- Email: [email protected]
Structure stability and electronic properties of PtmIrn (m + n = 2–7) clusters: A DFT study
Computational and Theoretical Chemistry 1138 (2018) 168–175
Contents lists available at ScienceDirect
Computational and Theoretical Chemistry journal homepage: www.elsevier.com/locate/comptc
Structure stability and electronic properties of PtmIrn (m + n = 2–7) clusters: A DFT study
T
⁎
Kun Gaoa, Xiu-Rong Zhangb, , Zhi-Cheng Yub, Pei-Ying Huob a b
School of Material Science and Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China School of Science, Jiangsu University of Science and Technology, Zhenjiang 212003, China
A R T I C LE I N FO
A B S T R A C T
Keywords: PtmIrn (m + n = 2–7) clusters Structure and stability Electronic property DFT
Structure, stability and electronic properties of PtmIrn (m + n = 2–7) clusters have been systematically investigated by using density functional theory (DFT) with considering the generalized gradient approximation (GGA). The results reveal that the ground state structures change from planar to three-dimensional structures with the increase of the number of atoms, and Ir atoms play a decisive role in the formation of PtmIrn clusters. The addition of a small amount amount of Ir improves the stability of pure Pt clusters. The stability analysis indicates that most of the Pt-rich clusters are more stable than those of the Ir-rich with same cluster size. The PtIr cluster charge transfer analysis illustrates that it not only occurs in different orbits, but also occurs between different atoms. PtIr3, Pt4Ir, Pt4Ir2, Pt3Ir3, Pt2Ir4, PtIr5 and Ir7 clusters exhibit comparatively large magnetism.
1. Introduction The transition-metals play important roles in the field of metallurgy and catalysis due to containing d electrons, which make formed clusters exhibit special electronic structures and physical-chemical properties. High-temperature alloy materials, magneto-optical recording materials, shape memory materials and the most important catalyst of chemical industry are all transition metal alloy materials. The chemical and physical properties of transition metal clusters can be changed by doping with other metal, and bimetallic clusters have a wide application prospect in catalysis science, surface science, nanoscience and nanotechnology. Therefore, transition metal doped clusters have been extensively investigated [1–10]. For example, the magnetic properties of Co12X (X = Ni, Ag, Pt, Au) clusters were analyzed by LU [9], which show that the impurities of the X atom break the symmetry of molecular orbitals of Co13. They induce the redistribution of the electrons, which dramatically alters the magnetism of Co12X clusters, and the total magnetic moments of Co12Pt cluster is 22 μB. And the geometrical structure, stability, electronic and magnetic properties of PdnIr (n = 1–8) clusters have been systematically studied by Bouderbala et al. [10]. They found that the total magnetic moment of PdnIr clusters is mainly localised on the Ir atom for Pd1-6Ir clusters. Meanwhile, the 5d orbital plays the key role in the magnetic moment of the Ir atom. Our research group has done some other atomic clusters studies [11–14]. For example, all the possible geometrical structures of PtnNim (n + m = 7, n,m ≠ 0) clusters
⁎
Corresponding author. E-mail address: [email protected] (X.-R. Zhang).
https://doi.org/10.1016/j.comptc.2018.06.016 Received 25 April 2018; Received in revised form 20 June 2018; Accepted 22 June 2018 Available online 23 June 2018 2210-271X/ © 2018 Elsevier B.V. All rights reserved.
are optimized with density functional theory [14]. The results show that all the ground state structures of PtnNim clusters are cube structures. Pt5Ni2 is the most stable one of PtnNim clusters. Ni atom plays a leading role in magnetism of the binary PtnNim clusters. Noble platinum metallic clusters are often used as a catalyst in the chemical industry because of their exhibiting remarkably higher chemical stability and catalytic activity. Iridium is platinum-group metal which not only is one of the most corrosion-resistant metal, but also plays an important role in the catalytic process. At present, platinum or iridium metals have been extensively studied both theoretically [15–29,35–44] and experimentally [30]. Guo et al. [28] reported the possible geometrical configurations and stability of PtIrn0, ± (n = 1–5) clusters by using density functional theory. Based on the stability analysis, they found that thermodynamics stability of clusters improves with the increase of atoms. Iridium atoms play a dominant action in stability of PtIrn0, ± clusters. Moreover, the energetic stability, electronic structure and magnetic properties of Pt8-nIrn clusters have been investigated by N Long et al. [29]. They found that the average binding energy of all the clusters presents the linear increment trend versus iridium atoms, bader charge analysis shows how tiny charge transfers from iridium to platinum. Experimentally, Pt–Ir catalysts with different atomic ratios were synthesized by Hu et al. [30], which illustrate that the addition of an appropriate amount of Ir improves the catalytic activity of pure Pt. In this paper, we have comprehensively studied the optimized structure, stability and electronic properties of PtmIrn bimetallic clusters
Computational and Theoretical Chemistry 1138 (2018) 168–175
K. Gao et al.
considering the spin multiplicity. The structure with lowest energy and real frequency was defined as the ground state stable structure. The lowest-energy optimized configurations of PtmIrn (m + n = 2–7) clusters are shown in Fig. 1. The symmetry, spin multiplicity and average bond lengths are listed in Table 2.
with m + n = 2–7 to explore the effect of different ratio of Pt and Ir elements on the properties aforementioned. Which may provide a theoretical reference for the preparation of platinum iridium nanomaterials. 2. Computational method
3.1.1. Pure Ptn and Irn clusters (n = 2–7) In order to investigate the ground state structures of bimetallic PtmIrn clusters, we first discuss the structures of pure Ptn and Irn clusters (n = 2–7) by using the method in Section 2. This range has also been studied by other workers [16–20,26,27,35,39,41–44], but in some cases, our ground state structures are different. For pure Ptn clusters, the ground state structures of our calculated results are consistent with the previous theoretical results [44] except that Pt4 and Pt7. But the lowest-energy geometry of Pt4 cluster is in agreement with the theoretical result [42]. The isomer of Pt7 with C3v symmetry is evaluated to be the ground state structure which can be regarded as capping one Pt atom on the vertex of the triangular prism structure. For pure Irn clusters, the ground state structures of our calculated results are in accordance with the theoretical results [20] except for Ir7. We obtain the ground state structure of Ir7 cluster with C2v symmetry by optimizing the side-face-capped triangular prism.
All calculations of the optimized configuration, stability and electronic properties of PtmIrn (m + n = 2–7) clusters were performed using DFT semi-core pseudopots in the Dmol3 package in Material Studio. The exchange-correlation interaction of between electrons was treated within the generalized gradient approximation (GGA) [31] using PW91 [32] functional. The double numerical basis set augmented with polarization functions (DNP) [33] was utilized. The convergence criterion of self-consistent field (SCF) was set to be 10-5Hartree. And the direct inversion in an iterative subspace (DIIS) [34] approach was used to accelerate the speed of SCF convergence. We considered the smearing in calculation, and the smearing of molecular orbital occupation was set to be 0.005 Hartree. In the process of geometric optimization of the system, converge thresholds of the forces, displacement and energy were set to be 0.004 Hartree/Å, 0.005 Å and 2.0 × 10−5 Hartree, respectively, and the other parameters all adopted the default values. Then ground state structures was selected to analyze structure stability and electronic properties. To check the validity of the computational method in our work, we firstly performed the calculation on the Pt2 and Ir2 clusters and the correlation data are as listed in Table 1. For Pt2, the bond length we obtained is 2.395 Å, which is in good agreement with previous theoretical data of 2.38 Å [17,22], 2.40 Å [35] and 2.34 Å [18,37,38,39], and the experimental values of 2.34 Å [36] and 2.45 Å [40]. Meanwhile, the binding energy (1.733 eV) is very close to previous theoretical data of 1.76 eV [38]. Similarly, for Ir2, our calculated bond length (2.284 Å) and Eb (2.233 eV) are in excellent agreement with the previous theoretical values (2.22 Å [22], 2.209 Å [27], 2.228 Å [41] and 2.28 eV [3]). All these results validate that our approach provides an efficient way to investigate PtmIrn clusters.
