Evolution of the structural and electronic properties of small alkali metal-doped aluminum clusters

Accepted Manuscript Evolution of the structural and electronic properties of small alkali metal-doped aluminum clusters K.O. Alcantar-Medina, M. Herrera-Trejo, A. Tlahuice-Flores, S. MartinezVargas, J. Oliva, A.I. Martinez PII: DOI: Reference:

S2210-271X(16)30447-9 http://dx.doi.org/10.1016/j.comptc.2016.11.008 COMPTC 2294

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Computational & Theoretical Chemistry

Received Date: Revised Date: Accepted Date:

28 September 2016 6 November 2016 7 November 2016

Please cite this article as: K.O. Alcantar-Medina, M. Herrera-Trejo, A. Tlahuice-Flores, S. Martinez-Vargas, J. Oliva, A.I. Martinez, Evolution of the structural and electronic properties of small alkali metal-doped aluminum clusters, Computational & Theoretical Chemistry (2016), doi: http://dx.doi.org/10.1016/j.comptc.2016.11.008

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Evolution of the structural and electronic properties of small alkali metal-doped aluminum clusters

K. O. Alcantar-Medina1, M. Herrera-Trejo1, A. Tlahuice-Flores2, S. Martinez-Vargas3, J. Oliva1, and A. I. Martinez1,4,*

1

2

Cinvestav-Saltillo Industrial, Zona Industrial, 25900 Ramos Arizpe, Coahuila, Mexico.

CICFIM-Facultad de Ciencias Físico-Matemáticas, Universidad Autónoma de Nuevo León, San Nicolás de los Garza, NL 66450, Mexico. 3

Facultad de Ingeniería, Universidad Autónoma del Carmen, Ciudad del Carmen, Campeche, 24115, Mexico.

4

Departamento de Física, Facultad de Ciencias, Universidad Católica del Norte, Casilla 1280, Antofagasta, Chile

*Corresponding author: [email protected], [email protected]

Abstract The atomic arrangement of Aln and AlnM clusters (n = 2 - 14, M = Li, Na o K) was determined by combining both the basin hopping (BH) algorithm using the Gupta potential, and density functional theory (DFT) calculations. The BH yielded hundreds of structures that were refined by DFT using the PBE framework, and Ahlrichs-VDZ basis sets. Anions, neutrals and cations of Aln and AlnM clusters were calculated by DFT resulting in a set of ground state structures. These structures were considered for studying different stability criteria such as binding energy,

dissociation energy, second-order difference of energies, and HOMO-LUMO gaps. Furthermore, the calculated ionization potential, and electron affinity of the clusters yielded values comparable to the experimental ones. A further bonding analysis of the clusters was carried out by the quantum theory of atoms in molecules (AIM) and by using the electronic localization function (ELF). Based on the stability criteria, we determinate the following clusters as relative stable against neighbors: Al7+, Al13-, Al2M-, Al4 M-, Al6 M-, and Al13M. Except by the Al4 M- clusters, all clusters are closed shell structures and they follow the jellium model predictions. The high relative stability of the Al4M- clusters was attributable to their aromaticity. Moreover, AIM and ELF results revealed that when the size of the clusters increases then the transition from covalent to metallic Al-Al bonding emerges. Otherwise, in the case of AlnM clusters, it was found that the nature of Al-M bonds is modified with the size, from metallic for Al2M- to ionic when their size increases.

Keywords: Aluminum clusters; basin hopping algorithm; density functional theory; electronic localization function; quantum theory of atoms in molecules.

1. Introduction The field of pure and doped aluminum clusters is very active, prompted by both fundamental research and their potential applications. In this regard, the origin of the existence of magnetic moments in small pure aluminum clusters has been studied recently [1]. Additionally, it has been demonstrated by experiments that the addition of aluminum atoms to helium nanodroplets forms Aln+ clusters as major products, instead of aluminum foams, which may be useful for the production of new cluster materials [2]. Therefore, the radical attached clusters have been studied as an alternative for the stabilization of small aluminum clusters, which opens the opportunity for the fabrication of stable cluster complexes [3]. Otherwise, even when bulk aluminum is totally inactive towards carbon-halogen bond dissociation, small Aln clusters catalyze this reaction in a similar way to Pd catalysts [4]. The size dependency of selectivity for

