Effect of alkali atom doping on the electronic structure and aromatic character of planar and quasi-planar Al13+ clusters

A set of three Al13+ clusters, one perfectly planar, and two quasi-planar structures, have been recently reported by our group (Guin et al. Journal of Molecular Graphics and Modeling, 2020, 97, 107544). All three clusters possess bilateral symmetry with identical structural features—a set of ten aluminum atoms encircle a triangular core. The symmetry axis passes through one of the Al atoms of the central triangular core and two Al atoms located on the periphery at two opposite ends of the cluster. This set of three aluminum clusters is an example of a rare metallo-aromatic system where highly anti-aromatic islands are embedded within an aromatic sea. In the present study, we have explored the effect of doping alkali atoms (Li, Na, and K) at the positions of the Al atoms that lie on the symmetry axis of the cluster intending to understand the structural stability and the effect on the aromatic character as compared to the undoped parent clusters. Besides the electronic structural analysis, NICS and ELF studies have also been carried out to characterize the aromatic nature of the doped clusters. Interestingly, it has been found that even with the incorporation of the alkali atoms, the bilateral symmetry of the clusters remains intact, but the alkali atoms are pushed out of the original location toward the edge of the cluster, whereas the aluminum atoms remain grouped. The dipole moment of the clusters systematically increases, and the overall aromaticity of the cluster systematically decreases with the increase in the atomic number of the doped alkali atoms. Effect of alkali atom doping to Al13+ cluster Effect of alkali atom doping to Al13+ cluster


Introduction
During current times, nano-clusters, as well as doped nanoclusters, have drawn inquisitive attention of scientists due to their versatile properties and potential applicability in various fields like optics [1], electronics [2], catalysis [3], and sensors [4]. Nano-clusters quite often exhibit unanticipated properties which are vastly different from their bulk counterpart. Especially, doped metal nano-clusters have additional advantages compared to the undoped clusters as this brings out the opportunity to amalgamate the properties of different metal atoms into a single entity. Studies of these nano-clusters also provide deeper understanding regarding the origin of stability as well as different possible isomers due to various geometric configurations [5]. Among various metal nano-clusters, aluminum nano-clusters have been found to have a wide range of applications in various fields like catalysis [6], storage of hydrogen [7], and splitting of water to produce hydrogen [8]. Aluminum is a cheaper material due to its higher natural abundance as well as the ease with which it can be tailored in various architectures like nano-rods [9], nano-disks [10], and nano-shells [11]. Recently Jiang et al. have reported various structural possibilities for Al n B m (n = 1-7 and m = 1-2) [12]. Q. L. Lu et al. have reported the cage-like structure of Al 12 by DFT calculation which has revealed that the presence of Mg and Ca metals enhance the stability of the aluminum cluster significantly [13]. In 2017, Li et al. investigated geometries, stabilities, and electronic properties of palladium-doped aluminum clusters having general formula Al n Pd m (n = 1-10, m = 1,2) by using DFT calculation [14]. In 2017, Jia et al. have reported low lying isomers of Al n As q (q = −1,0,+1; n = 1-16) [15].
Here, we report the effect of doping alkali atoms Li, Na, and K in place of the aluminum atoms that lie on the symmetry axis of the recently reported planar and quasi-planar Al 13 + clusters by our group [16,17]. It was found that Al 13 + cluster can exist in three closely lying isomeric forms, a perfectly planar cluster and two quasi-planar clusters, slightly puckered in opposite directions relative to the planar cluster. Among these two quasi-planar clusters, one is a true minimum structure (GS), and the other one is a transition state (TS). This ground state (GS) structure was found to be more aromatic compared to the planar and TS structure. These clusters have a common structural feature-in each of these a triangular core is encircled by a set of ten aluminum atoms (Fig. 1a). These clusters all possess a bilateral symmetry, where the symmetry line passes through one of the three aluminum atoms (Al1) of the central triangular core and two peripheral aluminum atoms Al4 and Al9 which are located respectively at the top and bottom of the cluster. The aim of the current study is to explore the effect of alkali atom doping at the position of Al1, Al4, and Al9 which line on the symmetry axis of the cluster. It is quite interesting that bilateral symmetry is a robust feature of this system which is maintained even after alkali atom doping. Also, the alkali atoms prefer the outward positions with respect to the parent cluster even if the doping is done at the bulk position. Detailed electronic structure analysis of these doped clusters has revealed the origin of structural rearrangement induced by doping. A study of Nucleusindependent chemical shift (NICS) indicates an overall loss of aromaticity compared to the parent cluster on alkali atom doping. Electron localization function (ELF) which is also a modern tool in theoretical chemistry to characterize aromaticity has provided insight into the nature of aromaticity of these doped systems. This study has also revealed that alkali atom doping can be effectively utilized to systematically tune the dipolar nature of these clusters.

