Unveiling the effects of doping small nickel clusters with a sulfur impurity

Unveiling the effects of doping small nickel clusters with a sulfur impurity Abdelaziz Chikhaoui, Mohamed Ziane, Slimane Tazibt, Said Bouarab ·Andr´es Vega Received: date / Revised version: date Abstract Small free-standing Ni clusters have been widely investigated during the last decade, but not many of their derived chalcogenides, despite their interest in technology and the new prospects that the nanoscale may open. The present work uncovers the effects of the S-doping on the structural, electronic and magnetic properties of Nin,n=1-10 clusters. Density functional theoretic calculations within the generalized gradient approximation for the exchange and correlation were conducted to explore the structural, electronic, and magnetic properties of the resulting NinS chalcogenide nanoparticles. The sulfur impurity is always adsorbed on the 3-fold holow sites available on the nickel host, in qualitative agreement with recent results of S adsorption on Ni(111) surfaces. S-doping tends to enlarge the average Ni-Ni inter-atomic distance but enhaces the thermodinamical stability of Ni clusters. It also increases the vertical ionization energy and electron affinity. However, S-doping has a small effect on the magnetism of small Ni clusters. According to the spin-dependent HOMO-LUMO gap, most of these clusters are good candidates as molecular junctions for spin filtering at low bias voltage. Keywords Ab initio calculations ·Doping ·Electronic properties ·Magnetic properties ·Nickel ·Sulfur 1 Introduction The chalcogenides are an important class of materials from the technological viewpoint due to their significant electrical, optical and chemical characteristics. The applications of chalcogenide materials include a variety of chalcogenide glasses, infra-red sensors, solar energy conversion and window layer (1; 2; 3; 4; 5; 6). A. Chikhaoui, Mohamed Ziane, Slimane Tazibt, Said Bouarab Laboratoire de Physique et Chimie Quantique, Facult´e des Sciences, Universit´e Mouloud Mammeri de Tizi-Ouzou, B.P. No17 RP, 15000 Tizi-Ouzou, Algeria E-mail: aziz [email protected] Andr´es Vega Departamento de F´ısica Te´orica, At´omica y ´ Optica, Universidad de Valladolid, Paseo Bel´en 7, E-47011 Valladolid, Spain. 2 A. Chikhaoui et al. Among chalcogenide nanomaterials, nickel sulfide NiS presents potential applications in photoconduction (7). In general, sulfur compounds such as transition metal sulfides have important applications in superconduction (8; 9), biochemical systems (10; 11) and catalysis (12; 13; 14). As thin films and at the nanoscale, the chalcogenides as it happens with most materials, present a wide range of new properties inherent to the quantum confinement, which deserve to be explored by the Scientific Community. The main characteristic of nanomaterials comes from the sensitivity of their electronic properties with their morphologies, size and composition, that can be completely different from their mesoscopic and macroscopic counterparts, thus offering new prospects for developing a wide range of new applications. Small free-standing Ni clusters have been widely investigated from different theoretical approaches (22; 23; 24; 25; 26; 27; 29; 30; 31; 28; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50) and experimentally (55; 56) during nearly two decades. However, no studies have been carried out so far regarding the effects of doping small nickel clusters with a light impurity. Oxygen and sulfur impurities are particularly interesting in this context, due to their abundance, their different electronegativity as compared with Ni, and the relevance of nickel oxide and chalcogenides. By doping the pure Ninclusters with an electronegative element like sulfur, local charge transfer is expected which could induce a partial ionic contribution to the local bonding in the system. The aim of the present work is to perform a systematic theoretical study of the evolution of the structural, electronic, and magnetic properties of small Ni clusters when doped with a single sulfur inpurity. We performed density functional theoretic calculations of NinS clusters in the size range of n=1-10. We determined the most stable atomic arrangements, the absolute and relative stabilities, the electronic structure and magnetic properties, and electronic indicators such as ionization potentials and electron affinities. A description of our theoretical approach is done in the next section. The results are