitals via a local pseudo potential are included for direct inversion in a subspace method (DIIS). Self consistent field (SCF) procedures are utilised with a 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 electron density are the boundary conditions. Symmetry restricted calculations are performed at higher spin multiplicities in order to compare energy values with the ground state geometries. Magnesium doped even atom rhodium clusters are optimized with

multiplicities (M= 1, 3, 5 and 7) while odd atom rhodium clusters are optimized with multiplicities (M= 2, 4, 6, and 8) to evaluate stable geometrical isomers. Frequencies are calculated at the same level of theory to confirm whether the geometries are the local minima (no imaginary frequencies) or transition states (only one imaginary frequency). Results and discussion Structures and energetics of RhnMg (n=2-8) clusters DFT optimized geometries of RhnMg (n=2-8) clusters are shown in Fig. 1 and their corresponding spin multiplicities (M), symmetries, bond lengths and binding energies per atom are reported in Table 1. Magnesium atom is doped at different location to obtain the stable ground state isomer of magnesium doped rhodium clusters. All the stable isomer of RhnMg (n=2-8) clusters possesses three dimensional configurations with Mg atom at the surface.

2a

2b

3a

3b

3c

4a

4b

4c

5a

5b

5c

5d

5e

5f

6a

6b

6c

6d

6e

7a

7b

7c

7d

7e

7f

7g

8a

8b

8c

8d

Fig 1. DFT optimized stable ground state structure of RhnMg cluster (n=2-8). Linear geometrical structure is observed for magnesium doped rhodium (RhMg) cluster with binding energy of 0.74 eV/atom. Rh−Mg bond length is 2.388 Å which is found to be in between Rh2 (1.5067 Å) and Mg2 (3.890 Å) bond distances with point group symmetry C∞v. Singlet state having isosceles triangular structure (2a) with symmetry point group C2v and 1B1 electronic state is found to be the ground state for Rh2Mg cluster. DFT evaluated binding energy of Rh2Mg is 1.46 eV/atom. Average Rh−Rh and Rh−Mg bond distances of Rh2Mg clusters are calculated to be 2.459 and 2.486 Å, respectively. Another isomer of Rh2Mg (2b) is mono caped magnesium with linear geometry having symmetry point group C∞v and singlet multiplicity. This isomer possesses 0.004 eV more energy than the lowest energy isomer. Triangular rhodium with bi-coordinated caped atomic magnesium (3a) for Rh3Mg cluster is evaluated to be a stable ground state structure with C3v symmetry point group in the doublet multiplicity. Average Rh−Rh and Rh−Mg bond lengths are found to be 2.535 and 2.536 Å, respectively. Electronic state of lowest energy neutral Rh3Mg cluster is 2 A2. Binding energy of the lowest energy Rh3Mg cluster is 1.96eV/atom. Isomer 3b, a triangular pyramidal geometry of Rh3Mg cluster with C3V point group and doublet multiplicity possesses slightly higher energy (0.07 eV) than the lowest energy structure. Another structure (3c) of Rh3Mg cluster with Cs symmetry having doublet multiplicity bears 0.094 eV more energy in comparison to the ground state. Binary Rh4Mg cluster attains trigonal bipyramidal geometry (4a) in the ground state with singlet multiplicity and C3v point group symmetry. Binding energy per atom and electronic state observed to be 2.25eV/atom and 1 A2, respectively. Average Rh−Rh and Rh−Mg bond distances are calculated to be 2.539 and 2.672 Å. The other isomers 4b and 4c contain 0.001

and 0.07 eV higher energy than the lowest energy structure 4a (ground state). 4b isomer is bicoordinated Mg caped tetrahedral geometry having singlet multiplicity with Cs point group and 4c isomer is mono caped magnesium with tetrahedral geometry having point group C1 in the singlet state. Table 1. DFT evaluated spin multiplicity, binding energy, average bond lengths and symmetry values of stable RhnMg (n=2-8) clusters. Clusters

