Prediction of the Iron-Based Polynuclear Magnetic Superhalogens

Jun 28, 2017 - Department of Optoelectronic Science & Technology, College of Elecrical & Information Engineering, Shaanxi University of Science. & Tec...
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Prediction of the Iron-Based Polynuclear Magnetic Superhalogens with Pseudohalogen CN as Ligands Li-Ping Ding,† Peng Shao,*,† Cheng Lu,*,‡,¶ Fang-Hui Zhang,† Yun Liu,† and Qiang Mu† †

Department of Optoelectronic Science & Technology, College of Elecrical & Information Engineering, Shaanxi University of Science & Technology, Xi’an 710021, China ‡ Department of Physics, Nanyang Normal University, Nanyang 473061, China ¶ Department of Physics and High Pressure Science and Engineering Center, University of Nevada, Las Vegas, Nevada 89154, United States ABSTRACT: To explore stable polynuclear magnetic superhalogens, we perform an unbiased structure search for polynuclear iron-based systems based on pseudohalogen ligand CN using the CALYPSO method in conjunction with density functional theory. The superhalogen properties, magnetic properties, and thermodynamic stabilities of neutral and anionic Fe2(CN)5 and Fe3(CN)7 clusters are investigated. The results show that both of the clusters have superhalogen properties due to their electron affinities (EAs) and that vertical detachment energies (VDEs) are significantly larger than those of the chlorine element and their ligand CN. The distribution of the extra electron analysis indicates that the extra electron is aggregated mainly into pseudohalogen ligand CN units in Fe2(CN)5¯ and Fe3(CN)7¯ cluster. These features contribute significantly to their high EA and VDE. Besides superhalogen properties, these two anionic clusters carry a large magnetic moment just like the Fe2F5¯ cluster. Additionally, the thermodynamic stabilities are also discussed by calculating the energy required to fragment the cluster into various smaller stable clusters. It is found that Fe(CN)2 is the most favorable fragmentation product for anionic Fe2(CN)5¯ and Fe3(CN)7¯ clusters, and both of the anions are less stable against ejection of Fe atoms than Fe(CN)n−x.

1. INTRODUCTION The negative ions with superhalogen property have attracted considerable attention due to their commercial role in forming salts and oxidizing and purifying agents in the chemical industry.1,2 A striking feature of these polyatomic systems is the ultrahigh electron affinities (EAs), as high as 14 eV,3 which are significantly higher than those of the halogen atoms. These molecules or clusters are termed as superhalogens4 or hyperhalogens.5,6 Superhalogens were first predicted by Gutsev and Boldyrev.4 They described them using the simple formula MXk+1 (M is a main-group or transition-metal atom with maximal formal valence k, and X is a halogen atom). As became clear later on, this formula is, in fact, more general and to be (MnLnk+1)¯,7,8 which can be used to indicate polynuclear superhalogens, possessing more than one central atom. Moreover, the superhalogen can also be created by substituting halogen atom with oxygen or hydrogen.9−12 In 2009, dramatic progress was made in studying superhalogen systems. Smuczynska et al.13 studied the superhalogen anionic species with monovalent pseudohalogens as ligands. The pseudohalogens are polyatomic analogues of halogens, whose chemistry resembles that of the true halogens. The results shows that the pseudohalogens, such as cyanide CN, can be used as ligands while designing novel superhalogen anions, and the CN ligand leads to the species with the vertical detachment energy (VDEs) in the 7.1−8.9 eV range. Much work, both theoretical © 2017 American Chemical Society

