Zn17 Superatom Cage Doped with 3d Transition-Metal (TM) Impurities

Article pubs.acs.org/JPCC

Zn17 Superatom Cage Doped with 3d Transition-Metal (TM) Impurities (TM = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and Cu) Alexandre Lebon,† Andrés Aguado,*,‡ and Andrés Vega‡ †

Laboratoire de Magnétisme de Bretagne, Université de Bretagne Occidentale, EA 4225, 29285 Brest, Cedex, France Departamento de Física Teórica, Atómica y Ó ptica, Universidad de Valladolid, Valladolid 47071, Spain

‡

ABSTRACT: A systematic theoretical study of the doping of Zn17 nanoparticle with 3d transition-metal (TM) impurities is presented. Calculations are conducted within the density functional framework as implemented in the VASP code at the generalized gradient approximation for the exchange and correlation effects. The ground state of Zn17 has been recently shown to be a dihedral superatom hollow cage in a singlet state [Angew. Chem., Int. Ed. 2015, 54, 2111]. We show that, among the 3d elements, endohedral doping of a quasi-undeformed cage results favorable only for Cr and Cu, which as free atoms display a very stable (half-filled and fully occupied, respectively) d shell electron configuration. This structural configuration allows to maximize the spin magnetic moment of the chromium-doped cage. Co and Ni also adopt an endohedral configuration, but with a strong deformation of the cage and a rather compact structure due to the large electron hybridization between the TM states and those of the Zn host. Doping with the other TM impurities results in an exohedral arrangement, also concomitant with a marked electron hybridization. Most of the TM impurities retain a large part of the spin magnetic moment that they have in a vacuum due to localization of part of their 3d states. The Zn atomic environment is found to be spin-polarized and modulates the total spin moment of these molecular magnets depending on the induced moments and magnetic couplings.

1. INTRODUCTION Nanoparticles containing magnetic elements together with other elements are often classified as molecular magnets. The chemical and geometrical environment of the magnetic element confers the molecular magnet certain functionalities that make it interesting in a variety of possible technological advances in spintronics, molecular electronics, or biomedical applications. Understanding the cooperative effects between the different elements forming the molecular magnet is a goal from the fundamental point of view but is also crucial for its design (in the case that it was not a natural molecule) and/or for optimizing its performance. Because of quantum confinement effects arising at the nanoscale, electronic structure calculations are required to achieve this goal and to complement existing or future experimental data concerning their synthesis and characterization. Obviously, the main property of a molecular magnet is its magnetic moment, so that it is necessary that the environment of the magnetic atom or subcluster does not quench it through electron hybridization. Finding such an environment is therefore appealing, and several groups have contributed in this context, finding a variety of TM-based molecular magnets.1−7 In many cases, the resulting magnet is a cage host endohedrally doped with a TM impurity of high stability. In a previous work,8 we explored the structural and electronic properties of neutral and charged pure ZnN clusters by means of an unbiased structural search at the DFT level. The reliability of the ground state configurations was demonstrated through a © 2015 American Chemical Society

benchmark of the resulting electronic structure against photoelectron spectroscopy measurements. In the particular case of Zn17, we obtained a hollow cage structure with perfect D5h symmetry as the global minimum (GM). An analysis of the size dependence of the binding energies of ZnN clusters8 showed a marked local maximum at N = 17, implying the enhanced stability (magic character) of this cluster with an exact filling of jellium electronic shells. In a separate work,7 we found that the cluster Zn17 endohedrally doped with a Cr impurity can be qualified as a magnetic superalkali cluster, with high stability, low ionization potential, and a high total spin magnetic moment of 6 μB, exactly the value of the isolated Cr atom. The electronic density of states (EDOS) showed that almost the totality of the Cr EDOS is concentrated in a single narrow peak, an indication of the weak hybridization between the localized 3d electrons of Cr and the delocalized orbitals of the Zn cage, which in turn contributes to preserve a large amount of the magnetic moment that Cr has as an isolated atom and, at the same time, to induce a spin-polarization in the electrons of the Zn host. The fact that Cr@Zn17 behaves as a superalkali cluster despite its total number of valence electrons (40) would fit an exact filling of jellium electronic shells clearly indicates that not all the valence electrons of Cr participate in the jellium cloud. In fact, since Received: September 10, 2015 Revised: November 17, 2015 Published: November 18, 2015 27838

DOI: 10.1021/acs.jpcc.5b08837 J. Phys. Chem. C 2015, 119, 27838−27847

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The Journal of Physical Chemistry C

Table 1. Relevant Structural and Electronic Data for Both the Putative GM Structure and the Structure Obtained after Relaxing the D5h Endohedral TM@Zn17 Configurationa system

X

Sc

Ti

V

Cr*

Mn

Fe

Co*

Ni*

Cu*

Zn−Zn (Å) Zn−X (Å) QB (e) Zn−Zn (Å) Zn−X (Å) QB (e) VB (Å3)

rc (Å)

2.68 2.84 3.78 2.69 2.70 3.75 13.19 1.70(7)

2.66 2.74 3.23 2.66 2.70 3.16 14.16 1.60(8)

2.66 2.72 4.40 2.64 2.76 4.47 15.25 1.53(8)

2.67 2.98 5.53 2.67 2.98 5.53 15.35 1.39(5)

1.323

1.217

1.323

2.64 2.54 9.27 2.64 2.66 9.22 15.56 1.26(3) 1.50(7) 1.302

2.65 2.95 11.08 2.65 2.95 11.08 15.93 1.32(4)

1.429

2.66 2.62 7.94 2.66 2.96 7.79 15.73 1.32(3) 1.52(6) 1.302

2.65 2.63 10.29 2.63 2.84 10.20 15.61 1.24(4)

rWS (Å)