3.1.2. PtmIrn clusters (m + n = 2–7) Here we explore about bimetallic PtmIrn clusters. The Pt-Ir bond length in PtIr cluster with C∞v symmetry is 2.356 Å. The lowest-energy geometries of Pt2Ir and PtIr2 clusters are all planar isosceles triangle structures with C2v symmetry. The Pt-Ir bond length of Pt2Ir cluster (2.497 Å) is less than of PtIr2 cluster (2.509 Å). In the case of Pt3Ir, the ground state structure is a tetrahedral structure with C3v symmetry which can be regarded as a Pt atom at the top of the Pt4 cluster replaced by a Ir atom. The Pt-Pt bond length in Pt3Ir (2.660 Å) is longer than the Pt-Pt bond length (2.637 Å) in Pt4 cluster. For Pt2Ir2 cluster, the planar quadrilateral structure with C2v symmetry is found to be ground state structure. The ground state structure of PtIr3 cluster can be viewed as a Ir atom of the Ir4 cluster substituted and connected all Pt-Ir bond, the configuration is C2v symmetry and the Ir-Ir bond length (2.360 Å) is less than the bond length (2.396 Å) in Ir4 cluster. The isomer of Pt4Ir with C4v symmetry whose structure is the rectangular pyramid with Ir atom on the vertex is evaluated to be the ground state structure The Pt-Pt bond length (2.625 Å) is smaller than the Pt-Pt bond length (2.660 Å) in Pt3Ir clusters. For Pt3Ir2 cluster, the ground state structure is the Ir edge capped the triangular structure of tetrahedral structure with Cs symmetry. In the isomer of Pt2Ir3 cluster, the ground state structure is trigonal pyramid structure with Pt on the vertex and D3h symmetry. The structure of PtIr4 cluster with C2v symmetry is selected as the ground state structure. For PtmIrn (m + n = 6), the ground state structure of Pt5Ir cluster is an oblique triangular prism structure with Cs symmetry which can be seen as filling a Pt atom on Pt4Ir cluster ground state structure. The PtPt bond length (2.657 Å) is greater than the Pt-Pt bond length (2.625 Å) in Pt4Ir cluster. Pt4Ir2, Pt3Ir3, Pt2Ir4 and PtIr5 clusters are all triangular prism structures which can be regarded as substituting atoms in the ground state structure of Ir6 cluster. Their symmetries are C2v, C3v, C2v and Cs, respectively. Finally, we investigate the PtmIrn (m + n = 7). The lowest-energy geometry of Pt6Ir cluster is similar to the lowest-energy structure of the Ir7 cluster with C2v symmetry and the Pt-Pt bond length is 2.634 Å. For Pt5Ir2 cluster, it can be obtained by capping a Pt atom to the Pt4Ir2 cluster. The isomer of Pt4Ir3 with C2v symmetry is evaluated to be the ground state structure which is resemble to the ground state structure of the Ir7 cluster. In the Pt3Ir4 cluster, the Ir edge capped the triangular structure with Cs symmetry is the most stable one. The calculations show that the isomer Pt2Ir5 with Cs symmetry is the ground state structure, which can be obtained by by capping a Pt atom to the ground state structure of PtIr5 cluster. The isomer PtIr6 with C3v symmetry is found to be the most stable structure among all optimized
3. Results and discussion 3.1. Geometrical structures In general, finding the ground state structure of binary alloy cluster is much more difficult than that of corresponding single pure cluster due to there exists non-equivalence of spatial geometric structure of atoms exchange position, and the quantity of possible configurations clusters increases exponentially with the increasing number of atoms. In order to find the ground state structures of PtmIrn (m + n = 2–7) clusters, we considered about 500 possible initial configurations, and constructed the initial configurations in two ways: (i) is guess the initial configuration directly; (ii) use the ground state structures of pure Ptn and Irn clusters as the basic framework, and then construct the initial configuration by capping, replacing and filling at different locations of the framework. The structure optimization and frequency calculation were carried out for each size of specific cluster on the premise of fully Table 1 Calculated bond length, binding energy; the experimental results and previous theoretical studies. Dimer Pt2
Ir2
Bond length (Å)
Eb (eV/atom) 1.733 1.76 [38]
Experimental
2.395 2.38 [17,22] 2.40 [35] 2.34 [18,37,38,39] 2.34 [36] 2.45 [40]
Our work Theoretical
2.284 2.22 [22] 2.209 [27] 2.228 [41]
2.233 2.28 [3]
Our work Theoretical
169
Computational and Theoretical Chemistry 1138 (2018) 168–175
K. Gao et al.
Fig. 1. The ground state structures of PtmIrn (m + n = 2–7) clusters.
isomers, which can be obtained by capping a Ir atom to the ground state structure of Ir6 cluster. By the above analysis, the ground state structures generally change from planar to three-dimensional structures with the increase of the number of atoms in general. We can seen that for PtmIrn (m + n = 2–4) clusters, all the optimized configurations are planar structure except that Pt4 and Pt3Ir which are tetrahedral structures. While for
m + n = 5–7, all the optimized geometries are three-dimensional structure except Pt5, Pt6 and PtIr4 which are planar structures. Especially m + n = 6–7, which all are triangular prism structures or the capped triangular prism structures. In the ground state structures, most of clusters use pure Irn (n = 2–7) clusters as basic structural units, indicating that the incorporation of Pt atoms in clusters did not destroy the formation of Ir-Ir bonds. But a fat lot clusters use pure Ptm 170
Computational and Theoretical Chemistry 1138 (2018) 168–175
K. Gao et al.
Δ2 En = E(PtmIrn + 1) + E(PtmIrn − 1)−2E(PtmIrn)
Table 2 Symmetry, multiplicity and average bond length of PtmIrn (m + n = 2–7) clusters. m+n
Cluster
Symmetry
Multiplicity
LPt-Pt/Å
LPt-Ir/Å
LIr-Ir/Å
2
Pt2 PtIr Ir2
D∞h C∞v D∞h
1 4 1
2.395 – –
– 2.356 –
– – 2.284
3
Pt3 Pt2Ir PtIr2 Ir3
D3h C2v C2v D3h
1 2 2 4
2.533 2.547 – –
– 2.497 2.509 –
– – 2.401 2.437
4
Pt4 Pt3Ir Pt2Ir2 PtIr3 Ir4
Td C3v C2v C2v D4h
1 4 1 6 1
2.637 2.660 2.523 – –
– 2.563 2.457 2.778 –
– – 2.349 2.360 2.396
5
Pt5 Pt4Ir Pt3Ir2 Pt2Ir3 PtIr4 Ir5
C2v C4v Cs D3h C2v C4v
1 6 1 2 3 4
2.523 2.625 2.628 – – –
– 2.583 2.597 2.645 2.346 –
– – 2.442 2.500 2.373 2.517
6
Pt6 Pt5Ir Pt4Ir2 Pt3Ir3 Pt2Ir4 PtIr5 Ir6
D3h Cs C2v C3v C2v Cs D3h
1 4 7 6 7 6 1
2.581 2.657 2.600 2.625 2.591 – –
– 2.641 2.553 2.507 2.572 2.559 –
– – 2.395 2.481 2.447 2.467 2.467
7
Pt7 Pt6Ir Pt5Ir2 Pt4Ir3 Pt3Ir4 Pt2Ir5 PtIr6 Ir7
C3v C2v Cs C2v Cs Cs C3v C2v
3 2 1 2 1 4 3 6
2.607 2.634 2.624 2.622 2.652 – – –
– 2.631 2.576 2.612 2.547 2.620 2.673 –
– – 2.399 2.507 2.465 2.470 2.485 2.492
Where E represents the binding energy of its most stable structure. The average binding energies reflect the binding ability of clusters. The larger the average binding energy is, the more stable the cluster will be. It can be seen from Figs. 2 and 3 that the average binding energies of clusters all increase with the increasing of size except PtmIr6 cluster in Fig. 2. And all the average binding energy of pure Irn clusters are larger then those of Ptn clusters, illustrating that the stability of iridium clusters is better then that of platinum. As seen from Figs. 2 and 3, it is obvious that the growth rate of average binding energies of different size clusters with Pt atoms is slower than that Ir atoms. The result reveals that iridium plays a major role in platinum-iridium doped clusters. The analysis results are in accordance with the previous analysis geometrical structures. It also can be seen from Fig. 3 that six are slight lifts corresponding to Pt3Ir2, Pt1,4,5Ir, Pt1,2Ir3, respectively. The emergence of these local magnitude maxima means that these clusters have stronger stabilities relative to their neighbours, and the addition of a small amount of Ir improves the stability of pure Pt clusters. The second-order energy difference (Δ2E) is a sensitive physical quantity to measure the thermodynamic stability of the cluster. The larger the value is, the higher the stability of the cluster will be. It can be found from Figs. 2 and 3 that the second-order energy difference of Pt2,3,5, Pt3Ir2, Pt1,4,5Ir, Pt2Ir3 and Ir2,4,6 clusters are positive. This means that these clusters are more stable, which is coincident with the result of the average binding energies. From Fig. 3, it is evident that there exist even-odd oscillations in the curves of Irn and Pt1,2Irn clusters, indicating that Ir2,4,6, Pt2Ir3 and PtIr1,5 clusters are more stable than their neighbors. The Δ2E values of PtIr, Ir2, Ir6, Pt2Ir3 and Pt5Ir clusters are much larger than those of other clusters, suggesting that the five clusters are more stable. 3.2.2. HOMO-LUMO energy gap (Eg) The chemical stability and activity of clusters are analysed by discussing the energy gaps of clusters. The variation curves of the energy gaps of PtmIrn cluster with the clusters size are plotted in the Fig. 4. The energy gap can be calculated by the following formula:
(m = 2–7) clusters as basic structural units, which suggests that the incorporation of Ir atoms in clusters destroys the formation of Pt-Pt bonds. And it is easy to form Pt-Ir bonds, which shows that Ir atoms play a decisive role in the formation of PtmIrn clusters.