aluminum cluster anions in the production of H2 from water has been demonstrated [5], and the production of H2 by reactions of Al6+ with water, resulted in the formation of Al6 O+ cluster [6]. Aluminum clusters have been doped with different atoms, such as the main-group elements and transition metals. During the formation of AlnXm clusters (n > m), different proportions of doping atoms (X) and Aln clusters has been considered in the literature. The study of AlnX clusters has relevance nowadays, because their remarkable catalytic, optical, and magnetic properties. The use of AlnSi and AlnP clusters as catalyst was proposed for the reduction of N2 at low temperatures, opening an alternative method for nitrogen fixation [7]. In order to modify the magnetic properties of aluminum clusters, the doping with the first-row transition metals has been recently explored [8,9]. For example, the Al12Cu cluster can be considered as a superatom that forms chains of ionic salts, which can be used as building blocks for the development of future nanostructured materials [9]. In such manner that the search of global minima of anionic AlnMg (n = 3–20) clusters was reported, where the Al6 Mg cluster is a magic number with 20 valence electrons, exhibiting Al6-Mg ionic bonding [10]. On the other hand, the construction of materials with excellent nonlinear optical properties has been proposed through the construction of dimers and trimers of Al7Na salts [11]. Likewise, Al12Li and Al12Na has been explored as potential low cost alternatives to Ag and Au for plasmonic applications [12]. Moreover, the study of lithium doped aluminum clusters has been useful to understand the microscopic properties of lithium/aluminum alloys which are widely used for the construction of high energy density batteries and aerospace structures [13]. Given the importance of aluminum clusters doped with one foreign atom, the study of alkali metal doped aluminum clusters is relevant for understanding the development of new materials. To the best of our knowledge the study of a complete series of AlnM (M = Li, Na, and K) including charged and neutral clusters has not been done. Instead, only isolated systems have been considered in the literature, such as AlnLi- (n = 3-13) [14], Al2Na [15], Al4M- (M = Li+, Na+, K+, Rb+, Cs+) [16], Al12Li- [17], Al6 M- (M = Li, Na, K) [18], AlnNa (n = 1-4) [19], AlnNam (n = 2-4; m = 1-8) [20], AlnNam (n = 2-22, m = 1-5) [21], AlnM (n ≤ 8, M = Li, K) [22], AlnCsm(n = 5–11, m = 1–3) [23], and Al13M (M = Li, Na, K, Rb, Cs) [24–28]. In order to fill-up the gap, we carried out a systematic study of charged and neutral clusters of AlnM (n = 2-14, M = Li, Na, and K). This manuscript includes important features regarding geometric configurations of the

pure and alkali-doped aluminum clusters and our computational results are comparable to the experimental values. Finally, our systematic study analyzes the relative stability of the clusters and the bonding nature of the most stable clusters.

2. Computational methods The structure of pure Aln and AlnM clusters was determined by combining both Gupta potential (GP) and DFT calculations. The potential energy surface generated by the GP has been sampled through the basin hopping (BH) algorithm [29], which has been demonstrated to be a highly efficient algorithm for global minimization of clusters, and it is implemented in the GMIN program package [29,30]. The Gupta parameters for homoatomic interactions are listed in Table 1. For the heteroatomic Al-M interactions, the parameters were calculated using the simple Lorentz mixing rules (arithmetic mean) [31]. For each composition, circa of 50 lower energy isomers from the GP runs were fully optimized at the DFT level using the Orca 3.0.1 software package [32]. The DFT calculations were performed at the PBE level [33] using DZVP and SV/J auxiliary basis sets, considering different spin states for each geometry. Harmonic vibrational frequencies were computed for the optimized geometries, and all lowest-energy isomers, hold real or positive frequencies, which confirmed each structure as a minimum.