Computational methodology
Gaussian 03 package [18] has been employed to explore the optimized geometry of alkali-doped Al 13 + clusters using the DFT methodology employing the B3LYP hybrid density functional [19,20] and 6-311G(d) basis set [21]. Threshold values of convergence criterion in the optimization process for maximum force and displacement are 0.000450 a.u. and 0.001800 a.u., respectively, whereas that for the RMS force and displacement are 0.000300 a.u. and 0.001200 a.u., respectively [22].Once the current values of all four criteria fell Fig. 1 Optimized geometries of alkali atom doped above the core atom (Al1) on planar and quasi-planar (Al 12 X) + (X = Li, Na, and K) clusters along with pure planar and quasi-planar Al 13 + cluster. (a) Undoped planar below the threshold, the nature of the optimized structures were characterized by frequency analysis. All quasi-planar structures correspond to true minimum structure with zero imaginary frequency. Graphics for canonical orbitals and electrostatic potential (ESP) [23] were generated using Molekel [24] and Chemissian package [25], whereas ELF analysis has been carried out using Multiwfn-3.7 package [26]. NICS(0) values have been computed using Gaussian 03 package.

Results
Alkali atom doping at position 1 A set of three Al 13 + clusters (one planar and two quasiplanar) with interesting metallo-aromatic properties have been recently reported by our group [16,17]. In all of these clusters, a central triangular core is encircled by a set of ten Al atoms in the form of a belt (Fig. 1a). Also, these clusters have a unique commonality-all of these possess a bilateral symmetry where the symmetry line passes through the middle of the cluster bisecting the central triangular core with one of the Al atoms (Al1) situated on this symmetry line. Two peripheral Al atoms (Al4 and Al9) also lie on the symmetry axis of the clusters. The present study aims to understand the effect of doping alkali atoms Li, Na, and K for three atoms that lie on the symmetry line of the cluster. In this section, we present the results of alkali atom doping over the position of Al1. In the process of searching the optimized structures in the presence of doped alkali atoms, besides the quasi-planar true minimum structure characterized by the presence of zero imaginary frequency in the vibrational analysis of the structure, we have also obtained planar Li-, Na-, and K-doped Al 13 + clusters having 3, 3, and 6 imaginary frequencies, respectively. The electronic structures of these planar structures have been explored along with the quasi-planar minimum energy structures to understand the nature of the distortion and the effect on aromaticity as the clusters evolve from planar to the quasiplanar puckered structures.
Optimized geometries of alkali atom (Li, Na, and K)-doped Al 13 + clusters have been depicted in Fig. 1. It is to be noted that previously reported planar and quasi-planar Al 13 + clusters possess a bilateral symmetry (Fig. 1a). The doping of alkali atoms over the position of Al1 does not destroy this bilateral symmetry; rather, the alkali atoms occupy their positions on this symmetry line. In the case of planar clusters (which are not true minimum structures), the alkali atoms remain within the bulk of the cluster, but for the quasi-planar true minimum structures, the alkali atoms occupy the peripheral position on the symmetry line (Fig. 1b, c, d).
In the case of Li doping, lower part of the cluster is affected most, and the upper portion remains nearly undistorted. Two rhombic grids at the middle of the planar Al 13 + clusters are diagonally joined by the effect of the Li atom at position 1 which establish two shorter bonds Li1-Al6 = 2.929 Å and Li1-Al12 = 2.929 Å as compared to 2.736 Å between Al1-Al3 and Al1-Al2 in the undoped planar Al 13 + cluster. Atoms Al13 and Al5 go away from the position of atom 1 which give rise to two approximate rectangular grids at the lower half of the cluster. The Li1-Al4 distance is 2.665 Å which is smaller compared to Al1-Al4 distance (2.714 Å).