Multiplicity

Rh2Mg Rh3Mg Rh4Mg Rh5Mg Rh6Mg Rh7Mg Rh8Mg

Singlet Doublet Singlet Quartet Singlet Doublet Singlet

Binding energy per atom (Eb/atom) 1.46 1.96 2.25 2.49 2.66 2.74 2.89

Rh-Rh bond length Å 2.459 2.535 2.539 2.572 2.517 2.585 2.489

Rh-Mg bond length Å 2.486 2.536 2.672 2.640 2.704 2.614 2.767

Symmetry

C2v C3v C3v C4v C2v Cs C4v

Square pyramidal Rh5 cluster becomes octahedral (5a) on doping with Mg atom is the lowest energy state in the quartet multiplicity. The electronic state and symmetry point group of the ground state of Rh5Mg is found to be 4B1 and C4v, respectively. Binding energy of the most stable Rh5Mg cluster is calculated to be 2.49 eV/atom. Average Rh−Rh and Rh−Mg bond distances are measured to be 2.572 and 2.640 Å, respectively. The next stable isomer, 5b (bi caped magnesium) have 0.006 eV energy higher than the ground state isomer with Cs point group and doublet multiplicity. Square pyramid with mono caped magnesium geometry 5c with quartet multiplicity and C s symmetry is found to have 0.35 eV higher in energy than the stable 5a cluster. Tri coordinated Mg doped Rh5 isomer (5d) having point group Cs and doublet multiplicity with energy 0.357 eV higher than stable isomer. Bi-coordinated Mg atom with square plane of rhodium 5e have symmetry point group C4v and doublet multiplicity with energy 0.359 eV higher than the 5a. 5f (doublet multiplicity) isomer with C1 point group and having structure mono coordinated caped magnesium at square plane of rhodium possesses energy 0.367 eV higher than the stable isomer 5a. Bridge type coordination of magnesium in vertical plane of prismatic rhodium (Rh6) cluster to form Rh6Mg (6a) is noticed to be the ground state having singlet multiplicity and C 2v symmetry. The electronic state and binding energy of the most stable structures are calculated to be 1B1 and 2.66 eV/atom, respectively. Average Rh−Rh and Rh−Mg bond lengths evaluated at BLYP/DNP level are 2.517 and 2.704 Å, respectively. Another isomer (6b)

having structure bi-coordinated magnesium doped with two edge of prismatic Rh6 with symmetric point group C2v and singlet multiplicity is found to be less stable by 0.002 eV than 6a. The next stable isomer 6c with symmetry C2v and triplet multiplicity is 0.008 eV higher in energy than ground state. Tetra coordinated magnesium with square plane of rhodium of Rh6Mg cluster (6d) with singlet multiplicity and C2v symmetry is having 0.016 eV higher in energy than ground state. While, tetrahedral capped prismatic structure of Rh6Mg (6e) with singlet multiplicity and C3v symmetry is identified to possesses 0.059 eV higher in energy than the ground state (6a). The most stable structure of Rh7Mg cluster (7a) is mono coordinated magnesium doped caped prism Rh7 with Cs symmetry and doublet multiplicity. Electronic state and binding energy of the ground state geometry are seen to be 2 A// and 2.7454 eV/atom, respectively. The geometrical parameters such as average Rh−Rh and Rh−Mg bond distances are evaluated to be 2.585 and 2.614 Å, respectively. Next stable isomer 7b with doublet multiplicity and Cs point group which is energetically higher than that of the stable isomer by 0.069 eV. Another isomer 7c with tetra coordinated magnesium capped with Rh7 cluster having point group Cs and quartet multiplicity is less stable by 0.125 eV from ground state geometry. Isomer 7d is bi coordinated magnesium to the upper vertical side of capped trigonal prismatic geometry with doublet multiplicity and Cs point group symmetry has 0.127eV higher energy than the most stable isomer. Again, mono coordinated magnesium to capped trigonal prismatic geometry (7e) with C1 symmetry at doublet multiplicity possesses almost similar stability with 7d. Next stable isomer 7f is tri coordinated caped magnesium with prismatic Rh7 cluster having doublet multiplicity and C1 point group with energy 0.299 eV higher than ground state stable Rh7Mg isomer. Isomer 7g having C s point group symmetry with doublet multiplicity is found to be less stable than 7a isomer by energy 0.341 eV. The lowest energy structure of Rh8Mg cluster is found to be tetra coordinated magnesium capped cubic geometry (8a) with singlet multiplicity and C4v symmetry. Binding energy and electronic state of the stable structure is obtained to be 2.89 eV/atom and 1B1, respectively. DFT evaluated average Rh−Rh and Rh−Mg bond distances are 2.489 and 2.767 Å, respectively. Next stable isomer 8b with tri coordinated magnesium capped cubic structure having point group C4v and singlet multiplicity is less favourable than isomer 8a by 0.006 eV. Bi coordinated magnesium capped with cubic isomer 8c having singlet multiplicity and C4v symmetry possesses total energy 0.01 eV higher than to 8a. Isomer 8d with singlet multiplicity and Cs point group is less stable than the stable ground state of Rh8Mg (8a) by

0.012 eV. Magnesium doped Rhn clusters (n=2, 3, 4, 5, 6, 8) are three dimensional higher symmetric structures having vertical plane of symmetry. Rh7Mg cluster possesses lower symmetry with no vertical plane of symmetry. Stability of RhnMg (n=2-8) cluster Relative stabilities of the lowest energy structure of RhnMg (n=2–8) clusters are evaluated on the basis of the following mathematical expressions such as binding energies per atom (Eb), the second order difference of energies (Δ2E), and fragmentation energies (Δ E f).