Table 1: Gupta parameters for homoatomic interactions. Parameter Interaction

A

p

q

xi

r0

Al-Al

0.122

8.612

2.516

1.316

2.864

Li-Li

0.033

8.181

0.737

0.325

5.490

Na-Na

0.0159

10.131

1.302

0.291

3.699

K-K

0.0205

10.580

1.340

0.263

4.367

3. Results and discussion

3.1. Geometrical structures For pure aluminum clusters, different ground-state structures have been reported; in contrast, for alkali-metal-doped clusters, only some clusters have been analyzed in the literature. In order to facilitate the discussion, Fig. 1 shows the relative energies of isomers (ΔEi) for Aln- and Aln-1M clusters that are within 1.5 eV of the ground state. For example, the Al3 - cluster presented two isomers, the ground-state at 0 eV, and the second isomer at ΔEi = 0.217 eV. On the other hand, for clusters with more than eight atoms, two energetically quasi-degenerated ground-state isomers were found. For example, in the case of the Al8 Li- cluster, 28 isomers were found in a 1.5 eV range, and two quasidegenerated structures were obtained with a relative energy of 0.02 eV. In order to facilitate the discussion, structures and properties of lowest energy isomers are discussed. The structures of the ground-state isomers for anionic clusters are displayed in Figs. 2 and 3. It was found that the symmetries of clusters do not change when one or two electrons are extracted from the anionic clusters with up to five atoms (see Fig. 2). Otherwise, anionic clusters with more than five atoms, showed symmetry changes when one or two electrons are extracted, and similar statements have been found by other authors [34]. The structures of cluster anions with more than five atoms are shown in Fig. 3.

Fig. 1. Relative energies of isomers (ΔEi) for Aln- and Aln-1M- clusters.

Fig. 2. Ground-state geometries found for Aln- and Aln-1M- clusters with up to five atoms.

Fig. 3. Ground-state geometries found for Aln- and Aln-1M- clusters comprised by 6 to 15 atoms.

A small pure aluminum cluster, such as the Al3- cluster exhibits a D3h point group with bond lengths of ca. 2.52 Å and angles of ~60°. The Al4 - cluster shows a D2h point group with four bond lengths around 2.55 Å and one of bond of circa 3.04 Å. The Al5 - cluster exhibits a planar structure with a C2v point group with five bond lengths of ~2.56 Å and two of 2.69 Å. It can be concluded that when the number of aluminum atoms increases in the cluster, the length of Al-Al bonds increases. Otherwise, for small doped aluminum clusters, such as the Al2M- clusters shown a C2v point group with an elongated Al-Al distance near to 2.55 Å, and larger Al-M distances which depends on the alkali metal as shown in Fig. 4. The Al3 M- clusters show a distorted C3v point group with Al-Al distances similar to those found in the Al4 - cluster; the Al-M average bond lengths are shown in Fig. 4. The Al4M- clusters show a C4v point group with Al-Al distances of ~2.6 Å exhibiting a square pyramidal structure with the alkali metal on the top. This structure has been reported as ground-state for Al4 M- (M = Li, Na, K) [14,16,35], and a distorted square pyramid has been reported for Al4M- (M = Li, K) [22]. Clusters comprised by more than five atoms, display either Cs or C1 point groups, except some pure and doped clusters (see Fig. 3). More symmetric pure aluminum clusters are as follows: Al6, Al7 -, Al8-, Al9-, Al13-, Al15-, which point groups are shown in Fig. 3. Pure aluminum clusters built by n = 6-10, evolve to 3D geometries following a growth pattern based on the octahedron of Al6-, see Fig. 3. In the case of aluminum clusters including n = 11-15 atoms, the icosahedron shape of Al13- is preserved, even after one or two atoms are removed or added. The growth pattern for Al14- and Al15- clusters is mainly based on the reported mechanism of capping extra atoms on the Al13 - icosahedron [36]. It is worthy to notice that the geometries of pure Alnclusters are consistent or nearly identical to other studies which used functionals such as BPW91, PBE0, and B3LYP, with different basis sets such as LANL2DZ, aug-cc-pVTZ, and 6-311G(2d), respectively [34,37,38]. The same concepts apply for the structures of Aln and Aln+ clusters (structures not shown here) [34,36–38]. For doped clusters with more than five atoms, the more symmetric systems are: Al5M- and Al6 Msee Fig. 3. The structures of the AlnM- clusters for n = 5-10 follow the framework of the Al6octahedron. These types of structures have been reported for different cluster anions such as Al6Li-, Al6Na-, Al6 K- [18], AlnLi- (n = 6-10) [14], and AlnCs- (n = 6-10) [23]. The AlnM- clusters for n = 11-14 follow the growth pattern of the icosahedral structure of Al13 -; i.e., for n = 11 the

clusters show a deformed icosahedral without one Al atom at the bottom and one alkali metal on the top. For n = 12 the alkali metal takes the position of the Al atom on the top of the Al12 cluster. For structures with n ≥ 13, the alkali metal occupies a site on the face of the Al13 icosahedral. Similar structures have been reported for aluminum doped clusters such as: Al(1113)Li