2.66 2.73 6.70 2.63 2.82 6.62 15.56 1.39(5) 1.61(8) 1.323

1.286

1.312

GS

D5h

a

Impurities noted with an asterisk are those that preserve an endohedral configuration after relaxation. Zn−Zn refers to the average Zn−Zn nearest neighbor distance; Zn−X is the average nearest neighbor distance between Zn and the corresponding TM atom. QB is the Bader charge on the impurity (for Sc, Ti, and V the calculation included the semicore p states in the active space; the quoted Bader charges do not include those semicore electrons); VB is the Bader volume. VB is quoted only for the endohedral configuration as its value is not very meaningful when the impurity is on the cluster surface. We also report the values of the covalent radii for the TM atoms15 and the Wigner−Seitz radii used by the VASP code to project out the spd contributions to the EDOS. The two different rc values for Mn, Fe, and Co correspond to different spin states or chemical valencies.

(PAW) approach. For the exchange and correlation potential we used the Perdew−Burke−Ernzerhof form of the generalized gradient approximation.11 The plane wave basis set was extended up to an energy cutoff of 300 eV, and we used an energy criterion of 10−4 eV for converging the electronic density. The individual clusters were placed in a cubic supercell of 20 × 20 × 20 Å3, a size large enough as to make the interaction between the cluster and its replicas in neighboring cells negligible, allowing to consider only the Γ point (k = 0) when integrating over the Brillouin zone. Initial geometries were generated as in our previous work7 of Cr@Zn17, namely, by considering a set of low-lying isomers predicted for the host Zn17 cluster to which the TM atom was added in different positions as well as low-lying isomers of Zn18 in which Zn atoms were substituted by TM ones. Structures were relaxed without any symmetry or spin constraints until interatomic forces were smaller than 0.01 eV/Å. In all cases different spin isomers were checked in order to ensure the location of the correct ground state. Local electronic charges and magnetic moments were evaluated using Bader’s method 12 which is based on partitioning the cluster into atomic volumes by locating the zero-flux surfaces of the electron density field. This method is implemented in a open source code due to the group of Henkelmann.13 Using this method, the sum of local charges and moments recovers the total electronic charge and magnetic moment. In order to assess the partial s, p, and d contributions to the spin polarization of each atom, VASP employs a projection onto spherical atomic volumes. The results of this procedure are sensitive to the radius chosen for the integration sphere, which is taken to be equal to the Wigner−Seitz radius of the corresponding elemental solid. While for homoatomic systems this may be a sensible option, for heteroatomic systems there is no unique way of defining appropriate radii for the different atomic species; moreover, the volumes of the Wigner−Seitz spheres will not necessarily be similar to the Bader volumes, and in any case some interstitial charge is always lost. As an example, we provide in Table 1 values for the Bader volumes of an endohedral impurity and also the Wigner−Seitz radii employed by VASP. The volumes of the WS spheres are systematically smaller than the Bader volumes. Moreover, the

most of the 3d states of Cr do not hybridize with the cage, and are well localized in the TM impurity, the Zn cage is preserved as an anionic jellium-like subcluster, and the endohedral doping is the most stable configuration. Therefore, the structural and electronic properties of this system finally depend on the subtle role played by the 3d electrons of the transition metal impurity in contact with the Zn host and the degree of hybridization. In view of the above findings, several questions arise if doping the Zn17 superatom cage with other 3d TM impurities different from Cr: (i) What is the role played by the 3d states of that TM impurity having a different electronic configuration from Cr? (ii) Is the cage structure of the Zn host preserved and is the resulting doping endohedral or exohedral? (iii) Up to which extent is the spin magnetic moment of the isolated TM atom preserved upon doping? The aim of the present study is to complement our two previous works7,8 by addressing the above issues. For this purpose we have carried out systematic density functional theory calculations of the spin-polarized electronic structure and total energy of the Zn17 cage doped with a 3d TM atom (TM = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn). Note that the cases TM = Cr and Zn were explored in detail in our previous works. We have analyzed the total and projected densities of electronic states and also the Bader partitioning of the spin-polarized electronic charge distribution. The computational details are outlined in section 2. In section 3 we first discuss the main trends regarding the morphology of the clusters in connection with the electronic structure in their global minimum structures. Next we discuss in detail the magnetic properties resulting from the spin polarization, with particular attention also to those metastable isomers resulting from the optimization of the endohedral D5h environment (global minima only in the case of Cr and Cu). The final part of section 3 is devoted to rationalize general trends for the absolute and relative stabilities of these systems in terms of different contributions, some of which have been unveiled in the two previous sections. Our conclusions are summarized in section 4.

2. COMPUTATIONAL METHODS We performed fully self-consistent DFT calculations using the plane-wave code VASP,9,10 which solves the spin-polarized Kohn−Sham equations within the projector-augmented wave 27839


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The Journal of Physical Chemistry C evolution trend is exactly the opposite in both cases: while the Bader volumes tend to increase from Sc to Cu along the 3d TM series, the WS radii show an overall decrease and are more in line with the evolution of covalent radii, also shown in Table 1. Therefore, there is no a priori reason to expect that the sum of s, p, and d contributions for one atom will recover the corresponding Bader local value of a given physical property. We have performed some test calculations modifying the WS radii so that the volume of the WS sphere matches the Bader volume. Integration over those bigger spherical domains still underestimates the atomic charges or local magnetic moments as compared to Bader results, but it allowed us to quantify in a first approximation the relative sp and d charge lost in the interstitial region when integrating onto WS spheres, which served to normalize the orbital-projected EDOS. We also checked that Bader’s distribution of the per-atom charge and magnetic moments preserves to a large extent the relative proportions directly provided by VASP through the projection of plane waves onto spherical atomic volumes, so we believe the percentages of s, p, and d contributions extracted are at least physically meaningful, if not fully quantitative, for discussing trends.