Eb( RhnMg )  [nE ( Rh)  E (Mg )  E ( RhnMg )] /(n  1) 2 E ( RhnMg )  E ( Rhn  1Mg )  E ( Rhn  1Mg )  2E( RhnMg ) Ef ( RhnMg )  E( Rhn  1Mg )  E( Rh)  E( RhnMg )

Where E(Rh) and E(Mg) represent the energies of the rhodium and magnesium atom while, E(RhnMg), E(Rhn+1Mg), and E(Rhn-1Mg) are the total energies of the ground state geometry of RhnMg, Rhn+1Mg, and Rhn-1Mg clusters, respectively. Table 2. stability function, fragmentation energy and HOMO-LUMO gap values of DFT optimized stable RhnMg (n=2-8) clusters. Cluster

Stability Function (eV)

Rh2Mg Rh3Mg Rh4Mg Rh5Mg Rh6Mg Rh7Mg Rh8Mg

-0.5199 0.0253 -0.3084 0.0993 0.2847 -0.7392

Fragmentation Energy (eV) 2.92 3.44 3.41 3.72 3.62 3.34 4.08

HOMO-LUMO gap (eV) 0.34 0.27 0.25 0.28 0.28 0.18 0.27

Variations of binding energies with cluster size for the most stable Rh nMg clusters are plotted in Fig. 2. It is seen from the Fig. 2 that the binding energies increase monotonically with the cluster size, which reveals that with the increase of the size of magnesium doped rhodium clusters binding energies are found to be increased. However, binding energy per atom of RhnMg clusters obtained in this study are lower than the pure rhodium clusters [38]. These findings reveal that the magnesium doped rhodium clusters are less chemically stable than the pure Rhn clusters. Therefore, chemical reactivity of RhnMg clusters is evaluated to be higher than the corresponding pure rhodium clusters.

Second order difference of energy (Δ2E), LUMO-HOMO gap and fragmentation energy (ΔEf) are important reactivity parameters to understand the stability and chemical reactivity of metal clusters. Variation of stability function, fragmentation energy and LUMO-HOMO gap of magnesium doped rhodium clusters with the cluster size are shown in Fig. 3, Fig. 4 and Fig. 5. It is seen from Fig. 3 that Rh5Mg and Rh6 Mg are comparatively more stable than their neighbouring clusters as these two clusters have highest value of stability function. Again, Fig. 4 reveals that Rh5Mg and Rh8 Mg clusters have higher values of fragmentation energy than the other magnesium doped rhodium clusters. Higher fragmentation energy signifies that these clusters are quite hard to fragment into smaller clusters or atoms. Larger LUMOHOMO gap of a chemical system represents higher kinetic stability and lower chemical reactivity. Fig. 5 shows that magnesium doped Rh2, Rh5 and Rh8 clusters possess higher value of LUMO-HOMO gap and hence, signifies the higher stability of these clusters. All the reactivity parameters mentioned above reveal that Rh5Mg, Rh6Mg and Rh8Mg are more stable than the other Mg doped rhodium clusters. Therefore, it may be concluded that among Rh5Mg, Rh6Mg and Rh8Mg clusters Rh5Mg is found to be somewhat more stable.

0.4 3.0

0.2

2.6

Stability Function (eV)

Binding energy/atom (eV)

2.8

2.4 2.2 2.0 1.8

0.0 -0.2 -0.4 -0.6

1.6

-0.8

1.4 Rh2Mg

Rh3Mg

Rh4Mg

Rh5Mg

Rh6Mg

Rh7Mg

Rh8Mg

Cluster

Fig 2.Binding energy/ atom of RhnMg cluster (n=2-8)

2

3

4

5

6

7

Number of Rh atom

Fig 3. Stability Function of RhnMg cluster (n=2-8)

4.2

0.36 0.34 0.32

HOMO-LUMO gap (eV)

Fragmentation Energy (eV)