[14], Al12Li- [17], and Al13M- (M = Li, Na, K, Cs) [24–28]. All AlnM- clusters, feature an

average distance between the alkali metal and their first three neighbor aluminum atoms, see Fig. 4. It is observed that the average Al-M distance do not vary strongly with the size of the cluster, and Al-M distance increases with the atomic radii of the alkali atoms. Therefore, the clusters with potassium atoms had larger distances in comparison with Li and Na doped clusters.

Fig. 4. Average distance between the alkali metal and their three nearest aluminum atoms in the AlnM- clusters. Vertical bars indicate the maximum and minimum Al-M distances.

3.2. Relative stability Experimentally, the relative stability of the clusters has been studied through the measurement of the mass ion intensities and fragmentation channels. Theoretically, the first insight for analyzing the relative stability of clusters is by plotting the binding energy per atom (Eb) as a function of cluster size [39]. A better parameter to study the relative stability of the clusters is the first

derivative of the total energy, also known as the dissociation energy (E), which is the energy needed for one atom separated from the host cluster [40]. Moreover, the relative stability of clusters can be analyzed through the second-order difference of energies (∆2E) [39]. For neutral clusters, these quantities are defined as [40]:

Eb ( Al n ) 

Eb ( Al n M ) 

nE ( Al )  E ( Al n ) n

(1)

nE ( Al )  E ( M )  E ( Al n M ) n 1

E ( Aln )  E ( Aln 1 )  E ( Al )  E ( Aln )

(2)

(3)

E ( Aln M )  E ( Aln 1M )  E ( Al )  E ( Aln M )

(4)

E( Aln M )  E( Aln )  E(M )  E( Aln M )

(5)

2 E ( Aln )  E ( Aln 1 )  E ( Aln 1 )  2E ( Aln )

(7)

2 E( Aln M )  E( Aln 1M )  E( Aln 1M )  2E( Aln M )

(8)

And for cluster anions:

(n  1) E ( Al )  E ( Al  )  E ( Aln ) Eb ( Al )  n  n

Eb ( Al n M  ) 

(9)

(n  1) E ( Al )  E ( Al  )  E ( M )  E ( Al n M  ) n 1

E ( Aln )  E ( Aln1 )  E ( Al )  E ( Aln )

(10)

(11)

E ( Aln M  )  E ( Aln )  E (M )  E ( Aln M  ) E ( Aln M  )  E ( Aln 1M  )  E ( Al )  E ( Aln M  ) 2 E ( Aln )  E ( Aln1 )  E ( Aln1 )  2E ( Aln ) 2 E ( Aln M  )  E ( Aln 1M  )  E ( Aln 1M  )  2E ( Aln M  )

(12) (13) (14) (15)

Where E represents the total energies of the corresponding systems. Fig. 5 shows the variation of Eb vs. n for the anions, neutrals, and cations of Aln and AlnM clusters. Eb vs. n is a rough estimation of clusters stability because only minor bumps are observed in Fig. 5. In the case of anions, the bumps are displayed by Al7 -, Al13 -, Al4M-, and Al6 M-. On the contrary, it can be observed two different changes of slope as the size of the Aln- and AlnM- clusters increases. Firstly, for Aln- clusters Eb increases rapidly for n = 3-6, and then it increases moderately for n = 6-15. It is important to note a correlation between the slope of Eb vs. n and the changes in the structure of the Aln- clusters: for n = 3-5, the structures are planar; for n = 6-15, the structures become 3D, following the growth pattern of the octahedral structure of Al6 (n ≤ 10), and the icosahedral-like shape for n = 11-15. Similar statements have been reported for Aln clusters [36]. Regarding the AlnM- clusters, the Eb vs. n curves follow the same trend obtained for pure aluminum clusters, where the changes in the growth pattern are closely related to the binding energy changes. For n = 2-4, the Al atoms are in the same plane; for n = 5, it starts to develop the 3D structure of an Al5 square pyramidal; and for n ≥ 6, the 3D structures are based on both the octahedral structure of Al6 and icosahedral-like shape of Al13. In the case of neutrals and cations of the clusters, similar correlations between the slope and the structure are observed; however, only bumps are displayed for Al7+, and Al13 M.

