Endohedral (X@ZniSi)i=4-160,± Nanoclusters, X = Li, Na, K, Cl, Br

or halogens such as Cl and Br, 4 e i e 16, and q ) -1, 0, 1. In these structures, the atoms are trapped inside previously characterized spheroid hollo...
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3560

J. Phys. Chem. C 2007, 111, 3560-3565

0,( Endohedral (X@ZniSi)i)4-16 Nanoclusters, X ) Li, Na, K, Cl, Br

Jon M. Matxain* and Leif A. Eriksson Department of Natural Sciences and O ¨ rebro Life Science Center, O ¨ rebro UniVersity, 70182 O ¨ rebro, Sweden

Elena Formoso, Mario Piris, and Jesus M. Ugalde Kimika Fakultatea, Euskal Herriko Unibertsitatea and Donostia International, Physics Center (DIPC), P.K. 1072, 20018 Donostia, Euskadi Spain ReceiVed: October 19, 2006; In Final Form: January 3, 2007

Endohedral (X@ZniSi)q structures have been characterized, with X being alkali metals such as Li, Na, and K or halogens such as Cl and Br, 4 e i e 16, and q ) -1, 0, 1. In these structures, the atoms are trapped inside previously characterized spheroid hollow structures with positively charged Zn atoms and negatively charged S atoms. Moreover, although the radii of all atoms are similar, Zn atoms are located more inside the structure. The alkali metals are found to be trapped inside a larger number of spheroid structures than the halogens. The parameters determining the stability of the endohedral structures are the charge and size of the trapped atom, along with the sphericity of the cluster.

I. Introduction Semiconductors are materials of great importance in the development of nanotechnology. Among these materials, we find the II-VI compounds, whose interest has increased notably because of their paramount technological potential. Applications such as photovoltaic solar cells,1-4 optical sensitizers,5 photocatalysts,6,7 or quantum devices8 have led to extensive investigation of their properties. Band gap control appears crucial at this point since the size of the band gap largely determines the properties and hence applications of the material. A good way of controlling the band gap is by doping the material, that is, inserting a small amount of an element or elements that are different from the major components. For instance, Si may be doped with P or Al to obtain p- or n-type semiconductors, respectively, increasing or decreasing in that way the band gap of Si.9 Nanoparticles or nanoclusters differ in properties and structure from bulk material.10 Similar to their bulk counterparts, nanoclusters may also be doped to obtain materials with different properties.11 Among all nanoclusters, interest in hollow spherical structures has increased since the discovery of buckminsterfullerene, C60,12 and other fullerenes. These structures are able to build up molecular solids, in which each molecule keeps its structure similar to that of the isolated molecule.13 The electronic properties of these molecules and solids may be altered by the introduction of dopants, thereby yielding new materials with tailored properties. Fullerenes may be doped in three different ways: (i) substituting one or several carbon atoms with other similar atoms, like B, N, and Si, yielding the so-called heterofullerenes. The first heterofullerenes were produced by Smalley et al. in 1991.14 (ii) The second way is exohedrally, where atoms are placed outside the fullerene cages. The conductivity of such doped solids can be altered from the nondoped insulator to superconductors15,16 or semiconductors.17 (iii) The third way is endohedrally, where atoms or molecules are trapped inside the fullerenes, regardless of the position of the * Corresponding author. E-mail: [email protected].