4.0 3.8 3.6 3.4 3.2

0.30 0.28 0.26 0.24 0.22 0.20

3.0 0.18 2.8

0.16 2

3

4

5

6

7

8

2

3

Number of Rh atom

4

5

6

7

8

Number of Rh atom

Fig 4. Fragmentation energy of RhnMg cluster (n=2-8)

Fig 5. HOMO-LUMO gap of RhnMg cluster (n=2-8) 3.0

0.8 2.8

0.6

Dipolemoment (D)

Magneticmoment (µ)

0.7

0.5 0.4 0.3 0.2 0.1

2.6 2.4 2.2 2.0 1.8

0.0 2

3

4

5

6

7

8

Increase of rhodium atom

Fig 6. Magnetic moment per atom with cluster size

2

3

4

5

6

7

8

Increase of rhodium atom

Fig 7. Dipole moment of RhnMg cluster (n=2-8)

Electric dipole and magnetic moments Fig. 6 and Fig. 7 represent variation of magnetic and electric dipole moment values of RhnMg (n=2-8) clusters with cluster size and calculated values of magnetic and electric dipole moment are summarised in Table 3. It is noticed from Fig. 6 that magnetic moment per atom of magnesium doped rhodium clusters become zero for Rh4Mg, Rh6Mg and Rh8Mg while, Rh2Mg, Rh3Mg, Rh5Mg, Rh7Mg have non zero magnetic moment. Odd-even oscillation of magnetic moment is noticed in magnesium doped rhodium clusters. Magnesium doped odd atomic rhodium clusters possess non zero magnetic moment while, magnesium doped even atomic rhodium clusters have zero magnetic moment except for Rh2Mg. In the case of RhnMg clusters, magnetic moment mostly depends on the spin of d-electrons of rhodium atoms. For Mg doped odd atomic rhodium clusters, electronic spins of d-electrons are not

paired up completely while in even atomic rhodium clusters d-electrons spins are found to be paired up. Higher dipole moment values are observed in the Rh2Mg, Rh3Mg and Rh5 Mg clusters (Fig. 7). On the other hand, irregular variation of dipole moment values are also noticed in the RhnMg clusters. Dipole moment is developed in a chemical system due to the higher charge separation or higher electronic delocalization. Rh2Mg, Rh3Mg and Rh5Mg clusters possesses higher charge separation i.e. higher dipole moment. Table 3. Values of magnetic moment per atom and dipole moment of DFT optimized stable RhnMg (n=2-8) cluster Cluster Rh2Mg Rh3Mg Rh4Mg Rh5Mg Rh6Mg Rh7Mg Rh8Mg

Magnetic moment per atom (µ) 0.76 0.25 0.00 0.50 0.00 0.13 0.00

Dipole moment (Debye) 2.6202 2.8296 2.0743 2.3116 2.1326 1.7894 2.0566

Spin density, Mulliken charge analysis, deformation density and Fukui function analysis: DFT evaluated spin and deformation density diagrams are presented in Fig. 8 and Fig. 9. Fig. 8 reveals that Rh2Mg has only spin up electronic density which leads to the non zero magnetic moment. While, resultant spin density is calculated to be zero due to the neutralization of spin up and spin down density in the case of Rh4Mg and Rh8Mg clusters. However, total spin up density is not nullified by cancellation of spin up with spin down density in Rh3Mg and Rh5Mg clusters. Therefore, magnesium doped odd atomic rhodium clusters possess non zero magnetic moment where as Mg doped even atomic rhodium cluster except Rh2 have zero magnetic spin density. Mulliken charges evaluated based on Mulliken population analysis (MPA) of magnesium atoms as well as the rhodium atoms directly connected to magnesium are evaluated at BLY/DNP level and the values are listed in Table 4. Table 4 shows that Mulliken charge is found to be always transferred from magnesium atom to rhodium. That is rhodium atoms possess negative charges and magnesium atom possesses positive charges. Therefore, it can be mentioned that magnesium atom is electron donor and rhodium atoms are electron acceptor. Charge transfer is observed because of the large electronegativity differences between Rh (2.28) and Mg (1.31). Higher positive charge is seen on the magnesium atom in

