Structural, Electronic, and Magnetic Properties of Iron Disulfide

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Article

Structural, Electronic and Magnetic Properties of Iron-Disulfide FeS (n=1-6) Clusters n

20/±

Slimane Tazibt, Aziz Chikhaoui, Said Bouarab, and Andres Vega J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b00942 • Publication Date (Web): 25 Apr 2017 Downloaded from http://pubs.acs.org on May 2, 2017

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The Journal of Physical Chemistry

Structural, Electronic and Magnetic Properties of 0/±

Iron-disulfide FenS2

(n=1-6) Clusters

S. Tazibt ,† A. Chikhaoui,‡ S. Bouarab,∗,‡ and A. Vega¶ Faculté du Génie Electrique et d’Informatique, Université Mouloud Mammeri de Tizi-Ouzou, B.P. No 17 RP, 15000 Tizi-Ouzou, Algeria., Laboratoire de Physique et Chimie Quantique, Faculté des Sciences, Université Mouloud Mammeri de Tizi-Ouzou, B.P. No 17 RP, 15000 Tizi-Ouzou, Algeria., and Departamento de Física Teórica, Atómica y Óptica, Universidad de Valladolid, Paseo Belèn 7, E-47011 Valladolid, Spain. E-mail: [email protected]

∗ To

whom correspondence should be addressed du Génie Electrique et d’Informatique, Université Mouloud Mammeri de Tizi-Ouzou, B.P. No 17 RP, 15000 Tizi-Ouzou, Algeria. ‡ Laboratoire de Physique et Chimie Quantique, Faculté des Sciences, Université Mouloud Mammeri de TiziOuzou, B.P. No 17 RP, 15000 Tizi-Ouzou, Algeria. ¶ Departamento de Física Teórica, Atómica y Óptica, Universidad de Valladolid, Paseo Belèn 7, E-47011 Valladolid, Spain. † Faculté

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Abstract 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0/±

The structural, electronic and magnetic properties of neutral and charged Fen S2 , n=1-6 clusters have been calculated in the framework of the density functional theory in the generalized gradient approximation for the exchange and correlation. The calculated adiabatic electron affinity and the vertical detachment energy are found to be in good agreement with the available experimental data. The impact of disulfide doping of the small iron clusters on the atomic structure, stability, magnetic moment and reactivity is determined through the analysis of the binding energy per atom, electronic charge transfer, spin-polarized electronic density of states and global reactivity indicators like the electronegativity and chemical hardness. Our results provide an exhaustive characterization of these small iron-sulfide particles in vacuum, a first step for completely understand their role as components of proteins.

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Introduction 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Transition-metal (TM) sulfide clusters are appealing in many fields ranging from catalysis to biology and material science. Their potential relationships with biology and nanotechnology, in particular, are exemplified by the iron-sulfide clusters which are involved in the electron transfer process as well as in many other functions such as substrate binding, catalysis, regulation and sensing. 1–4 From the fundamental point of view, TM-sulfide clusters are interesting. Both metallic and partially ionic bondings are expected to coexist due to the marked different electronegativity of the TM element and sulfur and the atomic and covalent radii of the TM elements are much larger than that of S. Therefore, doping TM clusters with an element like S could modify the magnetic exchange coupling in the TM host and its reactivity due to possible electronic charge redistributions and structural changes. Since the pioneering work of Cheshnovsky et al. 5,6 and Ganteför et al., 7,8 the photoelectron spectroscopy (PES) technique has been proved to be a powerfull tool to study atomic and molecular clusters, due to its ability to combine size selectivity with spectral sensitivity. In PES experiments, a mass selected cluster anion is crossed with a pulsed laser of fixed energy (wavelength), and photodetached electrons are detected according to their kinetic energies. In this process of transition from the ground state of anions into the ground state or electronic excited states of the corresponding neutrals, the electronic properties of the clusters are readily observed from the PES and some other informations can be derived from their analysis as it was done for pure iron clusters 9,10 or iron-sulfide clusters. 11–23 Thus, using PES, Zhai et al. 11 determined vertical detachment energies (VDEs), electronic affinities (EAs) and vibrational frequencies of anionic FeS− n and neutral FeSn (n=1-6) clusters. A noticeable increase of EA was only observed from FeS to FeS2 , whereas all larger clusters FeSn − (n=3-6) have EAs comparable to that of FeS2 . Nakat et al. 12 studied anionic FeS− 6 and FeS7

clusters through collision-induced dissociation (CID) experiments. Loss of neutral S2 fragments was observed as the major dissociation channel. In the context of reactivity of Fe clusters to S, Carlin and coworkers 13 observed at least six sulfur attachments in experimental reactivities of bare 3



Fe+ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ions with ethylene sulfide, to generate FeS+ n

species. By using Fourier transform ion cyclotron

resonance mass spectroscopy, bare Fe+ ions were also allowed to react with S8 in gas phase to 14,15 Fe-sulfide cluster anions (Fe S− , produce FeS+ n m n clusters; species with n=1-8 were observed.

n, m=1-6) have also been investigated using a magnetic-bottle type photoelectron spectroscopy where the electron affinities and the vertical detachment energies were measured for neutral and anionic species. 16 The most stable anions were found to be those with n=m or n=m ± 1, showing that Fen S− m , n = m=2,3,4,6 (which are iron-sulfur centers in proteins) are also stable species in a gas phase in the condition of supersonic jet expansion. Nakajima and coworkers 18 reported PES data and inferred geometric properties of iron-sulfide anionic clusters (Fen S− m n=1-8, m=2-6), together with chemical probe measurements for the corresponding cations. They observed a noticeable change of the EAs of Fen S− m clusters at the equiatomic composition (n = m). They also observed that the reactivity of iron-sulfide clusters toward NH3 and C2 H2 is enhanced around the equiatomic composition. These results suggest that their structures seem to be formed by alternate Fe and S bonds, resembling those of an active site in iron-sulfide proteins. 1 Some other experimental works were devoted to neutral or charged iron-sulfide dimers 19–23 or FeS2 clusters. Most theoretical investigations focus on such small clusters, 24–29 and few DFT calculations are carried out for larger Fen Sm ones. 11,24,30 Preliminary DFT calculations were per11 Two of us formed to determine structural shapes of FeS− n (n=1-6) consistent with PES data.