3. RESULTS AND DISCUSSION Geometrical and Electronic Structures of TM-Doped Zn17 Clusters in Their Ground State. In Figure 1, we show the putative GM structures of Zn17 doped with the different 3d TM atoms (including X = Zn also as an “impurity”). Table 1 summarizes structural and electronic data that are relevant to the discussion. We find that doping with Cr and Cu results in an endohedral structure with the TM impurity inside a nearly undeformed D5h host cage due, as we will see below, to the rather weak hybridization between the 3d electrons of the impurity and the sp electrons of the Zn host. In this D5h structural arrangement, the TM−Zn interatomic distance is the longest one (about 3 Å on average), and the cage has a slight prolate distortion, being elongated along its 5-fold symmetry axis. “Doping” with Zn is similar, except that the cage undergoes a C2v distortion, becoming elongated along a direction perpendicular to the original 5-fold symmetry axis. Co and Ni also adopt an endohedral configuration, but with a stronger deformation of the cage, leading to a lower point group symmetry (C1) and to much more compact structures (here we find the shortest TM−Zn interatomic distances are about 2.6 Å). As we will see, the electron hybridization with the cage orbitals is noticeable for Co and Ni. Doping with other 3d TM atoms results in an exohedral arrangement, with Cs symmetry in most cases (Ti, V, Mn, and Fe). Those Cs structures are in fact very similar to the C2v structure of Zn18, in which the C2 axis is lost after substitution of a surface atom of Zn18 with the TM atom. In all cases, Zn−Zn interatomic distances hardly differ from 2.65 Å, while differences in the TM−Zn distances are significant and reflect different degrees of electron hybridization between the TM impurity and the Zn host. The average TM−Zn first-neighbor distance is longer than Zn−Zn distances for all clusters except for Fe, Co, and Ni impurities. Therefore, there is a clear trend for late TM elements to make the structure more compact as compared to early TM impurities. In Figures 2 and 3 we plot the total EDOS, as well as its projections on the 3d and sp states of the TM impurity, for the GM structures of the doped clusters. We focus first on Cr and Cu impurities which are stable in an endohedral D 5h

Figure 1. Putative global minimum structures of Zn17 doped with a 3d transition metal impurity. We indicate the point group symmetry. P or AP indicates parallel or antiparallel magnetic coupling between TM and the Zn host. If not stated, the coupling is competing between P and AP or simply negligible. NM indicates that the electron density is not spin-polarized.

configuration. This particular structural arrangement is associated with a very weak hybridization between the d levels of the TM impurity and the levels of the host. As those two atoms feature a very stable d-electron configuration (associated with either a half-filled d-shell with a large exchange splitting or a fully occupied d-shell), it seems that the ultimate reason for the stability of the endohedral configuration is that the d-shell is perturbed as little as possible under the close-to-spherical environment provided by the cage and thus preserves much of its stability when placed in the center of the zinc cage. Additionally, both the d5 and d10 configurations are spherically symmetric and thus have a shape which is most congruent with the shape of the cage, which is also nearly spherical. This is why these two impurities do not induce significant distortions in the shape of the cage. The EDOS of Cr@Zn17 was already described in our previous work,7 in terms of the delocalized jellium-like states of the host cage. The isolated peaks below −5 eV are 1P states of the jellium cage (occupied with 6 electrons); the 1D states of the jellium cage (with 10 electrons) are located between −3.0 and −4.5 eV. The 1F and 2S superatom states come next and are located above −2.0 eV. The singly occupied level just below the Fermi level and about 1 eV above the (1F, 2S) states is a 2Pz state (or A2″ state according to the labels of the irreducible representations of the D5h point group). The 27840


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the projection onto the d orbitals of Cr recovers most of the whole peak height. Only a small fraction of the d electrons of Cr hybridizes with the superatom orbitals of the cage, as seen by the small contributions of the 3d-projected EDOS to other peaks of the total EDOS. Additionally, one electron of Cr (with mixed 4s and 4p character) is involved, through hybridization, in the bond formation, contributing in particular to the HOMO of the doped cluster but also to many other peaks. Overall, there is only one additional unpaired electron in the delocalized jellium cloud as compared to the empty cage, namely the one that populates the 2Pz orbital of the superatom (that orbital is the LUMO of the Zn17 cage). Apart from the deep impuritylike level, the EDOS of the doped cage preserves the jelliumlike shell structure of the empty cage with minor modifications and resembles that of an alkali atom so Cr@Zn17 was qualified as a superalkali.7 The total magnetic moment of 6 μB (see Figure 5) results from a parallel arrangement of the single unpaired electron in the superalkali cage and the five polarized electrons contained in the localized, impurity-like, level of dominant Cr-3d character. The situation is essentially the same for the Cu impurity, with the localized 3d states of Cu located now about 2.5 eV below the Fermi level and containing 10 electrons instead of 5. The magnetic moment of 1 μB is now completely due to the single unpaired electron occupying the HOMO which is delocalized over the whole cage. Therefore, Cu@Zn17 is also a superalkali. Both Cr@Zn17 and Cu@Zn17 would be very stable as cations and thus might be able to form ionic compounds with suitably chosen anions. The EDOS of Zn@Zn17 is in many respects similar to that of Cu@Zn17, featuring also a clear jellium-like electron shell structure. Two main differences arise: (1) in Zn@Zn17 the HOMO is a doubly occupied 2Px orbital, similar to an alkaline-earth atom; (2) the impurity level is buried deeper below the Fermi level, in fact right below the manifold of levels arising from the d electrons of the Zn17 cage. The large disparity between the energies of the impurity levels of Cu and Zn embedded impurities is just due to a similar difference in the d levels of the corresponding free atoms. The Bader analysis and projected EDOS provide two different ways to estimate the percentage of electrons that remain localized on the impurity. The 3d-projected EDOS around the Cr impurity contributes about 4.1 electrons of the five electrons contained under the narrow impurity-like level, so the remaining 0.9 electrons under that peak are assigned as being distributed over the sp orbitals of the Zn cage by the projection analysis. With these ratios, the large spatial localization of that state around Cr is obvious. We conclude that approximately one d electron of Cr is involved in hybridization with the cage, while about four d electrons remain strictly localized on the impurity (in other words, remain atomic-like and do not overlap with the cage orbitals). A comparison of the projection and Bader results is illuminating in order to understand the precise meaning of the last sentence. On one side, the projection analysis predicts that 1.9 electrons of Cr (or about 1.2 electrons for Cu) contribute to delocalized states of the superatom cage; on the other hand, the Bader charges (Table 1) suggest a charge transfer of only 0.5 electrons from the Cr impurity to the cage and no charge transfer at all in the case of Cu. In other words, a significant fraction of the impurity electrons that according to the EDOS analysis contribute to the delocalized states are reassigned to the impurity by the Bader partitioning of space and not to the cage. Both pictures are not reconcilable in