Eg = ELUMO−EHOMO
Based on the optimized ground state structures, the relative stability of PtmIrn (m + n = 2–7) clusters are studied by calculating the average binding energies (Eb), second-order energy difference (Δ2E) and HOMOLUMO energy gap (Eg) physical parameters. 3.2.1. Averaged atomic binding energies (Eb) and Second-order energy difference (Δ2E) Figs. 2 and 3 show the variation of Eb and Δ2E of ground state structures of PtmIrn (m + n = 2–7) clusters with the number of Pt (Ir) atoms. The Eb and Δ2E of Xm (X = Pt or Ir) clusters are calculated using the following formulas: (1)
Δ2 E = E(Xm + 1) + E(Xm − 1)−2E(Xm)
(2)
The Eb of PtmIrn clusters is evaluated using the following expressions:
Eb = [mE(Pt) + nE(Ir)−E(PtmIrn)]/m+n
(3)
3.3. Electronic property
The Δ2E of PtmIrn clusters as a function of the number of Pt and Ir atoms can be calculated as:
Δ2 Em = E(Ptm + 1Irn) + E(Ptm − 1Irn)−2E(PtmIrn)
(6)
Where ELUMO is the lowest unoccupied molecular orbital energy, and EHOMO is the highest occupied molecular orbital. The values of the energy gaps reflect the ability for the electrons to transit from the HOMO orbital to LUMO orbital. The lager the value is, the stronger the chemical stability will be. To the contrary, smaller value represents high activity. It can be seen from Fig. 4 that Pt2,5, Pt1,2,3Ir and Ir2,3,7 clusters show higher energy gaps than other clusters, indicating that these clusters are stronger in chemical stability. It also can be found that most of energy gaps of the Pt-rich clusters are larger than those of the Ir-rich with same cluster size, which is coincident with the conclusion obtained from the average binding energy. In order to explore the process of charge transfer, PtIr is mainly discussed as representative, because it shows better stability compared to other clusters in the above analysis. The natural electronic population for Pt and Ir are 5s25p66s15d96p0 and 5s25p66s25d76p0, respectively. It can be found that charge transfer from 6 s orbits to 6p, 5d orbits in the Ir atom, and charge transfer from 5d orbits to 6 s, 6p orbits in the Pt atom. After electron transfer, The electronic population for Pt and Ir are 5 s(2.000) 5p(5.996) 6 s(1.147) 5d(8.939) 6p(0.055) and 5 s (2.000) 5p(5.999) 6 s(1.277) 5d(7.630) 6p(0.056), respectively. It also can be found that a part of charge transfer from Ir atom to Pt atom.
3.2. Stabilities of PtmIrn (m + n = 2–7)
Eb = [mE(X)−E(Xm)]/m
(5)
In order to study the electronic properties of PtmIrn clusters, we analyzed the partial and total density of states (DOS) for ground state structures of PtIr3, Pt4Ir, Pt4Ir2, Pt3Ir3, Pt2Ir4, PtIr5 and Ir7 clusters for
(4) 171
Computational and Theoretical Chemistry 1138 (2018) 168–175
K. Gao et al.
Fig. 2. The averaged atomic binding energies and second-order energy differences of the ground state structures of PtmIrn clusters as a function of the number of Pt atoms.
their spin multiplicities are relatively larger. The s, p, d orbitals and the total orbital up-spin and down-spin density of states distributions of these clusters are plotted in Fig. 5. Due to the contribution of the f orbitals on the total density of states is very small, it is not considered in our analysis. The clusters Fermi level is at zero presented as a solid vertical line, the upper and lower sides of Fig. 5 represent up-spin and down-spin electrons, respectively. It is obvious from Fig. 5 that the local state density curves of the dorbit of all clusters are narrow and sharp, which indicates that distribution of d orbital electrons are relatively localized. and the total density of states (TDOS) mainly come from contribution of d orbital in the range of −5–2 eV, whereas the contribution from s and p orbital electrons are relatively less. As is shown in the Fig. 5, the upper and lower curves of DOS of all clusters show low symmetry, indicating that there exist large number of unpaired electrons around these clusters, which is consistent with the situation reflected by spin multiplicity. So the contribute to magnetic moments are greater. As the spin of the unpaired electrons can produce magnetic moment, and the greater the spin multiplicity is, the larger the number of unpaired electrons will be. Then we can conclude that the seven selected clusters have high magnetism, and they show better propensity to adsorb small molecule. In order to study the magnetic properties of PtmIrn (m + n = 2–7) clusters, we also studied the local magnetic moments of each atom in PtmIrn clusters. Fig. 6 shows the electron spin density around individual atoms of these clusters, where the blue and yellow represent electronic states of up-spin and down-spin, respectively. The corresponding local and total magnetic moment of the seven selected clusters are listed in
Fig. 4. The Eg of PtmIrn clusters at ground state.
Table 3. The larger the electron spin density is, indicating that the more unpaired electrons around atoms, the larger the local magnetic moment will be. It is clearly seen from Fig. 6 that there are a large number of electron spin density around each atom in PtIr3, Pt4Ir, Pt4Ir2, Pt3Ir3, Pt2Ir4, PtIr5 and Ir7 clusters, illustrating that each atom in clusters
Fig. 3. The averaged atomic binding energies and second-order energy differences of the ground state structures of PtmIrn clusters as a function of the number of Ir atoms. 172
Computational and Theoretical Chemistry 1138 (2018) 168–175
K. Gao et al.
Fig. 5. The DOS of PtIr3, Pt4Ir, Pt4Ir2, Pt3Ir3, Pt2Ir4, PtIr5 and Ir7 clusters at ground state.
the Pt3Ir3 cluster, indicating that iridium atoms make a great contribution to the total magnetic moment. In addition to the total magnetic moment of all the chosen clusters is approximately 5 or 6μB. The results of the magnetic moment is coincident with the previous analysis about the density of states.
contributes a great deal to local magnetic moment. Moreover, there only exists up-spin electronic states without spin-down, which indicates that almost all of the electrons around these atoms are unpaired, so that it obtains larger total magnetic moment than other clusters. It can be seen from Table 3 that local magnetic moment of Ir atoms in each cluster all are larger than local magnetic moment of Pt atoms, except 173
Computational and Theoretical Chemistry 1138 (2018) 168–175
K. Gao et al.
Fig. 6. The electron spin density maps of PtmIrn (m + n = 2–7) clusters.
4. Conclusion
clusters generally us pure Irn (n = 2–7) clusters as basic structural units rather than pure Ptm (m = 2–7) clusters, illustrating that iridium atoms play a decisive role in the formation of PtmIrn clusters. In addition, it can be seen that the average binding energy (Eb) of clusters increases with the increasing of size except PtmIr6 cluster and the growth rate of average binding energies of different size clusters with Pt atoms is
The geometrical structures, stability and electronic properties of PtmIrn (m + n = 2–7) clusters have been systematically investigated by using density functional theory (DFT) with considering the generalized gradient approximation (GGA). The study results indicated that most of
174
Computational and Theoretical Chemistry 1138 (2018) 168–175
K. Gao et al.
Table 3 The local and total magnetic moments (μB) of PtIr3, Pt4Ir, Pt4Ir2, Pt3Ir3, Pt2Ir4, PtIr5 and Ir7 clusters. Atom number
1 2 3 4 5 6 7 Total
Clusters PtIr3
Pt4Ir
Pt4Ir2
Pt3Ir3
Pt2Ir4
PtIr5
Ir7
1.464 1.615 1.494 0.396(Pt)
0.916 0.916 0.916 0.916 1.336(Ir)
0.943 0.943 0.943 0.943 1.114(Ir) 1.114(Ir)
0.617(Ir) 0.620(Ir) 1.066 1.065 0.577(Ir) 1.054
1.130 1.130 1.131 1.131 0.739(Pt) 0.739(Pt)
1.292 0.762 0.696 1.231 0.351 0.668(Pt)
4.969
5.000
6.000
4.999
6.000
5.000
0.641 1.045 0.641 0.346 0.641 1.045 0.641 5.000
slower than that Ir atoms. The result also reveals that iridium plays a major role in platinum-iridium dopant clusters and the addition of a small amount amount of Ir improves the stability of pure Pt clusters. The second-order energy difference (Δ2E) of Irn and Pt1,2Irn clusters show “odd-even” oscillation. Thermodynamic stability of PtIr, Pt5Ir, Pt2Ir3 and PtIr5 clusters show stronger than other ground state clusters, and Pt2, PtIr, Ir2, Pt2Ir, Ir3, Pt3Ir, Pt5 and Ir7 clusters show higher energy gap (Eg) than other clusters, indicating that these clusters are stronger in chemical stability than other clusters. The PtIr cluster charge transfer analysis illustrates that the it not only occurs in different orbits, but also occurs between different atoms. As the DOS and electron spin density analyzed, PtIr3, Pt4Ir, Pt4Ir2, Pt3Ir3, Pt2Ir4, PtIr5 and Ir7 clusters exhibit comparatively large magnetic owing to there exist a large amount of unpaired electrons around all atoms.