reported DFT calculations of the geometric, electronic and magnetic properties of free standing Fe2 S2 , Fe3 S4 and Fe4 S4 clusters, which are those most frequently contained in proteins. 30 We showed that their ground-state geometries are consistent with the conformations they have in core proteins and that those geometries do not change much with the charge state, apart from slight distortions. In view of the above findings, and particularly of the lack of theoretical studies devoted to Fesulfide clusters in the rich Fe phase, for which experimental data is available, we decided to inves0/±

tigate Fen S2

clusters, n=1-6, in a systematic way using an accurate DFT implementation such as

the Vienna Ab-initio Simulation Package (VASP), 31,32 which solves the spin-polarized Kohn-Sham

4


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(KS) equations in a plane-wave basis set and employs the Projector Augmented Waves (PAW) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

method to treat the core interactions. The theoretical and computational details are described in the next section. In order to understand the impact of the disulfide doping on free-standing iron clusters, we determined first the structural, magnetic and electronic properties of pure iron clusters with our theoretical approach. Part of these data are collected at the beginning of Section III. Our study on both neutral and anionic species of the iron disulfide clusters allows us to make contact with the experiments on negative ion photodetachment spectra described above. These and other properties (structure, stability, reactivity indicators, magnetism) are discussed along the rest of sections in comparison with the results for the corresponding pure Fen hosts. The main conclusions are summarized at the end.

Computational method As we mentioned in the introduction, the calculations were performed in the framework of HohenbergKohn-Sham’s density-functional theory 33,34 as implemented in the Vienna ab initio simulation package. 31,32 This code solves the spin-polarized Kohn-Sham equations in an augmented planewave basis set by using the projector augmented wave method 35,36 which is an approximate allelectron approach with frozen cores. We treated the exchange and the correlation effects in the generalized gradient approximation by using the Perdew-Burke-Ernzerhof functional. 37 The clusters were placed in a cubic supercell with an edge of 15 Å, and periodic boundary conditions were imposed. The KS wave functions in the interstitial region were expanded in a plane-wave basis set with a kinetic energy cutoff of 500 eV. A smearing of the KS levels was introduced in order to improve the numerical stability. We have used a Gaussian smearing method 38 with a very small final standard deviation σ = 0.05 eV, which keeps the entropy of the non-interacting (KS) gas below 106 eV/K atom. The calculations were carried out by considering only the Γ point in reciprocal space since we are dealing with isolated clusters. For charged clusters, corrections to the total energy were taken into account by considering the full dipole moment in all directions. The corrections to

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the total energy are calculated as the energy difference between a monopole/dipole/quadrupole in 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

the current supercell and the same monopole/dipole/quadrupole placed in a vacuum. We note that also quadrupole corrections coming from the expectation value of r2 are taken into account. The lowest-energy structures of the considered clusters were obtained by choosing various initial configurations, up to 15, with different interatomic distances, and relaxing them using a conjugate gradient method and quasi-Newton methods until the interatomic forces were smaller than 0.001 eV/Å. Our structural sampling included Fen skeletons (ground state and low-energy isomers of the pure Fen clusters) capped with the S atoms, but also geometries based on FeS units, so as to extend the sampling to arrangements in which a strong Fe-S bonding would prevent the nucleation of compact iron subclusters. Obviously, we checked that the results remain unchanged for higher cut-off energies and even more stringent convergence criteria. The relative stability of different isomers was further checked by performing calculations in different spin sates, including non-collinear magnetic arrangements, to be sure of the total spin of the putative ground state. Although we did not employ an unbiased structural search, we believe that our sampling is sufficient due to the small size of these clusters. Furthermore, in order to confirm that the putative ground states correspond to true minima, we reoptimized the structures with a small random change of the atomic positions and we recovered the same structures. We have also performed a vibrational analysis (within the standard harmonic approximation with finite differences in the atomic displacements) for some selected clusters for which the ground state and the first isomer enter in an energy window smaller than about 3 times room temperature, in order to estimate the zero-point energy corrections and to confirm the lowest energy of the ground states. VASP computes the local charges and spin magnetic moments by projecting the plane-wave components of the eigenstates onto spherical waves inside slightly overlapping atomic spheres of Wigner-Seitz radius. Because this projection depends on the choice of the atomic radius, the sum of the local charges and moments is not necessarily identical to the total cluster values. In order to check the accuracy of the calculated local magnetic moments, we performed an analysis by using Bader’s method 39–41 which is based on partitioning the cluster into atomic volumes by locating the

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zero-flux surfaces of the electron density field. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The accuracy of the theoretical approach used is demonstrated by the calculated bond length, vibrational frequency, VDE, adiabatic electron affinity (AEA) and ionization potential (IP) of 0/±

Fe2

0/±

, S2

and FeS0/± dimers, compared to experimental data. The results of the test, sum-

marized in Table 1, show a fairly good agreement between the calculated and the measured values of the different quantities considered. Let us note that even the ground state of Fe2 has been the subject of a great number of calculations performed at different ab initio and DFT levels, 42–49 and the results were not always consistent.

Results and discussion 0/±

Fen

clusters

The results obtained for the pure Fen clusters (n=2-6) in their neutral anionic and cationic states will serve as a reference for determining the change in their electronic properties upon disulfide doping. 0/±

We note that neutral and charged Fen

clusters have been the subject of several theoretical stud-

ies 50–73 against which we can benchmark our theoretical approach. Apart from slight relaxations, 0/±

our optimized geometries of Fen

(n=2-6) clusters, collected in Figure 1, are consistent with other

previously published results. Depending on the exchange and correlation functional used, the spin multiplicity differs in some cases. A different treatment of the core interactions or basis sets seems not to be the origin of discrepancies regarding the spin multiplicity. We performed calculations of the pure iron clusters using the code SIESTA 74,75 with the same approximation for exchange and correlation as with VASP, obtaining the same results except minor structural relaxations. SIESTA employs Troullier Martins pseudopotentials instead of PAWs for the core interactions, and numerical pseudoatomic orbitals instead of plane waves as basis sets. The total moment of the lowest energy states of charged clusters is usually 1 µB higher or lower than that of their neutral counterpart. Here, the violation of this rule (± 1 µB ) is only found for the cationic Fe+ 4 . Its lowest energy state is a trigonal pyramid of Td symmetry with a total moment of 11 µB , whereas its cor7