Figure 2. Total EDOS (red line) of the putative GM structure for TM = Sc, Ti, V, Cr, and Mn together with the EDOS projected on the 3d (green line) and sp (black line) states of the TM impurity.

Figure 3. Same as Figure 2 for TM = Fe, Co, Ni, Cu, and Zn.

remaining 2P states are unoccupied and thus above the Fermi level. In the middle of the (1F, 2S) states there is an additional narrow peak containing five fully polarized electrons, which mostly corresponds to 3d states localized in the Cr impurity and so do not participate in the jellium cloud. This state does not significantly hybridize with the electrons of the Zn host, as 27841


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The Journal of Physical Chemistry C quantitative terms, as the Bader analysis predicts that 5.5 electrons (and not 4.1) are localized on the Cr basin, for example. To further analyze this issue, we have performed additional calculations for Cr@Zn17 including the semicore 3p orbitals in the active valence space and compared the energy of the 3p levels of the embedded impurity with the 3p levels of the isolated Cr atom and Cr+ cation. Assuming that the 3p orbital already behaves as a core orbital, and imposing a linear interpolation between Cr and Cr+ results (which would be strictly satisfied in an exact DFT treatment), we have found that the 3p core level shift corresponds to a charge of +0.4e on the chromium impurity, much closer indeed to the Bader result of +0.5e than to the projected EDOS result. Although the different methods may not be exactly comparable, the trends obtained allow at least to extract the following physical picture: the impurity does contribute to many of the delocalized jellium-like electronic states, and so its spectral weight is considerably spread on the energy scale employed in the EDOS plots, but that contribution is restricted mostly to the inner side of the zinc shell when analyzed in real space, so the charge transferred to the cage according to core level shifts or Bader analysis is not as large as suggested by the EDOS partial integration. With this caveat in mind, we will continue to use the projections of the EDOS in the rest of this paper to estimate the number of d electrons not involved in hybridization and the Bader charges to estimate the degree of charge transfer. Another interesting feature of Cr and Cu impurities is that the impurity-like level has a very small ligand-field splitting, while for all other impurities we will see that the splitting of the impurity d levels is significant. The impurity-like states may apparently be associated with the compact and spherically symmetric d5 and d10 in vacuo configurations of Cr and Cu, respectively, which would correspond to 6S or 1S states both with L = 0. The weak interaction between the impurity and the cage orbitals would then explain the absence of substantial crystal-field splitting of the spherically symmetric impurity level. Notice that the 1D levels of the superatom, for example, have a sizable crystal-field splitting because the D5h cage has a slight prolate deformation, so an approximately S state and a weak interaction are both really needed to explain the absence of splitting. In fact, the D5h symmetry does not allow for orbital degeneracies higher than 2, and a d5 configuration must split according to A′1 + E″1 + E″2 irreducible representations. This is indeed observed although the splitting for Cr is so small that with the broadening employed in the figure only a high-energy shoulder is visually appreciated, corresponding to the dz2 orbital that transforms according to the totally symmetric A 1′ representation (for the case of Cu, the splitting is only slightly more visible). The picture of a very weakly perturbed spherical S state seems thus to be valid to a good approximation. To support this claim, we show in Figure 4 a spatial plot of the local density of states (LDOS) associated with the impurity peak. It indeed allows to visualize the approximately spherical shape of the electron distribution in that energy range (left plot), and that shape is compatible only with approximate d5 and d10 electronic configurations centered on the impurity. The fact that the corresponding peak in the EDOS (see Figure 2) has a 20% contribution from the sp atomic orbitals of zinc atoms is just due to the extended tails of the orbitals centered around the Cr impurity and is a measure of the degree of overlap. For a more precise description, we show in Figure 4 several LDOS isosurfaces. We notice that due to the prolate distortion of the D5h cage, the S state associated with the

Figure 4. Spatial plot of the local density of states (LDOS) associated with the impurity-like states of Cr@Zn17. The isosurface values shown are 0.05e, 0.03e, and 0.01e from left to right. The approximately spherical shape (left plot) of the electron distribution in that narrow energy range is consistent with an approximate d5 (6S) state and the absence of substantial crystal-field splitting. At very low electron density values the orbital develops a quadrupolar deviation from a perfect spherical shape and can be described as an S−D hybrid with a weak contribution from the superatom Dz2 orbitals.