the magnesium doped odd atomic rhodium clusters. That is more charge transfer is observed in the magnesium doped odd atomic rhodium clusters than the even atomic rhodium clusters. Iso-surface diagram of deformation electron density on RhnMg clusters are evaluated at BLYP/DNP level shown in Fig. 9. Rh3Mg, Rh5Mg and Rh7Mg clusters possess higher deformation density along both Rh−Rh and Rh−Mg bonds which suggests that the degrees of covalency decreases (ionic character increases) on these bonds. Therefore, it is observed that Rh−Mg bond distances are found to be smaller in the Rh5Mg and Rh7Mg. That is, electrons are more delocalised among rhodium and magnesium bonds. Higher deformed electron density suggests higher stability of the bonds and higher deformed density is seen in the Rh5Mg cluster. Whereas, in the magnesium doped even atomic rhodium clusters deformed electron density is noticed at the rhodium atoms only. Hence, even atomic rhodium clusters are found to be less stable. Table 4. Mulliken charge distribution (Q) between Mg atom and Rh atom directly connected with Mg in RhnMg clusters. Cluster Rh2Mg Rh3Mg Rh4Mg Rh5Mg Rh6Mg Rh7Mg Rh8Mg

Rh2Mg

QMg/e 0.422 0.532 0.269 0.461 0.343 0.369 0.378

Rh3Mg

Rh4Mg

QRh/e -0.211 -0.144 -0.056 -0.091 -0.061 -0.042 -0.085

Rh5Mg

Rh8Mg

Fig 8. Pictorial representation of spin density for DFT optimized RhnMg cluster. (Green colour= spin up and blue colour= spin down density)

Rh3Mg

Rh4Mg

Rh5Mg

Rh6Mg

Rh7Mg

Rh8Mg

Fig 9. Deformed electron density diagrams of DFT optimized Rh nMg cluster Fukui function analysis

 The local reactivity parameter, Fukui function, f (r ) [45], is defined as the first  derivative of electron density,  (r ) , with respect to the number of electrons at a constant  external potential,  (r ) .     (r )  f (r )    N  ( r )

Applying finite difference approximation, three types of condensed Fukui functions [46] are found from electronic population analyses.  f k (r )  qk ( N )  qk ( N  1) , electrophilic attack on the system

 f k (r )  qk ( N  1)  qk ( N ) ,

nucleophilic attack on the system

 f k0 (r )  qk ( N  1)  qk ( N  1)/ 2 ,

free radical attract on the system

DFT evaluated Fukui function values ( f  ) of the atoms of some of the pure Rh n and mixed metal Rhn-1Mg clusters summarized in Fig 10. It is noticed from Fig.10 that all the atoms of pure Rhn have almost uniform electron density ( f  value), while electron densities are not uniform at all the atoms of the mixed metal clusters. Fukui function

values ( f  ) of the rhodium atoms in pure rhodium clusters are found to be lower than the magnesium atom of Rh5Mg. These results show that magnesium atom of Rhn-1Mg cluster is more prone to nucleophilic attack in comparison to other rhodium atoms. It is also seen that ( f  ) values of atoms in pure cluster is smaller than the atoms of doped cluster.

Fig 10 Comparison of Fukui ( f  ) values of some pure rhodium and Mg doped rhodium clusters.

Electron density and electrostatic potential (contour) Electrostatic potential,V(r) developed in a molecule due to the nuclei and electrons, is used to interpret and predict molecular reactivity. The electrostatic potential V(r), is defined by the following mathematical equation [47]. V( r )  

ZA dr '    (r ' ) RA  r r'  r

ZA is the charge on nucleus located at RA and  (r) is the electronic density function of the molecule. Electrostatic potential, V(r) is a sum of a positive and negative contribution coming from the nuclei and electrons. Sign of the electrostatic potential is positive if major contribution comes from nuclei or negative if major contribution is from electrons. In this study, electrostatic potential of magnesium doped rhodium clusters are evaluated by quantum chemical method and their iso-surface diagrams are shown in Fig. 11. Fig. 11 represents the overall electron density (blue coloured region) and negative electrostatic potential (orange in colour) of magnesium doped rhodium clusters.