[18] A. Sebetci, Z.B. Güvenç, Energetics and structures of small clusters: PtN, N =2–21, Surf. Sci. 525 (2010) 66–84. [19] D.R. Isakov, G.M. Khrapkovskii, A.G. Shamov, Quantum-chemical study of methane dehydrogenation on neutral, cationic, and anionic clusters Pt2–5 by DFT method, Russ. J. Gen. Chem 81 (2011) 781–782. [20] J. Du, X. Sun, J. Chen, G. Jiang, A theoretical study on small iridium clusters: structural evolution, electronic and magnetic properties, and reactivity predictors. J. Phys. Chem. A. 114 (2010) 12825–12833. [21] F. Li, B.C. Gates, Synthesis and structural characterization of iridium clusters formed inside and outside the pores of zeolite NaY, J. Phys. Chem. B. 107 (2003) 202–203. [22] P. Bloński, J. Hafner, Magnetic anisotropy of transition-metal dimers: Density functional calculations, Phys. Rev. B. 79 (2009) 1377–1381. [23] J. Wu, S.M. Sharada, C. Ho, A.W. Hauser, M. Head-Gordon, A.T. Bell, Ethane and propane dehydrogenation over PtIr/Mg(Al)O, Appl. Catal. A-Gen. 506 (2015) 25–32. [24] A. Grushow, K.M. Ervin, Ligand and metal binding energies in platinum carbonyl cluster anions: Collision-induced dissociation of Pt m − Pt m − and Pt m (CO) n − Pt m (CO) n −, J. Chem. Phys. 107 (1997) 8210. [25] T. Pawluk, Y. Hirata, L. Wang, Studies of Iridium Nanoparticles Using Density Functional Theory Calculations, J. Phys. Chem. B. 109 (2005) 20817–20823. [26] K. Bhattacharyya, C. Majumder, Growth pattern and bonding trends in Ptn(n = 2–13) clusters: Theoretical investigation based on first principle calculations, Chem. Phys. Lett. 446 (2007) 374–379. [27] X. Liang, X. Wu, X. Huang, Y. Su, J. Hu, J. Zhao, Magnetic anisotropy of small Irn clusters (n = 2–5), J. Clust. Sci. 27 (2016) 935–946. [28] W.L. Guo, Q. Rao, X.R. Zhang, Theoretical study on structure and stability of PtIrn(0, ± )(n=1-5) clusters, Chinese J. Comp. Phys. 29 (2012) 453–458. [29] N. Long, J. Du, G. Jiang, The influence of the composition of eight-atom Pt–Ir clusters on the magnetic properties, Molec. Phys. 113 (2015) 3628–3636. [30] S. Hu, L. Xiong, X. Ren, C. Wang, Y. Luo, Pt–Ir binary hydrophobic catalysts: Effects of Ir content and particle size on catalytic performance for liquid phase catalytic exchange, Int. J. Hydrogen Energ. 34 (2009) 8723–8732. [31] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 78 (1997) 3865. [32] J.P. Perdew, Y. Wang, Accurate and simple analytic representation of the electrongas correlation energy, Phys. Rev. B. 45 (1992) 13244. [33] B. Delley, From molecules to solids with the DMol3 approach, J. Chem. Phys. 113 (2000) 7756–7764. [34] P. Pulay, Improved SCF convergence acceleration, J. Comput. Chem. 3 (1982) 556–560. [35] S.H. Yang, D.A. Drabold, J.B. Adams, P. Ordejon, K. Glassford, Density functional studies of small platinum clusters, J. Phys-Condens Mat. 9 (1997). [36] S.K. Gupta, B.M. Nappi, K.A. Gingerich, Mass spectrometric study of the stabilities of the gaseous molecules diatomic platinum and platinum-yttrium, Inorg. Chem. 20 (1981) 966–969. [37] Y. Xu, W.A. Shelton, W.F. Schneider, Effect of particle size on the oxidizability of platinum clusters, J. Phys. Chem. A. 110 (2006) 5839. [38] L. Xiao, L. Wang, Structures of platinum clusters: Planar or spherical?†, J. Phys. Chem. A. 108 (2004) 8605–8614. [39] B. Hamad, Z. El-Bayyari, A. Marashdeh, Investigation of the stability of platinum clusters and the adsorption of nitrogen monoxide: First principles calculations, Chem. Phys. 443 (2014) 26–32. [40] U. Müller, K. Sattler, J. Xhie, N. Venkateswaran, G. Raina, Scanning tunneling microscopy of single platinum atoms and small platinum clusters on highly oriented pyrolytic graphite, J. Vac. Sci. Technol. B. 9 (1991) 829–832. [41] M. Chen, D.A. Dixon, Low-lying electronic states of Ir(n) clusters with n = 2–8 predicted at the DFT, CASSCF, and CCSD(T) levels, J. Phys. Chem. A. 117 (2013) 3676–3688. [42] M. Carmona-Pichardo, R.L. Camacho-Mendoza, L.A. Zarate Hernandez, J. CruzBorbolla, C.A. González-Ramírez, T. Pandiyan, N. Jayanthi, Activation of Pt–O and Pt–H bonds: DFT studies on adsorption of [Gd(H 2 O) n ] 3+, (n =8–9) with Ptn (n =3–7) cluster, Comput. Theor. Chem. 1047 (2014) 47–54. [43] P. Błoński, S. Dennler, J. Hafner, Strong spin-orbit effects in small Pt clusters: geometric structure, magnetic isomers and anisotropy. J. Chem. Phys. 134 (2011) 1495–1953. [44] V. Kumar, Y. Kawazoe, Evolution of atomic and electronic structure of Pt clusters: Planar, layered, pyramidal, cage, cubic, and octahedral growth, Phys. Rev. B. 77 (2008) 998–1002.
Acknowledgement This project was supported by the National Natural Science Foundation of China (Grant No. 51402131) References [1] A. Estejab, G.G. Botte, DFT calculations of ammonia oxidation reactions on bimetallic clusters of platinum and iridium, Comput. Theor. Chem. 1091 (2016) 31–40. [2] F. Aguileragranja, R.C. Longo, L.J. Gallego, A. Vega, Structural and magnetic properties of X12Y (X, Y = Fe Co, Ni, Ru, Rh, Pd, and Pt) nanoalloys, J. Chem. Phys. 2010 (132) (2010) 1882. [3] J.B. Davis, S.L. Horswell, R.L. Johnston, Global optimization of 8–10 atom palladium-iridium nanoalloys at the DFT level, J. Phys. Chem. A. 118 (2014) 208–214. [4] J.X. Yang, J.J. Guo, D. Dong, Ab initio, study of AunIr (n = 1–8) clusters, Comput. Theor. Chem. 963 (2011) 435–438. [5] R.N. Zhao, Y.H. Yuan, J.G. Han, Transition metal Mo-doped boron clusters: A computational investigation, J. Theor. Comput. Chem. 2014 (13) (2014) 1450036. [6] S. Sicolo, G. Pacchioni, A DFT study of PtAu bimetallic clusters adsorbed on MgO/ Ag(100) ultrathin films, Phys. Chem. Chem. Phy. 12 (2010) 6352–6356. [7] E. Florez, F. Mondragon, F. Illas, Theoretical study of the structure and reactivity descriptors of CunM (M=Ni, Pd, Pt; n = 1–4) bimetallic nanoparticles supported on MgO(001), Surf. Sci. 606 (2012) 1010–1018. [8] M.B. Javan, Structural, electronic and magnetic properties of small bimetallic zirconium–palladium clusters: Ab initio study, J. Alloys Compd. 643 (2015) 56–63. [9] Q.L. Lu, J.C. Jiang, J.G. Wan, G.H. Wang, Structure and magnetic properties of Co12X(X = Ni, Ag, Pt, Au) clusters, Int. J. Mod. Phy. B. 21 (2007) 5091–5098. [10] W. Bouderbala, A.G. Boudjahem, A. Soltani, Geometries, stabilities, electronic and magnetic properties of small PdnIr (n = 1–8) clusters from first-principles calculations, Mol. Phy. 112 (2014) 1789–1798. [11] X.R. Zhang, Y.N. Cui, L.L. Hong, Aromatic character studies on M0, ± n (M = Ir, Pt; n = 3, 4) clusters via nucleus-independent chemical shifts (NICS) calculation and geometric structure, J. Comput. Theor. Nanos. 6 (2009) 640–643. [12] C.H. Gao, X.R. Zhang, Geometries and physical properties of WnNim (n + m ≤7) clusters, J. Comput. Theor. Nanos. 7 (2010) 612–618. [13] X.R. Zhang, M. Luo, F.X. Zhang, X.Y. Zheng, G.K. Hu, B. Structure stability and magnetic properties of OsnB (n, = 11–20) clusters ‡. B, Mater. Sci. 38 (2015) 425–434. [14] X.R. Zhang, X. Yang, Y. Li, W.L. Guo, Structure stability and magnetic properties of PtnNim (n+m=7, n, m≠0) clusters, Acta. Chim. Sinica 69 (2011) 2063–2069. [15] P. Błoński, J. Hafner, Magneto-structural properties and magnetic anisotropy of small transition-metal clusters: a first-principles study, J. Phys-Condens Mat. 23 (2011) 136001. [16] A. Sebetci, Does spin-orbit coupling effect favor planar structures for small platinum clusters? Phys. Chem. Chem. Phy. 11 (2009) 921–925. [17] M.N. Huda, M.K. Niranjan, B.R. Sahu, L. Kleinman, Effect of spin-orbit coupling on small platinum nanoclusters, Phys. Rev. A 73 (2006) 053201.