presented in section III in which we first present the structural properties and then we discuss the stability and electronic properties. The main conclusions are summarized at the end. 2 Computational method Calculations were conducted within the density functional theory, using a plane wave basis set and the Projected Augmented Wave (PAW) approach for the core interactions, as implemented in the VASP code (15). We considered the 3d84s2 valence configuration for Ni, and 3s23p4for S. A plane wave energy cutoff of 300 eV was taken. The exchange and correlation effects were treated in the Generalized Gradient Approximation (GGA) by using the Perdew-Burke-Ernzerhof functional (16). A cubic supercell with lateral size of 15 ˚ A was employed for all the calculations. Only the Γpoint was taken for integrations in the Brillouin zone. The cluster geometry was optimized, without symmetry constraints, until the force on each atom was less than 0.001 eV/˚ A, and the total energy was converged to 10−6 eV. For charged clusters, corrections to the total energy were included by considering the full dipole moment in all directions. The corrections were calculated as the energy difference between a monopole, dipole, or quadrupole in the current supercell and the same monopole, dipole or quadrupole placed in a vacuum. Fur- Unveiling the effects of doping small nickel clusters with S impurity 3 thermore, the quadrupole corrections originating from the expectation value of r2 were also taken into account. The lowest-energy structures of pure Ninclusters were obtained by considering various initial configurations with different symmetries. Most of the inputs used were taken from previous published works. For doped NinS clusters, we considered various initial atomic arrangements with the S atom occupying the different sites, and also by adsorbing it on all possible sites of several bare Ninlow-lying isomers (first, second and sometimes third isomers) calculated beforehand. We checked that the results remain unchanged after small displacements of the atoms around their equilibrium positions and also 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 states to be sure of the total spin of the putative ground state. Although we did not employed an unbiased structural search, we believe that our sampling should be sufficient due to the small size of the clusters. With the VASP code, the local charges and spin magnetic moments are computed 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 and always identical to the total cluster values. In order to overcome this issue when analyzing the local magnetic moments distribution, we performed the analysis by using Bader’s method (17; 18; 19) which is based on partitioning the cluster into atomic volumes by locating the zero-flux surfaces of the electron density field. The accuracy of the calculation method is checked by comparing the calculated bond length, vibration frequency, ionization potential and electronic affinity of both Ni2and S2dimers, with available experimental data. The results for Ni2, summarized in Table 1, show a fairly good agreement between the calculated and the measured values of the different quantities considered. As for the calculations for S2, the consistency of the results with the experimental data can be found in our previous paper on FenS2clusters (21). Moreover, aditional test calculations for hexagonal bulk NiS (NiAs structure) give lattice parameters of 3.45 and 5.20 ˚ A in good agreement with the measured values of 3.44 and 5.32 ˚ A (20). 3 Results and discussion 3.1 Structural properties In order to extract conclusions about the effect of S doping on the structural and electronic properties, we have first determined the putative ground state of the corresponding pure Ninclusters which we also compare with previous results available in the literature. The atomic configurations adopted by the putative minimum energy structure of Ninand NinS (n=1-10) clusters are displayed in Fig.1 and Fig.2. Only the geometries of the putative ground state is described along the text, except if certain isomers are energetically competitive with the ground state. Information about all the low-lying isomers found in the present work can be obtained from the authors upon request. 