Fig. 5. Binding energy/atom as a function of size for charged and neutral Aln and AlnM clusters, anions (squares), neutrals (circles), and cations (triangles).

Fig. 6. Dissociation energy (E) as a function of size for Aln and AlnLi clusters: (a) anions, (b) neutrals, and (c) cations.

For clarity, Figures 6 to 8 show only the data for AlnLi clusters because the AlnNa and AlnK exhibit the same trend. Fig. 6 shows the E for anionic, neutral and cationic clusters, in the case of Aln- clusters, the curves indicate the dissociation energy as the fracture into Aln-1 - clusters and one Al atom. Otherwise, for AlnM- clusters, the dissociation energy can be calculated as the fracture into (i) Aln- clusters and one M atom, see Eq. (12); and (ii) into Aln-1 M- clusters and one Al atom, see Eq. (13). The calculations indicated that the cases (i) are lower than (ii), this suggests that the AlnM- clusters are likely to dissociate into Aln- clusters and one M atom. In Fig. 6, some peaks are observed for Al13-, Al7, Al13, Al7+, Al14+, Al6Li, Al13Li, and Al13Li+; and although the maximums for AlnLi- are almost at the same level, some relative maximums are observed for Al2Li-, Al4Li-, Al6 Li-, and Al12Li-. Fig. 7 shows ∆2E values for anionic, neutral and cationic Aln and doped AlnLi clusters. Clusters with larger ∆2E are Al13-, Al7, Al7+, Al2Li-, Al4 Li, Al6Li-, Al13Li, and Al7 Li+. An additional quantity related with the chemical stability of a cluster is its larger HOMO-LUMO gap. Fig. 8 shows the HOMO-LUMO gaps for the neutral and charged Aln and AlnLi clusters; in the curves odd-even oscillations can be noted for most of the clusters. Large HOMO-LUMO gaps are displayed for Al13-, Al2 Li-, Al4Li-, Al6 Li-, Al13Li, and Al7+, see Fig. 8.

Fig 7. Second-order difference of energies (∆2E) as a function of size for Aln- and AlnLi- clusters: (a) anions, (b) neutrals, and (c) cations.

Fig. 8. HOMO-LUMO gap as a function of size for Aln- and AlnLi- clusters: (a) anions, (b) neutrals, and (c) cations.

It is important to note that simultaneous maximums in Eb, E, 2E and HOMO-LUMO gap were found for Al13-, Al2 M-, Al4M-, Al6 M-, Al13M, and Al7+ clusters. It has been reported that aluminum clusters exhibit improved stability with respect to their neighbors when the closedshell electronic structure is achieved, in other words, when the electron counting corresponds with magic numbers such as 8, 18, 20, 34, 40, 58, … [21]. In the case of alkali metal doped aluminum clusters, due to the lower ionization potential of the alkali atoms, the transfer of an electron from the alkali atom to the aluminum cluster is expected. In the series of stable clusters analyzed here, the Al13- is a closed-shell stable cluster within the spherical jellium model because it has 40 valence electrons; in addition, its structure is an icosahedron nearly to a regular Platonic solid [28,41]. On the other hand, the Al2 M- clusters have 8 valence electrons if a valence of 3 is assumed; the Al2Na- cluster anion has been reported as closed-shell, but its relative stability has not been assured experimentally [21,42]. Otherwise, Al4 M- cluster anions are a special case, where the closed electronic shell structure is not achieved, because it has 14 valence electrons. However, their high stability has been confirmed experimentally in the Al4Li- and Al4Na -