175
Contents lists available at ScienceDirect
Computational and Theoretical Chemistry journal homepage: www.elsevier.com/locate/comptc
Structure stability and electronic properties of PtmIrn (m + n = 2–7) clusters: A DFT study
T
⁎
Kun Gaoa, Xiu-Rong Zhangb, , Zhi-Cheng Yub, Pei-Ying Huob a b
School of Material Science and Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China School of Science, Jiangsu University of Science and Technology, Zhenjiang 212003, China
A R T I C LE I N FO
A B S T R A C T
Keywords: PtmIrn (m + n = 2–7) clusters Structure and stability Electronic property DFT
Structure, stability and electronic properties of PtmIrn (m + n = 2–7) clusters have been systematically investigated by using density functional theory (DFT) with considering the generalized gradient approximation (GGA). The results reveal that the ground state structures change from planar to three-dimensional structures with the increase of the number of atoms, and Ir atoms play a decisive role in the formation of PtmIrn clusters. The addition of a small amount amount of Ir improves the stability of pure Pt clusters. The stability analysis indicates that most of the Pt-rich clusters are more stable than those of the Ir-rich with same cluster size. The PtIr cluster charge transfer analysis illustrates that it not only occurs in different orbits, but also occurs between different atoms. PtIr3, Pt4Ir, Pt4Ir2, Pt3Ir3, Pt2Ir4, PtIr5 and Ir7 clusters exhibit comparatively large magnetism.
1. Introduction The transition-metals play important roles in the field of metallurgy and catalysis due to containing d electrons, which make formed clusters exhibit special electronic structures and physical-chemical properties. High-temperature alloy materials, magneto-optical recording materials, shape memory materials and the most important catalyst of chemical industry are all transition metal alloy materials. The chemical and physical properties of transition metal clusters can be changed by doping with other metal, and bimetallic clusters have a wide application prospect in catalysis science, surface science, nanoscience and nanotechnology. Therefore, transition metal doped clusters have been extensively investigated [1–10]. For example, the magnetic properties of Co12X (X = Ni, Ag, Pt, Au) clusters were analyzed by LU [9], which show that the impurities of the X atom break the symmetry of molecular orbitals of Co13. They induce the redistribution of the electrons, which dramatically alters the magnetism of Co12X clusters, and the total magnetic moments of Co12Pt cluster is 22 μB. And the geometrical structure, stability, electronic and magnetic properties of PdnIr (n = 1–8) clusters have been systematically studied by Bouderbala et al. [10]. They found that the total magnetic moment of PdnIr clusters is mainly localised on the Ir atom for Pd1-6Ir clusters. Meanwhile, the 5d orbital plays the key role in the magnetic moment of the Ir atom. Our research group has done some other atomic clusters studies [11–14]. For example, all the possible geometrical structures of PtnNim (n + m = 7, n,m ≠ 0) clusters
⁎
Corresponding author. E-mail address: [email protected] (X.-R. Zhang).
https://doi.org/10.1016/j.comptc.2018.06.016 Received 25 April 2018; Received in revised form 20 June 2018; Accepted 22 June 2018 Available online 23 June 2018 2210-271X/ © 2018 Elsevier B.V. All rights reserved.
are optimized with density functional theory [14]. The results show that all the ground state structures of PtnNim clusters are cube structures. Pt5Ni2 is the most stable one of PtnNim clusters. Ni atom plays a leading role in magnetism of the binary PtnNim clusters. Noble platinum metallic clusters are often used as a catalyst in the chemical industry because of their exhibiting remarkably higher chemical stability and catalytic activity. Iridium is platinum-group metal which not only is one of the most corrosion-resistant metal, but also plays an important role in the catalytic process. At present, platinum or iridium metals have been extensively studied both theoretically [15–29,35–44] and experimentally [30]. Guo et al. [28] reported the possible geometrical configurations and stability of PtIrn0, ± (n = 1–5) clusters by using density functional theory. Based on the stability analysis, they found that thermodynamics stability of clusters improves with the increase of atoms. Iridium atoms play a dominant action in stability of PtIrn0, ± clusters. Moreover, the energetic stability, electronic structure and magnetic properties of Pt8-nIrn clusters have been investigated by N Long et al. [29]. They found that the average binding energy of all the clusters presents the linear increment trend versus iridium atoms, bader charge analysis shows how tiny charge transfers from iridium to platinum. Experimentally, Pt–Ir catalysts with different atomic ratios were synthesized by Hu et al. [30], which illustrate that the addition of an appropriate amount of Ir improves the catalytic activity of pure Pt. In this paper, we have comprehensively studied the optimized structure, stability and electronic properties of PtmIrn bimetallic clusters
Computational and Theoretical Chemistry 1138 (2018) 168–175
K. Gao et al.
considering the spin multiplicity. The structure with lowest energy and real frequency was defined as the ground state stable structure. The lowest-energy optimized configurations of PtmIrn (m + n = 2–7) clusters are shown in Fig. 1. The symmetry, spin multiplicity and average bond lengths are listed in Table 2.
with m + n = 2–7 to explore the effect of different ratio of Pt and Ir elements on the properties aforementioned. Which may provide a theoretical reference for the preparation of platinum iridium nanomaterials. 2. Computational method
3.1.1. Pure Ptn and Irn clusters (n = 2–7) In order to investigate the ground state structures of bimetallic PtmIrn clusters, we first discuss the structures of pure Ptn and Irn clusters (n = 2–7) by using the method in Section 2. This range has also been studied by other workers [16–20,26,27,35,39,41–44], but in some cases, our ground state structures are different. For pure Ptn clusters, the ground state structures of our calculated results are consistent with the previous theoretical results [44] except that Pt4 and Pt7. But the lowest-energy geometry of Pt4 cluster is in agreement with the theoretical result [42]. The isomer of Pt7 with C3v symmetry is evaluated to be the ground state structure which can be regarded as capping one Pt atom on the vertex of the triangular prism structure. For pure Irn clusters, the ground state structures of our calculated results are in accordance with the theoretical results [20] except for Ir7. We obtain the ground state structure of Ir7 cluster with C2v symmetry by optimizing the side-face-capped triangular prism.
All calculations of the optimized configuration, stability and electronic properties of PtmIrn (m + n = 2–7) clusters were performed using DFT semi-core pseudopots in the Dmol3 package in Material Studio. The exchange-correlation interaction of between electrons was treated within the generalized gradient approximation (GGA) [31] using PW91 [32] functional. The double numerical basis set augmented with polarization functions (DNP) [33] was utilized. The convergence criterion of self-consistent field (SCF) was set to be 10-5Hartree. And the direct inversion in an iterative subspace (DIIS) [34] approach was used to accelerate the speed of SCF convergence. We considered the smearing in calculation, and the smearing of molecular orbital occupation was set to be 0.005 Hartree. In the process of geometric optimization of the system, converge thresholds of the forces, displacement and energy were set to be 0.004 Hartree/Å, 0.005 Å and 2.0 × 10−5 Hartree, respectively, and the other parameters all adopted the default values. Then ground state structures was selected to analyze structure stability and electronic properties. To check the validity of the computational method in our work, we firstly performed the calculation on the Pt2 and Ir2 clusters and the correlation data are as listed in Table 1. For Pt2, the bond length we obtained is 2.395 Å, which is in good agreement with previous theoretical data of 2.38 Å [17,22], 2.40 Å [35] and 2.34 Å [18,37,38,39], and the experimental values of 2.34 Å [36] and 2.45 Å [40]. Meanwhile, the binding energy (1.733 eV) is very close to previous theoretical data of 1.76 eV [38]. Similarly, for Ir2, our calculated bond length (2.284 Å) and Eb (2.233 eV) are in excellent agreement with the previous theoretical values (2.22 Å [22], 2.209 Å [27], 2.228 Å [41] and 2.28 eV [3]). All these results validate that our approach provides an efficient way to investigate PtmIrn clusters.