Rh2

Rh2Mg

Rh5

Rh3

Rh3Mg

Rh6

Rh4

Rh4Mg

Rh7

Rh5Mg

Rh7Mg

Rh6Mg

Fig 11. Pictorial representation of electron density and electrostatic potential (blue colourelectron density and orange colour- negative electrostatic potential) Uniform electron density is noticed around all rhodium and magnesium atom in the case of bare rhodium clusters whereas for doped clusters less uniformity is noticed. Negative electrostatic potential is generated opposite to magnesium atom at the RhnMg clusters. Dumbbell shaped total electron density surrounds the rhodium atoms (blue) in the bare Rh2 but negative electrostatic potential is found to be above and below the plane of rhodium atoms due to π-electron overlapping of d-orbitals. In magnesium doped cluster of Rh2 electrostatic potential develops only on rhodium atoms. In all Mg doped rhodium clusters electrostatic potentials are found to be scattered around only rhodium atoms. Electron density is found to be maximum near edge and minimum on the surfaces of the clusters. Hole or less potential crowd of electron density is noticed around the magnesium atom suggesting no electrophilic and nucleophilic attraction towards magnesium atom. Negative electrostatic potential develops at rhodium atoms opposite to magnesium in all Mg doped rhodium clusters make these rhodium atoms prone to nucleophilic attract. Electrostatic charge population contours have also been generated for Rh nMg clusters and are shown in Fig. 12. Fig. 12 shows that maximum negative potential (red in colour) density develops on the rhodium atoms and on Rh−Rh bonds opposite to doped magnesium atom.

Rh4Mg

Rh5Mg

Rh6Mg

Rh7Mg

Fig 12. Electrostatic potential contour plot of RhnMg clusters. (Red colour contour represents negative potential) Force vector analysis Fig. 13 represents the resultant force vector analysis of Mg doped rhodium clusters. Stability of the metal nano clusters can also be explained on the basis of force vector analysis. Brown arrows indicate the net force of individual atoms and green arrow shows the resultant force vector. It is seen from Fig. 13 that individual force vector of all the atoms in Rh4 Mg are in different direction while resultant force vector is found to be in the opposite direction to magnesium atom. The resultant force vector as well as the force vectors of individual atoms are in the same direction which leads to the formation of Rh5Mg cluster. In the case of Rh6Mg and Rh7Mg clusters, direction of the resultant force vector is seen to be towards opposite to magnesium atom while in the case of Rh8Mg resultant force vector is found to be towards magnesium atom. The resultant force vector in Rh5Mg and Rh8Mg clusters is noticed to be towards same direction (towards Mg atoms also) which reveal that the electrons of the magnesium atom involved strongly with the electrons of rhodium atoms to stabilize the magnesium doped rhodium clusters. As the number of electrons in the rhodium atom is more than the magnesium (stable ns2 configuration) atom hence the stability of the magnesium doped rhodium clusters depend primarily on the stronger electronic force acceleration of the rhodium atoms. Therefore, extra stability of Rh5Mg and Rh8Mg clusters is exhibited by the involvement of electrons of magnesium as well as rhodium atoms and force vector is found to the in the same vector direction.

Rh4Mg

Rh6Mg

Rh5Mg

Rh7Mg

Rh8Mg Fig 13. Force vector representation of RhnMg cluster (n=4-8) (brown arrow for individual atoms and green arrow for resultant vector).

Density of states (DOS) and LUMO and HOMO iso-surface analysis Density of states of magnesium doped rhodium clusters are shown in the Fig. 14. It is observed from Fig. 14 that DOS of d electrons are found to be maximum near Fermi region (bonding region) than other s, p and f electrons while DOS of p electrons are seen to be maximum near the anti-bonding region. Population of s, p and d electrons are found to be higher at zero energy level (Fermi region) in the Rh5Mg and Rh8Mg clusters which suggests the stronger interaction among rhodium and magnesium atoms. Hence, Rh5 Mg and Rh8 Mg are observed to be more stable due to stronger interaction of electrons among rhodium and magnesium atoms. Partial spin density of state diagrams of RhnMg are given in the Fig.15. The spin up density is plotted as positive value and spin down as negative. Fig. 15 reveals that spin of the d-