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responding neutral of D2d symmetry has 14 µB . This result is, nevertheless, in agreement with 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

some previous theoretical predictions. 50,55,62 As explanation it was noticed that the excited states of Fe4 and its ions may have planar or near planar geometries. 50,62 We indeed found, as isomer, a rhombus geometrical configuration of C2v for Fe+ 4 with total moment of 13 µB , although far away (∆E=0.70 eV) from the putative ground state of Td symmetry (see Figure 1). The lowest energy structures of Fe+ 4 with 1 µB higher or lower than that of the neutral cluster have all the same geometry (D2d symmetry) but higher energies (+1.08 and +0.44 eV) than the ground state cationic cluster of Td symmetry and total moment of 11 µB . In Figure 2 we plot the density of states (DOS) of the neutral and cationic ground states of the iron tetramer. The electron is not simply extracted from the HOMO (of majority spin character), but an electronic redistribution takes place with an electron transfer from the majority to the minority spin states. Thus, the adiabatic ionization is not a one electron process in this case, since the spin multiplicity of the ground state of the neutral and cationic cluster changes significantly; the electron is not simply extracted from the HOMO of the neutral cluster without structural and electronic relaxation. The question concerning the stability of the noncollinear magnetic ordering in iron clusters is still open. Up to date, the answer is not clear in view of some discrepancies still existing between available theoretical results. 57,59–61,68,71 In the present work, we also considered possible noncollinear arrangements by exploring an important number of spin configurations (up to 15 for Fe5 and Fe6 ). Most of them converged to collinear states; the few noncollinear states that resulted as local minima (only for Fe3 and Fe5 ), are high-energy spin excitations (see Figure 1). The general trends of stability and magnetic moment as a function of cluster size are used as a reference in comparison with those of the iron disulfide clusters discussed in the following subsection. 0/±

Fen S2

clusters

In this subsection we discuss the induced structural and electronic changes upon the disulfide dop0/±

ing of the Fen

0/±

clusters. The putative ground states of neutral, anionic and cationic Fen S2 8


(n=1-

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6) clusters, with their point-group symmetry and total spin magnetic moment are collected in Fig1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ure 3. As for the pure Fen clusters, we have also explored a great number of possible noncollinear magnetic arrangements. Most of them converged to collinear states and when they resulted as local minima, they were quite far in energy with respect to the ground state. Those noncollinear spin excitations were found in Fe3 S2 and Fe5 S2 clusters, and are illustrated in Figure 4. Before discussing general trends, let us describe in some detail each of the iron disulfide clusters. 0/±

FeS2

clusters:

0/±

The geometrical structures of FeS2

clusters depend on the S-Fe-S angle, i.e

on the presence or not of the S-S bond. They all have the same point-group symmetry C2v . The putative neutral ground state is the bent structure without the S-S bond. The S-Fe-S angle and Fe-S bond length are 113.5˚and 2.00 Å , respectively. The total cluster moment of 4 µB results from a parallel magnetic coupling between the iron atom (3.16 µB ) and the S atoms which are substantially polarized (0.42 µB ). For the anionic FeS− 2 cluster, the putative ground state is also a bent structure without the S-S bond. The S-Fe-S angle and the Fe-S bond length are increased to 143.8˚and 2.09 Å respectively, as compared to the neutral cluster (113.5˚and 2.00 Å). This gives rise to a less compact cluster, to an Fe spin moment of 3.80 µB and an induced moment on S atoms of 0.60 µB , leading to a total cluster moment of 5 µB . The ionization process leads to an isosceles triangular configuration of the cationic FeS+ 2 cluster, with C2v symmetry with an S-S bond of 2.08 Å , and an S-Fe-S angle of 57.5˚. The enlargement of the Fe-S bond to 2.17 Å and the important induced moment on S atoms (0.73 µB ) lead to total cluster moment of 5 µB . So, an S-S bond creates when extracting an electron from the neutral FeS2 cluster. From the charge transfer (Figure 5) we see that in the neutral state the S atoms have a larger excess of charge than in the cationic state. Consequently, the S atoms suffer a strong electrostatic repulsion to each other in the neutral cluster and separate not forming a bond. The fact that in the cationic state the charge transfer is small as compared to that in the neutral state, and the formation of S-S bond upon electron extraction indicates that a large part of the electron is extracted from S,

9



so that the HOMO of the neutral should have S character and with no charge density in the region 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

between the two S atoms, consistent with the strong electrostatic repulsion between the S atoms. The atom-projected electronic density of states and the spatial location of the charge density of the HOMO confirm these facts (Figure 6). However, the shape of the HOMO seems more consistent with non-bonding atomic orbitals, the charge density being located also on the Fe site. For more information, the dipole moments of the anionic and the cationic species are 0.81 and 1.75 electrons × Å. 0/±

Fe2 S2

clusters:

The putative neutral lowest-energy structure is a 3D buckled rhombus of Cs

symmetry, with alternating Fe and S atoms and Fe-Fe and Fe-S bond lengths of 2.21 and 2.20 Å , respectively. The dihedral angle between the Fe2 S1 entities is of 155.9˚. The Fe-Fe magnetic coupling is parallel and the resulting total cluster moment is 8 µB , contributed by both Fe and S atoms with 3.50 and 0.50 µB , respectively. The putative ground state of anionic and cationic Fe2 S± 2 clusters are found to be spin isomers of planar rhombus of C2v group-point symmetry, with alternating Fe and S atoms. These structures are similar to the structural entity most frequently contained in proteins. 80 They differ in their local magnetic moment distribution. In the anionic cluster, the Fe-Fe spin arrangement is ferromagneticlike (F) with a total moment of 7 µB resulting from the spin polarization of Fe (3.25 µB ) and S atoms (0.25 µB ). In the putative ground state of the cationic Fe2 S+ 2 cluster, the Fe atoms are coupled antiferromagnetically (AF) with local moments of ± 3.17 µB , giving rise to a quenched total magnetic moment. The magnetic frustration associated to the antiparallel magnetic coupling between the iron atoms is released by the expansion of the Fe-Fe bond length (2.44 Å) as compared to those found for neutral and anionic clusters (2.21Å ). One can notice that the energy differences between the cationic cluster in its ground state (zero magnetic moment) and in the excited states with moments of 7 and 9 µB are 0.23 eV and 0.65 eV, respectively. 0/±