clusters, this unusual stability has been related to the planar structure of the Al42- unit which exhibits aromaticity with two delocalized π-electrons [43]. Al6M- clusters feature an electron counting of 8 if a valence of 1 is assumed for aluminum, or it has 20 electrons if a valence of 3 is assumed. Given that 8 and 20 are both shell closings in the spherical jellium model, the Al6M- clusters has the potential of being closed-shell species. Experimentally, the high relative stability has not been analyzed for Al6Na- clusters, but the high ionization potential of Al6Na with one electron less than the closed-shell speaks about the high relative stability of the neutral cluster [42]. Moreover, the discussion of the relative stability of a closed-shell cluster such as Al6Na2 has been extensively analyzed by both experimental evidence and DFT calculations [21]. It has been concluded that the system can be considered as a Zintl salt with high relative stability of the neutral Al6Na2 cluster with closed-shell electronic structure [21]. It was established, despite of the calculated charges by natural population analysis (NPA) yielded a net donation by Na atoms of 1.54e, instead of 2.0e, to the Al6 cluster [21]. Based on abinitio calculations, it has been concluded that the Al6M- clusters can be viewed as Zintl salts with the Al62- dianion and the M+ cation, where the dianion is the fusion of two aromatic Al3 - units [18]. Furthermore, it has been argued that every face of the Al62- octahedron still possesses both π- and σ-aromaticity [18]. Then, the aromaticity may also contribute to the stability of Al6M clusters. If the alkali atom transfers 1e to the Al13 cluster, the Al13M clusters will exhibit electronic shell closure with 40 valence electrons. In has been found that the structure, stability, and properties of the Al13M clusters are similar [24]. Although, given the competition between the size and the ionization potential of the alkali atoms, the Eb of M to Al13 systematically decreases from Li to K [28]. It has been reported that experimental and theoretical results are in agreement for the electron affinities and vertical detachment energies, concluding that the ground state geometries of the Al13M clusters have been identified, which are analogous to those reported here [24]. Due to the high stability of the Al13M clusters, their complexes with Lewis bases such as NH3, H2O, C6H6, and HLi have a negligible or small effect on the structure of Al13M, developing alkalibonding interaction through the M+ cations [27]. It indicates the high stability of the Al13M Zintl salts. Regarding the cluster cations, the Al7+ cluster has enhanced stability due to its closed-shell electronic structure with 20e -, and the high relative stability of this cluster cation has been

verified experimentally through electron impact mass spectrometry measurements of Aln clusters formed inside helium droplets [2].

3.3 Electronic properties

Fig. 9. Calculated IP (filled squares) for the clusters: (a) Aln, (b) AlnLi, (c) AlnNa, and (d) AlnK. The open squares indicate experimental reported values with error bars: (a) extracted from Ref. [44], and (c) extracted from Ref. [42].

It has been found that closed-shell clusters should exhibit higher ionization potential (IP) than its immediate-size neighbors. Fig. 9 shows the calculated IP for the Aln and AlnM clusters, in addition, the experimental reported values are included for some cases. For Aln clusters, calculated IP values are very near to the experimental ones; some peaks for Al6 and Al13 are observed. The high IP of Al6 may be caused by both the electronic shell closure with 18 valence electrons and its Platonic solid octahedral structure. The high IP of Al13 can be associated to its icosahedral structure which is a Platonic solid, and because it has one electron less than the closed-shell structure. For Al7 and Al14, the sudden decrease in their IP values is attributed to their proximity to the shell closure, respectively. On the other hand, the calculated IP values for

AlnNa clusters are very near to the experimental values and follow the same trend, see Fig. 9. To the best of our knowledge, we are reporting for the first time the theoretical IPs values for the AlnLi and for AlnK systems (n = 2-15), and it is observed a systematical decrease in IP from Li to K. For AlnM clusters, two peaks are observed for Al6M and Al13M clusters, the high relative stability for both kind of clusters is because they have one electron less than the closed-shell structure including 19 and 39 electrons, respectively. Additionally, a sudden decrease in the IP value for n = 7 and 14 (Fig. 9) for the AlnM clusters is attributed to their electron counting larger than the shell closing requirement.