and experimental, has been done about the polynuclear superhalogens based on new other ligand than halogen. These studies have demonstrated that polynuclear superhalogens possessed higher VDE value, namely, they possess more obvious superhalogen properties.8,14−16 On the one hand, polynuclear superhalogen is the possibility of increasing the number of ligands while avoiding the increase of interligand repulsion, which usually exist in mononuclear superhalogens.8 On the other hand, the VDEs of superhalogens with new ligand (e.g., pseudohalogen) as building block may even exceed that of traditional superhalogen.17 As to the polynuclear superhalogens, however, the previous studies are limited to halogen ligands,3,15,16,18−23 including our work on iron-based magnetic superhalogens,24 with only a few exceptions.5,9,25,26 It seems that there remain many problems to be studied further from the theoretical point of view. To examine the limitations of pseudohalogens in forming polynuclear superhalogens, we here mainly focus on the neutral and anionic Fe2(CN)5 and Fe3(CN)7 clusters. Both of them meet the general formula (MnLnk+1)¯, because the Fe atom has predominate oxidation states of +2. The reason why we select CN as ligand is that it is the simplest pseudohalogen and has high EA value (4.07 eV), which mimics the chemistry of Received: March 15, 2017 Published: June 28, 2017 7928

DOI: 10.1021/acs.inorgchem.7b00646 Inorg. Chem. 2017, 56, 7928−7935

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Inorganic Chemistry

Table 1. Calculated Valuesa of Bond Length r (Å), Frequency ωe (cm−1) and Dissociation Energy De (eV) for Fe2, CN, and FeC Dimers at Different Levels Fe2

FeC

basis set

r

ωe

De

r

ωe

De

r

ωe

De

B3LYP

6-311+g* 6-311+g(2df) 6-311+g(3df) aug-cc-pvdz 6-311+g* 6-311+g(2df) 6-311+g(3df)

1.99 1.98 1.98 1.98 2.01 1.99 1.99 2.02 ± 0.02b

359 359 360 428 410 415 413 300 ± 15c

0.49 0.51 0.52 0.64 1.05 1.00 0.96 0.78 ± 0.17d

1.17 1.16 1.16 1.17 1.17 1.17 1.17 1.172e

2147 2150 2151 2138 2130 2158 2158 2069e

7.64 7.77 7.80 7.54 6.67 7.02 7.08 7.75 ± 0.2f

1.62 1.61 1.60 1.63 1.55 1.54 1.53 1.596g

606 605 607 591 1037 1031 1036

4.04 4.09 4.10 3.45 3.31 3.45 3.45 3.9 ± 0.3g

CCSD

Exp. a

CN

method

The boldface values represent the experimental values. bReference 43. cReference 44. dReference 45. eReference 46. fReference 47. gReference 48.

3. RESULTS AND DISCUSSION 3.1. Geometries. We first discuss the structures of anionic and neutral Fe2(CN)5 and Fe3(CN)7 clusters. According to our structure search, it is found that CN moieties bind to Fe atoms individually. C pointing toward Fe is the most favorable form for different modes of CN attachment, such as dimer (CN)2 and trimer (CN)3. So, the decisive factor on the relative stabilities of these clusters is the way of the terminal CN unit binds Fe atom, and the binding Fe atom with C atom leads to lower energy. A similar scenario was also observed in the Mg2(CN)5 anion.26 However, it is found that the CN ligands maintain integrity in different structures. In Figures 1 and 2, we

halogen atoms. In particularly, it has been confirmed to be capable of forming mononuclear superhalogens.13,25,27,28 Furthermore, we have found that Fe2F5 cluster exhibits superhalogen behavior, and its anion carries a large magnetic moment of 8 μB.24 However, to the best of our knowledge, almost there are no reports on polynuclear magnetic superhalogen with pseudohalogen as ligand. Thus, it will be interesting to see if Fe2(CN)5 and Fe3(CN)7 clusters exhibit superhalogen properties, and their anions can also carry a large magnetic moment as Fe2F5¯ cluster?