Fe3 S2

clusters:

The putative lowest-energy structure of the neutral cluster is a trigonal bipyra-

mid of C2v symmetry, where the two S atoms occupy the vertices. Its total moment of 10 µB results 10


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from a parallel magnetic coupling between the Fe atoms (3.16, 3.16 and 3.24 µB ) and the induced 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

moments of 0.22 µB on the S atoms. The putative ground state of the anionic Fe3 S− 2 counterpart has a 3D structure formed by a triangular iron trimer of C2v symmetry, capped by the two sulfur atoms in bridge sites over the smallest Fe-Fe bonds (2.31 Å). The dihedral angle between the Fe2 S entities and the iron trimer plane is 159.3˚. The local Fe spin moments (3.16, 3.61, 3.61 µB ) and the induced one on S atoms (0.31 µB ) are parallel giving rise to a high total moment of 11 µB . For the cationic Fe3 S+ 2 cluster, a trigonal bipyramid of D3h symmetry has been found as the putative ground state. Its total cluster moment results from Fe local moments of 3.40 µB and S moments of 0.40 µB . 0/±

Fe4 S2

clusters:

The neutral Fe4 S02 cluster has a structure with C2v symmetry formed by an

Fe4 tetrahedron capped by the two sulfur atoms on its opposite 3-fold hollow sites. Its total cluster moment of 14 µB results from parallel magnetic moments of the iron atoms (two nonequivalent sites of 3.22 and 3.50 µB ) and of the induced moments on S atoms (0.28 µB ). The ground state of the anionic Fe4 S− 2 clusters is formed also by the Fe4 tetrahedron where one sulfur atom occupies a bridge position and the other caps one of the 3-fold hollow sites. It is of Cs symmetry and has a total moment of 13 µB . The ionization process does not substantially modify the geometry and symmetry (C2v ) of the neutral cluster, apart from slight relaxations. The magnetic moment decreases to 13 µB resulting from the spin polarization of two nonequivalent Fe atoms (3.12 and 3.18 µB ) and the induced S moments (0.20 µB ). Comparing the local magnetic moments distribution of Fe4 S2 in the neutral and cationic states, we see that most of the decrease of the total magnetic moment as going from the neutral (14

µB ) to the cationic state (13 µB ) is contributed by two equivalent Fe atoms. This could indicates that the HOMO is essentially localized on those Fe atoms and the fact that the geometry does not change appreciably could mean that such eigenstate of the molecular Hamiltonian is neither clearly

11



bonding nor antibonding. The density of states, however, shows that the HOMO has both Fe and 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

S character, and the plot of the HOMO in the real space shows that it is delocalized in the whole cluster (Figure 7). 0/±

Fe5 S2

clusters:

The ground states of the neutral, anionic and cationic clusters are spin isomers

of a structure formed by an Fe5 distorted (buckled) square pyramid capped by the two sulfur atoms on opposite 3-fold hollow sites. Due to their C2v symmetry, they are formed by two nonequivalent pairs of Fe atoms of the base, one Fe atom at the vertex and by the two equivalent S atoms. The electron excess (defect) increases (decreases) the total moment by ±1 µB up to 17 (15µB ) in the anionic (cationic) clusters, with respect to the neutral state. 0/±

Fe6 S2

clusters:

The putative ground states of the neutral, anionic and cationic clusters are spin

isomers of a structure formed by an iron rectangular based bipyramid of C2v symmetry, capped by the S atoms on two opposite 3-fold hollow sites. The total magnetic moments of the neutral, anionic and cationic clusters are 20, 19 and 21 µB , respectively. Most of the first isomers are, at least, about 1eV less stable than the ground state, and are structurally similar, so that the zero-point energy correction is not expected to be noticeable. We have selected those clusters for which the ground state and the first isomer enter in an energy window smaller than about 3 times room temperature, and have performed a vibrational analysis. + Those clusters are: the neutral Fe2 S2 , the anion Fe3 S− 2 , the neutral Fe5 S2 and the cation Fe5 S2 .

In total, 8 clusters that cover different sizes and charge states. The energy differences between the respective ground states and first isomers, without the zero-point energy correction, were: 86 meV, 44 meV, 48 meV, and 87 meV, respectively. Those differences, including now the correction become 74 meV, 44 meV, 48 meV, and 85 meV, respectively. The zero-point energy correction is thus rather small, and insufficient to reverse the energetic order or to substantially modify the binding energy.

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General trends 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0/±

Structural stability of Fen S2

clusters

This subsection is devoted to the stability trends, for which we analyze some descriptors, namely the binding energy (BE) per atom and the second energy difference ∆2 E(n). These are defined in terms of the total energy of the clusters and component atoms:

BE(Fen S2 ) = [n × E(Fe) + 2 × E(S) − E(FenS2 )]/(n + 2),

(1)

BE(Fen S2+ ) = [E(Fe+ ) + (n − 1) × E(Fe) + 2 × E(S) − E(FenS2+ )]/(n + 2),

(2)

BE(Fen S2− ) = [n × E(Fe) + E(S) + E(S−) − E(Fen S2− )]/(n + 2),

(3)

and

∆2 E(n) = E(n + 1) + E(n − 1) − 2E(n).