3.1.2. PtmIrn clusters (m + n = 2–7) Here we explore about bimetallic PtmIrn clusters. The Pt-Ir bond length in PtIr cluster with C∞v symmetry is 2.356 Å. The lowest-energy geometries of Pt2Ir and PtIr2 clusters are all planar isosceles triangle structures with C2v symmetry. The Pt-Ir bond length of Pt2Ir cluster (2.497 Å) is less than of PtIr2 cluster (2.509 Å). In the case of Pt3Ir, the ground state structure is a tetrahedral structure with C3v symmetry which can be regarded as a Pt atom at the top of the Pt4 cluster replaced by a Ir atom. The Pt-Pt bond length in Pt3Ir (2.660 Å) is longer than the Pt-Pt bond length (2.637 Å) in Pt4 cluster. For Pt2Ir2 cluster, the planar quadrilateral structure with C2v symmetry is found to be ground state structure. The ground state structure of PtIr3 cluster can be viewed as a Ir atom of the Ir4 cluster substituted and connected all Pt-Ir bond, the configuration is C2v symmetry and the Ir-Ir bond length (2.360 Å) is less than the bond length (2.396 Å) in Ir4 cluster. The isomer of Pt4Ir with C4v symmetry whose structure is the rectangular pyramid with Ir atom on the vertex is evaluated to be the ground state structure The Pt-Pt bond length (2.625 Å) is smaller than the Pt-Pt bond length (2.660 Å) in Pt3Ir clusters. For Pt3Ir2 cluster, the ground state structure is the Ir edge capped the triangular structure of tetrahedral structure with Cs symmetry. In the isomer of Pt2Ir3 cluster, the ground state structure is trigonal pyramid structure with Pt on the vertex and D3h symmetry. The structure of PtIr4 cluster with C2v symmetry is selected as the ground state structure. For PtmIrn (m + n = 6), the ground state structure of Pt5Ir cluster is an oblique triangular prism structure with Cs symmetry which can be seen as filling a Pt atom on Pt4Ir cluster ground state structure. The PtPt bond length (2.657 Å) is greater than the Pt-Pt bond length (2.625 Å) in Pt4Ir cluster. Pt4Ir2, Pt3Ir3, Pt2Ir4 and PtIr5 clusters are all triangular prism structures which can be regarded as substituting atoms in the ground state structure of Ir6 cluster. Their symmetries are C2v, C3v, C2v and Cs, respectively. Finally, we investigate the PtmIrn (m + n = 7). The lowest-energy geometry of Pt6Ir cluster is similar to the lowest-energy structure of the Ir7 cluster with C2v symmetry and the Pt-Pt bond length is 2.634 Å. For Pt5Ir2 cluster, it can be obtained by capping a Pt atom to the Pt4Ir2 cluster. The isomer of Pt4Ir3 with C2v symmetry is evaluated to be the ground state structure which is resemble to the ground state structure of the Ir7 cluster. In the Pt3Ir4 cluster, the Ir edge capped the triangular structure with Cs symmetry is the most stable one. The calculations show that the isomer Pt2Ir5 with Cs symmetry is the ground state structure, which can be obtained by by capping a Pt atom to the ground state structure of PtIr5 cluster. The isomer PtIr6 with C3v symmetry is found to be the most stable structure among all optimized
3. Results and discussion 3.1. Geometrical structures In general, finding the ground state structure of binary alloy cluster is much more difficult than that of corresponding single pure cluster due to there exists non-equivalence of spatial geometric structure of atoms exchange position, and the quantity of possible configurations clusters increases exponentially with the increasing number of atoms. In order to find the ground state structures of PtmIrn (m + n = 2–7) clusters, we considered about 500 possible initial configurations, and constructed the initial configurations in two ways: (i) is guess the initial configuration directly; (ii) use the ground state structures of pure Ptn and Irn clusters as the basic framework, and then construct the initial configuration by capping, replacing and filling at different locations of the framework. The structure optimization and frequency calculation were carried out for each size of specific cluster on the premise of fully Table 1 Calculated bond length, binding energy; the experimental results and previous theoretical studies. Dimer Pt2
Ir2
Bond length (Å)
Eb (eV/atom) 1.733 1.76 [38]
Experimental
2.395 2.38 [17,22] 2.40 [35] 2.34 [18,37,38,39] 2.34 [36] 2.45 [40]
Our work Theoretical
2.284 2.22 [22] 2.209 [27] 2.228 [41]
2.233 2.28 [3]
Our work Theoretical
169
Computational and Theoretical Chemistry 1138 (2018) 168–175
K. Gao et al.
Fig. 1. The ground state structures of PtmIrn (m + n = 2–7) clusters.
isomers, which can be obtained by capping a Ir atom to the ground state structure of Ir6 cluster. By the above analysis, the ground state structures generally change from planar to three-dimensional structures with the increase of the number of atoms in general. We can seen that for PtmIrn (m + n = 2–4) clusters, all the optimized configurations are planar structure except that Pt4 and Pt3Ir which are tetrahedral structures. While for
m + n = 5–7, all the optimized geometries are three-dimensional structure except Pt5, Pt6 and PtIr4 which are planar structures. Especially m + n = 6–7, which all are triangular prism structures or the capped triangular prism structures. In the ground state structures, most of clusters use pure Irn (n = 2–7) clusters as basic structural units, indicating that the incorporation of Pt atoms in clusters did not destroy the formation of Ir-Ir bonds. But a fat lot clusters use pure Ptm 170
Computational and Theoretical Chemistry 1138 (2018) 168–175
K. Gao et al.
Δ2 En = E(PtmIrn + 1) + E(PtmIrn − 1)−2E(PtmIrn)
Table 2 Symmetry, multiplicity and average bond length of PtmIrn (m + n = 2–7) clusters. m+n
Cluster
Symmetry
Multiplicity
LPt-Pt/Å
LPt-Ir/Å
LIr-Ir/Å
2
Pt2 PtIr Ir2
D∞h C∞v D∞h
1 4 1
2.395 – –
– 2.356 –
– – 2.284
3
Pt3 Pt2Ir PtIr2 Ir3
D3h C2v C2v D3h
1 2 2 4
2.533 2.547 – –
– 2.497 2.509 –
– – 2.401 2.437
4
Pt4 Pt3Ir Pt2Ir2 PtIr3 Ir4
Td C3v C2v C2v D4h
1 4 1 6 1
2.637 2.660 2.523 – –
– 2.563 2.457 2.778 –
– – 2.349 2.360 2.396
5
Pt5 Pt4Ir Pt3Ir2 Pt2Ir3 PtIr4 Ir5
C2v C4v Cs D3h C2v C4v
1 6 1 2 3 4
2.523 2.625 2.628 – – –
– 2.583 2.597 2.645 2.346 –
– – 2.442 2.500 2.373 2.517
6
Pt6 Pt5Ir Pt4Ir2 Pt3Ir3 Pt2Ir4 PtIr5 Ir6
D3h Cs C2v C3v C2v Cs D3h
1 4 7 6 7 6 1
2.581 2.657 2.600 2.625 2.591 – –
– 2.641 2.553 2.507 2.572 2.559 –
– – 2.395 2.481 2.447 2.467 2.467
7
Pt7 Pt6Ir Pt5Ir2 Pt4Ir3 Pt3Ir4 Pt2Ir5 PtIr6 Ir7
C3v C2v Cs C2v Cs Cs C3v C2v
3 2 1 2 1 4 3 6
2.607 2.634 2.624 2.622 2.652 – – –
– 2.631 2.576 2.612 2.547 2.620 2.673 –
– – 2.399 2.507 2.465 2.470 2.485 2.492
Where E represents the binding energy of its most stable structure. The average binding energies reflect the binding ability of clusters. The larger the average binding energy is, the more stable the cluster will be. It can be seen from Figs. 2 and 3 that the average binding energies of clusters all increase with the increasing of size except PtmIr6 cluster in Fig. 2. And all the average binding energy of pure Irn clusters are larger then those of Ptn clusters, illustrating that the stability of iridium clusters is better then that of platinum. As seen from Figs. 2 and 3, it is obvious that the growth rate of average binding energies of different size clusters with Pt atoms is slower than that Ir atoms. The result reveals that iridium plays a major role in platinum-iridium doped clusters. The analysis results are in accordance with the previous analysis geometrical structures. It also can be seen from Fig. 3 that six are slight lifts corresponding to Pt3Ir2, Pt1,4,5Ir, Pt1,2Ir3, respectively. The emergence of these local magnitude maxima means that these clusters have stronger stabilities relative to their neighbours, and the addition of a small amount of Ir improves the stability of pure Pt clusters. The second-order energy difference (Δ2E) is a sensitive physical quantity to measure the thermodynamic stability of the cluster. The larger the value is, the higher the stability of the cluster will be. It can be found from Figs. 2 and 3 that the second-order energy difference of Pt2,3,5, Pt3Ir2, Pt1,4,5Ir, Pt2Ir3 and Ir2,4,6 clusters are positive. This means that these clusters are more stable, which is coincident with the result of the average binding energies. From Fig. 3, it is evident that there exist even-odd oscillations in the curves of Irn and Pt1,2Irn clusters, indicating that Ir2,4,6, Pt2Ir3 and PtIr1,5 clusters are more stable than their neighbors. The Δ2E values of PtIr, Ir2, Ir6, Pt2Ir3 and Pt5Ir clusters are much larger than those of other clusters, suggesting that the five clusters are more stable. 3.2.2. HOMO-LUMO energy gap (Eg) The chemical stability and activity of clusters are analysed by discussing the energy gaps of clusters. The variation curves of the energy gaps of PtmIrn cluster with the clusters size are plotted in the Fig. 4. The energy gap can be calculated by the following formula:
(m = 2–7) clusters as basic structural units, which suggests that the incorporation of Ir atoms in clusters destroys the formation of Pt-Pt bonds. And it is easy to form Pt-Ir bonds, which shows that Ir atoms play a decisive role in the formation of PtmIrn clusters.