2. COMPUTATION DETAILS The unbiased structure search is performed using the CALYPSO (Crystal structure Analysis by particle Swarm Optimization) method combined with B3LYP (Becke’s threeparameter hybrid exchange functional with the Lee-Yang-Par correlation) functional.29−31 It has been successfully used to predict the ground state structures of various systems.32−37 For neutral and anionic Fe2(CN)5 and Fe3(CN)7 clusters, the first generation of structures is produced randomly and subsequently optimized. Each generation contains 30 structures. For the next generation, 60% of the structures are generated from the lowest enthalpy structures provided by previous generation, evolved using particle swarm optimization. Different spin multiplicities are considered in the geometric optimization process. We usually followed 50 generations to achieve convergence. Next, the top 50 low-lying structures are collected as candidates for the lowest-energy structure. These isomers with energy difference from the lowest energy isomers less than 2 eV are further reoptimized with frequency calculations at B3LYP/6-311+G* level.38−40 In the reoptimization procedure, the isomers with various spin states are reoptimized until the minimum energy come along. This level of theory has been successful in predicting the geometries of a large number of halogen-transition metal complexes correctly.9,24,25,41,42 To verify the reliability of our chosen computational method and basis set, we have calculated the bond lengths r, vibrational frequencies ωe and dissociation energies De of the dimers Fe2, CN and FeC. This procedure is shown to yield results in good agreement with experimental values,43−48 as listed in Table 1. In structure optimization, the structures are fully optimized without any symmetry constraints. All calculations are performed using the Gaussian09 program.49

Figure 1. Obtained geometries of anionic and neutral Fe2(CN)5 cluster along with their symmetries, electronic states and relative energies. Meanwhile, some bond lengths are also shown in Figure. All the bond lengths are given in Å and relative energies are in eV.

show several low-lying isomers of Fe2(CN)5 and Fe3(CN)7, respectively. The nomenclature of the anionic isomers are designated by nA-a, nA-b, ... according to their energy from low to high; the neutrals are designated by nN-a, nN-b, ..., where n stands for the number of CN moiety. In addition, the corresponding bond lengths, electronic states, symmetries and relative energies are also presented in Figures 1 and 2. The ground-state structure of the Fe2(CN)5¯ anion (5A-a) has one bridging CN unit which connects two Fe atoms. Each of the two Fe atoms is linked with two terminal CN units. These four terminal CN units bind to Fe atoms with C pointing toward Fe. The distances between Fe and C atoms range from 7929

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moiety. For the latter case, the C might use one electron to bind Fe, whereas N might form a dative bond with Fe. This ground state structure is similar to the corresponding Fe2F5 cluster.24 The low-lying isomer 5N-d, which is similar to the ground-state of anion with slight distortion, is 0.87 eV higher in energy than the ground state structure. For anionic and neutral Fe3(CN)7 clusters, the Fe atom carries oxidation state of +2. In the ground-state structure of anion Fe3(CN)7¯, two Fe atoms have 4-fold coordination, while the third Fe atom is 3-fold coordinated. The terminal CN units retain the bond length of 1.16 Å. The distances between Fe and C atoms are in the range from 1.94 to 2.12 Å, while the Fe−C bond lengths of anionic FeCN7¯ are ranging in 1.94−1.99 Å. The second isomer is 0.52 eV higher in energy as compared to the first one. The low-lying isomers 7A-c and 7A-d, whose energies are quite close to each other, are higher in energy than that of the ground-state by 1.62 and 1.69 eV, respectively. The most important results for the three isomers (7A-a, 7A-b and 7A-c) of anionic Fe3(CN)7¯ is that the terminal CN units bind Fe atom with C atom. While in the fourth isomer 7A-d, the terminal CN units bind Fe atom with N atom. So, we conclude that the binding between Fe and C atoms will lead to lower energy. Although the ground-state geometry (7N-a) of neutral Fe3(CN)7 are completely different from its corresponding anion, which displays an open linear structure, the terminal C− N bond lengths are still 1.16 Å. This means that the C−N bond is not affected when the CN ligand binds with Fe. The isomer (7N-c), in which two of the CN units dimerize and the other five CN moieties bind separately to Fe atoms, is found to be 0.86 eV higher in energy than the ground state structure. The geometry (7N-d), which is similar to the ground-state structure of anion, is higher in energy by 0.98 eV. 3.2. Superhalogen Properties. 3.2.1. Electron Affinity and Vertical Detachment Energy. The EA and vertical detachment energy (VDE) could be used to judge the nature of superhalogen. We calculate the EA and vertical detachment energy of anionic Fe2(CN)50/‑ and Fe3(CN)70/‑ clusters based on B3LYP hybrid functional with 6-311+G* basis set. Unfortunately, there is no any experimental value available. Thus, we have recalculated the VDE and EA for the lowestenergy Fe2(CN)50/‑ and Fe3(CN)70/‑ clusters at CCSD(T) (coupled-cluster method with singles, doubles and noniterative inclusion of triples)51 and MP2 (second order Møller−Plesset perturbation)52 levels of theory based on the geometries obtained at B3LYP levels. The calculated results of EAs and VDEs at different levels of theory are shown in Table 2. The vertical detachment energy (VDE) is calculated as the energy difference between the anion and its neutral counterpart both at the ground-state geometry of anion. The adiabatic EA is the energy difference between the ground-state of anion isomer and the corresponding lowest-energy neutral isomer. It can be