atom inside the fullerene. The earliest, La@C60, was discovered by Heath et al. in 1985,18 and after that, many others have been found.18-21 Carbon fullerenes were the first hollow structures discovered, but since then, interest in hollow structures of other materials has increased considerably. BN clusters are the ones most widely studied because of the fact that a BN unit is isoelectronic to C2. A large amount of BN fullerenes have been investigated, such as BiNi, i ) 10-15, 24, 28.22-26 Hollow nanoclusters of elemental metals have also been synthesized. For instance, experimental evidence of “free-standing” hollow clusters consisting of gold atoms, Au3227 and Aun)16-18 ,28 has recently been given. As these gold cages have an average diameter > 5.5 Å, it has been hypothesized that they could easily accommodate a guest atom inside. Similarly, Sn-2 12 has also been characterized29 as a hollow cluster with icosahedral Ih symmetry and a large enough diameter (>6 Å) as to incarcerate atoms inside. Binary hollow nanoclusters of semiconductor elements, such as II-VI elements, have also been investigated.30-37 However, studies of the properties of endohedral compounds made of these hollow nanoclusters are scarce. Of particular relevance to the present research is the recent study38 of the Mn@Zn12O12 endohedral compound. The aim of this work is to study the endohedral (X@ZniSi)q compounds: X ) Li, Na, K, Cl, and Br; i ) 4-16; and q ) -1, 0, 1. The structures of these hollow ZniSi nanoclusters were characterized in previous work30,31 and were experimentally synthesized very recently.36,37 The structural pattern found in these nanospheroids resembles that of carbon fullerenes. Carbon fullerenes are built of pentagons, hexagons, and, in a few cases, also heptagons. For ZniSi spheroids and more generally for heteroatomic XiYi cluster structures, the number of rings can be predicted by the simple rules obtained from Euler’s law:

N6-ring ) i - 4 - 2N8-ring

(1)

N4-ring ) 6 + N8-ring

(2)

10.1021/jp0668697 CCC: $37.00 © 2007 American Chemical Society Published on Web 02/13/2007

0,( Endohedral (X@ZniSi)i)4-16 Nanoclusters

J. Phys. Chem. C, Vol. 111, No. 9, 2007 3561

Figure 1. Scheme of the ZniSi spheroid structures.

which states that, in a closed structure formed by polyhedra, the number of vertexes plus the number of faces will always equal the number of edges plus two. In the spheroids considered in this work, ZniSi, i ) 4-16, there are no octagons. In addition, it was observed that the Zn atoms are closer to the center of the cluster than the S atoms and that the atomic charges are close to those of the bulk, either wurtzite or zincblende. Therefore, the size of the cavities available inside the hollow nanoclusters for trapping other atoms is determined by the Zn atoms, as depicted in Figure 1. We have considered either trapped alkali (Li, Na, K) atoms or trapped halogen (F, Cl, Br) atoms. Alkalies have small ionization energies, and therefore once trapped inside the ZniSi nanocluster, they could donate their valence electron to the nanocluster. Conversely, halogen atoms could withdraw an electron from the nanocluster because of their large electron affinities. These two effects will affect distinctively the electronic properties of the resulting endohedral compound. Three parameters seem, a priori, to determine whether alkali or halogen atoms will be trapped inside these clusters and whether the resulting structures will be thermodynamically stable or not: (i) the appropriate matching between the size of the nanocluster, rcavity, and the size of the trapped atom. If rcavity is big, then the nanocluster will be able to trap larger atoms. If the size of the atom is too big, then it would not fit inside the cage. However, if the trapped atom is too small, then it would have high mobility and would not remain in the center of the cage. (ii) The second parameter is the shape of the nanocluster. Most spherical ones maintain the trapped atoms in the center easier than irregular ones. (iii) The third parameter is the charge of the trapped atom. If the charge of the trapped atom is positive, then it will repel the positively charged Zn atoms that lie closer to the cavity center than the S atoms. If the charge is negative, then it will be attracted by Zn atoms. In the first case, it will be easier to keep atoms in the center of the nanocluster, but the stability would be larger in the second case. II. Methods All geometries have been fully optimized using the gradient corrected hybrid B3LYP39-41 functional within the Kohn-Sham implementation42 of the density functional theory.43 Harmonic vibrational frequencies are determined by analytical differentiation of gradients in order to determine whether the structures found are true minima or not and to extract zero-point energies and Gibbs free energy contributions. The relativistic compact effective core potentials and sharedexponent basis set44 of Stevens et al. has been used for Zn and S, as in the study of the isolated clusters,31 and the all-electron 6-311+G(d) basis set was used for the trapped atom. The 3d electrons of Zn were included in the valence. In order to perform the geometry optimizations and harmonic frequency calculations,

