BAI Xi LIANG Rui-Rui LV JinWU Hi-Shun

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Structural, Electronic and Magnetic Properties of CoO (= 2～10) Clusters: A Density Functional Study①

BAI Xia, bLIANG Rui-RuiaLV Jina②WU Hai-Shun

a(041004)b(046000)

The structural, electronic, and magnetic properties ofCoO (2～10) clusters have been systematically investigated within the framework of the generalized gradient approximation density functional theory. The results indicate that the O atom occupies the surface-capped position on CoO (2～10) clusters. The stabilities of the host clusters are improved by adding one O atom. Maximum peaks of the second-order difference energy of the ground-state CoO clusters are found at3, 6 and 8, indicating higher stability than their neighboring clusters. Compared with corresponding pure Coclusters, the O-doped cobalt clusters have larger gaps between the HOMO and LUMO energy levels, indicating their higher chemical stabilities. In addition, the doping of O atom exhibits different influence on the magnetism of the clusters. This is also further investigated by the local magnetic moment, deformation charge density and partial local density of states analysis.

density functional theory, cobalt-based clusters, geometries, electronic structures, magnetic properties;

1 INTRODUCTION

Transition metal oxide clusters are widely used in high temperature chemistry, materials science, mi- croelectronics and nanotechnology areas, and have attracted extensive theoretical and experimental attention in the past ten years. For example, Clemmer[1]reported experimental measurement of Sc–O bond energies and ionization potentials of ScO2using guided ion beam reactions between ScO+and NO2. Wang[2]have calculated the structural and magnetic properties of small transition metal oxide clusters TMO(TM = Sc, Ti, V, Cr and Mn;1, 2;= 1～6) by usingdensity functional theory approach, and revealed that the geometries of clusters are closely correlated with the ratios of TM to O and the number of valence electrons of the TM atoms. Yang.[3, 4]studied the structural and electronic properties of LaO (2～12) clusters using the density functional theory (DFT), and found the doping of O atom prefers to stay outside the cluster, and can greatly improve the stability of small Laclusters. In addition, the structures, electronic, and magnetic properties of transition metal (M = Cr, Mn, Fe, and Ni) oxide clusters and their anions and cations have been studied largely[5-12].Gutsev G. L..[13]studied the polarizability per atom of the MO monomers (M = Fe, Co, and Ni), and found that the doping resulted in a steep decrease of polarizability ascompared to the atomic values. However, it is obvious that the existing theoretical study on CoO clusters is not sufficient, and that the detailed structural and electronic properties of the large size of CoO (≥5) clusters are still unclear. Therefore, it is desirable to extend the study of CoO clusters to larger size so as to glean a comprehensive unders- tan-ding of their exotic physical and chemical properties. We hope that our work can provide po- werful guidelines for the corresponding experiments and promote the functional design of the clusters cohesive material. In the past decades, on the experi- mental side, the mass selected cobalt oxide cluster anions CoO?(5～21,= 0～2) are studied by using photodetachment photoelectron spectroscopy (PES), indicating that O atom causes a minor influence on the electronic structures[14]. Jacobson and Freiser[15]have performed Fourier transform mass spectrometry investigation on the reaction of cationic Co dimers and trimers with O2. This was followed by a kinetic study of the reaction of small Co+clusters (2～9) with O2. On the theoretical side, Kosuke.[16]reported the results of structures of cobalt oxide cluster cations CoO+by ion mobility spectrometry (IMS), combined with the theoretical calculation in order to verify the struc- tures of the clusters, and concluded that (CoO)3-5+ions are monocyclic-ring structures and (CoO)6,7+has compact tower structures. Therefore, structural transition from the ring to compact structures occurs at (CoO)6+. The ground states of CoO(1～4) and their anions [CoO]–were studied by density functional theory, with the BLYP exchange- correlation functional[17]. However, the researches on single O atom doped cobalt clusters are seldom investigated except Liu[18]who study the structure and magnetic properties of the small-sized CoO (1～5) clusters by using the density functional approach.

As far as we know, there is no systematical first principle calculation on the large size of CoO (2～10) clusters. Our work aims to make clear how the O atom binds with the Co(2～10) clusters by theoretical calculation with density functional theory method, and try to explore how the stability changes after O atom’s doping with cobalt clusters, and how the magnetic properties of the host clusters are influenced by doping, finally to disclose the physical origin of the magnetic behavior of CoO clusters. We hope that our research work would provide a certain theoretical guidance for the prac- tical application of cobalt oxide clusters assembling materials.