4 A. Chikhaoui et al. Ninclusters. We note that neutral Ninclusters have been the subject of several theoretical studies (22; 23; 24; 25; 26; 27; 29; 30; 31; 28; 32; 33; 34; 35; 36; 37; 39; 40; 41; 42; 43; 44; 46; 47; 48; 49; 50) against which we can benchmark our theoretical approach. Let us note that our group already performed DFT calculations (50) for pure Ni clusters by using the SIESTA code (51; 52) with the same approximation for exchange and correlation (GGA-PBE) as in the present work. This method is based on norm-conserving pseudopotentials and linear combinations of atomic orbitals as basis sets for which we used triple-ζwith double polarization functions. In general, our present results for nickel clusters are similar to those previously obtained with the SIESTA code (50). It exist nevertheless some exceptions like Ni5 for which VASP gives a trigonal bipyramid of D3hsymmetry and total moment of 4µB, whereas SIESTA gave a square pyramid of C4vsymmetry and 6 µBof total moment. However, we point out that the first isomer of Ni5with total moment of 6 µBis found at only 0.03 eV of energy above the putative ground state with total moment of 4 µB. Apart from slight relaxations, our optimized geometries of neutral Ninclusters, displayed in figures 1 and 2, are also consistent with previous results published elswhere, except for few sizes in which a similar scenario as in the previously mentioned case of Ni5in the SIESTA vs VASP benchmark occurs. Different approaches at the DFT level are known to give rise sometimes to slightly different energetic ordering of the low-lying isomers. It is for this reason that recalculating the pure Ni clusters at the same level of accuracy as the S doped clusters is appealing for providing a consistent analysis. NinS clusters. We discuss first the general trends. We find that the S atom tends to occupy a 3-fold hollow site on the Ninhost clusters, in qualitative agreement with recent DFT calculations (53) where it was shown that the sulfur adsorption on the Ni(100) and Ni(110) surfaces takes preferably place on the most coordinated sites. The computed average Ni-Ni distance (AD) in both Ninand NinS clusters is plotted as a function of cluster size nin Fig. 3a. In pure nickel clusters, it increases up to n=5 and then it keeps nearly constant to stabilize around a value of 2.35 ˚ A. The situation is different in the S-doped clusters, where the Ni-Ni distance increases with respect to that of the pure Ninclusters although with a lower slope. Let us now analyze in some detail the structures of the different clusters. The ground state of Ni2S is an isosceles triangle (C2vsymmetry), with Ni-S and Ni-Ni bond lengths of 2.03 and 2.32 ˚ A, respectively. Its total magnetic moment of 2µBresults from a parallel magnetic coupling between the Ni atoms (2×0.82 µB) and the S atom (0.36 µB). We note that S doping considerably enhances the Ni-Ni bond length, as in the pure Ni3(D3h) these bond lengths are 2.21 ˚ A, and even smaller in Ni2(2.09 ˚ A), both pure clusters having also 2µB. For Ni3S, the putative ground state is a trigonal pyramid of Cssymmetry and total moment of 2µB, as that of Ni3. The local moments on Ni atoms are 2×0.64 and 0.66 µBwhereas the induced moment on S is very small 0.06 µB. A trigonal pyramid of C3vis the first isomer, lying at just 0.02 eV above the ground state. The pure Ni4is a tetrahedron (D2) with total moment of 4 µB. In this case, substitutional doping reduces the total magnetic moment. Doping also enhances the average Ni-Ni inter-atomic distance. Ni4S is a trigonal bipyramid of C3vsymmetry and 4 µBof total moment. The two non-equivalent Ni-Ni bond lengths (2.32 and 2.29˚ A) are slightly larger Unveiling the effects of doping small nickel clusters with S impurity 5 than those of Ni-S bonds (2.18 ˚ A). The local Ni moments are 3×0.98 and 0.93 µB whereas the S atom is noticeably polarized (0.13 µB). The same atomic arrangement but with a Cssymmetry and the same total moment (4 µB) is found as the first isomer at only 0.01 eV above. The pure Ni5is a trigonal bipyramid of D3h symmetry and total moment of 4 µB, meaning that doping here does not modify the magnetic moment. The putative lowest-energy structure of Ni5S is a Ni5distorted trigonal pyramid capped by the S atom on one of its 3-fold hollow sites. It has Cssymmetry and a total moment of 4 µB. The pure Ni6cluster is a square bipyramid of D4h symmetry and 8 µBof total moment resulting from the distribution of the moments of the base atoms (4×1.33 µB) and the apex atoms (2×1.34 µB). This Ni6 structure with D4hsymmetry is energetically quasi-degenerated (∆E=0.01 eV) with the same atomic arrangement having Cisymmetry. Substitutional doping reduces the total moment and leads to an important atomic rearrangement. For