Figure 2. Electron density distribution, D(r), as a function of the radial distance, r, from the guest atom’s nucleus position (cavity center). Solid line: endohedral cluster. Dashed line: free-standing guest atom. Top plot: Li@Zn4S4. Bottom plot: Br@Zn12S12.

an extra d function was added on Zn and S because of their importance for the proper description of the high coordination of the atoms in the three-dimensional cluster structures. Note that pure angular momentum functions were used throughout this study. The radial electron density distributions of the endohedral nanoclusters have been calculated with the origin of the coordinate system placed on the endohedral atom’s nucleus (cavity center), when possible. Recall that it is not necessary that the trapped atom is located in the middle of the endohedral compound to define it as endohedral. However, for the methodology defined below to calculate the charge of the guest atom, it is essential that it is placed exactly in the center of the cage. Using the Kohn-Sham orbitals {ψσi }, we have constructed the electron density function, F(r), as

F(r) )

σ ∑σ ∑i ψσ,/ i (r) ψi (r)

(3)

The index σ runs over the spins R and β. Following the algorithm of Sarasola et al.,45 the radial electron density distribution is obtained by integrating F(r) over the solid angle Ωr of the vector r as

∫

D(r) ) r2 F(r) dΩr

(4)

The function D(r) represents the probability of finding an electron at a distance between r and r + dr from the origin and is well-known to exhibit the expected number of spherical shells for the atoms of the first three periods.46-48 Inspection of Figure 2 reveals that D(r) also reflects the atomic shell structure for atoms incarcerated in the nanocluster cages. In such a way, the guest atom is seen to retain its identity upon incarceration. The question remains as to determine its charge. We have chosen to evaluate the charge of the guest atom in the endohedral cluster of Bader.49 Namely, we locate the critical distance, rc, of the electron density F(r) along its radial coordinate

∇F(r)|rc ) 0

(5)

and then assign the charge of the guest atom to the difference between the cumulative electron density versus the number of electrons, NX, of the free atom:

3562 J. Phys. Chem. C, Vol. 111, No. 9, 2007

q X ) NX -

∫0r D(r) dr c

Matxain et al.

(6)

All of the geometry optimizations and frequency calculations were carried out with the GAUSSIAN03 package.50 In the geometry optimization process, the geometry is adjusted until a stationary point on the potential surface is found, by the use of gradients, according to the Berny algorithm.51,52 It has to be pointed out that this methodology is not valid to study the dynamical processes of the molecules but just to locate stationary points in the potential energy surface. III. Results The effect of the charge state on the geometry of the nanoclusters will be analyzed in subsection III.A. We anticipate that the most salient geometrical feature of the charged nanoclusters is the cavity size compared to their neutral counterparts. In this subsection the ionization energies and the electron affinities of the bare nanoclusters are also discussed. In subsection III.B the endohedral compounds of these nanoclusters are studied. We have focused on alkali metal guests Li, Na, and K and halogens F, Cl, and Br. A. Isolated Clusters and Atoms. Initially, the structures of the cationic and anionic bare nanoclusters were characterized. Starting from the neutral nanoclusters, an electron was removed (for the cations) or added (for the anions) followed by geometry optimizations and frequency calculations to obtain and characterize minima structures of the nanocluster ions. Using the optimized structures, the adiabatic ionization energies (IE) and electron affinities (EA) were calculated. The structures of the cationic and anionic nanoclusters follow the same squarehexagon rule as do their neutral counterparts. In Table 1, the average radii of the sphere defined by the Zn atoms, rZn, along with their standard deviation and of the cavity of the cluster, rcavity, are given along with ionization energies and electron affinities for the neutral clusters. The radius of the cavity inside the spheroidal nanoclusters is defined by the Zn ionic ionic atoms and is given by rcavity ) rZn - rZn 2+, with rZn2+ ) 0.74 Å. Comparing rcavity for the neutral and ionic nanoclusters, we can conclude that this in general increases slightly from neutral to ionic structures. The maximum increase is 0.07 Å. However, the sphericity of the nanoclusters is not the same. A way of measuring the sphericity of these clusters is the standard deviation (σ) of the distances between the Zn atoms and the center of the nanoclusters. The smaller the σ, the more spherical the nanocluster is. It may be seen that nanoclusters ZniSi with i ) 4, 6, 12, 16 have σ ) 0 and are fully spherical. The i ) 9 nanocluster has only a small sphericity deviation: σ ) 0.15. Consequently, TABLE 1: Average Radius of the Sphere Defined by the Zn Atoms, rZn, the Standard Deviation (σ) in Brackets, the Cavity Inside the Clusters, rcavity, in Å, and the Ionization Potentials (IE) and Electron Affinities (EA) in eV q)0