2 COMPUTATIONAL DETAILS

All calculations were performed at the DFT level with the DMol3package in the Materials Studio of Accelrys Inc[19]. The exchange-correlation interaction was treated within the GGA using PW91 function (GGA-PW91)[20].The double numerical basis set augmented with-polarization and-polarization functions (DNP) was utilized. For the numerical integration, a fine quality mesh size was used, and the real space cutoff of the atomic orbital was set at 5.5 ?. The convergence criteria for structure optimization and energy calculations were set to fine with the tolerance for density convergence in SCF, energy, gradient and displacement 1 × 10-6eV/?, 1.0 × 10-5a.u, 0.002 Hartree/? and 0.005 ?, respectively.In geometry optimization procedure, we considered a number of initial structures including linear chains, planar and three-dimensional structures in this work to maximize our chance to find the ground state configurations of the alloy clusters. Meanwhile, we also look over other structures of LaO, ScO, YO, MnO, NbO, CoRh, CoMn, CoV and CoFe[5, 21-28]clusters. In addition, owing to the spin polarization, all optimized geometry was optimized again at various possible spin multiplicities.Consequently, the number of possible initial isomers increased very rapidly with the size increase of clusters.The cal- culations are implemented until the minimum energy is reached. We confirm the stability of the lowest- energy structures as minima of the potential energy surface by considering no imaginary frequency.

To check the validity of the computational method in our work, we first perform the calculation on the Co2and CoO dimers using PW91, PBE and BLYP, respectively. As listed in Table 1, we choose the PW91 method finally because the results are consistent with previous theoretical and experimental data well, and these data are sufficient to show that it is effective and reliable to study CoO (2～10) clusters with this method.

Table 1. Calculated Bond Lengths and Binding Energy per Atom of the Co2 and CoO Clusters Using Different Density Functional Theory Methods

3 RESULTS AND DISCUSSION

3. 1 Geometrical structures of theConO (n = 2～10) clusters

The low-lying geometries, symmetries, magnetic moment and energy relative (Δ) of CoO (2～10) clustersare shown in Figs. 1 and 2.The lowest energy structures of pure Coclusters are also in- cluded for comparison. The lowest frequencies of Coand CoO clusters are listed in Table 2.

Table 2. Frequencies (cm-1), HOMO-LUMO Gaps (eV) and Total Spin Magnetic Moments (μB) of Con/ConO Clusters. The Charges (e) on O Atoms of ConO Clusters Are also Presented

Fig. 1. Ground-state geometries of the corresponding bare Coclusters and the lowest-energy structures and low-lying isomers of CoO (2～6) clusters. Distances are given in ?

Fig. 2. The same as those in Fig. 1 but for7, 8, 9 and 10. Distances are given in ?

For CoO clusters, a number of different stable configurations for each size cluster are found, but only three of them are shown in this paper. In the case of Co2O cluster, the lowest-energy structure is an isosceles triangle (2v) with the O atom located at the apex. It has a total magnetic moment of 4 μB, which is consistent with previous theoretical calcula- tion results exactly[19]. A less stable structure with 0.106 eV higher energy than the most stable one has more relaxed Co–Co and Co–O bonds to bring with a higher magnetic moment of 6μB.

The most stable Co3O cluster adopts a planar structure (2v) with 7 μBof total magnetic moment.Its metastable structure (3 μB), which shares the same geometric structure with the lowest-energy of Co3O, is energetically less favorable than the most stable one by just 0.022 eV, so they are two energetically degenerate states and magnetic bistable states.The third stable isomer is a tetrahedron (C) which is different from theground state andmetastable state totally. It is 5 μBin magnetic moment and 0.107 eV less stable in energy than the lowest energy structure.

A triangular bipyramid (8 μB) with the O atom located at the apex is found to be the most stable structure of Co4O withCsymmetry, which is in good agreement with the previous theoretical results[19]. In comparison, the second lowest-energy structure has similar geometry with the3vsymmetryand lies 0.021 eV higher in energy with respect to the ground state.The next low-lying energy isomer (2v), which is energetically less stable than the most stable structure by 0.034 eV, exhibits double coordinating of O atom to the tetrahedron.

For the Co5O cluster, we considered a lot of initial geometries including capped triangular bipyramid, octahedron and pentagonal pyramid. The lowest- energy structure is a capped triangular bipyramid (C) with an 11 μBof total magnetic moment, in which the O atom is located at the capped position. The second stable isomer (9 μB), which shares the same geo- metric structure and symmetry, is just 0.003 eV higher in energy than the lowest-energy structure. By contrast, the other stable isomer at a higher energy (0.012 eV) is different from the first two because the O atom tends to bind preferably to the bridge site of the Co5O cluster.