impurity can overlap only with the 2S and 1D superatom orbitals (S−D hybridization is allowed by the quadrupolar distortion of the cage). This observation rationalizes the contribution of the 3d levels of Cr to only some particular superatom orbitals and also the detailed shape of the LDOS at low electron density values. As the electron density is decreased, the equatorial zinc atoms (those closest to the impurity due to the prolate shape of the cage) are the first to contribute to the LDOS (middle plot), while the rest of zinc atoms contribute at even lower density values. This progression illustrates that the impurity level is in fact an S−D hybrid with a weak admixture of the Dz2 orbitals of the cage. For other TM dopants, the hybridization between the states of the TM impurity and the electrons of the Zn host is stronger, as illustrated in Figures 2 and 3. This may result in exohedral (Sc, Ti, V, Mn, Fe) or endohedral (Co, Ni) arrangements. The structure is either completely different from the dihedral D5h one (for Sc, Co, and Ni impurities) or at least significantly more compact (for the rest of impurities). In all cases, the sp electrons of the TM impurity strongly hybridize with the electrons of the Zn host, as already found for Cr and Cu impurities; but additionally, a larger fraction of the 3d electrons of the TM also participates in the bond formation. For the early TM impurity Sc, most of their 3d electrons hybridize indeed with the sp electrons of Zn. For the rest of impurities, the EDOS still show some peaks of nearly pure 3d character, corresponding to a number of 3d electronic states which remain localized in the TM atom. Those localized electrons are fully spin-polarized for most TM impurities and lead to a magnetic moment localized in the impurity (Ni is the only exception). Moreover, there is a measurable crystal-field splitting of those localized impurity levels (Ni is again an exception) for several reasons: first, the configuration of the impurity atom is no longer d5 nor d10, at least in principle; second, there are significant distortions of the cage upon relaxation; third, the exohedral impurities have a local coordination environment of lower symmetry. The jellium-like shell structure pattern in the host is quite lost in the valence region as a consequence of such nonnegligible hybridization between the directional d electrons of the TM atom and the sp electrons of Zn, which also lowers the D5h symmetry of the original cage and thus produces a bigger fragmentation of the jellium orbitals. Nevertheless, the more internal 1P and 1D electronic shells can always be distinguished due to the large gaps separating them from other electronic levels. 27842


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The Journal of Physical Chemistry C Magnetic Properties. Endohedral versus Exohedral Arrangements. In this section we discuss the magnetic properties resulting from the electron spin polarization in connection with symmetry aspects and hybridization effects. Here we also focus on those metastable isomers resulting from the local optimization of the endohedral D5h environment, which are relevant from the magnetic point of view and also for the discussion of the relative stability of endohedral and exohedral arrangements. In Figure 5 we plot, as a function of the TM dopant, the total spin magnetic moment, the contribution of the TM impurity to

Figure 6. Isomers obtained after relaxing the D5h endohedral TM@ Zn17 configuration. We also report the total energy difference (in meV) with respect to the GM structures shown in Figure 1. The rest of the caption is the same as in Figure 1.

Figure 5. Total spin magnetic moments for the ground state (black circles) and the D5h endohedral TM@Zn17 isomers (red squares) are plotted in the upper panel. The central panel shows the contribution of the TM impurity to the total moment, extracted from the Bader analysis. In the lower panel we plot the number of 3d electrons localized in the TM atom obtained through the projection of the EDOS. Lines are included as a guide for the eye.

that magnetic moment according to the Bader partitioning method, and the number of 3d electrons that are localized in each TM impurity according to the projected EDOS. This last value, although not fully consistent with the Bader analysis, is at least consistent with the trend of the magnetic moment which tends to increase with half-band filling, thus confirming the localized nature of most of the moment of the cluster and the nearly magnetic saturation of the mid-TM impurities. The Cr impurity exhibits a highly localized 3d electron contribution of 4.05 μB to the magnetic moment. This is the dominant contribution to the 4.80 μB local moment on this atom extracted from the Bader analysis. In particular, the Bader prediction is much closer to the 5 μB limit value that would only be expected for a d5 state that does not overlap at all with the cage. The 6 μB total moment of the endohedral ground state is attained via the polarization of Zn surface atoms, which as mentioned above is essentially due to the single unpaired electron occupying the superatom orbitals but also to the weak contribution of Zn atoms to the d5 impurity state. We obviously considered the D5h endohedral doping as a possible input structure for all TM impurities. The corresponding relaxed isomers are depicted in Figure 6. We note that except for Cr, Cu, Zn, and Fe, a noticeable hybridization between part of the impurity d states and the Zn host takes place after relaxation of the D5h initial structure, which is reflected in the corresponding EDOS, plotted in Figures 7 and

Figure 7. Same as Figure 2 for TM = Sc, Ti, V, Cr, and Mn but for the endohedral isomers appearing in the left column of Figure 6. The dashed blue vertical lines position the energy of the d levels of the isolated TM atom within the EDOS of the TM@Zn17 cluster.

