+ (n = 1

Article pubs.acs.org/JPCC

Structural, Vibrational, and Magnetic Properties of FeCoOn0/+ (n = 1− 6) Bimetallic Oxide Clusters M. B. Torres,† A. Aguado,*,‡ F. Aguilera-Granja,¶ A. Vega,‡ and L. C. Balbás‡ †

Departamento de Matemáticas y Computación, Universidad de Burgos, Burgos, Spain Departamento de Física Teórica, Atómica y Ó ptica, Universidad de Valladolid, Valladolid, Spain ¶ Instituto de Física, Universidad Autónoma de San Luis Potosí, San Luis Potosí, México ‡

ABSTRACT: FeCo nanostructures are very interesting for storage media, sensing, and biomedical applications. To learn how an oxidizing environment may affect the physical and chemical properties of FeCo nanoparticles in the molecular limit, we investigated, by means of density functional theoretic calculations, the structural, electronic, and magnetic properties of neutral and ionized oxides of the magnetic dimer FeCo as a function of the oxygen content (FeCoOn and FeCoOn+ with n = 1−6). Our aim was to rationalize the structural pattern, energetics, effects of oxidation on the local and total magnetic moments and magnetic couplings, and effect of the ionization on all those properties. The binding energy shows saturation for an oxygen content in the range of n = 4−6. The metal−metal bond weakens with increasing oxygen content. This is reflected in the metal-to-oxygen charge transfer although not systematically in the magnetic properties because the total spin moment oscillates as a function of n between high-spin states (characterized by parallel magnetic couplings) and low-spin states (characterized by antiparallel couplings). Oxide clusters in the high-spin state retain the same total moment as the bare FeCo dimer because of the direct contribution of the oxygen atoms. Upon ionization, the weakening of the metal−metal bond is less marked and the overall magnetic moment decreases because of the increasing tendency toward antiparallel couplings. We calculated the vibrational frequencies and IR intensities of certain isomers of different geometries and spin states, from which future IR spectroscopy experiments could confirm the structural pattern and, indirectly, the magnetic state.

1. INTRODUCTION Transition-metal (TM) oxide clusters have attracted the attention of the scientific community and are presently a hot topic for several reasons. From the technological point of view, these systems have been shown to be good models for characterizing reactive sites in heterogeneous oxidation reactions.1−5 TM oxide clusters formed with the elements of bulk ferromagnets are also interesting to evaluate the influence of the oxidation on their inherent magnetic properties,6−8 the oxidation being a process difficult to avoid in real systems subject to environmental conditions. Designing a nanoparticle that retains a net magnetic moment in those realistic conditions is appealing in many contexts. For instance, Co-oxide nanoparticles are useful in storage media and biomedical sensors.9−13 From the fundamental viewpoint, the physics and chemistry of TM oxides is quite rich. Just characterizing the metallic or insulating character of bulk TM oxides is a challenge for the theoretical models which often have to accurately describe the electronic correlations; NiO or ZnO are good examples. At the molecular limit, a HOMO−LUMO gap always exists because of the finite size, even if the corresponding bulk counterpart is metallic, but the bonding pattern can be different from that in the bulk regime. In addition, the geometry is not necessarily a fragment of the bulk crystal. Understanding the © XXXX American Chemical Society

evolution of the electronic and structural properties (strongly interconnected) as size increases from the simplest TM-O molecule to the bulk limit is necessary knowledge if we want to achieve the technological goals. The present work focus on the molecular limit of TM oxide clusters formed with the elements of 3d bulk ferromagnets, in particular those based on the Fe−Co dimer. Fe−Co alloys are quite interesting for magnetic applications in soft magnets. At 30−40% of Co content the Fe−Co alloy is the material with the highest saturation magnetization, even larger than that of pure Fe bcc.14 Fe−Co alloys also have high Curie temperatures. Thus, alloys of nearly equal parts of iron and cobalt are widely used in commercial magnetic devices like, for instance, solenoids in which an extremely high saturation magnetization is required together with a small magnetic anisotropy. The magnetic properties of those alloys can be tuned at the nanoscale, as in thin films,15 nanocrystals,12 or nanoparticles or small clusters,13 which under realistic environmental conditions Special Issue: Current Trends in Clusters and Nanoparticles Conference Received: December 5, 2014 Revised: January 23, 2015

A

DOI: 10.1021/jp5121349 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

certain isomers so as to provide useful information for future IR-MPD experimental measurements to confirm the putative global minimum (GM) structures of those clusters and the corresponding electronic and magnetic properties. The rest of the paper is organized as follows. In section 2 we describe our theoretical method and computational details. Sections 3 and 4 describe the structural, electronic, and magnetic properties. The vibrational spectra of several isomers of FeCoO4+ and FeCoO6+, which can be used as a structural fingerprint in future experiments, are discussed in detail in section 5. The main conclusions are summarized in the last section.

can be subject to oxidation. Core−shell nanocrystals based on CoFe2O4/MnFe2O4 have been synthesized and shown to have unique features in blocking temperature and coercivity, which is of potential interest in storage media, sensing, and biomedical applications.12 Oxidation can be also useful in the synthesis process itself. A way to produce monodisperse Fe−Co nanoparticles with high magnetic anisotropy and controlable size, also of interest for storage and biomedical applications, is by means of CoFe2O4 nanoparticles of different sizes subjected to chemical reduction processes.13 Because the electronic properties are strongly connected to the structural properties, both properties have to be determined when investigating clusters. Unambiguous structural characterization of free-standing clusters from the experimental side is not possible at present. However, several spectroscopic techniques have been developed which, in combination with density functional theoretic calculations, allow us to obtain the plausible geometric arrangement of the cluster. Examples are photoelectron spectroscopyi (PES),16−19 infrared multiple photon dissociation spectroscopy (IR-MPD),3,20,21 ion mobility spectrometry (IMS),22,23 reactivity with CO,24,25 and collisioninduced dissociation.26−28 Recently, the fragmentation patterns of cobalt oxide clusters observed in mass spectrometry of jets of clusters produced by laser ablation29,30 were rationalized by Aguilera-del Toro et al. by means of density functional theoretic calculations.31 A similar study including pure and Cr-doped cobalt oxide cations was performed by Tung et al.32 for a small range of sizes. In regard to Co−Fe oxides, infrared spectroscopy experiments have been carried out only for the pure oxides. Kirilyuk et al. carried out IR-MPD experiments for cationic Fe oxide clusters of several sizes and stoichometries.21 Comparing with density functional theory (DFT) calculations of the vibrational spectrum allowed them to determine the putative spin magnetic configuration of certain clusters. Ota et al. studied Co oxide clusters by means of IMS. Again in combination with DFT calculations they identified the structures present in the cluster beam, some of which were of low-dimensional character (linear chains or rings).22 A particularly interesting question is how the magnetic interactions between the metal atoms, mediated by the successive addition of oxygen atoms, leads to a rich variety of magnetic states. These magnetic states depend not only on the number of oxygen atoms but also on the total charge of the cluster. For example, the two Fe atoms in Fe2O5+ (Fe2O5−) have parallel (antiparallel) spins, leading to a quadruplet (doublet) ground state.24,25 Instead, the two Fe atoms in Fe2O6+ (Fe2O6−) have parallel spins, but now leading to a doublet (quadruplet) ground state.24,25 In addition to the number of oxygen atoms and charge state, the mixed-metal oxide clusters present an additional freedom to set the magnetic state of the cluster, namely the different charge on the two metallic species, resulting from their interactions with oxygen and with the other metal. In view of the interest in understanding the electronic, magnetic, and structural properties of Fe−Co oxides and the existing experimental techniques, we conducted DFT calculations on small neutral and cationic Fe−Co oxides, namely FeCoOn0/+ (n = 1−6) with oxygen concentrations up to the saturation limit (we note that most experiments are performed on cationic clusters). The structural search was carried out by relaxing an exhaustive sampling of initial geometries. We also calculated the vibrational frequencies and IR intensities of