(4)

The first equation is the binding energy per atom of the neutral clusters, the second (third) is that of the cationic (anionic) clusters, and the fourth equation is the second energy difference (∆2 E) which provides the relative stability of a cluster of a given size n with respect to its neighboring sizes, being E(n) the energy of Fen S2 in the corresponding charge state. 0/±

Figure 8 shows those quantities for neutral and charged Fen S2

clusters as function of n. The

binding energy per atom increases as increasing n, an indication of the strong contribution of Fe-Fe bonding to the stability, but it tends to saturate fast. An Fe subcluster, similar to the corresponding 0/±

pure Fe counterpart, can be identified in the structures of Fen S2

, which corroborates that the

metallic Fe-Fe bonding is strong. Since n grows while keeping constant the number of S dopants, the binding energy per atom would tend, obviously, to the value of the bulk for infinite n. It is interesting to note that the average interatomic Fe-Fe distance (not shown) rises to stabilize around a value of 2.45 Å in the neutral state (close to the nearest neighbors distance in bulk iron: 2.48 13



Å) already for n = 4 − 6. The binding energy of these iron disulfide clusters exceeds that of the 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

corresponding undoped iron clusters (compare left and right panels of Figure 8). This increase of the global stability upon disulfide doping is consistent with the partial ionic contribution to the bonding, a fact that is corroborated by the noticeable electronic charge transfer from the Fe atoms to the S ones (Figure 5) which itself is a consequence of the much more electronegative character of S (2.58 for S, 1.83 for Fe). The most significant feature regarding the relative stability is the remarkable peak at n=2 in 0/±

∆2 E, indicating the high stability of Fe2 S2

clusters with respect to their neighboring sizes. We

note that the Fe2 S2 entity is the basis of larger structures like those of Fe3 S4 and Fe4 S4 which are the most frequently iron sulfide clusters contained in proteins (together with Fe2 S2 ), but also of even larger iron-sulfur clusters. 1 The high stability of this Fe2 S2 entity in vacuum may be an important fact in the context of its fundamental role in protein synthesis. 30 These results are also in agreement with the experimental mass spectrum of iron-sulfur Fen S− m clusters anions produced by laser vaporization 16 showing that the most intense peaks correspond to the composition n ≈ m in gas phase. 0/±

Electronic properties of Fen S2

clusters

As we mentioned in the introduction, the determination of structures for both anionic and neutral clusters allows to make a link with the experiments on negative ion photodetachment spectra. In those experiments, the measured energies of the incident photon and the electron removed from the cluster could provide information on the electronic structure of the cluster. From the DFT calculations, one can determine the spin band origin of the extra electron. The change in the total spin magnetic moment upon both ionization and an electron excess can be explained as a one electron process, an exception being the ionization of Fe2 S2 . Thus, Figure 8 shows that the total moment of the cationic or anionic clusters differ in ±1µB from that of the neutral counterpart (except Fe2 S2 ). More specifically, the moment of the anionic clusters increases by 1 µB for odd n with respect to neutral ones, and decreases by 1 µB otherwise. This trend can be qualitatively 14


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Page 15 of 44


understood in a first approximation by analyzing the densities of electronic states (DOS) of the 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

neutral clusters (assuming a small electronic relaxation upon the electron deficit or excess). We have verified that the LUMO of odd n neutral clusters (except Fe1 S2 ) is of majority-spin character whereas for even n clusters the LUMO is of minority-spin character. Strong electronic relaxations are expected in Fe1 S2 which presents important structural changes as a function of the charge state. On the other hand, this odd-even behavior is not manifested in the cationic clusters for all n. However, when the total moment increases (decreases) by 1 µB upon ionization, we see in general that the HOMO of the neutral cluster is of minority- (majority-) spin character. We plot in Figure 9 0/±

the DOS of the neutral, anionic and cationic Fe3 S2

clusters. Here, structural changes are more

appreciable, and therefore electronic relaxations upon an electron deficit or excess are important. We remind that for the neutral state of this cluster we obtained a distorted trigonal bipyramid of C2v symmetry where the two S atoms occupy the vertices (see Figure 3). The corresponding anion has a quasi 2D structure formed by an iron triangular trimer (of C2v symmetry also) where the two sulfur atoms are adsorbed out of the iron plane, on bridge position over the smallest FeFe bonds (see Figure 3). The structure of the cation is a perfect based triangular bipyramid of D3h symmetry. As one can see from their respective DOS, the charge deficit or excess affects considerably the electronic structure of both spin components. Despite the fact that both charged states have an increased spin multiplicity, by one unit, with respect to the neutral state, both the HOMO and LUMO of the neutral cluster are of minority-spin character. As indicated above, Fe2 S2 is a particular case since ionization totally quenches the magnetic moment. This can not be explained as a one electron process. Indeed, a strong electronic relaxation, manifested in a change in the magnetic couplings, takes place. This cluster adopts an antiferromagnetic-like configuration (in contrast with the ferromagnetic-like coupling of the neutral state) leading to a singlet state despite the high local spin polarization (more than 3µB per Fe atom). We have also plotted the magnetic moments per atom as a function of cluster size n (Figure 10). The increase of the total moment as increasing cluster size correlates with the increase of the per atom value, independently of the charge state. This can be explained taking into account that most

15



of the spin polarization is contributed by the Fe atoms, and ferromagnetic-like coupling is found 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(as shown in the local moments distribution in Figure 3). Therefore, increasing the size of the iron subcluster leads to an increase of both the total moment and the per atom value, except Fe2 S2 where the spin polarization is AF giving rise to a quenched total magnetic moment. In Figure 11 we plot, as a function of cluster size n, the spin-up and spin-down LUMO-HOMO 0/±

gaps of Fen S2

in their putative lowest-energy structures. For neutral(anion) clusters, the cor-

responding spin-up gaps display an oscillatory behaviour with local maxima(minima) for species with even(odd) number of atoms. For spin-down gaps of neutral clusters, we obtain a relative minimum at n=3 and a relative maximum at n=5. For anionic clusters, the gaps corresponding to spin-down states are relatively small and do not vary significantly with the size as compared to spin-up states. Therefore, the LUMO-HOMO gap for one spin channel changes as a function of size upon S2 -doping, in contrast with the LUMO-HOMO gap for the other spin channel. Unlike for the anions, the neutral clusters have spin-up gaps not always larger than those of spin-down states; they are only for n=2,3,4 and 6. As for the cations, the spin-up and spin-down gaps values are equal for n=2,3,4,5 and differ otherwise. The spin-down gap oscillates with maxima for even-n sizes and minima for odd-n. To complete our analysis of the electronic properties, we calculated several electronic indicators for which experimental results are available. We plot in Figure 12a the variation of the adiabatic electron affinity of these clusters as a function of their size n, compared with experimental data. 11,18 The AEA is calculated as the difference of the total energy of the anionic and neutral ground states. Taking into account the measurement uncertainties, the calculated AEAs follow rather well the experimental data, except for n=1 for which the difference between both values reaches ∼ 0.6 eV. As a reference, we report the corresponding data for pure iron Fen clusters for which we also find a good agreement between the calculated and the experimental values. 9,10 We find that disulfide doping of the small Fe clusters (n=1-3) considerably increases the electronic affinity, as expected when doping a system with a much more electronegative element. This effect reduces as increasing the relative content of Fe with respect to S.