8. As a result of the unbalanced population of the d shell of the impurity, the impurities cannot be viewed as approximately spherically symmetric. The D5h symmetry is lowered upon relaxation, the cage contracts appreciably, and in many cases the impurity adopts an off-center position at the local minimum, trying to form stronger and shorter bonds with some of the Zn atoms. Fe@Zn17 is an exceptional case in this respect, as it 27843


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polarized electrons, compatible with a d5 configuration centered on the impurity, but fragmented by the C2v symmetry of the distorted cage. The partial EDOS analysis now attributes around a 50% weight to the cage, implying that the d orbitals centered on V are not so localized in space. This observation is consistent with the magnetic moment of 5 μB and at the same time compatible with the local moment of 3.3 μB on the V impurity deduced from the Bader analysis (Figure 5). Again, no additional electron populates the cage orbitals, but the HOMO−LUMO gap is now lower (about 0.6 eV) than for the Ni impurity. This type of analysis explains why, as shown in Figure 5, the endohedral doping maximizes the magnetic moment of the cluster, maintaining in most cases the magnetic moment of the TM atom in vacuo. In Mn@Zn17, for example, the electron configuration of the Mn impurity is close to d6. We can still clearly appreciate a very stable d5 configuration of majority spin electrons, while the minority spin d orbital is the HOMO of the cluster. Being much less stable than its majority spin counterpart, the minority spin d orbital is more extended in space, and so the HOMO peak shows a substantial contribution from the cage orbitals. Additionally, the HOMO−1 orbital is the Pz orbital of the cage, which is populated by the additional s electron of manganase. Altogether the results explain the magnetic moment of 5 μB seen in Figure 5. Similarly, in Fe@Zn17 the impurity is clearly in a d7 configuration with negligible participation of the cage orbitals, and the HOMO is of Pz character as in the Cr and Cu cases. This is consistent with the local magnetic moment of Fe, which is about 3 μB (Table 1). It is worth noticing that for both Mn@ Zn17 and Fe@Zn17 clusters two spin isomers enter in a narrow energy range (6 meV for Mn@Zn17 and 44 meV for Fe@Zn17). In Mn@Zn17, the most stable one has a magnetization of 5 μB (Figure 6) while the other has a magnetic moment of 3 μB (not shown here). In Fe@Zn17, the most stable one has a magnetization of 2 μB (Figure 6) while the other has a magnetic moment of 4 μB (not shown here). The difference lies in the magnetic coupling between the TM atom and the Zn surface atoms. For both clusters, a localized moment in the Mn (Fe) impurity of about 4 (3) μB induces spin polarization in the Zn atoms, either with antiparallel coupling (low-spin isomer) or with parallel coupling (high-spin isomer). Note that in Mn@ Zn17 both isomers are nearly degenerate while in Fe@Zn17 the low-spin isomer is stabilized. In other words, the spin state is dictated by the single unpaired electron that occupies the delocalized HOMO and its coupling with the localized moment in the impurity. In the case of Mn@Zn17, due to the practical degeneracy of both spin states, we also tested a noncollinear configuration, but no energy gain resulted via the additional degrees of freedom provided by the different local spin quantization axes. The rest of impurities (Sc, Ti, and Co) show a higher degree of hybridization, and the results are more difficult to rationalize in terms of simple indicators. In all cases, Figures 7 and 8 exhibit signatures of the distortion induced by the endohedral TM dopant. In fact, the band of (1F, 2S) states of the Zn17 cage centered around 1.5 eV is broadened. In the peculiar case of Sc, the broadening is especially marked which can be associated with the strong distortion incurred by the insertion of a large ionic radius doping element.15 The other interesting case is the strong hybridization limit exemplified by the Co doping atom, which is also associated with some broadening of this series of peaks of the jellium cage. Hybridization is also measured by the

Figure 8. Same as Figure 3 for TM = Fe, Co, Ni, Cu, and Zn but for the endohedral isomers appearing in the right column of Figure 6. For Zn@Zn17 we additionally include the jellium labels of the superatom orbitals, fragmented by the D5h point group symmetry. The rest of the caption as in Figure 7.

remains in the high-symmetry D5h configuration (this result has been checked by starting the optimization from off-center initial positions for the Fe impurity, and in all cases the centered D5h cage was recovered after relaxation), and in that case we see that hybridization is as weak as for Cr, Cu, and Zn. In other words, hybridization is always weak in the perfect D5h structures; for most TM impurities, it is the nonspherical shape of the d electron configuration of the impurity that prevents this high-symmetry structure from being a local minimum, and the distortion finally enforces a higher degree of hybridization. There are additional interesting issues to discuss about the metastable endohedral impurities. In Ni@Zn17, for example, the three nearly degenerate states closest to the Fermi level altogether integrate to 10 electrons and have no spin polarization. Similar to the case of Cu, the EDOS features a d10 configuration centered on the impurity but with an approximately 20% contribution of the zinc atoms to its tail region. This result is not significantly modified in the correct global minimum (Figure 3) as the impurity remains endohedral although with a more distorted cage that helps to stabilize the d band. This observation further supports the conclusion that a fully occupied d shell becomes stabilized for an atom at the center of the cage and is consistent with the complete quenching of the magnetic moment shown in Figure 5 as well as compatible with the Bader charge on Ni shown in Table 1. However, because d10 is not the natural configuration of a Ni atom, this effect competes with the energy cost of the 3d94s1 → 3d10 promotion, and as a result the d levels are much less stable than for Cu, forming indeed the HOMO of the doped cluster. Related to the d10 configuration, Ni@Zn17 is interesting also because it is a magic superatom in its neutral state, featuring a closed electronic shell with a large HOMO−LUMO gap of about 1 eV. Its magic nature demonstrates that no additional electron is introduced into the cage orbitals, so the 2P superatom orbitals are all empty. Its lowest energy excitations would be from levels localized on the impurity toward delocalized superatom levels of P character. V@Zn17 is similar as the peaks closest to the Fermi level contain five fully 27844