q)1

q ) -1

i

rZn

rcavity

IE

EA

rcavity

rcavity

4 6 8 9 10 11 12 13 14 15 16

1.72 (0.00) 2.22 (0.00) 2.66 (0.34) 2.81 (0.15) 3.00 (0.33) 3.16 (0.39) 3.28 (0.00) 3.48 (0.55) 3.60 (0.46) 3.72 (0.33) 3.88 (0.02)

0.98 1.48 1.92 2.07 2.26 2.42 2.54 2.79 2.86 2.98 3.14

8.63 7.97 8.47 8.18 8.00 7.87 8.28 7.94 7.87 8.05 8.05

2.00 1.97 1.95 1.96 2.07 2.03 1.97 2.10 2.10 2.07 2.10

1.04 1.51 1.98 2.08 2.26 2.42 2.56 2.73 2.85 2.99 3.11

1.03 1.55 1.98 2.13 2.31 2.47 2.59 2.79 2.91 3.03 3.15

these nanoclusters are highly spherical. The remaining structures are substantially less spherical. The ionization energies of these clusters oscillate around 8 eV, with the exceptions of i ) 4 and 8 which lie around 8.5 eV. The electron affinities of the spheroids oscillate around 2 eV. These large IEs and small EAs are indicative of the high stability of these nanoclusters.36,37 B. Endohedral Clusters. We have considered all possible (X@ZniSi)q endohedral compounds, i ) 4-16, q ) 0, 1, -1, and X ) Li, Na, K, F, Cl, Br. For alkali metals, neutral and cationic endohedral compounds have been characterized, and for halogens, neutral and anionic compounds have been characterized. Electron density distributions are used to calculate the charge of the caged atom, as indicated in section II. The thermodynamic stability of the minima will be assessed by the free energy, ∆G, of the incarceration reaction:

ZniSi + Xq f (X@ZniSi)q q ) 0, (1

(7)