On the other hand, the central triangle is also reformed maintaining its symmetry with Li1-Al2 = 2.643 Å and Li1-Al3 = 2.643 Å as compared to 2.736 Å between Al1-Al3 and Al1-Al2 in the undoped planar Al 13 + cluster. Even this effect of doping of lighter atom at position 1 also reduces bond distance among Al2-Al3 {2.567 Å from 2.736 Å}. A pair of squares at the bottom surface of the cluster has been formed due to doping. But geometry of top region of the cluster remains nearly unaffected. Maximum horizontal and vertical dimension for this cluster is 7.930 Å and 7.408 Å.
The minimum energy quasi-planar structure corresponding to the centrally Li-doped planar cluster has been depicted in the lower panel of Fig. 1b. It is interesting to note that now the Li atom has swapped its position with Al4 which was at the periphery of the pure Al 13 + clusters. This effect is a generic feature and is observed in the case of Na and K doping as well ( Fig. 1 c and d). Alkali atoms prefer to occupy the peripheral position compared to a bulk one. A comparison of the Lidoped true minimum structure with the corresponding quasiplanar Al 13 + shows that now not only the lower part of the cluster but all thirteen atoms of the cluster readjusts itself and Li-doped cluster is more puckered compared to the quasiplanar Al 13 + cluster. In this puckered configuration, the cluster assumes a flying bird-like shape with two symmetry-related edges (formed by Al5, Al6, Al7 and their symmetry-related Al13, Al12, and Al11) analogous to two wings, Li1 which is placed slightly downward of the mean plane forms the tail, and three aluminum atoms (Al8, Al9 and Al10) at the upper edge form the head portion of the cluster. An account of the bond distances and dihedral angles between adjacent triangular rings of the cluster has been provided in table S1 and table S2, respectively.
In the case of Na-doped Al 13 + cluster, doping of Na atom at position 1 enlarges the bond distance among Na1-Al2/Al3 {2.953 Å from 2.736 Å}.This effect of doping also enhances the bond distance among Al2-Al3 {2.857 Å from 2.736 Å}. Due to presence of the Na atom at position 1, Al4 is displaced more downward and knocked out from the bond connected by Na1, Al5, and Al13. The bilateral symmetry along y-axis remains intact even in the presence of Na. The maximum horizontal and vertical dimension extension of the cluster, in this case, is 8.082 Å and 8.460 Å. Bond distances and bond angles for the cluster has been summarized in table S1.
In the true minima Na-doped quasi-planar structure, Na1 and Al4 swap their locations along the symmetry line. Also Na1 atom is located 2.46 Å downward of the mean plane passing through the central Al 3 triangular core. Aluminum atoms Al5, Al6, and Al7 on the left edge, as well as their symmetry-related counterparts Al13, Al12, and Al11, move upward (0.54 Å, 1.95 Å, and 1.52 Å, respectively) of the mean plane passing through the central triangular core. This give rise to a puckered geometry of the cluster rendering the cluster a shape analogous to a flying bird with Na(1) occupying the tail region and three aluminum atoms Al8, Al9, and Al10 forming the head portion of the cluster. Al9 is placed slightly upward (0.43 Å) of the mean plane passing through the central triangular core.
In the case of K doping also, both the planar and the quasiplanar clusters have the analogous topologies like those of the Na-doped cluster. In the case of the planar cluster, K1-Al4 distance is relatively longer compared to Li-and Na-doped clusters. Bond distance of K1-Al2/Al3 (3.116 Å) is much longer than the corresponding distance of parent Al 13 + cluster (2.736 Å). This effect of doping slightly increases the bond distance among Al2-Al3 {2.927 Å from 2.736 Å} also. The maximum horizontal and vertical extension of the cluster in this case is 8.159 Å and 7.783 Å.