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which have been unveiled in the two previous sections. This will allow us to get insight into the relevant contributions for the stability of these systems, providing us with arguments to think of other optimal molecular magnets of this kind. In order to compare the stabilities of the different TM-doped clusters, we have calculated the energy involved in the doping process [E(TM) + E(Zn17) − E(TMZn17) ] and also the vertical ionization energy (VIE) [as the total energy difference between the neutral cluster and the TMZn17+ cation at the neutral geometry]. The doping energies are all positive, implying that doping is always an exothermic process, and range between 1.9 and 3.5 eV for all impurities except X = Zn, which has a very low formation energy of only 0.36 eV. Local maxima both in the doping energy and VIE values are obtained for V and Ni impurities, which is consistent with the electronic shell closing identified in the EDOS of these two systems. In fact, the VIE of NiZn17 is 5.99 eV, which is essentially the same as the VIE of pure Zn17.7 The VIE of VZn17 is lower, namely 5.52 eV, consistent also with the smaller HOMO−LUMO gap as compared to the Ni impurity. Local drops in the doping energy and VIE are observed for CrZn17 and CuZn17 due to the population of the 2Pz jellium orbital and the associated superalkali nature of those two clusters. The biggest drop in formation energy occurs between Cu and Zn because in Zn18 the quite unstable 2P jellium orbital is populated by two electrons. These results suggest that the trends in the absolute stabilities of TMZn17 clusters as a function of the TM atom are dominated by the contribution of the delocalized superatom orbitals. Apparently the Zn17 cage is hardly able to admit two additional electrons into its electron shell structure, so we expect that endohedral doping of this cage with a trivalent gallium atom would be a highly endothermic process. Analyzing, for each separate system, the relative stability of endohedral and exohedral configurations is not so simple, as the total energy difference between those two homotops results from the competition of several energy contributions that are inextricably linked. Nevertheless, we have made an attempt to rationalize in simple terms why the high-symmetry D5h endohedral structure is stabilized for some impurities and destabilized for others. First of all, we recall that the pure Zn17 cage is magic and so is very stable from the electronic point of view. There are several factors that can explain why the D5h endohedral arrangement is more stable than the exohedral one for Cu and Cr. In those two cases, doping involves combining a very stable superatom cage with a very stable d shell impurity configuration. The nearly spherical and hollow cage has enough room to host the spherical shape of the d electron cloud of the impurity. Being both very stable and of congruent shape, they tend to interact as little as possible: the EDOS of the cage is not significantly perturbed by the impurity, and vice versa. The cage retains also its high-symmetry shape so one expects a lower elastic energy penalization as compared to other impurities. The only destabilizing factor is the single unpaired s electron from the impurity that populates the 2Pz superatom orbital, as the energy of this level is considerably above the HOMO of the Zn17 superatom (it is precisely this factor the one that explains the local minimum of the doping energy and VIE obtained for these two impurities). However, this factor may be not so relevant in the comparison between endohedral and exohedral arrangements as both homotops contain the additional unpaired electron and differ just in the atomic site that the impurity occupies. Therefore, we expect the d electrons of the

number of localized 3d electrons on the impurity, and Co appears as a minimum in this respect (see Figure 5). In our previous work,7 we already demonstrated the stability and high magnetic moment of Cr@Zn17. Highly magnetic and stable TM@Zn17 nanoparticles are potentially interesting in applications because of the protection of the TM magnetic moment against environmental conditions that the Zn cage provides, as explicitly assessed7 for Cr@Zn17. The results of this work demonstrate that such endohedral ideal structures are only retained when doping with Cr and Cu. Cu@Zn17 is the most stable one of both although Cr@Zn17 is the most interesting one for possible magnetic applications. Concerning the rest of systems, even if the endohedral undistorted configuration is not the stable one, at least most of the TM impurities retain a large part of the spin magnetic moment that they have in a vacuum. Moreover, the local Bader magnetic moment on the TM impurity is rather insensitive to its Zn atomic environment, as shown in the central panel of Figure 5. This is due to the fact that a large part of the 3d electrons are localized in the TM atom and do not participate in the bond formation through hybridization. Thus, the TM impurity provides the nanoparticle with a localized moment that induces, via electron sharing or hybridization, a spin polarization in its Zn environment. The difference between the total moments obtained for the ground states (Figure 1) and the D5h-based isomers (Figure 6) thus comes essentially from the induced magnetic moments and their couplings with the localized moment that can be either parallel or antiparallel. In the endohedral configuration the magnetic moment tends to be maximized because the impurity states introduced into the cage remain of d character and centered on the impurity; i.e., they remain atomic-like even if the tails of those orbitals are contributed by Zn atoms from the cage. Because the approximate spherical symmetry is not destroyed, Hund’s rule of maximum multiplicity applies and fixes the direction of the induced magnetic moment. Some of these clusters (those with Cr, Mn, and Fe impurities) have an additional unpaired electron in a delocalized superatom orbital, which only in the case of Fe opposes the localized moment. Fe@Zn17 is thus the only endohedral system that does not maximize the total magnetic moment. A comparison of the EDOS of the two spin isomers demonstrates that the minority spin levels of the Fe impurity are destabilized in the 4 μB spin isomer, explaining why the spin of the delocalized electron tends to align with the minority spins of the impurity. In the exohedral configurations, the approximate local spherical symmetry around the impurity is lost, and no simple rule exists that rationalizes the sense of the induced moment. In any case, the observation that a significant local magnetic moment survives in the doped cluster is quite interesting since it shows that the Zn environment does not quench to a large extent the magnetic moment of the TM impurity through electron hybridization, but rather serves to modulate the total moment of the resulting molecular magnet. This is similar to recent experimental and theoretical findings on Cr-doped gold nanoparticles Cr@AuN with N = 2−7 for which high magnetic moments were reached in a so-called local magnetic regime yielding the largest magnetic moments.14 General Trends for the Absolute and Relative Stabilities. Once the electronic structure has been analyzed in detail, it is pertinent to rationalize the general trends about the absolute and relative stabilities of these systems (as a funcion of the 3d impurity or of the endohedral/exohedral environment) in terms of different contributions, some of 27845