Figure 2. Obtained geometries of anionic and neutral Fe3(CN)7 cluster along with their symmetries, electronic states and relative energies. Meanwhile, some bond lengths are also shown in Figure. All the bond lengths are given in Å and relative energies are in eV.

2.02 to 2.06 Å, which are longer than the Fe−C bond length (1.84 Å) in FeCN¯ anion. All the CN units possess the bond lengths of 1.16 Å irrespective of bridging CN or terminal CN, which almost are the same as those in a free CN moiety and slightly shorter than C−N bond length (1.17 Å) in FeCN¯. In the other low-lying isomers, the bond lengths of some of CN units have been slightly lengthened but they are in a relatively narrow 1.17−1.18 Å range as shown in Figure 1. Compared with the bond length of C−N (1.177 ± 0.004 Å)50 of CN¯ anion, it can be seen that the bond length of CN¯ ligand is almost not affected in the various different structures. This observation also remains valid for their corresponding neutral species, which will be discussed in the following. The ground-state structure of neutral Fe2(CN)5 is similar to the anionic low-lying isomer 5A-c. The bond lengths of the terminal CN units are always 1.16 Å, while those of the bridging CN are shorter by 0.02 Å. The distances between Fe and C atoms range from 2.02 to 2.08 Å, which are longer than the Fe−C bond length (1.89 Å) in neutral FeCN and 1.62 Å in pure FeC cluster. This leads to the improved symmetry from C2 of anion to C2v of neutral. In polynuclear Fe2(CN)5 clusters, the CN can act either as the terminal CN or as the bridging

Table 2. Calculated Values of Electron Affinity (EA) and Vertical Detachment Energy (VDE) of the Lowest-Energy Anionic Fe2(CN)5¯ and Fe3(CN)7¯ Clusters at Three Levels of Theory Fe2(CN)5¯ 5A-a