Ni6S, the putative ground state is obtained from the Ni6square bipyramid where the S atom is adsorbed on a 3-fold hollow site giving rise to a Ni-Ni bond breaking on the base. It has Cssymmetry and a moment of 6 µB. A similar atomic arrangement but with C3vsymmetry and the same total magnetic moment as pure Ni6(8 µB), is found as the first isomer at only 0.04 eV above. The Ni7cluster is an Ni6octahedron capped by the seventh Ni atom on one of its 3-fold hollow site. It is of Cssymmetry and bear a total moment of 8µB. As expected, the effect of enlarging the average Ni-Ni inter-atomic distance upon S doping decreases as increasing the size of the Ni cluster. The putative lowest-energy structure of Ni7S is a distorted pentagonal bipyramid of Cssymmetry where the S atom caps one of its 3-fold hollow sites. It bears a total moment of 6 µB. The reduction of the magnetic moment of the host cluster upon S doping (by 2 µB), that takes place for Ni7S, as well as for Ni6S is less marked than for the smaller clusters discussed above; for larger clusters, as we will see, this effect dissapears. We will come later to this point when discussing the electronic properties. Ni8has a bisdisphenoid configuration with C2vsymmetry and total magnetic moment of 8 µB. Ni8S is a Ni6octahedron capped by two Ni and one S atoms on 3-fold hollow sites. It has Cssymmetry and total moment of 8 µB. The putative lowest-energy structure of Ni9is a trigonal prism tricapped of C2vsymmetry and total moment of 8 µB. The putative ground state of Ni9S is an octahedron Ni6capped by three Ni atoms and the S atom, on 3-fold hollow sites. It has the same symmetry (C3v) and same total moment (8 µB) as the putative lowest energy structure of Ni10 where one of the Ni atoms is replaced by S (Fig. 2). Finally, the lowest-energy structure of Ni10S is a distorted pentagonal bipyramid of Cssymmetry and total moment of 8 µB, capped by three Ni atoms on 3-fold hollow sites. It was obtained by substiting the tenth atom of the Ni11 cluster by the S atom (Fig. 2). 3.2 Stability and electronic properties The binding energies (BEs) per atom for both Ninand NinS clusters (n=1-10) are plotted in Fig. 3c. BE is calculated from the following expressions 6 A. Chikhaoui et al. BE(Nin) = −[E(Nin) + nE(Ni)]/n, (1) BE(NinS) = −[E(NinS) + nE(Ni) + E(S)]/(n+ 1).(2) First, we notice that the general behavior of the BE of pure Ninclusters as function of size is consistent with previous theoretical results (33; 34; 39; 43; 46; 49; 50). BEs of NinS clusters are larger than those of pure Nin, particularly for the smallest sizes for which the Ni/S rate is larger. As expected, BEs of pure and doped clusters tend to converge to each other as increasing cluster size. This reflects the obvious fact that a single S atom is averaged with an increasing number of Ni atoms. For clusters larger than those investigated here, it is expected that the S atom will continue to occupy preferentially the most coordinated hollow sites, as it occurrs in surfaces (53), with concomitant local relaxations but without affecting the rest of the host cluster. The binding energy indicates that S-doping enhances the thermodinamical stability of the Ni clusters. This binding increase is related to the strong S-Ni bonding, reflected in the kind of adsorption site (the S-atom is bonded with three Ni atoms in a 3-fold hollow site). As we will see later, the strong S-Ni bond is favoured by a partial ionic contribution due to charge transfer from Ni to S as a consequence of the different electronegativities of the two elements (S is more electronegative than Ni). A further evidence of the strong S-Ni bonding is provided by the single-atom fragmentation energies. We considered two single-atom fragmentation channels of NinS, involving one Ni atom or the S atom. These quantities, plotted in Figure 4a are defined in terms of total energies as follows: ∆S=E[Nin] + E[S]−E[NinS],(3) ∆Ni =E[Nin−1S] + E[Ni]−E[NinS].