16


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Page 17 of 44


The VDE of iron disulfide clusters is calculated as the energy difference of the anionic cluster 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

and the neutral counterpart with the structure of the anionic cluster. It corresponds, therefore, with the vertical ionization potential (VIP) of the anionic cluster. For iron clusters the vertical detachment energies (VDE± ,s) are computed for two possible one-electron detachment channels corresponding to the neutral states whose spin multiplicities differ from the spin multiplicity of the anion parent by ± 1 at the geometry of the anion lowest total energy state,

− V DE± (Fe− n ) = E(Fen , 2S + 1) − E(Fen , (2S + 1) ± 1).

(5)

The calculated VDEs of pure Fen and disulfide doped Fen S− 2 clusters, compared to their respective measured values 9–11,18 are reported in Figure 12b. As one can see, the agreement between the theoretical and the experimental data is fairly good for both pure and doped clusters, which gives further support to our putative ground state configurations. The VIP of the pure iron and iron disulfide clusters are plotted in Figure 12c. Our computed adiabatic IP for both type of clusters show only small differences (less than 0.1 eV). However, there is no available experimental data for Fen S2 clusters, unlike for pure Fen clusters for which we include in Figure 12c the values obtained from the ionization thresholds of laser photoionization experiments. 84,90,91 To the best of our knowledge, only one experimental study was devoted to Fe2 and Fe3 clusters. 84 For larger clusters, Fe4 to Fe6 , there are more than one experimental data, but with some differences that reach ± 0.4 eV. 90,91 Our calculated values for Fen clusters are consistent with the experimental data for n=1,2,5,6. For Fe4 we obtained 5.82 eV which is within 0.48 eV from the lowest experimental value (6.4 ± 1 eV). 84 We note that similar disagreement was obtained elsewhere at the BPW91 level for the exchange correlation functional that is combining Becke’s exchange with Perdew-Wang’s correlation functionals. 92,93 This could be explained by the fact that the putative low-lying isomer of the ionized Fe+ 4 cluster does not follow the law of oneelectron process (± 1µB ) upon ionization of the neutral cluster. As discussed above, the putative ground state of Fe+ 4 has a total moment of 11µB (14±1µB its neutral counterpart). But when we

17



consider the spin isomer of 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fe+ 4

Page 18 of 44

with 13 µB , the calculated VIP (6.26 eV) agrees with the lowest

experimental value with an error of just 0.04eV. The same holds for Fe+ 3. Finally, in order to characterize the global reactivity of the iron disulfide clusters, we calculated conceptual DFT based global reactivity descriptors. 94 From the VIP and VEA (calculated with the same definition as the adiabatic ones but at the optimal neutral geometry for the charged states), we can determine the electronegativity (the negative of the electronic chemical potential µ ): 1 χ = −µ = (V IP +V EA), 2

(6)

and the chemical hardness (or fundamental gap, except for a constant factor): 1 1 η = Egap = (V IP −V EA). 2 2

(7)

These quantities are plotted in Figure 13, together with those obtained for the undoped iron clusters. Iron disulfide clusters are more electronegative than their pure iron counterparts. Therefore, disulfide doping of Fe clusters enhances their ability to attract and hold electrons, becoming less reactive towards electrophilic compounds. For instance, oxidation of the doped clusters is expected to be a slower process than in pure iron clusters. The chemical hardness of the disulfide iron clusters is higher than that of their pure iron counterparts. This means an enhancement of the sensitivity of the chemical potential to changes in the number of electrons. The larger the hardness, the less reactive the cluster is. Among the iron disulfide clusters, Fe2 S2 is the less reactive one. As we have seen in previous subsections, this cluster is also the one having the largest relative stability and the iron sulfide structure most frequently contained in proteins 80

Conclusions We have performed first-principles DFT calculations, in the generalized gradient approximation for exchange and correlation, to determine the putative ground state structures and related elec-

18


Page 19 of 44

The Journal of Physical Chemistry 0/±

tronic properties of neutral and charged Fen S2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

, n=1-6 clusters, and to analyze the impact of

disulfide doping on the fundamental properties of the smallest iron clusters. The good agreement between our calculated adiabatic electron affinity and vertical detachment energy with available experimental data gives support to the proposed ground state configurations. These iron disulfide clusters exhibit an Fe skeleton similar to the corresponding pure Fe host, an indication of the strong metallic bonding. Disulfide doping of small Fe clusters enhances the binding energy per atom, without substantially modifying the magnetic moment. This increase in the global stability is consistent with the partial ionic contribution to the bonding, a fact that is corroborated by the noticeable electronic charge transfer from the Fe atoms to the S ones. The preservation of most of the magnetic moment upon S doping is due to the robust parallel magnetic coupling between the Fe atoms, the only exception being Fe2 S+ 2 in which the induced antiparallel couplings lead to a singlet state accompanied by an expansion of the Fe-Fe bond length. Except in this case and few other exceptions, the change in the total spin magnetic moment upon both ionization and an electron excess can be explained as a one electron process, leading to a 1µB increase or decrease of the spin moment with respect to the neutral state. The exceptions are due to strong electronic relaxation, most of which associated to a structural change. Disulfide iron clusters are more electronegative than their pure iron hosts, and thus less reactive towards electrophilic compounds. They have also a larger chemical hardness, so that the sensitivity of their chemical potential to changes in the number of electrons is enhanced, becoming globally less reactive that their pure iron hosts. Fe2 S2 stands out as the less reactive and more stable of the smallest iron disulfide clusters. It is also the only one in which ionization quenches the magnetic moment, and it is similar to the structural entity most frequently contained in proteins. 80 We hope that our characterization of the smallest disulfide iron clusters in vacuum helps in achieving a complete understanding of the role of these compounds in biology and catalysis.