2. COMPUTATIONAL PROCEDURE We performed fully self-consistent DFT calculations using the SIESTA code,33 which solves the spin-polarized Kohn−Sham equations within the pseudopotential approach. For the exchange and correlation potential we used the Perdew− Burke−Ernzerhof form of the generalized gradient approximation.34 We employed norm-conserving scalar relativistic pseudopotentials35 in their fully nonlocal form,36 generated from the atomic valence configuration 3d74s1 for Fe (with core radii 2.60 a.u. for s, p, and d orbitals), 3d84s1 for Co (with core radii 2.50 a.u. for s, p, and d orbitals), and 2s22p4 for O (with core radii 1.00 au). Our pseudopotentials include nonlinear partial core corrections37 which are known to be important for transition metals. Valence states were described using double-ζ plus polarization basis sets for all the atomic species. The basis was variationally optimized by minimizing the total cluster energy with respect to the basis set parameters for selected atomic configurations. The energy cutoff used to define the real-space grid for numerical calculations involving the electron density was 500 Ry. The Fermi distribution function that enters in the calculation of the density matrix was smoothed with an electronic temperature of 300 K. We used an energy criterion of 10−4 eV for converging the electronic density matrix. With these computational settings, we conducted benchmark calculations on the diatomic molecules FeCo, FeO, CoO, and O2, both in their neutral and cationic states. Concerning the molecules that contain oxygen, we obtain good agreement with experimental results38−41 for the bond lengths, magnetic moments, electric dipole moments, and fundamental vibrational frequencies of the three molecules. The theoretical dissociation energies show, however, a significant overbinding of 0.6−0.8 eV as compared to experimental values. This problem is wellknown from previous DFT calculations of O2 employing semilocal orbitals.42 Its origin is well understood and can be traced back to the inaccuracy of present semilocal exchange functionals in capturing the effects of the different nodal structure of the orbitals of the oxygen atom as compared to those of molecular oxygen.43 Nevertheless, the good values obtained for the equilibrium bond length and vibrational frequencies suggest that the error in the energy does not significantly affect the shape of the potential energy curve in the chemically relevant bonding region in which we are interested. A similar conclusion has been reached in previous theoretical works.42 We also notice that our PBE results on the diatomics are of a similar quality (when compared to experimental values) as those obtained from the hybrid B3LYP functional employed in some of the previous works on similar systems.22 For the FeCo (FeCo+) molecule, we obtain Re = 1.99 Å (2.05 Å), a magnetic moment of 5 μB (4 μB), a harmonic frequency of 425 cm−1 (326 cm−1), and a dissociation energy B


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that partially emptying the more than half-filled 3d band in the TM atoms is usually a way to increase their local magnetic moments, at least in pure systems. Therefore, to get insight into the magnetic behavior of transition-metal oxide clusters as a function of the oxygen content, a dedicated calculation is required for each particular cluster. As we will show, it is hardly possible to extract well-defined general trends for the magnetic properties. Our results are organized as follows: Figure 1 displays the putative GM structures of FeCoOn0/+ complexes with n = 2−6, together with some of the low-lying structural isomers identified in this work. The structures will be referred to as n-i, where i is a roman number (I, II, III, ...) that identifies a specific structural isomer, according to the labels given in Figure 1. Excess energies with respect to the ground state

equal to 2.68 eV (2.70 eV). These numbers are in good agreement with previous DFT-generalized gradient approximation (GGA) calculations.44 The theoretical dissociation energy of FeCo+ compares very well with an experimental value of 2.69 ± 0.22 eV,45 which demonstrates that the overbinding problem occurs only with oxygen compounds. In the calculations, the individual clusters were placed in a cubic supercell of 20 × 20 × 20 Å3, a size large enough to make the interaction between the cluster and its replicas in neighboring cells negligible and to consider only the Γ point (k = 0) when integrating over the Brillouin zone. The equilibrium geometries resulted from an unconstrained conjugate-gradient structural relaxation using the DFT forces. Initial geometries were built by considering the different decorations of the oxygen atoms on the Fe−Co dimer. An exhaustive sampling of possible geometries was tested. Structures were relaxed without any symmetry constraint until interatomic forces were smaller than 0.001 eV/Å. In all cases, different spin isomers were checked to ensure the correct ground state. The vibrational frequencies were obtained by diagonalizing the Hessian matrix, obtained through finite differences under the harmonic approximation. Born effective charges were also determined through DFT perturbation theory to extract the relative line intensities (oscillator strengths) in an IF absorption experiment at the electric dipole level.46,47 Normal modes with a vanishing oscillator strength are silent at this level of theory, i.e., they can not absorb photons even if they have the appropriate resonant frequency. However, in experiments performed with high laser fluences, mechanical anharmonicity (which destroys the independence of normal modes), electrical anharmonicity, and higher-order multipolar effects may allow for the excitation of those “silent” modes.

3. STRUCTURAL AND MAGNETIC PROPERTIES In the following subsections, we will describe the detailed structural and electronic features separately for each value of n, as well as their relation with the geometrical and magnetic properties of Co2On0/+ and Fe2On0/+ clusters obtained in previous works,24,25,31,48,49 to provide useful information regarding the structural and magnetic excitations. Before presenting such a detailed and complex description, it is desirable to make a few general comments about the different physical factors that can influence the cluster magnetism and to provide an overview of the main results. It is well-known that clusters of ferromagnetic transition-metal elements (Fe, Co, and Ni) have high magnetic moments arising from parallel magnetic couplings and larger local (per atom) spin-polarization than in their bulk counterparts. Because oxygen is much more electronegative than those 3d elements, it is expected that charge transfer from TM to the oxygen atoms tends to reduce the total magnetic moment of the metal oxide clusters by favoring the occurrence of antiparallel couplings, particularly for Fe which will end with an effective d-band filling closer to that of Mn (that is in the frontier of the 3d antiferromagnets). Additionally, the strong metal−oxygen bonds may weaken the Fe−Co bond giving rise to a double exchange mechanism mediated by oxygen, which can also lead to antiparallel magnetic couplings in some cases. However, this interplay between metal−metal and metal−oxygen bonds is expected to depend on the composition, size, and geometry. On the other hand, one has to consider also the contribution of the oxygen atoms themselves to the total magnetic moment and the fact

Figure 1. Putative global minimum structures of FeCoOn0/+ (n = 2−6) clusters and some of their low-lying energy isomers. The colors are orange for Fe, pink for Co, and red for oxygen atoms.