Fig. 10. Calculated EA (filled squares) for the clusters: (a) Aln, (b) AlnLi, (c) AlnNa, and (d) AlnK. The open squares indicate experimental reported values with error bars extracted from: (a) Ref. [38,45], (b) Ref. [13], (c) Ref. [21], and (d) Ref. [24].

A cluster with one more electron than a closed-shell structure will lose easily that electron, similar to an alkali metal, and a cluster with one electron less the electronic shell closure will has a large electron affinity (EA), such as a halogen. The calculated EA for the Aln and AlnM clusters is shown in Fig. 10, in addition, the experimental EA is included in some cases. For pure and doped clusters, it is observed that the EA increases as n rises. The liquid drop model (LDM) -a classical electrostatic model that take a metal cluster such as a uniform conducting sphere

[46]-, predicts that more energy is released on adding an electron to a large cluster than to a smaller one, it means that the EA will increase with the cluster size. However, the curves shown in Fig. 10 reveal both the alternation in EA with n and some peaks of high intensity, which cannot be explained with the LDM. These deviations are due to quantum size effects which can be treated with the jellium model. For the pure Aln clusters, the peaks of high intensity relative to neighboring peaks are observed at n = 6 and 13, it is because these clusters have two and one electrons less than the electronic shell closure. For the AlnM clusters the same trend is observed for the three alkali metals, displaying maximums at n = 4, 6, and 12. For the Al4M clusters, the addition of one electron will generate their anions, which have high relative stability due to their aromaticity. Furthermore, the Al6M clusters have one electron less that the electron closure. On the other hand, the relative high EA values of Al12M clusters are due to the existence of very stable Al13M clusters which exhibit very low EA values due to their electron closure with 40 electrons.

3.5 Bonding analysis The characterization of bonding in bimetallic clusters has been analyzed through different methodologies [35,47–49]. However, for alkalized aluminum clusters, the quantum theory of atoms in molecules (AIM) has been proved as the best descriptor for the ionic character of Al-M bonds [49]. The AIM population analysis yields accurately the AIM charges, which describe the charge polarization in fragments of a cluster [47]. Table 2 shows the calculated AIM charges (Q) of the Aln and M fragments of the most stable AlnM clusters. The listed Q values for the Al4 fragments are very near to those reported for Al4Li- and Al4Na- calculated by AIM, whose values are -1.748 and -1.512, respectively [49]. Moreover, Q of the Al6 fragment is near to the charge of -1.54 calculated by NPA for the 2Na+(Al6)2- Zintl salt [21]. Regarding, natural bond orbital (NBO) charges, and the Al2Na- cluster, a value of -1.12 for the Al2 fragment was reported for the ground state [15], which is a little lower to the found here. Furthermore, for the Al3M clusters, reported NBO charges are 0.87, 0.86, and 0.94 for M = Li, Na, and K, respectively [24]. These values reveal the charge transfer from the alkali metals to the Al13 fragment. According to Table 2, Li exhibits a larger charge donation to the Aln fragments than K and Na atoms. Furthermore, it

is observed that larger clusters accept more charge than smaller ones, and this trend is related to the fact that EA values growth as n increases, see Fig. 10a. For Al2Na- and Al2 K- the low charge of the alkali atoms indicates that the bonding is more covalent than ionic while for the Al2Li-, the bonding is more ionic. For larger clusters, the large charge donation from the alkali metal to the Aln fragments indicates an important ionic character of the M-Al bonds and the formation of Zintl salts.

Table 2. Calculated AIM charges for the fragments of the AlnM clusters with higher relative stability. Cluster

Q

Q

(Aln fragment)

(M fragment)

Al2Li-

-1.495

0.495

Al2Na-

-1.233

0.233

Al2K-

-1.153

0.153

-1.755

0.755

-1.586

0.586

Al4K-

-1.591

0.591

Al6Li-

-1.805

0.805

Al6Na-

-1.643

0.643

Al6K

-1.635

0.635

Al13Li

-0.858

0.858

Al13Na

-0.798

0.798

Al13K

-0.835

0.835

Al4LiAl4Na

-

-

The bonding analysis was also studied by using the electron localization function (ELF). ELF is a measure of electron localization in molecular systems and permits to distinguish the electronic regions with metallic or covalent bonding [50]. In regions where electrons are alone or paired with opposite spins, the ELF gets a value close to 1 such as in atomic shells, chemical bonds, and