(4) One can see from Figure 4a that ∆Sis larger than ∆Ni, for any size n, showing that the desulfurization (removing the S atom) of NinS systems requires more energy than extracting the less bonded Ni atom of the cluster. In other words, it is easier to dissociate Ni than S atom from the NinS system which suggests that the Ni-S bonding is stronger than the Ni-Ni one. The lowest Ni fragmentation energy corresponds to the extraction of one Ni atom from Ni4S and the largest desulfurization energy corresponds to the removing the S atom from Ni3S and Ni4S. The maximum difference (2.77 eV) between the two energies is obtained for Ni4S. One can connect the low energy required to dissociate one Ni atom from the Ni4S cluster to the enlargement of the Ni-Ni inter-atomic distances which takes place upon S doping of Ni4(Fig. 3a). Besides, the apex Ni atom in the trigonal bipyramid of Ni4S is the less bounded atom due to the repulsion with its Ni neighboring atoms, induced by the charge transfer to the S atom (Fig. 4b). In order to discuss the relative stability of a cluster of a given size nwith respect to its neighboring sizes, we computed the second energy difference, defined as ∆2E(n) = E(n+ 1) + E(n−1) −2E(n). This quantity is plotted in Fig. 3b. For S-doped clusters, the most remarkable feature is the noticeable peak at n= 3 indicating the high stability of Ni3S for which the completion of the 3-fold bonding of S with Ni takes place. Notice that this correlates with the largest desulfurization Unveiling the effects of doping small nickel clusters with S impurity 7 energy corresponding to the remove of the S atom from Ni3S. For pure Ni clusters, Ni6stands out as particularly stable. As we will see later, these relative stabilities are also reflected in electronic properties like the ionization potential and the electronic affinity. The vertical ionization potential (VIP) and the vertical electronic affinity (VEA) are important quantities that can be used to characterize the global reactivity of the NinS clusters by means of conceptual DFT indicators (54). The VIP and VEA for both the pure and doped nickel clusters are plotted in Fig. 5, as a function of cluster size n, where we included the calculated values obtained for the pure Ninclusters as well as experimental data reported for them (55; 56). The VIP(VEA) of NinS clusters is calculated as the energy difference between the neutral clusters and the cationic (anionic) counterparts with the structure of the ground state neutral cluster. Except the result of Ni atom, for which the difference between the experimental and the calculated values reaches ∼0.68 eV, the calculated VIPs for Ninclusters follow the experimental data (55) rather well as a function of cluster size. This gives further support to our putative ground state structures. Unfortunately, experimental data concerning VIP and VEA of S-doped nickel clusters are not available so far. However, one can bring out some trends concerning the effect of S-doping on VIP of NinS by comparing their calculated values with those of the pure Ninclusters. From Figure 5, one can see that Sdoping produces in general a slight increase of the VIP, except for n=2 and 6. We also note that the VIPs decrease as a function of size in a more monotonic fashion for the S-doped Ni clusters than for the pure ones. As for the calculated values of VEAs for Ninclusters, they agree also rather well with the experimental data, except for n=3 for which the difference in the absolute values amounts to 0.28 eV. The VEA of pure Ni clusters increases quite lineary with nbetween n=2 and 9 and then decreases slightly for n=10. The VEA increases upon S-doping by about 11%. It follows almost the same slope as of pure nickel clusters as a function of cluster size n. The enhancements of both VEA and VIP of S-doped clusters with respect to those of pure Ninare consistent with the higher binding energy of the S-doped clusters as compared with the pure ones (Fig. 3c). From VIP and VEA one can evaluate the electronegativity (the negative of the electronic chemical potential µ): χ=−µ=1 2(V IE +V EA),(5) and the chemical hardness (or fundamental gap, except for a constant factor): η=Egap =1 2(V IE −V EA).(6) These quantities are plotted in Fig. 5 as a function of the cluster size nfor the pure and doped nickel clusters. Both χand ηof Ninclusters display qualitatively the same behaviour as the ionization energy as function of the size n. They decrease between n=2 and 4 and then increase up to n=6 after which it decreases again up to n=10. Thus, both quantities present a local maximum at n= 6 and a local minimum at n=4 which correlates with the relative high stability of Ni6clusters and the low stability of Ni4already observed through the second difference in the energy (Figure 3b). The electronegativity of S-doped Ni clusters is equal or higher 8 A. Chikhaoui et al. than that of the pure ones. The chemical hardness ηdoes not change much, and the most noticeable change occurs for n=4. Let us discuss now the magnetic behavior of the pure and S-doped nickel