The true minima K-doped quasi-planar cluster has a similar bird-like architecture as that was found in case of Li-and Nadoped cluster. The geometrical parameters (bond distances, bond angles, and dihedral angles between adjacent rings) have been provided in Table 1. Both the planar and quasi-planar Kdoped clusters possess bilateral symmetry along y-axis.
Among the three quasi-planar Li-, Na-, and K-doped clusters, the major differences prevail around the tail region. Dopant alkali atoms are displaced downward with respect to the mean plane passing through the central triangular core constituted by Al2, Al3, and Al4 (Fig. 2). Figure 2 depicts the superposed view of the three alkali-doped clusters in which the alignment has been done with Al4 as origin, yaxis passes through origin and the middle of the arm formed by Al2 and Al3, x-axis was taken parallel to this arm, and z = 0 was set for the plane passing this triangle. From Fig. 2(b), it can be seen that the distance of the alkali atoms from the origin (position of Al4) increases following the increasing atomic number of the alkali atoms. K is displaced downward highest (2.62 Å) from the mean plane, Na has an intermediate downward displacement (2.46 Å), and Li has the least (2.35 Å) downward displacement among the three alkali atoms. The distances of the projection points of K, Na, and Li on the symmetry axis (y-axis) from Al4 (which is at origin) are 2.32 Å, 1.75 Å, and 1.30 Å, respectively. As can be seen from Fig. 2, the central triangular core for all three clusters is almost identical. From Fig. 2(b), it is also evident that the upper part of the clusters (consisting of peripheral Al6, Al7, Al8, Al9, Al10, Al11, and Al12) deviates upward of the mean plane. Al5 and symmetry-related Al13 deviate downward of the mean plane. The magnitude of the upward deviation of the Al atoms at the upper portion of the cluster is maximum for Lidoped cluster, intermediate for Na-doped cluster, and least for Li-doped cluster, whereas for the lower portion of the cluster, this sequence is reversed, K-doped cluster has the maximum downward deviation, Li-doped cluster has the lowest downward deviation, and Na-doped cluster has intermediate value (see Fig. 2(a)). For all three clusters, the upward deviation for Al7 and symmetry-related Al11 is practically the same.
The dihedral angle between the central ring (R1) and the adjacent ring (R8) on top of the cluster is 48.13°, 42.04°, and 36.79°, respectively, for the Li-, Na-, and K-doped clusters. The highest dihedral angle is between R6 and R7 (92.28°, 92.75°, and 92.42°for Li-, Na-, and K-doped clusters), and Quasi-planar 0.000 this leads to maximum puckering at the upper left and upper right corner of the clusters. Next highest puckering is between the ring R3 and R4, and the least puckering is between the rings R4 and R5 (Table 2). This deviation leads to the architecture of the cluster analogous to the upwardly displacement of two wings of a flying bird.
Alkali atom doping at position 4 It has been previously observed that the lower tail region of the parent Al 13 + cluster is more flexible. It is thus interesting to explore the effect of doping alkali atoms at position 4 of the parent Al 13 + cluster. The effect of this doping has been depicted in Fig. 3. The alkali atom doping at the position 4 of the planar cluster leads to drastic reorganization of atoms at the lower region of the cluster, whereas the upper portion remains nearly undistorted. A rhombic grid is generated at the lower portion for each of the alkali atoms doping. Each alkali atom is di-coordinated and bonded to peripheral Al5 and Al13 on either side. Alkali atoms remain on the symmetry axis but move away from the central aluminum atom Al1. The Al1-Li4 distance is 4.300 Å, Al1-Na4 distance is 4.712 Å, whereas Al1-K4 distance is 5.370 Å. The peripheral Al5 and Al13 atoms also move away from the central Al1. The Al1-Al5/Al1-Al13 distance is 3.037 Å, 3.079 Å, and 3.060 Å, respectively, for Li-, Na-, and K-doped clusters as compared  to 2.857 Å for the parent Al 13 + cluster. It is interesting to note that this reorganization does not destroy the bilateral symmetry. The central triangle remains isosceles maintaining its symmetry. For the Li-doped cluster, Al1-Al2 = Al1-Al3 = 2.614 Å and Al2-Al3 = 2.655 Å. For the Na-doped cluster, A1-Al3 = A1-Al3 = 2.627 Å and Al2-Al3 = 2.653 Å, whereas for Kdoped cluster, Al1-Al2 = Al1-Al3 = 2.627 Å and Al2-Al3 = 2.654 Å. These can be compared with the corresponding bond distances of the undoped planar Al 13 + cluster which are Al1-Al2 = Al1-Al3 = 2.736 Å and Al2-Al3 = 2.619 Å. The geometry of top portion of each cluster remains almost same. In this case, maximum horizontal and vertical extensions of the clusters are 7.835 Å and 8.956 Å, 7.826 Å and 9.385 Å, and 7.812 Å and 10.034 Å, respectively, for Li-, Na-, and Kdoped clusters.