Eg = ELUMO−EHOMO
Based on the optimized ground state structures, the relative stability of PtmIrn (m + n = 2–7) clusters are studied by calculating the average binding energies (Eb), second-order energy difference (Δ2E) and HOMOLUMO energy gap (Eg) physical parameters. 3.2.1. Averaged atomic binding energies (Eb) and Second-order energy difference (Δ2E) Figs. 2 and 3 show the variation of Eb and Δ2E of ground state structures of PtmIrn (m + n = 2–7) clusters with the number of Pt (Ir) atoms. The Eb and Δ2E of Xm (X = Pt or Ir) clusters are calculated using the following formulas: (1)
Δ2 E = E(Xm + 1) + E(Xm − 1)−2E(Xm)
(2)
The Eb of PtmIrn clusters is evaluated using the following expressions:
Eb = [mE(Pt) + nE(Ir)−E(PtmIrn)]/m+n
(3)
3.3. Electronic property
The Δ2E of PtmIrn clusters as a function of the number of Pt and Ir atoms can be calculated as:
Δ2 Em = E(Ptm + 1Irn) + E(Ptm − 1Irn)−2E(PtmIrn)
(6)
Where ELUMO is the lowest unoccupied molecular orbital energy, and EHOMO is the highest occupied molecular orbital. The values of the energy gaps reflect the ability for the electrons to transit from the HOMO orbital to LUMO orbital. The lager the value is, the stronger the chemical stability will be. To the contrary, smaller value represents high activity. It can be seen from Fig. 4 that Pt2,5, Pt1,2,3Ir and Ir2,3,7 clusters show higher energy gaps than other clusters, indicating that these clusters are stronger in chemical stability. It also can be found that most of energy gaps of the Pt-rich clusters are larger than those of the Ir-rich with same cluster size, which is coincident with the conclusion obtained from the average binding energy. In order to explore the process of charge transfer, PtIr is mainly discussed as representative, because it shows better stability compared to other clusters in the above analysis. The natural electronic population for Pt and Ir are 5s25p66s15d96p0 and 5s25p66s25d76p0, respectively. It can be found that charge transfer from 6 s orbits to 6p, 5d orbits in the Ir atom, and charge transfer from 5d orbits to 6 s, 6p orbits in the Pt atom. After electron transfer, The electronic population for Pt and Ir are 5 s(2.000) 5p(5.996) 6 s(1.147) 5d(8.939) 6p(0.055) and 5 s (2.000) 5p(5.999) 6 s(1.277) 5d(7.630) 6p(0.056), respectively. It also can be found that a part of charge transfer from Ir atom to Pt atom.
3.2. Stabilities of PtmIrn (m + n = 2–7)
Eb = [mE(X)−E(Xm)]/m
(5)
In order to study the electronic properties of PtmIrn clusters, we analyzed the partial and total density of states (DOS) for ground state structures of PtIr3, Pt4Ir, Pt4Ir2, Pt3Ir3, Pt2Ir4, PtIr5 and Ir7 clusters for
(4) 171
Computational and Theoretical Chemistry 1138 (2018) 168–175
K. Gao et al.
Fig. 2. The averaged atomic binding energies and second-order energy differences of the ground state structures of PtmIrn clusters as a function of the number of Pt atoms.
their spin multiplicities are relatively larger. The s, p, d orbitals and the total orbital up-spin and down-spin density of states distributions of these clusters are plotted in Fig. 5. Due to the contribution of the f orbitals on the total density of states is very small, it is not considered in our analysis. The clusters Fermi level is at zero presented as a solid vertical line, the upper and lower sides of Fig. 5 represent up-spin and down-spin electrons, respectively. It is obvious from Fig. 5 that the local state density curves of the dorbit of all clusters are narrow and sharp, which indicates that distribution of d orbital electrons are relatively localized. and the total density of states (TDOS) mainly come from contribution of d orbital in the range of −5–2 eV, whereas the contribution from s and p orbital electrons are relatively less. As is shown in the Fig. 5, the upper and lower curves of DOS of all clusters show low symmetry, indicating that there exist large number of unpaired electrons around these clusters, which is consistent with the situation reflected by spin multiplicity. So the contribute to magnetic moments are greater. As the spin of the unpaired electrons can produce magnetic moment, and the greater the spin multiplicity is, the larger the number of unpaired electrons will be. Then we can conclude that the seven selected clusters have high magnetism, and they show better propensity to adsorb small molecule. In order to study the magnetic properties of PtmIrn (m + n = 2–7) clusters, we also studied the local magnetic moments of each atom in PtmIrn clusters. Fig. 6 shows the electron spin density around individual atoms of these clusters, where the blue and yellow represent electronic states of up-spin and down-spin, respectively. The corresponding local and total magnetic moment of the seven selected clusters are listed in
Fig. 4. The Eg of PtmIrn clusters at ground state.
Table 3. The larger the electron spin density is, indicating that the more unpaired electrons around atoms, the larger the local magnetic moment will be. It is clearly seen from Fig. 6 that there are a large number of electron spin density around each atom in PtIr3, Pt4Ir, Pt4Ir2, Pt3Ir3, Pt2Ir4, PtIr5 and Ir7 clusters, illustrating that each atom in clusters
Fig. 3. The averaged atomic binding energies and second-order energy differences of the ground state structures of PtmIrn clusters as a function of the number of Ir atoms. 172
Computational and Theoretical Chemistry 1138 (2018) 168–175
K. Gao et al.
Fig. 5. The DOS of PtIr3, Pt4Ir, Pt4Ir2, Pt3Ir3, Pt2Ir4, PtIr5 and Ir7 clusters at ground state.
the Pt3Ir3 cluster, indicating that iridium atoms make a great contribution to the total magnetic moment. In addition to the total magnetic moment of all the chosen clusters is approximately 5 or 6μB. The results of the magnetic moment is coincident with the previous analysis about the density of states.
contributes a great deal to local magnetic moment. Moreover, there only exists up-spin electronic states without spin-down, which indicates that almost all of the electrons around these atoms are unpaired, so that it obtains larger total magnetic moment than other clusters. It can be seen from Table 3 that local magnetic moment of Ir atoms in each cluster all are larger than local magnetic moment of Pt atoms, except 173
Computational and Theoretical Chemistry 1138 (2018) 168–175
K. Gao et al.
Fig. 6. The electron spin density maps of PtmIrn (m + n = 2–7) clusters.
4. Conclusion
clusters generally us pure Irn (n = 2–7) clusters as basic structural units rather than pure Ptm (m = 2–7) clusters, illustrating that iridium atoms play a decisive role in the formation of PtmIrn clusters. In addition, it can be seen that the average binding energy (Eb) of clusters increases with the increasing of size except PtmIr6 cluster and the growth rate of average binding energies of different size clusters with Pt atoms is
The geometrical structures, stability and electronic properties of PtmIrn (m + n = 2–7) clusters have been systematically investigated by using density functional theory (DFT) with considering the generalized gradient approximation (GGA). The study results indicated that most of
174
Computational and Theoretical Chemistry 1138 (2018) 168–175
K. Gao et al.
Table 3 The local and total magnetic moments (μB) of PtIr3, Pt4Ir, Pt4Ir2, Pt3Ir3, Pt2Ir4, PtIr5 and Ir7 clusters. Atom number
1 2 3 4 5 6 7 Total
Clusters PtIr3
Pt4Ir
Pt4Ir2
Pt3Ir3
Pt2Ir4
PtIr5
Ir7
1.464 1.615 1.494 0.396(Pt)
0.916 0.916 0.916 0.916 1.336(Ir)
0.943 0.943 0.943 0.943 1.114(Ir) 1.114(Ir)
0.617(Ir) 0.620(Ir) 1.066 1.065 0.577(Ir) 1.054
1.130 1.130 1.131 1.131 0.739(Pt) 0.739(Pt)
1.292 0.762 0.696 1.231 0.351 0.668(Pt)
4.969
5.000
6.000
4.999
6.000
5.000
0.641 1.045 0.641 0.346 0.641 1.045 0.641 5.000
slower than that Ir atoms. The result also reveals that iridium plays a major role in platinum-iridium dopant clusters and the addition of a small amount amount of Ir improves the stability of pure Pt clusters. The second-order energy difference (Δ2E) of Irn and Pt1,2Irn clusters show “odd-even” oscillation. Thermodynamic stability of PtIr, Pt5Ir, Pt2Ir3 and PtIr5 clusters show stronger than other ground state clusters, and Pt2, PtIr, Ir2, Pt2Ir, Ir3, Pt3Ir, Pt5 and Ir7 clusters show higher energy gap (Eg) than other clusters, indicating that these clusters are stronger in chemical stability than other clusters. The PtIr cluster charge transfer analysis illustrates that the it not only occurs in different orbits, but also occurs between different atoms. As the DOS and electron spin density analyzed, PtIr3, Pt4Ir, Pt4Ir2, Pt3Ir3, Pt2Ir4, PtIr5 and Ir7 clusters exhibit comparatively large magnetic owing to there exist a large amount of unpaired electrons around all atoms.