clusters. The total magnetic moment as a function of cluster size nof both sets of clusters is plotted in Fig. 6a. We have also plotted the magnetic moments per atom (Figure 6b) and included, for the sake of comparison, the available experimental data for pure Ninclusters (57). Our values are smaller than the experimental ones, as it is also the case for almost all ab initio calculations on nickel clusters (33; 40; 42; 47; 49). Those discrepancies between theory and experiment remain an open question, although the problem may arise from the additional orbital moment contributions or isomerization effects as suggested by some authors (38; 45). The S-doping of Ninclusters affects Ni6S and Ni7S by reducing their total moment from 8 µBin Ni6and Ni7to 6 µB. We note that for both Ni6S and Ni7S clusters, the magnetic state with 8 µBis only ∼0.03 eV higher in energy than the ground state with 6 µB. This small effect of S-doping on the total spin polarization of Ninclusters is consistent with the weak hybridization between the S and Ni orbitals. To analyze this with two examples, we compare the density of states (DOS) of Ni5S (Ni6S) with that of Ni5(Ni6). [Figures 7 and 8]. In both cases, the hybridization is weak and involves molecular orbitals far from the Fermi level. For Ni5S the geometry of the host Ni5cluster is essentially preserved (Fig. 1), and no significant rearrangement of both spin-up and spin-down states takes place upon S-doping, the total moment being preserved (Fig. 7). In Ni6S, however, we observe an important electronic states rearrangement for both spin components upon S doping (Fig. 8), associated to a structural change. The spectrum rearrangement is accompanied by a spin flip from the majority to minority spin states, giving rise to a decrease of 2 µBupon doping. Finally, we plot in Figure 9, as a function of cluster size, the spin-up and spin-down HOMO-LUMO gaps of NinS in their putative lowest-energy structures. The HOMO-LUMO gap of each spin channel is a key quantity for spin-dependent electronic transport at low voltages. The S-doped clusters with n≤4 and n=810, have relatively large HOMO-LUMO gaps for spin-up states (∼2.38 to 1.20 eV) whereas, except for n=3, spin-down states have small gaps (∼0.60 to 0.04 eV). The situation is somewhat different for pure Ninclusters where the largest HOMO-LUMO gaps for spin-up states are obtained for n=2-3 and for sizes larger than n=5. Ni6(Ni4) displays the largest(lowest) gap 2.46(0.23 eV) which reflects the high(low) stability of this cluster (Figure 3b). One can note that the total gap of Ni4is the smallest one as reflected in its low stability from the calculated second differences of energy for pure Ninclusters (Figure 3b). The gaps corresponding to spin-down states are relatively small, and nearly zero for n > 4, indicating that these clusters are good candidates as molecular junctions for spin filtering at low bias voltage. However, the absolute value of the HOMO-LUMO gap has to be taken with care, since it is not a well defined quantity in DFT that tends to underestimate it due to the lack of electronic correlations. Hybrid functionals such as BLYP, B3LYP, B3PW91, HSE06, among others, are designed to better describe part of the exchange and/or correlation effects and, thus, give better absolute values for the HOMO-LUMO gaps than functionals like PBE that otherwise are built from physical grounds and work well for a wide spectrum of properties. To the best of our knowledge only one theoretical work using B3LYP functional (61) was devoted Unveiling the effects of doping small nickel clusters with S impurity 9 to nickel sulfide clusters (NiS)n,n=3-5. In order to estimate the discrepancy between the HOMO-LUMO value obtained with PBE and B3LYP, we calculated at the PBE level the ring structure proposed for (NiS)3in this reference. The PBE HOMO-LUMO gap (0.50 eV) underestimates the B3LYP one (1.04 eV) in about 50%. Other quantities such as ionization potential (IP) and electron affinity (EA) and derived quantities are expected to be less affected since they are obtained as energy differences between ground states calculated at the DFT level, so that they are well defined indicators within the DFT as oppose to the HOMO-LUMO gap. This is confirmed by the calculated VIPs and VEAs for Ninclusters which follow the experimental data rather well as a function of cluster size, as indicated in Figure 5. For the ring structure proposed for (NiS)3in reference (61), our calculated values of VIP and VEA, 5.65 and 3.5 eV respectively, are within 13 and 18% of those of B3LYP, 5 and 4 eV respectively (61). 