A negative value of ∆G indicates that the endohedral nanocluster is more stable than the separated fragments. For the sake of clarity, the alkali metal and halogen endohedral nanoclusters will be discussed separately. 1. Alkali Endohedral Nanoclusters. In Table 2, the geometric, electronic, and energetic properties of the characterized alkali endohedral nanocluster structures depicted in Figure 3 are listed. Lithium is found to build neutral and cationic endohedral nanoclusters only for i ) 4. The obtained minimum energy structure for the neutral species is depicted in Figure 3. For larger nanoclusters, the lithium atoms move toward the surface of the nanoclusters and bind to a specific Zinc atom. This leads to the breaking of the nanocluster Zn-S bonds and ultimately to the fragmentation of the nanocluster. In both Li@Zn4S4 and (Li@Zn4S4)+, the cavity is significantly enlarged as compared to the isolated cluster, that is, from 0.98 to 1.39 Å and 1.34 Å, respectively. The ionic radius of Li+ is 0.73 Å, and since the cavity radius of the isolated Zn4S4 nanocluster is 0.98 Å, the lithium cation should be able to be trapped inside without distorting the nanocluster. However, our calculations predict that the cavity radius enlarges by 0.4 Å. The lithium atom becomes positively charged, qLi ) 0.99, after incarceration in Zn4S4, as seen in Table 2. This suggests that the endohedral atom transfers an electron to the cage yielding a charge separated radical species Li+@(Zn4S4-)•. This is confirmed by inspection of the singly occupied molecular orbital of Li@Zn4S4, shown in Figure 4, which is delocalized on the four zinc atoms of the Zn4S4 nanocluster. Further electron ionization yields a structure with the Li+ trapped inside Zn4S4. Observe that the charge of Li in (Li@Zn4S4)+ is qLi ) 0.98. This might account for the remarkable enlargement of the Zn4S4 cluster’s cavity upon Li incarceration. Indeed, the highly positively charged guest lithium repels with the inner positively charged Zn atoms of the nanocluster. The end result is the observed increment of the radius of the cavity. The ∆G’s of the incarceration process for both the neutral and the cationic (Li@Zn4S4)0,+1 endohedral nanoclusters are positive. Hence, these compounds are predicted to be thermodynamically unstable with respect to their corresponding separated compounds. Nonetheless, the height of the barrier for the evaporation of lithium atoms might render Li endohedral complexes with long enough lifetimes as to be amenable to experimental detection. Finally, we point out that the ionization energy of the Li@Zn4S4 endohedral nanocluster is 6.83 eV, midway between that of the isolated cluster (8.63 eV) and that of Li (5.62 eV).

0,( Endohedral (X@ZniSi)i)4-16 Nanoclusters

J. Phys. Chem. C, Vol. 111, No. 9, 2007 3563

TABLE 2: Cavity within the Cluster, rcavity, the Free Energy of Complexation, ∆G, in kcal/mol, the Charge of the Endohedral Atom, qX, and the Ionization Energies, in eV rcavity

∆G

qX

IE

rcavity

∆G

Li@Zn4S4

1.39

20.37

0.99

6.83

(Li@Zn4S4)+

1.34

48.32

0.98

Na@Zn9S9 Na@Zn12S12 Na@Zn13S13 Na@Zn15S15 Na@Zn16S16

2.28 2.54 2.89 2.99 3.11

4.94 4.13 -2.27 -2.33 -4.72

0.93 0.84

(Na@Zn9S9)+ (Na@Zn12S12)+ (Na@Zn13S13)+ (Na@Zn15S15)+ (Na@Zn16S16)+

2.25 2.64 2.87 3.08 3.21

6.00 4.85 -9.52 -10.60 -3.00

0.92 0.83

0.78

5.46 5.45 5.11 5.06 5.50

K@Zn9S9 K@Zn12S12 K@Zn15S15 K@Zn16S16

2.33 2.71 3.12 3.11

22.83 6.02 -2.13 0.91

0.85 0.87 0.86 0.74

5.61 5.13 4.93 4.81

(K@Zn9S9)+ (K@Zn12S12)+ (K@Zn15S15)+ (K@Zn16S16)+

2.29 2.67 3.09 3.18

48.61 20.74 8.07 8.19

Sodium is more versatile than lithium as a guest atom in ZniSi nanoclusters. Five stable structures have been found for both neutral and cationic endohedral compounds, namely, (Na@ZniSi)0,+1 with i ) 9, 12, 13, 15, 16, all of which are depicted in Figure 3. Nanoclusters with i < 9 have a too small cavity as to trap a

Figure 3. Structures of Li@Zn4S4, X@Zn9S9, X@Zn12S12, Na@Zn13S13, X@Zn15S15, and X@Zn16S16, X ) Na, K, Cl, Br.