19



Acknowledgement 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

We acknowledge the financial support from the Algerian Ministry of Higher Education and Scientific Research via the project CNEPRU B00L02UN150120130013, and from the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund (Project FIS2014-59279-P).

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Complexes Containing the Fe2 S2 Core and the Structures of Bis[o-xylyl-α , 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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α ′ -dithiolato-

µ -sulfido-ferrate (III)] and Bis[p-tolythiolato-µ -sulfido-ferrate (III)] Dianions. J. Am. Chem. Soc. 1975, 97, 1032-1045. (81) Moskowits, M.; DiLella, D. P. Di-Iron and Nickel-Iron. J. Chem. Phys. 1980, 73, 4917-4924. (82) Montano, P. A.; Shenoy, G.K. Exafs Study of Iron Monomers and Dimers Isolated in Solid Argon. Solid State Commun. 1980, 35, 53-56. (83) Purdum, H.; Montano, P. A.; Shenoy, G. K.; Morrison, T. Extended-X-Ray-Absorption-FineStructure Study of Small Fe Molecules Isolated in Solid Neon. Phys. Rev. B 1982, 25, 44124417. (84) Rohlfing, E. A.; Cox, D. M.; Kaldor, A.; Johnson, K. H. Photoionization Spectra and Electronic Structure of Small Iron Clusters. J. Chem. Phys. 1984, 81, 3846-3851. (85) Hunsicker, S.; Jones, R. O.; Ganteför, G. Rings and Chains in Sulfur Cluster Anions S− to S− 9 : Theory (Simulated Annealing) and Experiment (Photoelectron Detachment). J. Chem. Phys. 1995, 102, 5917-5936. (86) Moran, S.; Ellison, G. B. Photoelectron Spectroscopy of Sulfur Ions. J. Chem. Phys. 1988, 92, 1794-1803. (87) Celotta, R. S.; Bennett, R. A.; Hall, J. L. Laser Photodetachment Determination of the Electron Affinities of OH, NH2, NH, SO2, and S2. J. Chem. Phys. 1974, 60, 1740-1745. (88) Bender, H.; Carnovale, F.; Peel, J. B.; Wentrup, C. Dinitrogen Sulfide, N2S, Revealed by Photoelectron Spectroscopy. J. Am. Chem. Soc. 1988, 110, 3458-3461. (89) Liao, C. L.; Ng, C. Y. Molecular Beam Photoionization Study of S2. J. Chem. Phys. 1986, 84, 778-782. (90) Yang, S.; Knickelbein, M. B. Photoionization Studies of Transition Metal Clusters : Ionization Potentials for Fen and Con . J. Chem. Phys. 1990, 93, 1533-1539. 28


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(91) Parks, E. K.; Klots, T. D.; Riley, S. J. Chemical Probes of Metal Cluster Ionization Potentials. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

J. Chem. Phys. 1990, 92, 3813-3826. (92) Becke, A. D. Phys. Rev. A Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. 1988, 38, 3098-3100. (93) Perdew, J. P.; Wang, Y. Accurate and Simple Analytic Representation of the Electron-Gas Correlation Energy. Phys. Rev. B 1992, 45, 13244-13249. (94) Geerlings, P.; De Proft, F.; Langenaeker, W. Conceptual Density Functional Theory. Chem. Rev. 2003, 103, 1793-1874.

29



Graphical TOC Entry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

30


Page 30 of 44

Page 31 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1: Calculated values of bond length r, vibrational frequency ω , vertical detachment 0/± 0/± energy VDE, adiabatic electronic affinity AEA and ionization potential IP for Fe2 , S2 and FeS0/± dimers, compared to experimental data.

ω (cm−1 ) VDE (eV) 254 1.14 and 1.40 a 250±20 0.90 and 1.44a

Dimer r (Å) − Fe2 This work 2.03 Exp. works Fe2

This work 2.01 Exp. works 1.87±0.13b 2.02±0.02d

Fe+ 2

This work

2.10

340

S− 2

This work 2.01 Exp. works

573 589f

S2

This work 1.90 Exp. works 1.89j

715 726j 725±12f

S+ 2

This work 1.83 Exp. works

570

FeS−

This work 2.04 Exp. works 2.18m

460 450m

FeS

This work 2.00 Exp. works 2.04q

FeS+

This work 2.01 Exp. works 2.05t

537 540r 520±30m 478 448u

AEA (eV) 1.08 0.902±0.008a

290 299.6c

IP (eV)

6.50 6.30±0.01e

1.54 1.67±0.01g 1.66±0.04h 1.56±0.05i 9.38 9.40k 9.36l 1.54

1.72 1.85±0.10n 2.04±0.09o,p

1.69 1.72±0.10n 1.76±0.10o,p 8.00 8.3 ± 0.3s

a 9 b 82 c 81 d 83 e 84 f 85 g 86 h 87 i 85 j 77 k 88 l 89 m 11 n 78 o 16 p 17 q 76 r 19 s 79 t 79 u 79

31


8.00

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 1: Putative ground-state structures of Fen (n=2-6) clusters in the neutral (first column), anionic (second column) and cationic (third column) states with their corresponding point-group symmetry and total magnetic moment MM (µB ). Bond lengths are given in Å and the local spin moments are given (in µB ) inside the atomic spheres. The sixth row gives the noncollinear spin arrangements found for neutral Fe3 and Fe5 clusters with their relative total energies ∆E with respect to the ground state. The arrows are proportional to the values of the local spin moments, given (in units of µB ) inside the atomic spheres. 32


Page 32 of 44

Page 33 of 44

90 60 30 0

DOS (states/eV/spin)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-30 -60 -90 -5 90

(Fe4) -4

0

-3

-2

-1

0

1

2

3

4

5

-2

-1

0

1

2

3

4

5

60 30 0

-30 -60 -90 -5

(Fe4) -4

+

-3

Energy (eV)

Figure 2: Calculated spin-polarized (↑,↓) density of states for neutral Fe04 and cationic Fe+ 4 ground states. The vertical dashed line indicates the Fermi level.