Co6O cluster (14 μB) adopts an O-capped octahe- dron structure with3vsymmetry. In the metastable structure, the O atom coordinates with two con- necting Co atoms and is coplanar with four Co atoms of the octahedron. The other low-lying structure (C) with 0.029 eV higher in energy shares the same configuration with the ground state, while has a smaller total magnetic moment of 12 μBwhich maybe results from the decrease in average bond length.

The ground-state structure of Co7O (15 μB) is a bi-capped octahedron withCsymmetry, in which the O atom is located at the capped position. The next two low-lying states have the same structure (2v) in which atom O lays coplanarly with the 5-membered ring of the hexagonal bipyramid. With total magnetic moments of 13and 15 μB, their energies are higher than the ground-state structures by 0.044 and 0.051 eV, respectively.

The lowest-energy structure of Co8O cluster can be viewed as a tricapped octahedron (C) with an 18 μBof total magnetic moment and the O atom is capped on the Co8ground-state geometry. The metastable state is a bicapped pentagonal bipyramid (2v) where O atom lies in the middle plane and is opposite to the bicapped position. Its energy is 0.021 eV higher than the lowest energy structure. A side-capped tetrahedral prism geometrical isomer (C) with the O atom located at the capped position, which shares similar total magnetism with the ground state and the metastable state, is considered to be the next stable structure at a slightly higher energy (0.027 eV).

In terms of Co9O, three low-lying structures are similar, which are all the bi-capped tetragonal antiprisms. The difference lies in the way how tocap. For the ground state structure (19 μB) with4vsym- metry, the bi-capped atoms locate oppositely. While the metastable state and the third state are the same completely on structure (3v), in which the O impurity occupies an anterior capped position of pure Co9with notable instability (0.003 and 0.016 eV, respectively).

In the case of Co10O, the structure is different from the Co10cluster, which tends to form large layered structure of Co clusters. In addition, three low-lying structures have the same configuration and symmetry. The metastable state (18 μB) and the third state (14 μB)are higher in energy than the ground-state struc- ture (20 μB) by 0.027 and 0.0055 eV, respectively.

From the above analysis, geometry optimizations reveal that O atom tends to bind preferably to the bridge site of the Co2O and Co3O clusters. About geometries of CoO (5, 6, 7, and 8) clusters, we can see that O adds to bind preferably to three coordination sites with the ground state geometries of Co(5, 6, 7, and 8), forming surface-capped structures. Although O atom also binds with three Co atoms in clusters of Co4O and Co10O, the way in which O atom binds is different. Their structures are based on the Co atoms rearrangement instead of the original ground-state structure of pure cobalt clusters. Additionally, for Co9O, O binds to Co atom on the square edge in the most stable geometry. In a word, the results indicate that the O atom occupies the surface-capped position on Co(=2～10) clusters. Meanwhile, we also found that a number of similar low energy isomers exist as the low-lying structures of the CoO (= 2～10) clusters.

3. 2 Stabilities and electronic properties

To investigate the influence of doping of O on the stability of cluster, we computed and compared the average binding energies per atom of the lowest energy structures of CoO clusters and Coclusters (Fig. 3). The atomic average binding energyb() can be expressed by the following formulas:

b(CoO) = [(Co) +(O) –

E(CoO)]/(+ 1) (1)

b(Co) = [(Co) –

(Co)]/(2)

whereis the total energy of the respective atom or cluster.corresponds to the number of Co atoms in clusters. From Fig. 3, we can see that the average binding energies of CoO clusters are larger than those of Coclusters, indicating that the doping with O improves the stability of the main cluster. Moreover, the average binding energies of CoO clusters are increasing with the size, which indicates that these clusters can continuously gain energy during their growth. Specifically, in the initial stage (1～7),bincreases rapidly, whilegoes from 7 to 10, thebexhibits obvious convergence trend. The change trend ofbfor pure Co clusters matches with the previous theoretical results well[26, 28, 29].