Fe3(CN)7¯

5A-b

5A-c

5A-d

7A-b

7A-c

7A-d

method

EA

VDE

VDE

VDE

VDE

EA

VDE

VDE

VDE

VDE

B3LYP CCSD(T) MP2

5.47 6.23 6.44

7.01 6.70 7.56

5.98 6.85 7.45

5.17 6.32 7.16

5.50 6.80 7.54

5.33 6.02 6.41

5.90 6.35 6.74

5.47 5.87 6.31

5.94 6.12 6.62

4.92 5.73 5.45

7930

7A-a

DOI: 10.1021/acs.inorgchem.7b00646 Inorg. Chem. 2017, 56, 7928−7935

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Inorganic Chemistry seen from Table 2 that the Fe2(CN)5 and Fe3(CN)7 clusters displays to be superhalogen due to their EAs are significantly larger than the atomic values of F (3.48 eV), Cl (3.72 eV) and CN (4.95 eV) at the same B3LYP/6-311+G* level. Namely, cyanide (CN) is capable of forming polynuclear superhalogens. In addition, the VDEs of Fe2(CN)5¯ and Fe3(CN)7¯ are almost a factor of larger than those of F¯ (3.48 eV), Cl¯ (3.72 eV) and CN¯ (3.07 eV). This further indicates that these two complexes are indeed superhalogens. Such interesting properties can also be found in [Mg2(CN)5] .26 Furthermore, we observe that the values of EA and VDE for anionic Fe2(CN)5¯ are much higher than those of Fe2F5 cluster (EA = 3.791 eV and VDE = 4.555 eV).24 This indicates that replacing electronegative atom F by a pseudohalogen cyanide CN leads to a significant increase in EA and VDE values. The polynuclear superhalogen ligand can be formed by pseudohalogen CN. The reason that Fe 2 F 5 superhalogen has higher EA and VDE values than the Fbased one may be that the pseudohalogen CN has larger EA value (3.82 eV)53 than F (3.40 eV).54 For anion, based on our calculation, the VDE of CN¯ (4.08 eV) is also higher than that of F¯ (3.48 eV). Further, compared to the B3LYP and CCSD(T) methods, it is clearly found that MP2 overestimates EA values. 3.2.2. Electron Distribution. To further gain insight into the superhalogen properties of Fe2(CN)5 and Fe3(CN)7 clusters, we investigate the electron distribution of the lowest-energy configurations by analyzing the natural bond orbital (NBO) charge, as well as the highest occupied molecular orbitals (HOMOs). The results are shown in Figures 3 and 4,

Figure 4. Contour maps of the HOMOs of the ground-state anionic Fe2(CN)5¯ and Fe3(CN)7¯ clusters.

Fe1 atom (see Figure 3) acts as electron donator. According to the fundamental quantum mechanics,55 non-negligible extra electron distribution on all CN units will lead to large spatial extent of the extra electron and thus to lower electronic kinetic energy. This may be the reason for high VDE values of these two clusters. Molecular orbital (MO) analysis indicates that their HOMO has the most contribution from the Fe-d orbital and π orbitals of CN molecule, as illustrated in Figure 4. The content of HOMO, which only originates from CN ligands, is still not found in these two clusters. This is comparable with our studied Fe2Fn¯ (n = 2−7) clusters.24 3.2.3. Magnetic Moment. For the iron element, it carries a spin magnetic moment of 4 μ B /atom and is couple ferromagnetic in standard bulk phases. It is found that Fe2F5¯ carries a large magnetic moment of 8 μB.24 It will be, thus, a very interesting problem to elucidate how to change when Fe interacts with pseudohalogen CN. We calculated the spin magnetic moments of Fe2(CN)5¯ and Fe3(CN)7¯ clusters by using the multiplicity minus one, because the orbital magnetic moments are usually very small compared with the spin magnetic moments in clusters containing metal. It has been used successfully in earlier works.24,56,57 The magnetic moments of these two clusters are 8 and 10 μB, respectively. Namely, both of them continue to carry a large magnetic moment, as Fe2F5¯ cluster and the atomic magnetic moment of Fe atom is enhanced when it is decorated with pesudohalogen CN. Thus, Fe2(CN)5 and Fe3(CN)7 clusters can be termed as polynuclear magnetic superhalogens. To explore the origin of the magnetic behavior, we calculated the total spin density of states (TDOS) and partial spin density of states (PDOS) for polynuclear magnetic superhalogens Fe2(CN)5¯ and Fe3(CN)7¯. The calculated results of Fe2(CN)5¯ and Fe3(CN)7¯ are shown in left and right columns of Figure 5, respectively. From Figure 5, it can be noted that the total DOS shows clear spin polarization near the Fermi energy. By comparing the total and partial DOS, it is obviously found that the total DOS mainly come from the d-states of transitionmetal Fe atoms, while the magnetic moments of pseudohalogens CN-s and CN-p states are almost negligible, suggesting that the spin polarization is mainly localized on Fe atoms. This result is in good agreement with the finding of mononuclear iron-based magnetic superhalogen.24,32 Generally speaking, the hybridization between s, p, and d states causes the closed-shell Fe atoms to have an incomplete dshell configuration, which is usually responsible for the magnetism of transition-metal clusters. The sub-bands of the pseudohalogens CN-p states of Fe2(CN)5¯ cluster (Figure 5d) are more closely spaced with Fe-d states in comparison to that of Fe3(CN)7¯ cluster (Figure 5b), which enhances the depletion of Fe-d states through p−d hybridization. This results in the