[18] A. Sebetci, Z.B. Güvenç, Energetics and structures of small clusters: PtN, N =2–21, Surf. Sci. 525 (2010) 66–84. [19] D.R. Isakov, G.M. Khrapkovskii, A.G. Shamov, Quantum-chemical study of methane dehydrogenation on neutral, cationic, and anionic clusters Pt2–5 by DFT method, Russ. J. Gen. Chem 81 (2011) 781–782. [20] J. Du, X. Sun, J. Chen, G. Jiang, A theoretical study on small iridium clusters: structural evolution, electronic and magnetic properties, and reactivity predictors. J. Phys. Chem. A. 114 (2010) 12825–12833. [21] F. Li, B.C. Gates, Synthesis and structural characterization of iridium clusters formed inside and outside the pores of zeolite NaY, J. Phys. Chem. B. 107 (2003) 202–203. [22] P. Bloński, J. Hafner, Magnetic anisotropy of transition-metal dimers: Density functional calculations, Phys. Rev. B. 79 (2009) 1377–1381. [23] J. Wu, S.M. Sharada, C. Ho, A.W. Hauser, M. Head-Gordon, A.T. Bell, Ethane and propane dehydrogenation over PtIr/Mg(Al)O, Appl. Catal. A-Gen. 506 (2015) 25–32. [24] A. Grushow, K.M. Ervin, Ligand and metal binding energies in platinum carbonyl cluster anions: Collision-induced dissociation of Pt m − Pt m − and Pt m (CO) n − Pt m (CO) n −, J. Chem. Phys. 107 (1997) 8210. [25] T. Pawluk, Y. Hirata, L. Wang, Studies of Iridium Nanoparticles Using Density Functional Theory Calculations, J. Phys. Chem. B. 109 (2005) 20817–20823. [26] K. Bhattacharyya, C. Majumder, Growth pattern and bonding trends in Ptn(n = 2–13) clusters: Theoretical investigation based on first principle calculations, Chem. Phys. Lett. 446 (2007) 374–379. [27] X. Liang, X. Wu, X. Huang, Y. Su, J. Hu, J. Zhao, Magnetic anisotropy of small Irn clusters (n = 2–5), J. Clust. Sci. 27 (2016) 935–946. [28] W.L. Guo, Q. Rao, X.R. Zhang, Theoretical study on structure and stability of PtIrn(0, ± )(n=1-5) clusters, Chinese J. Comp. Phys. 29 (2012) 453–458. [29] N. Long, J. Du, G. Jiang, The influence of the composition of eight-atom Pt–Ir clusters on the magnetic properties, Molec. Phys. 113 (2015) 3628–3636. [30] S. Hu, L. Xiong, X. Ren, C. Wang, Y. Luo, Pt–Ir binary hydrophobic catalysts: Effects of Ir content and particle size on catalytic performance for liquid phase catalytic exchange, Int. J. Hydrogen Energ. 34 (2009) 8723–8732. [31] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 78 (1997) 3865. [32] J.P. Perdew, Y. Wang, Accurate and simple analytic representation of the electrongas correlation energy, Phys. Rev. B. 45 (1992) 13244. [33] B. Delley, From molecules to solids with the DMol3 approach, J. Chem. Phys. 113 (2000) 7756–7764. [34] P. Pulay, Improved SCF convergence acceleration, J. Comput. Chem. 3 (1982) 556–560. [35] S.H. Yang, D.A. Drabold, J.B. Adams, P. Ordejon, K. Glassford, Density functional studies of small platinum clusters, J. Phys-Condens Mat. 9 (1997). [36] S.K. Gupta, B.M. Nappi, K.A. Gingerich, Mass spectrometric study of the stabilities of the gaseous molecules diatomic platinum and platinum-yttrium, Inorg. Chem. 20 (1981) 966–969. [37] Y. Xu, W.A. Shelton, W.F. Schneider, Effect of particle size on the oxidizability of platinum clusters, J. Phys. Chem. A. 110 (2006) 5839. [38] L. Xiao, L. Wang, Structures of platinum clusters: Planar or spherical?†, J. Phys. Chem. A. 108 (2004) 8605–8614. [39] B. Hamad, Z. El-Bayyari, A. Marashdeh, Investigation of the stability of platinum clusters and the adsorption of nitrogen monoxide: First principles calculations, Chem. Phys. 443 (2014) 26–32. [40] U. Müller, K. Sattler, J. Xhie, N. Venkateswaran, G. Raina, Scanning tunneling microscopy of single platinum atoms and small platinum clusters on highly oriented pyrolytic graphite, J. Vac. Sci. Technol. B. 9 (1991) 829–832. [41] M. Chen, D.A. Dixon, Low-lying electronic states of Ir(n) clusters with n = 2–8 predicted at the DFT, CASSCF, and CCSD(T) levels, J. Phys. Chem. A. 117 (2013) 3676–3688. [42] M. Carmona-Pichardo, R.L. Camacho-Mendoza, L.A. Zarate Hernandez, J. CruzBorbolla, C.A. González-Ramírez, T. Pandiyan, N. Jayanthi, Activation of Pt–O and Pt–H bonds: DFT studies on adsorption of [Gd(H 2 O) n ] 3+, (n =8–9) with Ptn (n =3–7) cluster, Comput. Theor. Chem. 1047 (2014) 47–54. [43] P. Błoński, S. Dennler, J. Hafner, Strong spin-orbit effects in small Pt clusters: geometric structure, magnetic isomers and anisotropy. J. Chem. Phys. 134 (2011) 1495–1953. [44] V. Kumar, Y. Kawazoe, Evolution of atomic and electronic structure of Pt clusters: Planar, layered, pyramidal, cage, cubic, and octahedral growth, Phys. Rev. B. 77 (2008) 998–1002.
Acknowledgement This project was supported by the National Natural Science Foundation of China (Grant No. 51402131) References [1] A. Estejab, G.G. Botte, DFT calculations of ammonia oxidation reactions on bimetallic clusters of platinum and iridium, Comput. Theor. Chem. 1091 (2016) 31–40. [2] F. Aguileragranja, R.C. Longo, L.J. Gallego, A. Vega, Structural and magnetic properties of X12Y (X, Y = Fe Co, Ni, Ru, Rh, Pd, and Pt) nanoalloys, J. Chem. Phys. 2010 (132) (2010) 1882. [3] J.B. Davis, S.L. Horswell, R.L. Johnston, Global optimization of 8–10 atom palladium-iridium nanoalloys at the DFT level, J. Phys. Chem. A. 118 (2014) 208–214. [4] J.X. Yang, J.J. Guo, D. Dong, Ab initio, study of AunIr (n = 1–8) clusters, Comput. Theor. Chem. 963 (2011) 435–438. [5] R.N. Zhao, Y.H. Yuan, J.G. Han, Transition metal Mo-doped boron clusters: A computational investigation, J. Theor. Comput. Chem. 2014 (13) (2014) 1450036. [6] S. Sicolo, G. Pacchioni, A DFT study of PtAu bimetallic clusters adsorbed on MgO/ Ag(100) ultrathin films, Phys. Chem. Chem. Phy. 12 (2010) 6352–6356. [7] E. Florez, F. Mondragon, F. Illas, Theoretical study of the structure and reactivity descriptors of CunM (M=Ni, Pd, Pt; n = 1–4) bimetallic nanoparticles supported on MgO(001), Surf. Sci. 606 (2012) 1010–1018. [8] M.B. Javan, Structural, electronic and magnetic properties of small bimetallic zirconium–palladium clusters: Ab initio study, J. Alloys Compd. 643 (2015) 56–63. [9] Q.L. Lu, J.C. Jiang, J.G. Wan, G.H. Wang, Structure and magnetic properties of Co12X(X = Ni, Ag, Pt, Au) clusters, Int. J. Mod. Phy. B. 21 (2007) 5091–5098. [10] W. Bouderbala, A.G. Boudjahem, A. Soltani, Geometries, stabilities, electronic and magnetic properties of small PdnIr (n = 1–8) clusters from first-principles calculations, Mol. Phy. 112 (2014) 1789–1798. [11] X.R. Zhang, Y.N. Cui, L.L. Hong, Aromatic character studies on M0, ± n (M = Ir, Pt; n = 3, 4) clusters via nucleus-independent chemical shifts (NICS) calculation and geometric structure, J. Comput. Theor. Nanos. 6 (2009) 640–643. [12] C.H. Gao, X.R. Zhang, Geometries and physical properties of WnNim (n + m ≤7) clusters, J. Comput. Theor. Nanos. 7 (2010) 612–618. [13] X.R. Zhang, M. Luo, F.X. Zhang, X.Y. Zheng, G.K. Hu, B. Structure stability and magnetic properties of OsnB (n, = 11–20) clusters ‡. B, Mater. Sci. 38 (2015) 425–434. [14] X.R. Zhang, X. Yang, Y. Li, W.L. Guo, Structure stability and magnetic properties of PtnNim (n+m=7, n, m≠0) clusters, Acta. Chim. Sinica 69 (2011) 2063–2069. [15] P. Błoński, J. Hafner, Magneto-structural properties and magnetic anisotropy of small transition-metal clusters: a first-principles study, J. Phys-Condens Mat. 23 (2011) 136001. [16] A. Sebetci, Does spin-orbit coupling effect favor planar structures for small platinum clusters? Phys. Chem. Chem. Phy. 11 (2009) 921–925. [17] M.N. Huda, M.K. Niranjan, B.R. Sahu, L. Kleinman, Effect of spin-orbit coupling on small platinum nanoclusters, Phys. Rev. A 73 (2006) 053201.
175