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adopt an endohedral arrangement, but with a strong deformation of the cage and much more compact structures. Doping with the rest of 3d TM atoms results in an exohedral arrangement. Through the analysis of the orbital and siteprojected electronic densities of states as well as the local electronic charge distribution within the cluster, we demonstrate that the D5h endohedral configuration is concomitant with a very weak hybridization between the d levels of the TM impurity and the levels of the host. Both the d5 and d10 configurations of Cr and Cu, respectively, are spherically symmetric, thus having a shape which is most congruent with that of the cage, and have a radial extension that fits well within the size of the cage. As a result, the d shell in those cases is weakly perturbed and preserves much of its stability when placed in the center of the zinc cage. The additional s electron of the impurities has a considerably larger radial extension and is essentially donated to the cage orbitals. CrZn17 and CuZn17 can thus be qualified as superalkali clusters. The 3d orbitals of the rest of impurities, with atomic configurations different from half or total filling of the d shell, result more destabilized when placed inside the cage which explains their preference for less symmetric (often exohedral) arrangements which involve more hybridization with the Zn electrons. We conclude that the energetics of the impurity d orbitals is the dominant factor that suffices to rationalize the observed structural trends. These clusters have in general a large magnetic moment (up to 6 μB in the case of CrZn17) mostly localized in the 3d impurity, which tends to increase with half-band filling of the dopant, approaching magnetic saturation. Although the D5h endohedral configuration is the optimal environment in regard to maximizing the magnetic moment (due to the weak hybridization), a noticeable moment is also present for the other structures. Thus, we conclude that the TM impurity provides the nanoparticle with a localized moment that induces, via electron sharing or hybridization, a spin polarization in its Zn environment which couples with the localized moment either parallel or antiparallel. Therefore, the Zn environment does not quench to a large extent the magnetic moment of the TM impurity through electron hybridization, but rather serves to modulate the total moment of the resulting molecular magnet depending on the induced moment and magnetic couplings. Highly magnetic and stable TM@Zn17 nanoparticles are potentially interesting in applications because of the protection of the TM magnetic moment against environmental conditions that the Zn cage can provide.7 The results of this work demonstrate that such endohedral ideal structures are only retained when doping with Cr and Cu but can be metastable configurations for most of them. We hope that the present work will stimulate future experiments aiming at producing the predicted molecular magnets.

impurity to dominate the endohedral versus exohedral energetics. Our idea is thus to compare the energy of the d levels of the embedded impurity with those of the corresponding TM atoms in vacuo. The VIE of the clusters allows us to refer the HOMO to the vacuum level. Similarly, we have calculated the ionization energies of the TM isolated atoms at the PBE level. This allows to refer the “HOMO” of the atom to the same vacuum level, so that we can in the end plot the energy of the d levels of the isolated atoms in Figures 7 and 8 (dashed blue lines). We can see that the endohedral embedding always tends to destabilize the d states of the impurity as compared to the free atom but that the effect is close to negligible for Cr and very small for Cu. It is precisely for those two clusters, which feature a d level buried deep below the HOMO of the Zn17 cage, that the destabilization effect on the energy of the d states is the smallest one. For all other impurities the destabilization effect is much bigger, with the only exception of Mn for which the effect is nevertheless larger than for Cu. This analysis clearly demonstrates that endohedral doping is most stable for Cr and Cu and significantly less stable for the rest of impurities. Although the impurity levels are not so easily defined in the exohedral configurations, for some impurities such as Mn and Fe they can still be recognized (Figure 3), and the average energy of those levels is clearly lower than in the endohedral configuration. In summary, even if the relative stabilities result from a competition between several energy terms, our analysis suggests that the energetics of the impurity d orbitals suffices to rationalize the observed structural trends. As a final side note, we comment that the destabilization of the TM eigenvalues upon embedding is not in conflict with the exothermicity of the doping process mentioned above. In fact, it is well-known that KS eigenvalues are not additive quantities that can reproduce the total energy of a quantum system because such a sum would contain a double counting of the two-body electron−electron interaction terms. The eigenvalues of the embedded impurities contain more electron−electron double counting than the eigenvalues of the corresponding isolated TM atoms, so a comparison of the eigenvalues cannot be directly related with the cluster stability. If the double counting is corrected in order to obtain additive energies, the embedded impurities would be found to be more stable than the isolated TM atoms, but the systematic trends obtained above about the comparison of the different TM impurities would remain essentially the same. Thus, KS eigenvalues are enough for the purpose of analyzing stability trends across the TM 3d series.

4. CONCLUSIONS Fully self-consistent DFT calculations, using the plane-wave code VASP within the projector-augmented wave approach and the Perdew−Burke−Ernzerhof form of the generalized gradient approximation, were conducted to explore the doping with 3d transition-metal impurities of the dihedral hollow-cage Zn17 superatom. The doping process is always exothermic. Enhanced stabilities are obtained for VZn17 and NiZn17, consistent with the electronic shell closing identified in the electronic density of states of these two systems which can be qualified as closedshell superatoms. However, among the 3d elements, only doping with Cr and Cu results in a D5h endohedral configuration with the TM impurity placed inside the nearly undeformed hollow cage of the pristine Zn17. Co and Ni also

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (A.A.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the support of the Spanish Ministry of Science and Innovation and the European Regional Development Fund (Grant FIS2014-59279-P). A.V. ackowledges the financial support and kind hospitality from the University of Brest 27846


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The Journal of Physical Chemistry C (UBO), France. Facilities provided by the Pole de Calcul Intensif pour la Mer, CAPARMOR (Brest) are also acknowledged.

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REFERENCES

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Zn17 Superatom Cage Doped with 3d Transition-Metal (TM) Impurities

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