Figure 3. Electron distribution of the lowest-energy structures by analyzing the NBO charge.

respectively. For the NBO charges, we mainly focus on the distribution of the extra electronic charge as one cluster moves from neutral to anion. From Figure 3, it can be seen that Fe atoms are positively charged in both anionic clusters and their corresponding neutrals. This may be because the CN, possessing high EA, withdraws electron from Fe. Compared with Fe2(CN)5¯, Fe3(CN)7¯, and their neutral counterparts, the extra electron is aggregated mainly into four terminal CN units in Fe2(CN)5− cluster. This leads to a large EA value and makes it a superhalogen. As for anionic Fe3(CN)7¯ clusters, the extra electron is almost distributed over the entire cluster, except that 7931

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Figure 5. Calculated total DOS and partial DOS of the ground-state anionic Fe2(CN)5¯ (a and b) and Fe3(CN)7¯ (c and d) superhalogens. The Fermi level is indicated by the vertical dashed line.

fact that the magnetic moment of Fe3(CN)7¯ is larger than that of the Fe2(CN)5¯ cluster. 3.3. Thermodynamic Stabilities. Because of the complexity of the structures of anionic Fe2(CN)5¯ and Fe3(CN)7¯ clusters, their thermodynamic stabilities against fragmentation into smaller clusters were investigated by considering several of the most possible fragmentation channels. For Fe2(CN)5¯ cluster, the symmetrical fragmentation paths Fe(CN)x¯ + Fe(CN)n−x (0 ≤ x ≤ n) were calculated. For Fe3(CN)7¯ cluster, three dissociation pathways, such as asymmetry fragmentation channels Fe2(CN)5¯ + Fe(CN)2, Fe2(CN)5 + Fe(CN)2¯, as well as symmetry Fe(CN)x¯ + Fe(CN)n−x + Fe (0 ≤ x ≤ n) fragmentation path, were considered. The reason why we mainly focus on these fragmentation pathways is that FeFa¯ + FeFn−a fragmentation channels have been found to be the most preferred fragmentation channels in anionic Fe2Fn¯ clusters.24 We thus want to see if they are also the preferred fragmentation channels for anionic Fe3(CN)7¯. The fragmentation pathways and corresponding dissociation energies for both clusters are listed in Table 3. The fragmentation energies of anionic Fe2(CN)5¯ and Fe3(CN)7¯ against fragmentation products are calculated by the following formulas, respectively.

Table 3. Dissociation Energies of Anionic Fe2(CN)5¯ and Fe3(CN)7¯ Clusters against Various Fragmentation Channels Fe2(CN)5¯ channel Fe¯ + Fe(CN)5 Fe(CN)¯+ Fe(CN)4 Fe(CN)2¯+ Fe(CN)3 Fe(CN)3¯+ Fe(CN)2 Fe(CN)4¯+ Fe(CN) Fe(CN)5¯+ Fe

8.513 6.013 5.089 2.395 3.973 5.429

channel

energy (eV)

Fe2(CN)5 + Fe(CN)2¯ Fe2(CN)5¯ + Fe(CN)2 Fe¯+ Fe(CN)7 + Fe Fe(CN)¯+ Fe(CN)6 + Fe Fe(CN)2¯+ Fe(CN)5 + Fe Fe(CN)3¯+ Fe(CN)4 + Fe Fe(CN)4¯+ Fe(CN)3 + Fe Fe(CN)5¯+ Fe(CN)2 + Fe Fe(CN)6¯+ Fe(CN) + Fe Fe(CN)7¯+ 2Fe