energy are separately shown in Table 1 because there are several spin isomers for each structural isomer. Table 2 provides details about the lengths of the different bonds (Fe−Co, Fe−O, Co−O, and O−O) for the ground state of neutral and cationic complexes. Tables 3 and 4 contain the nominal charge excess and local magnetic moment on each atom for the GM structure of the neutral and cationic clusters, respectively. We next discuss the different stages in the oxidation process of the FeCo dimer from the structural point of view. The first two oxygen atoms prefer to occupy bridge positions, i.e., there is a clear tendency to maximize the number of metal−oxygen bonds at this initial stage. The next two oxygen atoms bind in atop positions along the Fe−Co molecular axis; the first of them binds to Fe, an observation consistent with the larger binding energy of the FeO dimer as compared to that of CoO. The fifth oxygen atom binds also on the iron side, without a C


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Some of the above trends change upon the ionization of the clusters. The structural pattern in the cation series slightly changes at n = 4, for which we identify two essentially degenerate stable structures. One of them is the same as the GM structure of the neutral, but the other one contains two oxygen atoms bonded to the Fe atom (structure 4-II). The GM structures of neutral and cation differ also for n = 5 (structure 5-II). The Fe−Co distance oscillates with n and ranges between 2.31 Å in the pure dimer and 2.49 Å in FeCoO4+. The lack of one electron also has consequences in the magnetic behavior. Overall the cluster cations are in a low spin-state of 0 μB or 2 μB characterized by an antiparallel coupling and low local spin polarizations. The only cluster that departs from this behavior is one of the two degenerate FeCoO4+ structures, which has a total spin moment of 4 μB associated with a parallel magnetic coupling. This is one of the clusters whose structure differs from its neutral counterpart. We notice that if the cation were to retain the neutral structure (isomer 4-I), it would have 0 μB instead, which is within the general trend for cations. This lowspin excitation of FeCoO4+ can be reached with an energy of just 20 meV. In view of the interest of this nano-oxide cation because of its high-spin state, and the tiny energy difference with respect to the first isomer, we performed a vibrational analysis of both isomers so that future experimental measurements of the vibrational spectrum can identify the correct ground state. Because both the structure and magnetic states are different, infrared spectra should be able to indirectly identify the magnetic state. We have performed similar calculations for n = 6 because of two spin isomers which are nearly degenerate. This is further discussed in the last section. 3.1. FeCoO0/+. The oxygen atom bridges the FeCo0/+ molecule forming a Fe−O−Co angle of 72.29° (149.06°) for the neutral (cation) state. The Fe−Co distance in the cation is large enough to consider that the oxidation process dissociates the Fe−Co bond, so each metal atom is bonded only to the oxygen atom. The cluster FeCoO+ is the only one in this study in which the Fe−Co bond is broken; therefore, all of its properties depart significantly from the global trends displayed by all the other clusters. Whereas the magnetic moment of the neutral oxide is 5 μB, for the cation it is only 2 μB because of an antiparallel coupling of the spins of Fe and Co. 3.2. FeCoO20/+. The quasi-rhombic structure 2-I, with both oxygen atoms in bridge positions, is the ground state of both neutral and charged clusters, with a magnetic moment of 1 μB and 2 μB, respectively. As seen in Table 1, the lowest energy excitations are associated with the spin isomers of this rhombic structure. We can compare our results with those obtained for Fe2O20/+ and Co2O20/+ in previous works. The GM structure of those pure metal oxides were found to be also the quasirhombic structure 2-I. The ground-state magnetic moment of the Fe2-dioxide, calculated with DFT-GGA methods, is 1 μB for cationic25 and anionic24 charge states and 2 μB for the neutral state,48 which implies that the spins of the two Fe atoms are in an antiparallel relative orientation. Concerning the Co2-dioxide, a zero magnetic moment was obtained for the neutral state49 using both B3LYP and CCSD(T) methods, whereas a ferromagnetic state with a magnetic moment of 5 μB was reported for the cation Co2O2+.31 Thus, the magnetic moment of FeCoO2+ (2 μB) is between those of Fe2O2+ (1 μB) and Co2O2+ (5 μB). The Fe−Co bond length in the 2-I structure is considerably longer than in the FeCo diatomic (this is true for both neutral and cationic states; see Table 2). On the other hand, the Fe−O

Table 1. Total Energy Differences (in Electronvolts), with Respect to the Global Minimum Energy, for the Structural Isomers of FeCoOn0/+ Clusters Shown in Figure 1a neutrals

cations

isomer

1 μB

3 μB

5 μB

0 μB

2 μB

4 μB

2-I 2-II 2-III 2-IV

0.00 0.65 0.63 1.54

0.11 0.76 0.88 0.91

0.24 0.83 0.61 1.15

0.21 0.60 0.74 −

0.00 1.26 1.11 2.53

0.57 1.45 1.23 1.75

3-I 3-II 3-III 3-IV

0.76 0.52 0.67 0.79

0.48 0.86 1.01 0.86

0.00 0.52 0.88 0.85

0.00 0.74 0.57 0.61

0.37 0.34 1.02 0.76

0.15 0.53 1.12 0.53

4-I 4-II 4-III 4-IV

0.11 0.86 1.05 1.48

0.22 0.59 0.76 1.43

0.00 0.60 1.03 1.25

0.02 0.31 0.71 −

0.36 0.13 0.84 0.87

0.08 0.00 0.52 −

5-I 5-II 5-III 5-IV

0.00 0.15 1.11 0.56

0.06 0.34 0.91 0.87

0.22 0.20 0.22 0.83

0.51 0.29 1.50 0.34

0.26 0.00 1.72 0.41

0.44 0.23 1.45 0.37

6-I 6-II 6-III

0.15 0.08 0.78

0.00 0.48 0.94

0.32 0.94 0.98

0.00 0.20 0.43

0.008 0.84 0.23

0.13 0.90 0.71

a

For each structural isomer, we include the energy of three different magnetic states.

direct O−O contact; finally, the sixth oxygen atom binds to Co and to another O atom with which it forms an oxygen dimer. The binding energy of the neutral FeCo-oxide clusters achieves saturation for this oxygen content, as discussed in a forthcoming section. As the oxygen content increases, the Fe−Co bond length systematically increases from 1.99 Å in the pure FeCo dimer to 2.54 Å in FeCoO6, and at the same time, the charge transfer from the metal to the oxygen atoms increases, both facts reflecting the weakening of the metal− metal bond. In spite of these structural and electronic trends, we could not find a systematic behavior of the total magnetic moment which oscillates between a high-spin state of 5 μB for FeCoO1, FeCoO3, and FeCoO4 and a low-spin state of 1 μB for FeCoO2 and FeCoO5. This means that the total spin moment does not decrease systematically with increasing oxygen content. In other words, one can find certain FeCo-oxide clusters with high oxygen content (close to the saturation limit) that retain the same total spin moment as the pure FeCo dimer (5 μB), an interesting result indeed for their potential technological use under oxidizing environmental conditions. A general trend is that high-spin states are due both to parallel magnetic couplings within the cluster and also to the direct contribution of the oxygen atoms. For instance, the local spin polarization on the metal atoms in FeCoO3 and FeCoO4 is lower than in the pure FeCo molecule because of their relatively high oxygen coordination, but the contribution of all the O atoms to the total moment is about 1 μB and the clusters retain the same moment as in the pure dimer. Low-spin states are mainly due to the occurrence of antiparallel magnetic couplings between the two metals. D