33



Figure 3: Putative ground-state structures of Fen S2 (n=1-6) clusters in the neutral (first column), anionic (second column) and cationic (third column) states with their corresponding point-group symmetry and total magnetic moment MM (µB ). Bond lengths are given in Å, and the local spin moments are given (in units of µB ) inside the atomic spheres. Big red and small yellow spheres represent Fe and S atoms respectively.

34


Page 34 of 44

Page 35 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4: Noncollinear spin arrangements found in neutral Fe3 S2 and Fe5 S2 clusters with their corresponding point-group symmetry, total magnetic moment MM (µB ), and the relative total energy ∆E with respect to the collinear state. Bond lengths are given in Å, red and yellow spheres represent Fe and S atoms respectively. The arrows are proportional to the values of the local spin moments, given (in units of µB ) inside the atomic spheres. Inter-atomic distances in Fe5 S2 are all different due to its C1 symmetry.

35



1.5

Charge transfer on S atom

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 44

1

(FenS2)

0.5

(FenS2) (FenS2) 0

0

1

2

3

4

5

6

0 +

7

Cluster size (n) 0/±

Figure 5: Calculated charge transfer to the sulfur atoms in neutral, anionic and cationic Fen S2 clusters as function of the cluster size n.

36


Page 37 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 6: Calculated spin-polarized (↑,↓) density of states for neutral FeS2 cluster where the vertical dashed line indicates the Fermi level. The oblique arrow shows the calculated spatial location of the charge density of the HOMO’s cluster.

37



Figure 7: Calculated spin-polarized (↑,↓) density of states for neutral Fe4 S2 cluster where the vertical dashed line indicates the Fermi level. The oblique arrow shows the calculated spatial location of the charge density of the HOMO’s cluster.

38


Page 38 of 44

Page 39 of 44

0/-/+

(Fen)

4

4

3.5

3.5

3

3

2.5

2.5

2

2

1.5 2

1.5

∆2Ε (eV)

BE (eV)

(FenS2)

0/-/+

1

1

0

0 -1 -2

-1

20

20

MM (µΒ)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


15

15

10

10

5

5

0

0

1

2

3

4

5

6

0

7 0

1

Cluster Size (n)

2 3 4 5 Cluster Size (n)

6

7

Figure 8: Binding energy (BE) per atom, second energy difference (∆2 E), and total magnetic moment (MM) of neutral (triangles), anionic (squares) and cationic (circles) Fen S2 (left panel) and Fen (right panel) clusters as function of size n=1-6.

39



60 40 20

0

(Fe3S2)

0 -20 -40

DOS (/states/eV/spin)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 44

60 40

-

(Fe3S2)

20 0

-20 -40 60 40 20

+

(Fe3S2)

0 -20 -40 -14 -12 -10

-8

-6

-4

-2

0

2

4

Energy (eV) 0/±

Figure 9: Calculated spin-polarized (↑,↓) density of states for neutral, anionic and cationic Fe3 S2 clusters. The vertical dashed line indicates the Fermi level.

40


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Total magnetique moment per atom (µB)

Page 41 of 44

3 2.5 2 1.5 (FenS2) (FenS2)

1

(FenS2)

0 +

0.5 0

0

1

2

3 4 Cluster size (n)

5

6

7 0/±

Figure 10: Calculated total magnetic moment per atom for neutral, anionic and cationic Fe3 S2 clusters as function of the cluster size n.

41



3

(FenS2)

2

0

1 0

LUMO - HOMO (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 42 of 44

3

0

1

2

3

4

6

5

7

spin up spin down

2 1

(FenS2)

0 0 3

1 (FenS2)

2

-

2

3

4

5

6

7

2

3

4

5

6

7

+

1 0

0

1

Cluster Size (n) Figure 11: LUMO-HOMO gap for spin-up and spin-down electrons of neutral and charged 0/± Fen S2 clusters as function of the cluster size n.

42


AEA (eV)

4.5 4 3.5 3 2.5 2 1.5 1

VDE (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4.5 4 3.5 3 2.5 2 1.5 1

VIP (eV)

Page 43 of 44

9.5 9 8.5 8 7.5 7 6.5 6 5.5

FenS2 (cal.)

(a)

FenS2 (exp.) Fen (cal.) Fen (exp.)

0

1

2

3

4

6

5

(b)

7

FenS2 (cal.) FenS2 (exp.) Fen (cal.) Fen (exp.)

0

1

2

3

4

6

5

7

FenS2 (cal.) Fen (cal.)

(c)

0

Fen (exp.)

1

2

3 4 5 Cluster Size (n)

6

7

Figure 12: (a): Calculated adiabatic electron affinity of Fen S2 (red open circles) and Fen clusters (blue open circles) as function of cluster size (n). The corresponding experimental values with their error bars for Fen S2 11,18 (red filled circles) and Fen 9,10 (blue filled circles) are also included for the sake of comparison. (b): Calculated vertical detachment energy (VDE) of Fen S2 (red open circles) as function of cluster size (n), with the corresponding experimental values 11,18 with their error bars (red filled circles). For pure Fen clusters two calculated values VDE+ and VDE− (VDE+ > VDE− ) (blue open circles), compared to the measured values 9,10 (blue filled circles). (c): Calculated vertical ionization energies of Fen S2 (red open circles) and Fen clusters (blue open circles). The corresponding experimental values with their error bars for Fen clusters 84,90,91 (blue filled circles) are also included for the sake of comparison.

43


Chemical hardness η (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Electronegativity χ (eV)


Page 44 of 44

6 5.5

Fen FenS2

5 4.5 4 3.5 3

0

1

2

3

4

5

6

7

0

1

2

3

4

5

6

7

4 3.5 3 2.5 2

Cluster size (n) Figure 13: Chemical hardness and electronegativity of pure Fen and Fen S2 clusters as function of the cluster size n.

44


Structural, Electronic, and Magnetic Properties of Iron Disulfide

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