The doping of alkali atoms at the location of Al4 of the quasi-planar Al 13 + cluster leads to a dramatic reorganization of the cluster-it assumes a bowl shape and the alkali atoms migrate toward the center of the cluster and position themselves over the central triangular core of the cluster (see lower panel of Figs. 3 and 4). As the alkali atoms move over to the central triangular core, Al5 and Al13 come closer to establish a bond among them. At the lower portion of the cluster, a new triangle is generated by Al1, Al5, and Al13 in this reorganization. The planes of the peripheral triangles deviate toward the same side of the central triangle to produce a bowl shape of the base Al 12 cluster. The alkali atoms remain on the concave side of this bowl. It is interesting again that the doped structure retains bilateral symmetry. The symmetry line now passes through Al9, Al1, and the midpoint of the bond between Al5 and Al13. The overall architecture of doped structures is identical. The core of each doped cluster is an isosceles triangle. The distances of the doped atoms from the mean plane of the central triangle is 2.487 Å, 2.913 Å, and 3.568 Å, respectively, for Li, Na, and K atoms which correlate with the size of the alkali atoms.
The dihedral angle between the central ring (R1) and the adjacent ring (R8) on top of the cluster is 152.72°, 153.53°, and 153.16°, respectively, for the Li-, Na-, and K-doped clusters. The dihedral angle between the central ring (R1) and the adjacent ring (R4) on the left of the cluster is 163.69°, 165.38°, and 167.81°, respectively, for the Li-, Na-, and K-doped clusters. The dihedral angle between R1 and the plane containing Al2, Al3, and X4 (X = Li, Na, K) are respectively 71.93°, 72.26°, and 73.67°for Li-, Na-and K-doped clusters. This indicates that the foot point of K is closer to Al1 compared to that of Li and Na. This is also discernible from Fig. 4b. Other relevant bond distances and dihedral angles have been summarized in table S1 and table S3, respectively. It is to be noted that the curvature of the curved bowl surface is very close to each other, but for the K-doped cluster, the radius of curvature is slightly higher, and for the Li-doped cluster, the radius of curvature is the smallest (Fig. 4b).
The search for optimized structures for doping of alkali atoms at position 9 on the symmetry axis was also attempted, but minimum energy structures could not be found. It was seen that the clusters, in this case, tend to assume a threedimensional geometry in contrast to the planar and quasiplanar geometry.

Relative energies of the doped cluster
The energies of the optimized doped clusters for doping of alkali atoms at position 1 and position 4 have been given in Table 1. It can be seen that alkali atom doping at position 4 of the quasi-planar Al 13 + cluster leads to lower energy doped clusters compared to the clusters obtained by doping alkali atoms at position 1. The true minima K-doped Al 13 + cluster (doped at 4th position) possesses the lowest energy, and the planar Li-doped Al 13 + cluster (doped at 1st position) has the highest energy among all of our reported clusters (Table 1). Relative energies (in Kcal/mol) of all these clusters have been estimated compared to the Li-doped Al 13 + cluster which has the lowest energy among all the doped clusters.