In cluster physics, the second-order difference of cluster energies is another important quality that can reflect the relative stability of clusters. The second- order difference energy Δ2() is also calculated using the following formulas below and plotted in Fig. 3:

Δ2(Co) =(Co+1) +(Co-1) –

2(Co) (3)

Δ2(CoO) =(Co+1O) +

(Co-1O) ? 2(CoO) (4)

whereis the total energy of cluster. As shown in Fig. 3, the Δ2() exhibits an obvious even-odd oscillatory behavior for Coclusters, indicating that the Coclusters with even number of atoms are more stable than their neighboring sizes. A similar trend is observed in CoO clusters except for Co3O. The local peaks are found at3, 6 and 8, which indicates that these clusters are relatively more stable than their neighboring clusters. Meanwhile, local mini- mum peaks appear at5, 7 and 9 identically. Overall, the doping of O atom does not influence the change trend of the stability of clusters.

Fig. 3. Average binding energies per atom and the second-order difference energiesof the most stable structures of Coand CoO clusters as a function of cluster size

In addition, the HOMO-LUMO gap is a charac- teristic quality of electronic structure and stability in clusters and is commonly used to measure the ability for clusters to undergo activated chemical reactions with small molecules. As shown in Table 2, the HOMO-LUMO gaps of CoO are usually larger than those of Coclusters except for8, suggesting their high chemical inertness of the doped CoO clusters. The reason for the largergapis that the O atom’s doping makes the Co–Co interaction weak in clusters, leading to the largegap[34]. That is consistent with the trend of the binding energies. Moreover, noticeable peaks ofgapare found at3, 6 and 10, indicating that these clusters must be more stable than the neighboring sizes. However, the stabilities of clusters for5 and 8 are low.

Fig. 4. 3isosurface HOMO and LUMO diagrams of Coand CoO clusters (2, 4, 6, 8)

We also perform Mulliken population analysis for the lowest-energy structures, and the atomic charges of O atom are presented in Table 2. It shows clearly that all of the O atoms are negatively charged. There is an obvious charge transfer from Co to O, indicating that the O atom is a Mulliken charge receiver. Furthermore, the charge transfer means the presence of ionic bonds between Co and O in CoO clusters. It is an important reason for the higher stability of the doped CoO clusters[35].

In order to understand the charge distribution between Co and O atoms of the doped clusters, we analyzed the charge difference density of Co3O and Co6O clusters. The difference charge density is defined as the difference between the total charge density of the cluster and a superposition of atomic charge densities with the same spatial coordinates in the cluster. As is shown in Fig. 5, the red color means charge accumulation, while the blue repre- sents charge depletion. Strong charge accumulation is observed around the O atom both in Co3O and Co6O, while the depletion of charge is found from vacuum to Co site. Significantly, the electron accumulation is highly localized, signifying the characteristic of ionic bond between O and its neighboring Co atoms. Additionally, we can con- clude that the extent of charge accumulation on O atom is greater in Co6O than in Co3O.

3. 3 Magnetic properties

Following, we will focus on the magnetic proper- ties of CoO (2～10) clusters. The total magnetic moment of the ground-state CoO (2～10) clusters has been calculated and the results are presented in Figs. 1 and 2. For comparison, the values of pure cobalt clusters are also plotted. Clearly, the total magnetic moments of CoO clusters increase with the size, which shows a similar trend with Coclusters. For2, 3, 6, 7 and 10, the total magnetic moments of clusters even remain constant after doping with the O impurity, and those of the Co(4, 5) clusters decrease while the values increase for8 and 9. Interestingly, whether the moment increases or decreases, it keeps a difference of 2 μB. The magnetic behavior of CoO (1, 3, 5) clusters is similar to that of the previous theoretical work[18].

Fig. 5. Calculated deformed charge density plots for Co3O (left) and Co6O (right)

In order to explore the magnetic origin further, we selected the ground state CoO (5, 7, 9) clusters as representatives to discuss the influence of the doping of O atom on local magnetic moment of the main clusters (Fig. 6). For comparison, the local magnetic moment per atom of corresponding pure Coclusters is shown in Fig. 6. As is evident from the figure, the magnetic moments of the CoO clusters are chiefly derived from the Co atom and the contribution of O atom is very small. Additionally,the magnetic moment reduction or enhancement upon doping stems from the reduced or increased local magnetic moments on the Co atoms. For instance, as for the Co5O cluster,the local magnetic moment of Co atom is reduced because of the doping of O atom, resulting in decrease on the total spin moment in contrast with the corresponding pure Co5cluster.In the case of9, accompanying the enhanced local magnetic moments on Co in the doped cluster, the total magnetic moment increases. For the cases of7, the O’s doping redistributes the spin moment on the Co atoms and the local moments decrease for the Co atoms near O and increase for those at a distance overall, thus the total magnetic moments of the clusters remain unaltered before and after loading O. A similar phenomenon also appears in previous study on the magnetism of atomic oxygen adsorbed Sc(2～14) clusters[36].