5.051 2.427 14.131 12.123 9.020 6.505 8.451 7.855 8.703 10.187

dissociation energies mean that products are more stable than the parents. From Table 3, we can obviously note that the dissociation into Fe(CN)3¯ + Fe(CN)2 is the most favorable fragmentation channel in the case of Fe2(CN)5¯, reflecting the fact that the negative charge resides on Fe(CN)3 part of cluster. Similar scenario is also observed in Fe2F5¯ cluster.24 The lowest dissociation energy of 2.395 eV in conjunction with the distribution of electron density of HOMO (see Figure 4) further confirms that the dissociation into Fe(CN)3¯ + Fe(CN)2 is the most favorable fragmentation channel for Fe2(CN)5¯. Thus, the Fe2(CN)5¯ can be seen as [Fe(CN)3]¯[Fe(CN)2] complex. As for Fe3(CN)7¯ cluster, it can be seen that the dissociation into Fe2(CN)5¯ and Fe(CN)2 is more favorable. The fragmentation through loss of Fe atoms is less stable than Fe(CN)n−x irrespective Fe2(CN)5¯ and Fe3(CN)7¯ cluster, and the cluster containing exactly one iron atom and two cyanide CN ligands is the predominant production during the dissociation procedure of Fe2(CN)5¯ and Fe3(CN)7¯ clusters.

ΔE = −{E[Fe2(CN)−5 ] − E[Fe(CN)−x ] − E[Fe(CN)5 − x ]} (1)

ΔE = −{E[Fe3(CN)−7 ] − E[Fe(CN)−x ] − E[Fe(CN)7 − x ] − Fe}

Fe3(CN)7¯ energy (eV)

(2)

The optimized lowest-energy structures of fragmentation products Fe(CN)n0/− (n = 1−7) are presented in Figure 6. For the former four neutral Fe(CN)n (n = 1−4) clusters, the structures in previous study58 are also employed as a guide during the optimized procedure. The positive dissociation energies mean that the parent clusters are more stable than the products, while negative 7932

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Figure 6. Obtained ground-state structures of neutral and anionic Fe(CN)n (n = 1−7) clusters at the same level of theory.

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Most importantly, these two anions are less stable against ejection of Fe atoms than Fe(CN)n−x.

AUTHOR INFORMATION

Corresponding Authors

*Phone/Fax: +86 29 86168320. E-mail: [email protected]. (P.S.) *E-mail: [email protected]. (C.L.)

4. CONCLUSIONS In summary, we perform a systematic study of the equilibrium geometries, magnetic superhalogen properties, and thermodynamic stabilities of Fe2(CN)5 and Fe3(CN)7 clusters. According to the unbiased structure search, it is found that CN moieties prefer to bind to Fe atoms individually with C pointing toward Fe, and the bond length of CN ligands maintain unchanged in different geometries. To judge the superhalogen properties of Fe2(CN)5 and Fe3(CN)7, we calculate their electron affinities and vertical detachment energies. The calculated results show that the values are significantly larger than that of the chlorine element. The feature of the extra electron distribution further confirms their superhalogen behavior. Both Fe2(CN)5¯ and Fe3(CN)7¯ anions are found to carry large magnetic moments, which can be termed as polynuclear magnetic superhalogens. The thermodynamic stabilities are investigated by considering several most possible fragmentation channels. It can be clearly seen that the fragmentation channels Fe(CN)3¯ + Fe(CN)2 and Fe2(CN)5¯ + Fe(CN)2 are the most favorable fragmentation pathways for Fe2(CN)5¯ and Fe3(CN)7¯ anionic clusters, respectively. We hope that this work can stimulate further experimental study on iron-based or other polynuclear magnetic superhalogens that confirms our predictions in the near future.

ORCID

Li-Ping Ding: 0000-0002-3793-9519 Cheng Lu: 0000-0003-1746-7697 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (Nos. 11604194, 11304167, and 21671114), The 973 Program of China (No. 2014CB660804), Natural Science Foundations of Shaanxi Province (Nos. 2016JQ1028 and 2016JQ1003), Scientific Research Plan Projects of Shaanxi Education Department (No. 16JK1098), the Shaanxi University of Science & Technology Key Research Grant (Nos. 2016BJ-01 and BJ1507), the Program for Science & Technology Innovation Talents in Universities of Henan Province (No. 15HASTIT020), and Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase) (No. U1501501). Calculations were performed using the Cherry Creek Supercomputer of the UNLV’s National Supercomputing Institute, as well as the National Supercomputer Center in Guangzhou. 7933

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