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Table 2. Interatomic Distances (in Angstroms) of the Several Bonds That Appear in the GM Structures of Neutral/Cation FeCo−On0/+ Clusters (n = 0−6)a FeCo n=0 1.990/2.306 1 n=1 2.144/3.405 1 n=2 2.281/2.424 1 n=3 2.308/2.368 1 n=4 2.437/2.494 1/1 n=5 2.471/2.393 1/1 n=6 2.540/2.424 1

FeO(b)

FeO(t)

CoO(b)

1.788/1.745 1

1.846/1.788 1

1.825/1.800 2

1.849/1.871 2

CoO(t)

O−O

O2

1.791/1.758 2

1.623/1.613 1

1.854/1.878 2

1.783/1.796 2/2

1.625/1.588 1/2

1.823/1.837 2/2

1.624 1/0

2.737 0/1

1.790/1.746 2/2

1.617/1.607 2/1

1.812/1.860 2/2

1.629/1.922 1/2

2.684 1/0

1.298 0/1

1.771/1.753 2

1.609/1.601 2

1.838/1.842 2

1.858/1.900 2

2.739/2.651 1

1.372/1.314 1

a

We use the symbol O−O to refer to the distance between two oxygen atoms that are bonded to the same metal atom, but not directly bonded to each other; the O2 symbol denotes instead molecular adsorption. Concerning the metal−O bonds, we distinguish between the bridge (b) and top (t) sites that can be occupied by an oxygen atom. The number of bonds of each type is given below the corresponding bond length. Note that for n = 4− 5 the number of Fe−O(t) and Co−O(t) bonds is different in neutral and cation states.

atom placed on top of the Fe atom and aligned with the Fe−Co molecular axis. In the neutral case, this causes a change of the Fe−Co spin coupling from antiparallel (2-I) to parallel (3-I). Instead, in the cationic case, the Fe−Co coupling remains antiparallel in both 2-I and 3-I structures. Thus, loss of a single electron (from neutral to cation) may lead to large changes in the magnetic coupling and total magnetic moment of that structure. The structural isomer 3-II shows an oxygen atom on top of the Co site and is more stable than some of the magnetic isomers of the GM structure. The other isomers shown in Figure 1 miss one of the bridging oxygen atoms and are generally less stable. Fe2O3+ (Fe2O3−) also adopt24,25 the rhombus structure with an additional oxygen on top of Fe, with an antiferromagnetic configuration and magnetic moments of 3 μB (1 μB). For Co2O3 (Co2O3+), calculations31 predict the 3-I structure as well, with a magnetic moment of 2 μB (5 μB). Thus, when a Fe atom of the antiferromagnetic Fe2O3 cluster is substituted with a Co atom, the resulting FeCoO3 becomes ferromagnetic. Considering the cationic counterparts, only the Co2O3+ shows a parallel arrangement of the spins of Co atoms. 3.4. FeCoO40/+. The neutral and cationic clusters show different GM ferromagnetic structures for this size, with magnetic moments of 5 μB and 4 μB, respectively. Both structures can be obtained by adding two oxygen atoms to the 2-I structure, which we take as a reference building block unit. In the neutral structure (4-I), the two oxygen atoms occupy atop positions which are approximately aligned with the Fe−Co axis. One of the oxygen atoms binds to iron, the other one to cobalt, and the structure as a whole is close to (although not perfectly) planar. In the cation structure (4-II), in contrast, the two oxygen atoms bind to the iron site at positions which are

and Co−O distances change only slightly upon the formation of the cluster. It is then sensible to visualize the structure of the FeCo-dioxide as resulting from the bonding between two polar molecular units (FeO and CoO) rather than by the attachment of two separated oxygen atoms to the covalent FeCo molecule. This point of view is further supported by the observation that the calculated lowest-energy dissociation channel results in FeO and CoO fragments. In the GM structure, the FeO and CoO units are in a parallel arrangement. The first structural isomer is 2-III for the neutral and 2-II for the cation. Both structures display a perpendicular arrangement of FeO and CoO units with a dangling oxygen atom and are just homotops of the same skeletal structure. The next structural excitation (2-IV) is no longer based on the very stable FeO and CoO units and thus it is much less stable. Interestingly, it is not possible to optimize a stable 2-IV cationic structure with zero magnetic moment because it transforms without barrier to the 2-I structure during the geometry optimization. The detailed quantitative data offered in Table 1 demonstrate the complex interplay between the charge state of the cluster and its structural and spin degrees of freedom, which causes, in general, the rich magnetic maps of the metal oxides, where exchange, double exchange, and superexchange magnetic interactions have been identified. We observe, for example, a strong influence of both the total charge and the spin on the relative stabilities of 2-II and 2-III structures (see Table 1). In other words, the excitation energy spectrum is determined by a complex competition between the structural and spin channels. 3.3. FeCoO 3 0/+ . The GM structure is the planar configuration 3-I for both neutral and cation states, with magnetic moments of 5 μB and 0 μB, respectively. This structure is obtained from 2-I by the addition of one oxygen E


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The Journal of Physical Chemistry C not aligned with the metal−metal axis so that the structure is no longer planar. There is no direct bond between the two oxygen atoms, so the adsorption of O2 to the Fe site is a dissociative chemisorption process. The local environment around the Fe site is approximately tetrahedral. The structure 4II is a high-energy excitation for the neutral cluster (0.59 eV, see Table 1). But the cationic 4-I structure with 0 μB is only 20 meV above the 4-II ground state. Given the expected accuracy of DFT-PBE calculations, the two cation structures can be considered to be nearly degenerate in practical terms. The rest of the isomers (4-III to 4-VII, not all of them are explicitly shown in Figure 1) represent high-energy excitations for both charge states. We note that there are isomers in which O2 attaches as a molecular unit to the Fe or Co sites. For the cation state, those isomers are indeed at excitation energies lower than that of the 4-III structure shown in Figure 1. These results suggest that molecular (nondissociative) chemisorption of O2 is more probable in cluster cations than in the neutral clusters. This is a sensible result as the total electronic charge on the oxygen atoms will be smaller in the cations (see Tables 3 and 4).

Table 4. Same as Table 3 for Cations type FeCo charge excess μ = 2 μB FeCoO charge excess μ = 2 μB FeCoO2 charge excess μ = 2 μB FeCoO3 charge excess μ = 0 μB FeCoO4 charge excess μ = 4 μB FeCoO5 charge excess μ = 2 μB FeCo-O6 charge excess μ = 2 μB

Table 3. Excess Electronic Charges (with Respect to the Nominal Atomic Charge) and Local Magnetic Moments (in μB) for the GM of Neutral Clustersa type FeCo charge excess μ = 5 μB FeCoO charge excess μ = 5 μB FeCoO2 charge excess μ = 1 μB FeCoO3 charge excess μ = 5 μB FeCoO4 charge excess μ = 5 μB FeCoO5 charge excess μ = 1 μB FeCoO6 charge excess μ = 3 μB

Fe

Co

O(b)

O(Fe)

0.149 1.807

−0.489 3.119

−0.259 1.737

0.748 0.144

−0.923 3.173

−0.673 −2.099

0.798 −0.036

−1.159 2.007

−0.771 1.987

0.725 0.349

0.479 0.309

−1.227 2.261

−0.996 1.354

0.662 0.252

0.428 0.604

0.469 0.277

−1.392 −0.852

−0.995 1.551

0.607 0.117

0.378 −0.294

0.417 0.657

−1.367 0.361

−0.962 1.648

0.590 0.168

0.385 0.000

0.189 0.326

Co

O(b)

O(Fe)