Electrostatic potential surface (ESP)
ESP surface for doped clusters at position 4 ESP surfaces of alkali-doped Al 13 + for position 4 have been depicted in Fig. 5. Dipole moment [27] of these clusters has been provided in Table 2. In the Li-doped planar cluster, the region connecting Al2 and Al3 is the most electron-rich (red) throughout the whole cluster, whereas electron-deficit region (indicated by blue color) is spread over the periphery of the cluster, most prominently at upper left, upper right corner, and the lower tip of the cluster. The net dipole moment of the cluster is aligned along the symmetry axis (y-axis) of the cluster (−3.01 Debye). The X-component of the dipole moment has a negligible value. Also, due to planarity, there is no Z-component of dipole moment. For Li-doped quasi-planar structure, the electron-rich red region has been moved to the Al1 position of the cluster, which is situated at the middle of the curved region (back view). There is a significant Zcomponent of dipole moment (+0.79 Debye), but the net dipole moment for this cluster is +0.87 Debye, which is slightly less than the planar counterpart (+3.01 Debye).
In the case of Na-doped planar cluster (at position 4) also, the region around Al1-Al2 is the most electron-rich (red), whereas electron-deficit region is located at the lower tip of the cluster, specifically on Al5 and Al13 atoms. In this case, also, the net dipole moment of the cluster is aligned along the negative y-axis . The Xcomponent of dipole moment has a negligible value. For quasi-planar structure, the electron-rich red region has shifted to the Al1 position of the cluster and slightly over Al2 and Al3 atoms of the cluster, at the middle of the curved region (back view). There is also a significant Z-component of dipole moment (+1. 17 Debye), but the net dipole moment for this cluster is +1. 27 Debye which is slightly less than the planar counterpart (+3.71 Debye).
For the K-doped cluster, like two previous clusters, the most electron-dense region appears around the region connecting Al2-Al3 atoms at the core of the cluster. Here, peripheral atom Al4 is the most electron deficit. The rest of the regions of the cluster has moderate electron density. The net dipole moment of the cluster is aligned along the symmetry line of the cluster (y-axis) and has a value of −5. 23 Debye.
For the corresponding quasi-planar cluster, the most electrondeficit region is located on the Al4 atom of the cluster. But, the back view shows that the electron-rich region has been spread over the triangular core of the cluster. The Zcomponent of dipole moment and the net dipole moment values are 2.04 Debye and 2.21 Debye, respectively.
The dipole moment of the clusters systematically increases with the atomic number of the doped alkali atoms. Like doping at position 1, in these clusters also, going from Li to Na to K doping, the dipole moment increases from 3.01 to 3.71 to 5.23 Debye and 0.87 to 1.27 to 2.21 Debye, respectively, for planar and quasi-planar clusters. So, it is also increasing with atomic number of the cluster. But in comparison with doping at position 1, series of planar clusters reveal higher dipole moments for doping at position 4, and it is less for set of quasi-planar clusters.

ESP surface for doped clusters at position 1
The ESP surface of the alkali-doped Al 13 + cluster has been depicted in Fig. S1. The dipole moment of these clusters has been provided in Table 2. In the Li-doped cluster, Li1 is the most electron-rich region (red) throughout the whole cluster, whereas electron-deficit region (indicated by blue color) are spread over the periphery of the cluster. The net dipole moment of the cluster is aligned along the symmetry axis (yaxis) of the cluster (−1.81 Debye). The X-component of the dipole moment has a negligible value. For Li-doped quasiplanar structure, there is a significant Z-component of dipole moment (−0.95 Debye), but the net dipole moment for this cluster is −1.64 Debye which is slightly less than the planar counterpart.
In the case of the Na-doped planar cluster, Na1 is the most electron-rich region (red) within the whole cluster, whereas the electron-deficit region is spread over the whole periphery of the cluster. In this case, the net dipole moment of the cluster is aligned along the negative y-axis ( The dipole moment of the clusters systematically increases with the atomic number of the dopant alkali atoms. For the quasi-planar clusters, going from Li to Na to K doping, the dipole moment increases from 1.64 to 2.40 to 3.70 Debye. This trend in the systematic increase in the dipole moment values can be understood from the fact that the higher atomic number alkali atoms are easily polarizable due to their soft nature. So, the present system is possibly a unique one where the dipole of the cluster can be tuned by doping alkali atoms of various sizes keeping the direction of the dipole fixed. Also, it is to be noted that whereas in the pure Al 13 + cluster the net dipole moment value is quite small (0.45Debye), the doping of alkali atoms can increase the polarity of the system by an order of magnitude.