4 Conclusions The main conclusions of our DFT-GGA study of S-doped NinS clusters (n=1-10) can be summarized as follows. (i) The S atom tends to occupy a 3-fold hollow site, in agreement with DFT calculations (53) of sulfur adsorption on Ni surfaces, which was shown to take place preferentially on the most coordinated sites. A further evidence of the strong S-Ni bonding is provided by the single-atom fragmentation energies: a Ni atom can be extracted from NinS with a lower energy cost that the S atom. (ii) S-doping enhances the thermodynamical stability of the Ni clusters. The increase of binding energy upon S doping is related to the strong S-Ni bonding, also favoured by a partial ionic contribution due to charge transfer from Ni to S. According to the second differences in energy, Ni3S is particularly stable with respect to the neighboring sizes. All atoms of this cluster are involved in the 3fold bonding, and it has the largest desulfurization energy among the investigated clusters. (iii) S-doping only affects the magnetic moment of Ni6S and Ni7S by reducing their total moment from 8 µBin Ni6and Ni7to 6 µB. The spin-polarized densities of states show a weak hybridization between the S and Ni orbitals, but strong enough structural changes upon doping, in few cases, to produce an electronic states rearrangement consistent with a change of total moment. (iv) S-doped clusters with n≤4 and n=8-10, have relatively large HOMOLUMO gaps for spin-up states. However, the gaps corresponding to spin-down states are small, and nearly zero for n > 4, indicating that most of these clusters are good candidates as molecular junctions for spin filtering at low bias voltage. Aknowledgements This study was funded by the Algerian Ministry of Higher Education and Scientific Research via the project CNEPRU B00L02UN150120130013, and by the Junta de Castilla y Len (Spain) (Project VA124G18) 16 A. Chikhaoui et al. 0 1 2 3 4 5 6 78 9 10 11 2 3 4 5 6 Fragmentation energy (eV) (a) (b) ∆Ni ∆S 0 1 2 3 4 5 6 78 9 10 11 Cluster Size (n) 0.3 0.4 0.5 0.6 Charge Transfer on S atom (e-) Fig. 4 Fragmentation energies of NinS clusters via the loss a Ni (∆Ni) or a S (∆S) atom, as a function of cluster size n=1-10 and calculated charge transfer to the sulfur atom in neutral NinS clusters, as function of cluster size n=1-10 (b). Unveiling the effects of doping small nickel clusters with S impurity 17 5 6 7 8 9 VIP (eV) NinS (cal) Nin (cal) Nin (exp) 1 1.5 2 2.5 3 VEA (eV) 4 4.5 5 χ (eV) 0 1 2 3 4 5 6 78 9 10 11 Cluster Size (n) 2 2.5 3 3.5 4 η (eV) Fig. 5 Vertical ionization potential (VIP), vertical electronic affinity (VEA), electronegativity (χ) and chemical hardness (η) of Nin(open triangle) and NinS (filled square) as function of the cluster size n=1-10. 18 A. Chikhaoui et al. 0 1 2 3 4 5 6 78 9 10 11 0 2 4 6 8 10 12 14 Total Magnetic Moment (µB) (a) (b) NinS Nin 0 1 2 3 4 5 6 78 9 10 11 Cluster Size (n) 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Magnetic Moment per Atom (µB) Fig. 6 Total magnetic moments (a) and magnetic moments per atom (b) of NinS and Ninas a function of cluster size n=1-10. Unveiling the effects of doping small nickel clusters with S impurity 19 -14 -12 -10 -8 -6 -4 -2 0 2 -40 -20 0 20 40 60 Total DOS Ni5 -14 -12 -10 -8 -6 -4 -2 0 2 Energy (eV) -20 -10 0 10 20 30 S Ni Ni5S Fig. 7 Total spin polarized density of states projected on the 5 Ni atoms and on the S atom of the putative ground-state of Ni5S (a), as compared to the total DOS of the host Ni5(b). The vertical dashed line indicates the Fermi energy. A Gaussian smearing (0.1 eV) of the states has been used in the plot. 20 A. Chikhaoui et al. -14 -12 -10 -8 -6 -4 -2 0 2 -60 -40 -20 0 20 40 60 Total DOS -14 -12 -10 -8 -6 -4 -2 0 2 Energy (eV) -30 -20 -10 0 10 20 30 40 50 S Ni Ni6 Ni6S Fig. 8 Total spin polarized density of states projected on the 6 Ni atoms and on the S atom of the putative ground-state of Ni6S (a), as compared to the total DOS of the host Ni6(b). The vertical dashed line indicates the Fermi energy. A Gaussian smearing (0.1 eV) of the states has been used in the plot. Unveiling the effects of doping small nickel clusters with S impurity 21 0 0.4 0.8 1.2 1.6 2 2.4 (a) - NinS (b) - Nin spin + spin - 0 1 2 3 4 5 6 78 9 10 11 Cluster Size (n) 0 0.4 0.8 1.2 1.6 2 2.4 Homo-Lumo Gap ( eV) spin + spin - Fig. 9 HOMO-LUMO gap for spin-up and spin-down electrons of NinS (a) and Nin(b) as function of cluster size n=1-10.