O(Co)

−0.536 3.868

−0.464 −1.868

−1.005 3.729

−0.834 −1.94

0.841 0.211

−1.344 3.686

−1.079 −2.291

0.712 0.302

−1.429 2.319

−1.156 −2.394

0.632 0.117

0.320 0.310

−1.474 0.390

−1.176 2.566

0.571 0.395

0.253 0.127

−1.437 2.209

−1.076 −1.712

0.580 0.022

0.318 0.322

0.017 0.563

−1.470 0.522

−1.070 −1.716

0.505 −0.253

0.241 0.272

0.022 0.578

1 and 2 μB, respectively. Both structures are obtained by adding three oxygen atoms to the 2-I reference structure. In the neutral 5-I GM structure, two oxygen atoms dissociatively bind to the iron site (O−O axis approximately perpendicular to Fe−Co axis) and the remaining oxygen atom binds to the Co site, with the Co−O bond approximately aligned with the Fe−Co axis. The structure is not planar. In the GM of the cation, one oxygen atom binds to the iron site and an O2 molecule binds to the Co site. The orientation of the adsorbed molecule is perpendicular to the Fe−Co axis and such that the cluster is planar. This is the first cluster for which an O−O bond occurs in the GM structure. This finding is consistent with our observation in the previous subsection that molecular chemisorption in the cationic oxides is more stable than that in the neutral oxides. The 5-III structure, with three oxygen atoms bridging the Fe−Co bond, is 0.22 eV higher than the neutral ground state, but it is not favorable at all for the cationic cluster (1.47 eV excitation energy). Instead, the cation prefers the 5-IV structure as a relatively low-energy excitation (0.34 eV), which has an O2 molecule on top of the Fe site. An isomer (not shown) with two dissociated oxygen atoms on top of Co and one oxygen on top of Fe is found at 0.69 eV (0.94 eV) for the neutral (charged) cluster. The ground state of Fe2O5− (Fe2O5+) shows a structure similar to 5-I with a magnetic moment of 1 μB (3 μB).24,25 Similar structures were found for Co2O5− (Co2O5+) with magnetic moments of 2 μB (3 μB).31 Thus, for n = 5 oxides, the ground states of pure and mixed clusters show low magnetic moments, indicating that the number of oxygen atoms is high enough to kill (to hinder) the magnetism of the diatom. This is further confirmed by the results for n = 6 shown in the following subsection. 3.6. FeCoO60/+. The GM of both neutral and charged clusters is the structure 6-I. Apart from the two bridging oxygen atoms which already appear in structure 2-I, it contains two terminal oxygen atoms on top of the Fe site, plus one oxygen molecule bonded to the Co site. The neutral cluster is

O(Co)

−0.149 3.193

Fe

a

Values for the two bridge oxygen atoms, O(b), are equal. Values for the oxygen atoms on top of Fe or Co are equal.

Previous theoretical reports on Fe2O4+ (Fe2O4−) also obtained the rhombus structure with one additional oxygen on top of each Fe atom in a nonplanar (planar) antiferromagnetic configuration with magnetic moments of 1 μB (1 μB).24,25 On the other hand, Co2O4 (Co2O4+) show GM structures of 4-I type with antiferromagnetic (ferromagnetic) coupling.31 In comparison, we obtain a ferromagnetic ground state for both the FeCoO40/+ neutral and cationic clusters. Thus, it seems that the mixing of Fe and Co enhances the magnetism of diiron and dicobalt tetraoxides. 3.5. FeCoO50/+. The neutral and cationic clusters have different GM structures as for n = 4, with magnetic moments of F


Article

The Journal of Physical Chemistry C ferromagnetic with a modest magnetic moment of 3 μB, and the cation is nonmagnetic (0 μB, although a spin excitation with 2 μB should be considered as essentially degenerate within the accuracy of our DFT-PBE model). Notice that the two O−O axis are perpendicular to the Fe−Co axis but only approximately perpendicular to each other, resulting in C2 point-group symmetry. The first structural excitation is the isomer 6-II, which differs from 6-I in two aspects: first, there are no O−O bonds in 6-II; second, the orientation of the two O− O axis relative to the Fe−Co axis is now the same, leading to C2v point-group symmetry. Isomer 6-III is quite similar in shape to 6-II, although 6-III is closer to planar and contains two O2 molecular units. Many other structural excitations (not explicitly shown in Figure 1) have been identified. Essentially, all of them involve either O2 molecular units of two O atomic units and differ just in the torsional angle of those units about the Fe−Co axis. In fact, we will see in a later section that those torsional modes determine together with bending modes the low-frequency tail of the vibrational spectrum. The lowest spin excitation of the GM structure is 0.15 eV (0 μB) above the ground-state energy for the neutral cluster and 0.008 eV (2 μB) for the cation (see Table 1). Note that the lowest-energy excitation channel for the neutral cluster is an isomerization to the 6-II structure, with an energy cost (0.08 eV) lower than that needed for the spin excitation. The reported GM structure of Fe2O60/+ clusters24,25 is of the 6-II type, with a magnetic moment of 3 μB (1 μB) for the anionic (cationic) species. Similarly, Co2O60/+ clusters also adopt the 6-II structure,31 with magnetic moments of 2 μB and 1 μB, respectively. Our results for mixed CoFeO60/+ clusters are generally consistent with those for pure clusters and confirm that the addition of more than four oxygen atoms tends to destroy the magnetism of the metal subsystem.

Figure 2. Upper panel: binding energy per atom as a function of the total number of atoms (N = n + 2). Lower panel: second energy difference as a function of the total number of atoms.

Peaks in Δ2(FeCoOn0/+) correspond to clusters that are highly stable relative to those with a neighboring number of O atoms. This quantity provides a local stability measure as it is essentially the curvature of the binding energy curve (which is an absolute stability measure). Δ2 is also plotted in Figure 2. We see that both neutral and cationic oxides are particularly stable for n = 2, which can be considered the stoichiometric composition of the metal-oxide if we assume oxidation states of +2 for both Fe and Co. In fact, cobalt acts usually as a divalent metal, while iron may act as either divalent or trivalent. It is then sensible to obtain a high stability for such an approximately stoichiometric oxide. Additionally, we find that the neutral cluster has also a high relative stability for n = 4. Instead, the cationic FeCoO4+ is less stable than his neighbors because the local maximum in the binding energy curve of the cations occurs at n = 5 instead of n = 4. The ionization potentials (IP) of the neutral FeCoOn clusters show an overall steady increase with oxygen content that saturates to a maximum value of about 9.7 eV for n = 4−6. The saturation in the IP (an electronic property) correlates with the saturation observed in the binding energies. The interatomic distances in FeCoOn0/+, reported in Table 2, show well-defined general trends as a function of oxygen content. Overall, the Fe−Co distance tends to increase with n, reflecting a gradual and quite steady weakening of the metallic bond. Bridge Fe−O and Co−O distances stay quite constant (with an average value of about 1.80 Å), which indicates that the FeCoO2 moiety is a quite rigid and identifiable unit in all these clusters. The distances between the metal atoms and the terminal oxygen atoms depend on the dissociative or molecular nature of the oxygen attachment. When the O2 binds as a

4. CLUSTER STABILITIES AND ELECTRONIC PROPERTIES Figure 2 shows the binding energy per atom, Eb0/+(FeCoOn0/+), as a function of the total number of atoms N = n + 2. This quantity is defined as E b0/ +(FeCoOn 0/ +) =