Fig. 6. Local atomic magnetic moments on each atom of the lowest energy structures of CoO (5, 7, 9)

To further understand the magnetic mechanism of CoO (1～9) clusters, we provide the partial (PDOS) and local (LDOS) contribution of different orbital components of Co5O, Co7O and Co9O clusters as representatives. As is evident from Fig. 7, firstly,we note that the magnetism of CoO is mainly from the contribution of Co atoms in which their electronic states below Fermi level come primarily fromelectron state and the contributions fromandelectron states are very small. For the O atom,below the Fermi level,the integral area of spin-upelectrons is nearly equal to the spin-downelectrons in LDOS, indicating that the doping of O atom can hardly affect the magnetism of clusters, which coincided with the above analysis about local magnetic moment of clusters. In addition, between the Fermi level of –4 and –6 eV, there is a clear indication of hybridization between O 2and Co 3,resulting in the rearrange of charge density and in turn influences the magnetic moment of cobalt clusters. Generally speaking, the relative shift between the spin-up and spin-down bands can indicate the degree of spin exchange splitting. Moreover, the greater spin exchange splitting, the larger spin polarization and magnetic moment of cluster[37]. As shown in Fig. 7, for Co5O cluster, we find that the spin-upelectrons integral area of Co5O/Co5is evidently smaller than that of the pure Co5cluster. Meanwhile, theelectron peak of spin-down of Co5O cluster is broadened around –5.5 eV below the Fermi level, which further counteracts the spin-upelectrons, indicating that the spin exchange splitting of DOS is decreased obviously. So, the total magnetic moment is decreased after O doping the pure Co5cluster. Compared with Co7cluster, there is no much change on spin exchange splitting of Co7O/Co7, and the differences of integral areas between spin-up and spin-downelectrons in pure Co7cluster and Co7O/Co7are similar, so the total spin moment of Co7O cluster remains unchanged. In addition, we find that the spin exchange splitting of Co9O/Co9is obvious, and the integral area of spin-upelectrons is evidently larger than that of spin-down below the Fermi level in LDOS, resulting in the increasing magnetism of the doping-O cobalt clusters.

Fig. 7. Partial (PDOS) and local (LDOS) density of states of Coand CoO (5, 7, 9) clusters. The broadening width parameter is chosen as 0.1 eV

4 CONCLUSION

By using the first-principles DFT-GGA calcula- tions, the geometries, stabilities, and magnetic pro- perties of the O doped Coclusters have been sys- tematically studied, with the results summarized as follows:

(1)In the most stable structures of CoO clusters, the O atom prefers to occupy the surface-capped position of Co(2～10) clusters. Geometry optimizations reveal that O atom tends to bind the bridge site in the Co2O and Co3Oclusters; the O atoms are capped by three coordination in CoO (5, 6, 7 and 8) clusters; for Co9O cluster, the O atom is capped by four coordination, in which the corresponding Comaintains its original ground state structure of pure cobalt cluster. In addition, by analyzing the most stable geometries of Co4O and Co10O clusters, we also found that the O atom prefers to bind with Co atoms in a way of three-coordinate, but Co atoms appear obvious rearrangement, and the Co10O cluster exhibits a layer structure model.

(2) From the analysis of the second-order energy difference, we can conclude that CoO clusters at3, 6, and 8 possess relatively higher stabilities than their neighbors, which means that the doping of O atom improves the stability of the Co3O, Co6O and Co8O clusters.

(3) By analyzing the HOMO and LUMO of Coand CoO (2, 4, 6, 8) clusters, we can conclude that the gap is mainly determined by the bonding strength between atomic orbitals.

(4) Compared to those of pure cobalt clusters, the magnetism calculations show that the total magnetic moments for CoO clusters emerge different chan- ging trends. Because of the hybridization between the 3state of Co and the 2state of doping-O,the local magnetic moments of Co atoms changed. However, the contribution of spin moments from O atom is negligible in CoO clusters. Thus, the magnetic moment reduction or enhancement by doping can be attributed to the decrease and increase of the local magnetic moments of the Co atoms.

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8 May 2017;

9 October 2017

10.14102/j.cnki.0254-5861.2011-1713

①Project supported by the National Natural Science Foundation of China (No. 21301112) and the Ph. D. Program Foundation of Ministry of China (No. 20131404120001)

②Born in 1978, professor, research field: cluster physics and computational chemistry. Tel/Fax: +863572051375, E-mail: lvjin_sxnu@163.com