Figure 4. SOMO of Li@Zn4S4. The atom in the middle is that of Li, the ones with a large orbital contribution are those of S, and those with a small contribution are those of Zn.

qX

0.91 0.77 0.89 0.88 0.88

sodium atom, and consequently, the nanoclusters break apart when Na is placed inside. The i ) 12, 13, 15, 16 nanoclusters remain almost intact upon incarceration of the sodium atom, but sodium incarceration enlarges the Zn9S9 nanocluster by incrementing its radius 0.2 Å. This effect is ascribed to the strong Coulomb repulsion due to the proximity of the partially charged Zn atoms of the small Zn9S9 nanocluster and the partially charged Na guest. Observe (see Table 2) that the guest sodium atom is positively charged in all of the endohedral nanoclusters characterized (qNa > 0.75). Unfortunately, we were not able to calculate the charge of the sodium atom when trapped in the (ZnS)13 clusters, both neutral and cationic cases, and in the neutral (ZnS)15 case because the guest atom is not located in the center of the cluster. The free energy of incarceration decreases as the size of the nanocluster increases, for both the neutral and the cationic species. For nanoclusters with i > 13, it is negative, indicating that thermodynamical equilibrium would be displaced toward the formation of the endohedral nanoclusters. It is worth noticing that the IE of the sodium endohedral nanoclusters lies between 5.0 and 5.5 eV, very close to the ionization energy of Na (5.42 eV) and remarkably smaller than the ionization energies of the bare nanoclusters (∼8 eV). Endohedral nanoclusters with a guest potassium atom are very similar to their corresponding sodium endohedral nanoclusters, which may be seen in Figure 3. Stable structures are found for both neutral and cationic endohedral structures for i ) 9, 12, 15, 16. The charge of the potassium atom is close to one atomic unit in all of the nanoclusters (qK > 0.75), as shown in Table 2. For the ionic K@Zn9S9 case, no charge is given for potassium, since it is not placed in the center. Observe also that incarceration of potassium enlarges the ZniSi nanocluster slightly more than sodium, and the incarceration free energies are now all positive except for the K@Zn15S15. Finally, according to our calculation, endohedral potassium doping of the ZniSi nanoclusters lowers the ionization energy from ∼8 eV to a value between 4.8 and 5.6 eV. 2. Halogen Endohedral Nanoclusters. Endohedral structures built by three different halogens have been studied in this work, namely, F, Cl, and Br. F was found to not be able to build any stable endohedral structure. For i ) 4, 6, the cluster is broken, and for the remaining structures, F is small and moves from the middle to one side of the cluster, forming bonds with other atoms. Cl and Br are able to build endohedral nanoclusters. For both elements, the anionic nanoclusters are more stable than the neutral ones. In the case of Cl, i ) 9, 12, 15, 16 are stable for the anionic cases, while only i ) 9, 12 are stable for the neutral species. The obtained structures are shown in Figure 3. The instability of the neutral species is even more critical for Br, where only the i ) 12 cluster was found to be stable. According to the cavity radii given in Table 3, the nanoclusters are contracted slightly upon halogen incarceration. This is expected in view

3564 J. Phys. Chem. C, Vol. 111, No. 9, 2007

Matxain et al.

TABLE 3: Cavity within the Cluster, rcavity, the Free Energy of Complexation, ∆G, in kcal/mol, the Charge of the Endohedral Atom, qX, and the Electron Affinity, in eV rcavity

∆G

qX

EA

Cl@Zn9S9 Cl@Zn12S12

2.04 2.47

-9.02 -34.84

-0.30 -0.45

4.73 5.27

Br@Zn12S12

2.49

-18.07

-0.28

5.28

of the Coulomb attraction between the guest halogen anion and the partially positively charged Zn atoms of the nanocluster. Both Cl and Br carry a negative charge upon incarceration. This electrostatic attraction makes the matching between the cavity and the guest ion critical. If they do not match precisely, the ion moves over the surface and interacts explicitly with one of the Zn atoms, which normally leads to fragmentation of the cluster structure. This accounts for the fact that it is only for the most spherical nanoclusters that endohedral halogen compounds are found. The incarceration free energies of all of the characterized halogen endohedral nanoclusters are negative. This is indicative of the very high thermodynamical stability of these structures. The calculated electron affinities of the halogen endohedral nanoclusters are substantially larger than those of the corresponding guest halogen atom (EA(Cl) ) 3.62 eV, EA(Br) ) 3.36 eV). Consequently, these endohedral nanoclusters may be seen as superhalogens.53,54 It has been observed for electron affinities that