1 [E(Fe) + E(Co0/ +) + nE(O) n+2

− E(FeCoOn 0/ +)]

(1)

where E(A) is the total energy of system A. For the cationic cluster, FeCoOn+, we assume that the Co atom becomes ionized after the atomization process. Eb initially increases with the oxygen content, reflecting the higher strength of the metal−oxide bonds as compared to that of the metal−metal bond. After the attachment of four oxygen atoms, however, the Eb(N) curve displays a plateau region which extends up to n = 6 for neutral and cation clusters. These trends correlate very well with the type of oxygen adsorption, which can roughly be classified as atomic-like up to n = 4 and molecular-like for n > 4. In other words, the cohesive energy ceases to increase appreciably once each metal atom is saturated by three oxygens. Another interesting quantity in this context is the second energy difference with respect to the oxygen content, defined as Δ2 (FeCoOn 0/ +) = E(FeCoOn + 10/ +) + E(FeCoOn − 10/ +) − 2 × E(FeCoOn 0/ +)

(2) G


Article

The Journal of Physical Chemistry C molecular unit, the TM−O distances are longer, indicating the expectedly weaker nature of a molecular adsorption. The O−O distance in the adsorbed molecule is in the range 1.3−1.4 Å, i.e., quite elongated as compared to the O2 molecule in vacuo. This is due to charge transfer and is indicative of an incipient superoxo state. For dissociative adsorption, the O−O distance is much longer, with an average value of 2.7 Å. Deviations from these general trends are of course observed. For example, the Fe−Co distance in cluster cations shows an oscillating, nonmonotonous behavior on top of the general trend to increase with n. Such oscillations about the average behavior are typically observed in the physical properties of small cluster systems. The Mulliken charges and local magnetic moments shown in Tables 3 and 4 also show the expected general trends, despite the nonmonotonous detailed size evolution. The charge transferred from the TM atoms to the oxygen atoms increases initially with n but saturates at n = 4. The calculations suggest a limiting Mulliken charge of about +1.5 for Fe and +1.0 for Co. Similarly, the local magnetic moments on the TM atoms tend to decrease with increasing number of oxygen atoms, although for intermediate values of n ∼ 2−4 they can be even larger than in the isolated FeCo molecule, mostly the cobalt local moment. The results for n = 5−7 are consistent with the general expectations, stated above, that oxidation will tend to destroy magnetism. It is interesting that Fe is much more sensitive than Co: while the magnetic moment of iron is reduced by almost 100%, that of Co is reduced by only 10−20%. However, the results for n = 2−4 demonstrate that a moderate addition of oxygen atoms can reinforce the local magnetic moments on TM atoms. It is precisely in this range of n-values characterized by finite-size oscillations of the physical properties that the highest total magnetic moments emerge, demonstrating the need of dedicated calculations as the ones shown here.

Figure 3. Simulated infrared vibrational spectra of FeCoO4+ and FeCoO6+ cluster cations. Results are shown for the two nearly degenerate GM structures that we obtain for these sizes: 4-I (upper left), 4-II (lower left), 6-I with 0 μB (upper right), and 6-I with 2 μB (lower right). The black curves are obtained after broadening each frequency with a Gaussian envelope of 10 cm−1 width and include the calculated IR intensities at the electric dipole level. The green spikes show all the frequencies without any broadening, to help in the visualization of the “silent” modes.

the very soft bending modes. This difference may be essential in an experimental assignment. For n = 6, in contrast, the lowfrequency part of the vibrational density of states is quite similar in both spin isomers. Apart from bending and torsional modes which are similar to those identified for n = 4, there are additional low-frequency modes for n = 6 associated with the rotations of the O2 molecular unit relative to the rest of the cluster. The intermediate frequency range (∼400−750 cm−1) contains essentially the vibrational modes of the FeCoO2 quasi-rhombic central unit, and thus involves the motion of the two bridge oxygen atoms. The frequencies of these modes are quite the same in all the structures, reflecting the high stability of the FeCoO2 unit. For n = 6, this frequency region additionally contains the stretching modes associated with the Co−O2 bond, i.e., modes in which the O−O distance in the adsorbed molecule does not change. These modes are strongly IR-active, explaining the high peaks seen in the n = 6 spectra. Moreover, they appear at quite different frequencies in the two spin isomers of n = 6, so they might be useful in a structural assignment. The peaks located around 900 cm−1 are assigned as being due to stretching of the Co−O and Fe−O bonds (only Fe−O bonds in the case of n = 6), with the Co−O peak at slightly lower frequency. Finally, the peaks located close to 1200 cm−1 for n = 6 are due to the stretching mode of the O2 adsorbed molecule. These peaks occur at significantly different frequencies in the two spin isomers, so they may serve as a probe of the magnetic moment of this cluster. Because the orientation of this molecule is approximately perpendicular to the Fe−Co symmetry axis, this mode has a very low infrared activity. In case it can be detected under IR-MPD conditions, the mere observation of this mode would evidence the presence of adsorbed molecular units. Additionally, if the two spin isomers of n = 6 are really degenerate, a doublet structure

5. INFRARED SPECTRA OF SELECTED ISOMERS Figure 3 shows the simulated vibrational spectra for the two nearly degenerate structures obtained for FeCoO4+ and FeCoO6+. These two sizes are interesting because in one case (n = 4) the degeneracy involves two different structural isomers while in the other (n = 6) it involves two different spin states of the same structural isomer. Therefore, our results examine the sensitivity of the vibrational spectrum to both structural and spin excitations in bimetallic oxides. Also, we expect to motivate future multiple-photon dissociation experiments which might ultimately decide if the two proposed structures are really degenerate (in which case the experimental spectrum would be due to a mixture of the two isomers) or not (in which case only one isomer, the true GM, would appear in the experimental beam). The low-frequency tail of the spectra, covering approximately the range 0−350 cm−1, contains mostly bending and torsional collective modes, but also a localized mode located around 170−210 cm−1 (depending on the cluster size) which can be essentially identified with the Fe−Co stretching. The significant reduction in this frequency as compared to its value in vacuo (326 cm−1 for FeCo+) demonstrates the weakening of the metal−metal bond induced by oxidation. The spectra of the two n = 4 isomers differ most markedly in this low-frequency region. The structure 4-I is planar and has a very soft mode at 77 cm−1 which is related to the bending motion of the two terminal oxygen atoms. The structure 4-II is nonplanar and displays a tetrahedral FeO4 unit with stiffer bonds, so it misses H


Article


We expect our results to be of interest for designing small magnetic nanoparticles subject to oxidizing environmental conditions. We also expect to motivate future multiple-photon dissociation experiments which might ultimately decide, through the comparison with our simulated vibrational spectra, the structural pattern and magnetic spin state of FeCoO4+ and FeCoO6+.

should be observed in the high-frequency end of the vibrational spectrum.