electrons are responsible for the non zero magnetic moment of Rh2Mg, Rh3Mg, Rh5Mg and Rh7Mg because population of d electrons are maximum near Fermi region than other p and s electrons. For the above mentioned clusters height of density of states is more (more than 1.5 eV) than Rh4Mg, Rh6Mg and Rh8Mg clusters where height of s and p electron density is maximum near Fermi region (in decimal, less than 10-5 eV). Due to higher penetration power of s and p electrons than d, electrons in s and p orbital are more attracted towards nucleus than d electrons. In comparison to s and p electrons d electrons are free due to less penetration power. In the case of magnesium doped even atomic rhodium clusters magnetism is depended on the core or inner s and p electrons where as for odd atomic rhodium clusters magnetism depends on d electrons. Due to paired electronic spin in the inner s and p orbitals zero magnetic moment is observed in the case of magnesium doped even atomic rhodium nano structures. However, a little magnetism is noticed in Rh3Mg, Rh5Mg and Rh7Mg because of the acceleration of free d electrons. Highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) isosurface diagrams of Mg doped rhodium clusters are presented in Fig 16. Isosurface diagram of Rh2Mg and Rh5Mg reveals that electrons of the HOMO is mainly localized at the d-orbitals of rhodium atoms and electrons of the LUMO is localized at the available orbitals of magnesium as well as rhodium atoms. Electron transfer occurs in these two clusters from LUMO to HOMO as from MPA analysis it is observed that electron transfer from magnesium to rhodium atoms. HOMO is found to be localized at the available orbitals of Mg as well as Rh atoms but LUMO is localised at the d-orbitals of rhodium atoms only in the Rh4Mg. Therefore, HOMO to LUMO electron transfer is possible in the Rh4Mg. Electrons in LUMO and HOMO is seen to be mainly localized at the d-orbitals of rhodium atoms in the Rh3Mg, Rh6Mg, Rh7Mg and Rh8 Mg. Hence, electrons are observed to be distributed among d orbitals of rhodium atoms for these clusters. Symmetry mismatch overlapping is noticed among rhodium atoms via dz2 and dx2-y2/dxy orbitals at HOMO of RhnMg clusters except for Rh2Mg and Rh8Mg. In case of Rh2Mg and Rh8 Mg, overlapping is seen to be observed among d z2 orbitals. In the case of LUMO of Rh2Mg positive overlapping is noticed whereas permissible overlapping in observed in LUMO of Rh5Mg among orbitals of rhodium and magnesium atoms.

Rh2Mg

Rh3Mg

Rh4Mg

Rh5Mg

Rh6Mg

Rh7Mg

Rh8Mg Fig 14. Electronic density of states of DNP/BLYP optimized RhnMg(n=2-8) clusters

Rh2Mg

Rh3Mg

Rh4MG

Rh5MG

Rh6MG

Rh7MG

Rh8MG

Fig 15. Spin density of states of DNP/BLYP optimized RhnMg (n=2-8) clusters.

Cluster

Rh2Mg

Rh3Mg

Rh4Mg

Rh5Mg

Rh6Mg

Rh7Mg

HOMO

LUMO

Rh8Mg

Fig 16. LUMO and HOMO isosurface diagrams of DFT optimized RhnMg(n=2-8) clusters Catalytic activity of Rh 5 and Rh5Mg clusters: In this study Rh5 and Rh5Mg clusters are chosen for the investigation of activation of methanol molecule. In contrast to Rh5, Rh5Mg cluster is found to be more favorable for nucleophilic attack. Variations of selected geometric parameters for the activation of methanol are shown in Table 6 and their structures are given in Fig 17. Due to the adsorption of methanol on Rh5Mg cluster, C−O and O−H bond lengths of methanol got slightly elongated in comparison to pure methanol molecule. Length of O−H is increased by 0.1 Å (0.984 Å) from pure CH3OH where as O−H bond length is 0.973 Å. In the case of methanol adsorbed Rh5Mg and pure Rh5 clusters, Mg−O and Rh−O distances are found to to be 2.009 Å and 2.211 Å, respectively. It is relevant to obtain thermodynamic stability parameter like ∆G

(formation)

adsorbed pure and mixed metal rhodium clusters. ∆G

for the formation of methanol (formation)

values are calculated by

using following mathematical formula. ∆G(formation) = G(complex) - G(cluster)+G(CH3OH) G(complex), G(cluster) and G(CH3OH) are the absolute free energy values of cluster-CH3OH complex, pure Rh5 or Rh5Mg and methanol molecule, respectively. ∆G(formation) (free energy of formation) of the Rh 5-(CH3OH) and Rh5Mg-CH3OH complexes are calculated to be 2.46 and 2.58 eV, respectively. Calculated ∆G(formation) values suggest that Rh5Mg-CH3OH is more stable in comparison to Rh5 -CH3OH. Transition state corresponding to the O–H bond dissociation of methanol catalyzed by Rh5Mg involves the breaking of the O–H bond and subsequent transfer of hydrogen atom to any one of the nearby rhodium atoms. The energy barrier (relative energy) for O–H bond dissociation is found to be 0.17 eV. Only one imaginary frequency of -328 cm1

is obtained in the transition state which corresponds to the movement of proton to one

of the rhodium atoms. The product formed on complete rupture of O–H bond is stabilized by 0.32 eV with respect to the reactant. In the case of pure Rh5 catalyzed dissociation of O–H bond, the activation free energy barrier is found to be 0.61 eV.