EA(ZnS) < EA(X) < EA(X@ZnS) and it has been observed for ionization energies that

IE(X) e IE(X@ZnS) < IE(ZnS) As may be observed in Figure 5, the isolated ZnS nanoclusters have a closed shell electronic structure. When an alkali is trapped inside the cage, an electron is transferred to the lowest unoccupied molecular orbital (LUMO; above, right). This electron can more easily be removed than one from the highest occupied molecular orbital (HOMO) of the isolated cluster, decreasing the ionization potential. Similarly, when a halogen

rcavity

∆G

qX

(Cl@Zn9S9)(Cl@Zn12S12)(Cl@Zn15S15)(Cl@Zn16S16)-

2.06 2.46 2.89 3.02

-32.27 -70.52 -77.99 -77.64

-0.31 -0.52 -0.55 -0.65

(Br@Zn9S9)(Br@Zn12S12)(Br@Zn15S15)(Br@Zn16S16)-

2.10 2.48 2.90 3.02

-3.21 -57.02 -68.54 -71.85

-0.26 -0.59 -0.67 -0.70

atom is trapped, it takes an electron from the surface, and now the HOMO orbital is singly occupied, therefore increasing the electron affinity with respect to the isolated cluster. The electron transfer occurring from the trapped atom to the surface is also responsible for the instability of neutral halogen endohedral clusters because of an increase in the Coulomb attraction between Zn atoms and halogen atoms. IV. Conclusions The geometrical structures and electronic properties of the 0,(1 endohedral (X@ZniSi)i)4-16 nanoclusters, with X standing either for the Li, Na, and K alkali elements or for the Cl and Br halogens, have been characterized. The stability of the resulting structures has been rationalized in terms of three parameters. (i) The first is the appropriate matching between the size of the nanocluster, rcavity, and the size of the trapped atom. (ii) The second is the shape of the nanocluster; most spherical ones are more prone to incarcerate atoms than the irregular ones. (iii) The third is the charge of the trapped atom; negatively charged guest atoms are found to be the thermodynamically most stable ones. Incarceration of halogen atoms results in endohedral nanoclusters with enhanced electron affinity relative to the guest halogen atom. These nanoclusters ought, therefore, to be considered as superhalogens in the same vein as the Al@Al12 cluster, where recent research has confirmed its predicted55 high electron affinity of EA ) 3.20 eV as well as its ability to form salts with electropositive elements like potassium.56 The Cl and Br endohedral nanoclusters studied in this work have electron affinities substantially larger than Al@Al12, namely, EA > 4.5 eV. Hence, they are expected to have a stronger superhalogen character which makes them suitable to form ionic clusterassembled materials. Furthermore, the electron affinities of the halogen endohedral nanoclusters and the ionization energies of the alkali endohedral nanoclusters of ZniSi are rather similar. This is an interesting property, since large IE/EA differences would yield substantial heat release during assembling that might destroy the assembled material as it is formed. Acknowledgment. This research was funded by the Swedish National Research Council and the Government of the Basque Country (SAIOTEK program). The SGI/IZO-SGIker UPV/EHU (supported by Fondo Social Europeo and MCyT) is gratefully acknowledged for the generous allocation of computational resources. J.M.M. and E.F. contributed equally to this work. References and Notes

Figure 5. HOMO and LUMO occupancies for isolated and endohedral nanoclusters, along with the orbital energies. Above is the scheme for isolated and alkali endohedral cases, and below is the scheme for isolated and halogen endohedral nanoparticles case.

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0,( Endohedral (X@ZniSi)i)4-16 Nanoclusters

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