6. CONCLUSIONS The main conclusions of our systematic DFT-GGA study of neutral and ionized oxides of the magnetic dimer FeCo as a function of the oxygen content, can be summarized as follows: (i) In the first stage of oxidation, there is a clear tendency to maximize the number of metal−oxygen bonds; oxygen binding to Fe is more favorable than to Co, in keeping with the larger binding energy of FeO as compared to that of CoO; when the oxygen content reaches 4−6 atoms, the binding energy (and ionization potential) of the FeCo-oxide clusters achieves saturation and further oxidation takes place through molecular adsorption; the FeCoO2 moiety is a quite rigid and identifiable unit in all these clusters. (ii) As the oxygen content increases, the metal−metal bond weakens, a fact reflected in the increasing Fe−Co bond length, in the increasing electronic charge transfer from the metal to the oxygen atoms, and in the softening of the Fe−Co stretching frequency. In the cationic oxides, these trends are relatively less marked. A rich map of spin and structural isomers is found. (iii) The total magnetic moment oscillates in the neutral oxides between a high-spin state of 5 μB for FeCoO, FeCoO3, and FeCoO4 and a low-spin state of 1 μB for FeCoO2 and FeCoO5. High-spin states are characterized by parallel magnetic couplings and a direct contribution of the oxigen atoms (up to 1 μB) to the total moment. This means that, despite the high degree of oxidation, certain FeCo-oxide clusters retain the same total spin moment as the bare FeCo dimer (5 μB), an interesting finding for their potential use in magnetic devices under oxidizing environmental conditions. Low-spin states are characterized by antiparallel magnetic couplings. (iv) The putative ground state of the cationic metal-oxides corresponds to low-spin states (0 μB or 2 μB), favored by the further emptying of the metal d-states upon ionization; the only exception could be FeCoO4+, for which the high-spin state with 4 μB is degenerate with the low-spin state (0 μB) within the accuracy of our theoretical approach. The change in spin state is accompanied by a change in the cluster structure which departs from the general trend. (v) The simulated vibrational spectra for the two nearly degenerate structures of FeCoO4+ differ most markedly in the low-frequency range (0−350 cm−1) containing bending and torsional collective modes as well as the Fe−Co stretching mode. We also calculated the spectra for two degenerate spin isomers of the same structural isomer of FeCoO6+, in which differences appear both in the intermediate frequency range (400−750 cm−1) in regard to the stretching modes associated with the Co−O2 bond and in the high-frequency range in the peaks located close to 1200 cm−1 that are due to the stretching mode of the O2 adsorbed molecule. Although our paper describes the oxidation process of a single FeCo molecule, we expect that the strong trends (such as conclusions (i) and (ii) above) identified here will hold also for the oxidation of bigger FeCo clusters. The conclusions about magnetic moment and ordering are not so easily extrapolated with confidence, however, as we did not identify clear-cut trends for the magnetic properties. In the future, it will be interesting to extend this work to include bigger bimetallic oxide clusters. Some preliminary calculations along these lines have been already initiated in our group.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We acknowledge the support of the Spanish “Ministerio de Ciencia e Innovación” and the European Regional Development Fund (Grant FIS2011-22957).

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REFERENCES

(1) Zemski, K. A.; Justes, D. R.; Castleman, A. W., Jr. Studies of Metal Oxide Clusters: Elucidating Reactive Sites Responsible for the Activity of Transition Metal Oxide Catalysts. J. Phys. Chem. B 2002, 106, 6136−6148. (2) Justes, D. R.; Mitrić, R.; Moore, N. A.; Bonacić-Koutecký, V.; Castleman, A. W., Jr. Theoretical and Experimental Consideration of the Reactions between VxOy+ and Ethylene. J. Am. Chem. Soc. 2003, 125, 6289−6299. (3) Fielicke, A.; Mitrić, R.; Meijer, G.; Bonacić-Koutecký, V.; von Helden, G. The Structures of Vanadium Oxide Cluster-Ethene Complexes. A Combined IR Multiple Photon Dissociation Spectroscopy and DFT Calculation Study. J. Am. Chem. Soc. 2003, 125, 15716−15717. (4) Xie, Y.; Dong, F.; Heinbuch, S.; Roccab, J. J.; Bernstein, E. R. Oxidation Reactions on Neutral Cobalt Oxide Clusters: Experimental and Theoretical Studies. Phys. Chem. Chem. Phys. 2010, 12, 947−959. (5) Wang, Z.-Ch; Yin, S.; Bernstein, E. R. Gas Phase Neutral Binary Oxide Clusters: Distribution, Structure, and Reactivity towards CO. J. Phys. Chem. Lett. 2012, 3, 2415−2419. (6) Tono, K.; Terasaki, A.; Ohta, T.; Kondow, T. Chemical Control of Magnetism: Oxidation-Induced Ferromagnetic Spin Coupling in the Chromium Dimer Evidenced by Photoelectron Spectroscopy. Phys. Rev. Lett. 2003, 90, 133402. (7) Roy, D. R.; Robles, R.; Khanna, S. N. Magnetic Moment and Local Moment Alignment in Anionic and/or Oxidized Fen Clusters. J. Chem. Phys. 2010, 132, 194305. (8) Wang, Y.; Gong, X.; Wang, J. Comparative DFT Study of Structure and Magnetism of TMnOm (TM = Sc-Mn, n = 1 − 2, m = 1 − 6) Clusters. Phys. Chem. Chem. Phys. 2010, 12, 2471−2477. (9) Kodama, R. H. Magnetic Nanoparticles. J. Magn. Magn. Mater. 1999, 200, 359−372. (10) Lu, A. H.; Salabas, E. L.; Schueth, F. Magnetic Nanoparticles: Synthesis, Protection, Functionalization, and Application. Angew. Chem., Int. Ed. 2007, 46, 1222−1244. (11) Benitez, M. J.; Petracic, O.; Tüysüz, H.; Schüth, F.; Zabel, H. Decoupling of Magnetic Core and Shell Contributions in Antiferromagnetic Co3O4 Nanostructures. Europhys. Lett. 2009, 88, 27004. (12) Song, Q.; Zhang, Z. J. Controlled Synthesis and Magnetic Properties of Bimagnetic Spinel Ferrite CoFe2O4 and MnFe2O4 Nanocrystals with Core-Shell Architecture. J. Am. Chem. Soc. 2012, 134, 10182−10190. (13) Poudyal, N.; Chaubey, G. S.; Rong, C. B.; Cui, J.; Liu, J. P. Synthesis of Monodisperse FeCo Nanoparticles by Reductive SaltMatrix Annealing. Nanotechnology 2013, 24, 345605. (14) Bozorth, R. M. Ferromagnetism; IEEE Press: Piscataway, NJ, 1993. I