lone electron pairs. Whereas metallic bonding is characterized by an ELF around 0.5 [50]. For a sake of comparison, Fig. 11 shows the ELF contour plots for the most stable clusters such as Al2Na-, Al4Na-, Al6Na-, Al7+, Al13-, and Al13Na. The corresponding series of AlnLi and AlnK are not shown because they have the same trend that the equivalent AlnNa clusters. For pure clusters, Fig. 11a shows a ELF contour plot for Al7+, and it shows red regions between each Al-atom and near the surface of the cluster. It indicates that exist covalent interactions between Al-Al atoms but also there are localized electrons near the surface; also a green region around the cluster surface is observed. Whereas for the Al13 - cluster (Fig. 11b), the green region of the ELF indicates that dominates the metallic bonding (see regions in the middle of the five Al-atoms and on the surface of the cluster). In addition, red regions of the ELF indicate more localized electron pairs around the Al-atoms near the surface of the cluster. It has also been observed in aluminum crystalline surfaces [50]. In the case of the Al2M- clusters, the covalent interaction between Al-Al is indicated as a red area located between Al-atoms, see the EFL contour of Al2Na-. For pure clusters, there are localized electrons on their surfaces, and the green region around the cluster is also observed. It indicates that the Al2Na- cluster presents very weak Li-Al covalent interactions because the electrons are not between the Al-Li atoms, and dominates a metallic-like bonding in this clusters. While the size of AlnNa clusters rises, the localized electrons near Na atoms diminishes, and most of the charge is donated to Aln fragments, see Fig. 11d-f. Larger donation of charge from the alkali metal to greater clusters was also observed in the calculated AIM charges. Additionally, the EFL contour plots reveal the strong ionic character of the Aln-M bonds for fragments with n = 4, 6 and 13. Finally, for small doped clusters dominate the Al-Al covalent interactions (see Fig. 11cd), while for greater Aln fragments, the metallic bonding character is the main bonding contribution (see Fig. 11e-f).

Fig. 11. ELF contour plots for: (a) Al7+, (b) Al13-, (c) Al2Na-, (d) Al4Na-, (e) Al6Na-, and (f) Al13Na. For doped clusters, the Na atom is on the top of the clusters. The color scale runs from 0 (blue) to 0.5 (green), and 1 (red), see bar located on the right side of (f).

4. Conclusions It was found that the atomic arrangement of Aln fragments of AlnM clusters follows the atomic arrangement of pure Aln clusters, except for some special cases such as the Al5 M clusters. Where the pure Al5 cluster exhibits a 2-D structure; while the Al5 fragment exhibit a square pyramidal structure with the M atom located at the center of the base. Additionally, larger clusters follow the framework of the Al6 octahedron or the Al13 icosahedron. The systematic calculation of the Aln and AlnM clusters was useful for analyzing different stability criteria. This analysis provided diverse relative stable clusters, some ones exhibiting the electron shell closure (Al7+, Al13 -, Al2 M, Al6M-, and Al13M); while the stability of other clusters was related to their aromaticity (Al4M-).

Moreover, it was demonstrated that DFT in the PBE framework provides relatively accurate adiabatic EA and IP values comparable to the available experimental data. It was demonstrated that the alkali metals diminish the IP and EA, where stronger effects were found in AlnK clusters. The bonding analysis realized by both AIM and ELF revealed that despite the low IP of the alkali atoms, the donation of charge from M to the clusters depends on the clusters size. This modify the nature of Al-M bonds; i.e., from metallic Al-M bonds for Al2M-, to the ionic character of the Al-M bonds for greater clusters. Otherwise, for pure Aln clusters and Aln fragments, while the cluster size rises, the transition from covalent to metallic Al-Al bonding emerges.

Acknowledgements KOAM thanks the Conacyt sponsorship. The authors are grateful for the facilities of the Xiuhcoatl-Cinvestav computer cluster.

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

Aln and AlnM clusters (n = 2 - 14, M = Li, Na o K) were studied



The bonding analysis revealed that the donation of charge from M to the Aln clusters depends on the clusters size



The ionic character of the Al-M bonds changes with the clusters size