Activation barrier height for O–H dissociation is higher for pure Rh5 in comparison to Rh5Mg. Product formed after O–H bond dissociation catalyzed by Rh5 is found to be bridged adsorbed hydrogen between two Rh atoms stabilized by 0.22 eV. Again, C–H bond dissociation catalyzed by Rh 5 has the activation barrier height of 0.79 eV. Dissociated hydrogen atom found to be bonded with one of the rhodium atom and product thus formed is endothermic by 0.19 eV. While, the barrier height of C−H dissociation catalyzed by Rh5Mg is found to be 0.34 eV. Imaginary frequency found for this transition state is -289cm-1. Product formed after C–H bond dissociation catalyzed by Rh5Mg is found to be singly coordinated hydrogen adsorbed on adjacent rhodium atom which is stabilized by -0.27 eV. Our results reveal that O−H dissociation is more favourable than C−H dissociation of methanol and activation barrier heights are found to be lower for Rh5Mg catalyzed reactions.

Activation of O-H by Rh5Mg

Activation of O-H by Rh5

Activation of C-H by Rh5Mg

Activation of C-H by Rh5

Fig 17: Activation barrier for O−H and C−H bonds dissociation for methanol activation by Rh5 Mg and Rh5 clusters. Table 6. DFT evaluated bond length parameters of reactant and transition state

Bond with cluster O-H (Rh5 Mg) O-H (Rh5 ) C-H (Rh5 Mg) C-H (Rh5 ) C-O (Rh5 Mg) C-O (Rh5 )

Reactant Bond length 0.984 0.976 1.098 1.091 1.474 1.463

Transition state Bond length 1.594 1.602 1.539 1.582 1.499 1.481

Conclusion DFT study is performed to understand the different orientation of magnesium atom on stable Rhn (n=2-8) clusters and to evaluate the stable ground state structure. Three dimensional configuration of magnesium doped rhodium clusters are obtained where location of magnesium is found on the surface. Rh5Mg, Rh6 Mg and Rh8Mg clusters are observed to be very stable based on the calculated reactivity parameters such as stability function, LUMOHOMO gap and fragmentation energy. Mulliken population analysis suggests that electrons are basically transferred from magnesium to rhodium atoms. Deformation electron density suggests Rh5 Mg cluster as stable one because more electron density is deformed for making

ionic character among bond (Rh−Rh and Rh−Mg). Force vector analysis and electronic density of states lead us to conclude that Rh5Mg and Rh8Mg are more stable. Our investigation also reveals that magnesium doped odd atomic rhodium clusters possess nonzero magnetic moment and even atomic rhodium clusters possess zero magnetic moment. LUMO and HOMO orbital analysis suggest that contribution of pi overlapping among orbitals in RhnMg clusters is more than sigma overlapping. From overall study it can be concluded that Rh5Mg, Rh6Mg and Rh8Mg clusters are more stable in comparison to other magnesium doped rhodium clusters. Calculated Fukui function values suggest that magnesium doped rhodium clusters are more reactive than pure rhodium clusters. Energy barrier for the activation of methanol catalyzed by magnesium doped rhodium clusters is found to be lower than the pure rhodium clusters. It is also observed that O−H bond dissociation of methanol is more favourable than C−H bond dissociation. Acknowledgement: Authors thank Department of Science and Technology (DST), New Delhi, India for financial support (SB/EMEQ-214 /2013).

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Some Highlights are 1. Rh5Mg, Rh6Mg and Rh8Mg clusters are observed to be very stable based on the calculated reactivity parameters such as stability function, LUMO-HOMO gap and fragmentation energy. 2. Deformation electron density suggests Rh5Mg cluster as stable. 3. Force vector analysis and electronic density of states lead us to conclude that Rh 5Mg and Rh8Mg are more stable. 4. Magnesium doped odd atomic rhodium clusters possess nonzero magnetic moment and even atomic rhodium clusters possess zero magnetic moment. 5. Rh5Mg is found to activate CH3OH by O-H dissociation rather than C-H.

Structural, electronic and catalytic properties of single magnesium atom doped small neutral Rhn (n=2-8) clusters: Density functional study Abhijit Dutta, Paritosh Mondal* Department of Chemistry, Assam University, Silchar 788011, Assam, India *Corresponding author: Email: [email protected] In this study RhnMg (n=2-8) clusters are investigated to evaluate the structure, stability, electronic and magnetic properties using density functional theory (DFT). Ii is observed from structural and electronic parameters that Rh5Mg, Rh6Mg and Rh8Mg cluster are sable. Other parameters such as density of states, force vector and deformation electron density suggests the stability of Rh5Mg and Rh8Mg cluster among other magnesium doped rhodium cluster.

More interaction among orbitals

More deformed electron density