Article

The Journal of Physical Chemistry C (15) Liu, X.; Morisako, A. Soft Magnetic Properties of FeCo Films with High Saturation Magnetization. J. Appl. Phys. 2008, 103, 07E726. (16) Majer, K.; Ma, L.; Hock, C.; von Issendorff, B.; Aguado, A. Structural and Electronic Properties of Oxidized Sodium Clusters: A Combined Photoelectron and Density Functional Study. J. Chem. Phys. 2009, 131, 204313. (17) Ma, L.; von Issendorff, B.; Aguado, A. Photoelectron Spectroscopy of Cold Aluminum Cluster Anions: Comparison with Density Functional Theory Results. J. Chem. Phys. 2010, 132, 104303. (18) Aguado, A.; Kostko, O. First-Principles Determination of the Structure of NaN and NaN− Clusters with up to 80 Atoms. J. Chem. Phys. 2011, 134, 164304. (19) Li, S.; Zhai, H. J.; Wang, L. S.; Dixon, D. A. Structural and Electronic Properties of Reduced Transition Metal Oxide Clusters, M4O10 and M4O10− (M = Cr,W), from Photoelectron Spectroscopy and Quantum Chemical Calculations. J. Phys. Chem. A 2012, 116, 5256−5271. (20) Kirilyuk, A.; Demyk, K.; von Helden, G.; Meijer, G.; Poteryaev, A. I.; Lichtenstein, A. I. Atomic Clusters of Magnetic Oxides: Structure and Phonons. J. Appl. Phys. 2003, 93, 7379. (21) Kirilyuk, A.; Fielicke, A.; Demyk, K.; von Helden, G.; Meijer, G.; Rasing, Th. Ferrimagnetic Cagelike Fe4O6 Cluster: Structure Determination from Infrared Dissociation Spectroscopy. Phys. Rev. B 2010, 82, 020405(R). (22) Ota, K.; Koyasu, K.; Ohshimo, K.; Misaizu, F. Structures of Cobalt Oxide Cluster Cations Studied by Ion Mobility Mass Spectrometry. Chem. Phys. Lett. 2013, 588, 63−67. (23) Aguado, A.; López, J. M. Structures and Stabilities of Aln+, Aln, and Aln− (n = 13−34) Clusters. J. Chem. Phys. 2009, 130, 064704. (24) Reilly, N. M.; Reveles, J. U.; Johnson, G. E.; Khanna, S. N.; Castleman, A. W., Jr. Experimental and Theoretical Study of the Structure and Reactivity of Fe1−2O≤6−Clusters with CO. J. Phys. Chem. A 2007, 111, 4158−4166. (25) Reilly, N. M.; Reveles, J. U.; Johnson, G. E.; del Campo, J. M.; Khanna, S. N.; Köster, A. M.; Castleman, A. W., Jr. Experimental and Theoretical Study of the Structure and Reactivity of FemOn+ (m = 1,2; n = 1 − 5) with CO. J. Phys. Chem. C 2007, 111, 19086−19097. (26) Li, M.; Liu, S.-R.; Armentrout, P. B. Collision-Induced Dissociation Studies of FemOn+: Bond Energies in Small Iron Oxide Cluster Cations, FemOn+ (m = 1 − 3, n = 1 − 6). J. Chem. Phys. 2009, 131, 144310. (27) Starace, A. K.; Neal, C. M.; Cao, B.; Jarrold, M. F.; Aguado, A.; López, J. M. Correlation between the Latent Heats and Cohesive Energies of Metal Clusters. J. Chem. Phys. 2008, 129, 144702; Electronic Effects on Melting: Comparison of Aluminum Cluster Anions and Cations. J. Chem. Phys. 2009, 131, 044307. (28) Aguado, A.; Jarrold, M. F. Melting and Freezing of Metal Clusters. Annu. Rev. Phys. Chem. 2011, 62, 151−172. (29) Yin, S.; Xue, W.; Ding, X.-L.; Wang, W.-G.; He, S.-G.; Ge, M.-F. Formation, Distribution, and Structures of Oxygen-Rich Iron and Cobalt Oxide Clusters. Int. J. Mass Spectrom. 2009, 281, 72−78. (30) Dible, C. J.; Akin, S. T.; Ard, S.; Fowler, C. P.; Duncan, M. A. Photodissociation of Cobalt and Nickel Oxide Cluster Cations. J. Phys. Chem. A 2012, 116, 2691−2697. (31) Aguilera-del-Toro, R. H.; Aguilera-Granja, F.; Vega, A.; Balbás, L. C. Structure, Fragmentation Patterns, and Magnetic Properties of Small Cobalt Oxide Clusters. Phys. Chem. Chem. Phys. 2014, 16, 21732−21741. (32) Tung, N. T.; Tam, N. M.; Nguyen, M. T.; Lievens, P.; Janssens, E. Influence of Cr Doping on the Stability and Structure of Small Cobalt Oxide Clusters. J. Chem. Phys. 2014, 141, 044311. (33) Soler, J. M.; Artacho, E.; Gale, J. D.; García, A.; Junquera, J.; Ordejón, P.; Sánchez-Portal, D. The SIESTA Method for Ab Initio Order-N Materials Simulation. J. Phys.: Condens. Matter 2002, 14, 2745−2779. (34) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (35) Troullier, N.; Martins, J. L. Efficient Pseudopotentials for PlaneWave Calculations. Phys. Rev. B 1991, 43, 1993−2006.

(36) Kleinman, L.; Bylander, D. M. Efficacious Form for Model Pseudopotentials. Phys. Rev. Lett. 1982, 48, 1425−1428. (37) Louie, S. G.; Froyen, S.; Cohen, M. L. Nonlinear Ionic Pseudopotentials in Spin-Density-Functional Calculations. Phys. Rev. B 1982, 26, 1738−1742. (38) Husband, J.; Aguirre, F.; Ferguson, P.; Metz, R. B. Vibrationally Resolved Photofragment Spectroscopy of FeO+. J. Chem. Phys. 1999, 111, 1433−1437. (39) Chestakov, D. A.; Parker, D. H.; Baklanov, A. V. Iron Monoxide Photodissociation. J. Chem. Phys. 2005, 122, 084302. (40) Sakellaris, C. N.; Miliordos, E.; Mavridis, A. First Principles Study of the Ground and Excited States of FeO, FeO+, and FeO−. J. Chem. Phys. 2011, 134, 234308. (41) Sakellaris, C. N.; Mavridis, A. Electronic Structure and Bonding of Cobalt Monoxide, CoO, and Its Ions CoO+ and CoO−: An Ab Initio Study. J. Phys. Chem. A 2012, 116, 6935−6949. (42) Behler, J.; Reuter, K.; Scheffler, M. Nonadiabatic Effects in the Dissociation of Oxygen Molecules at the Al(111) Surface. Phys. Rev. B 2008, 77, 115421. (43) Gunnarsson, O.; Jones, R. O. Total-Energy Differences: Sources of Error in Local-Density Approximations. Phys. Rev. B 1985, 31, 7588−7602. (44) Gutsev, G. L.; Mochena, M. D.; Jena, P.; Bauschlicher, C. W., Jr. Periodic Table of 3d-Metal Dimers and their Ions. J. Chem. Phys. 2004, 121, 6785−6797. (45) Hettich, R. L.; Freiser, B. S. Spectroscopic and Thermodynamic Investigations of Transition-Metal Cluster Ions in the Gas Phase: Photodissociation of MFe+. J. Am. Chem. Soc. 1987, 109, 3537−3542. (46) Giannozzi, P.; Baroni, S. Vibrational and Dielectric Properties of C60 from Density-Functional Perturbation Theory. J. Chem. Phys. 1994, 100, 8537−8539. (47) Baroni, S.; de Gironcoli, S.; Dal Corso, A.; Giannozzi, P. Phonons and Related Crystal Properties from Density-Functional Perturbation Theory. Rev. Mod. Phys. 2001, 73, 515−562. (48) Jones, N. O.; Reddy, B. V.; Rasouli, F.; Khanna, S. N. Structural Growth in Iron Oxide Clusters: Rings, Towers, and Hollow Drums. Phys. Rev. B 2005, 72, 165411. (49) Uzunova, E. L.; Mikosch, H. Electronic Structure and Reactivity of Cobalt Oxide Dimers and Their Hexacarbonyl Complexes: A Density Functional Study. J. Phys. Chem. A 2012, 116, 3295−3303.

J


+ (n = 1

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