Canonical molecular orbitals
A scrutiny of the nature of the molecular orbitals provides important information such as electron delocalization and molecular reactivity [28]. Delocalized electronic orbitals are directly related to the aromatic/anti-aromatic character of a system. The energy difference between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of a cluster is correlated with the reactivity of the cluster. Lower HOMO-LUMO gap clusters are expected to be more reactive. Figure 6 depicts the HOMO-LUMO orbitals and the HOMO-LUMO gap for all the clusters.
For the pure Al 13 + cluster, HOMO has substantial delocalization due to π-electrons, and LUMO has significant delocalization due to σ-electrons for the planar structure. On the other hand for the quasi-planar structure, this has π character. HOMO-LUMO gap for the planar cluster is 1.58 eV, and for the quasi-planar cluster, it is 1.37 eV. For Li-doped cluster at position 1, HOMO and LUMO both have substantially delocalization due to π-electron and σ-electron, respectively, for planar and the quasi-planar structure as well. In this case, the HOMO-LUMO energy gap is 0.53 eV and 1.25 eV, respectively, for planar and quasi-planar structures. For Na-doped Al 13 + cluster at position 1, the situation is a little bit different. Here, in both cases, HOMO has substantially delocalization due to σ-electron, but LUMO has significantly delocalization due to purely π-electrons. In this case, HOMO-LUMO gap energy is 0.38 eV and 1.23 eV, respectively, for planar and quasi-planar structures. In the case of K doping at position 1 of the Al 13 + cluster, HOMO has substantial delocalization due to π-electrons, and LUMO has significant delocalization due to σ-electrons. For quasi-planar structure, both HOMO and LUMO have σ character. In this case, the HOMO-LUMO gap is 0.83 eV and 1.33 eV, respectively, for planar and quasi-planar structures. From the HOMO-LUMO gap values, it is clear that for pure quasi-planar Al 13 + cluster, the gap is higher (1.37 eV) compared to the alkali-doped clusters, among which Na doping leads to the highest reduction in the energy gap value (1.23 eV). So, the doping of the alkali atom at the core tends to reduce the energy gap of the cluster.
In the case of doping at position 4, for Li-doped planar cluster, LUMO has substantial delocalization due to π-electron. For, the quasi-planar structure on the other hand, the LUMO has substantial π-electron delocalization. In this case, the HOMO-LUMO energy gap is 0.72 eV and 0.28 eV, respectively, for planar and quasi-planar structures. For Nadoped Al 13 + cluster at position 4, the situation is similar to that of the Li-doped cluster. Here, for planar clusters, LUMO has substantially delocalization due to π-electron, but LUMO has significantly delocalization contributed by the σ-electrons. For, quasi-planar cluster, it is the opposite. The HOMO-LUMO energy gap for Na-doped cluster is 0.63 eV and 2.02 eV, respectively, for planar and quasiplanar structures. For K-doped Al 13 + cluster, both HOMO and LUMO have substantial delocalization due to σelectrons for planar clusters. For the quasi-planar cluster, HOMO is π delocalized but LUMO has delocalization due to σ-electrons. In this case, the HOMO-LUMO gap is 0.56 eV and 1.90 eV, respectively, for planar and quasiplanar structures. From the HOMO-LUMO gap values comparing all clusters, it is clear that Na doping at position 4 leads to the highest energy gap value (2.02 eV). It is interesting to note that energy gap values are in the semiconducting region for the alkali-doped quasi-planar cluster at position 4.

Nucleus-independent chemical shift analysis
Nucleus-independent chemical shift (NICS) is the widely used magnetic criterion of aromaticity [29]. A high negative value of NICS indicates the aromatic character of a ring, a high positive value of NICS indicates anti-aromatic character, whereas a small value of NICS indicates the non-aromatic nature of a ring. NICS(0) is the value of NICS computed at the ring plane at z = 0 Å height at the centroid of a ring.
The cluster with pure and alkali doped at the 4th position of the periphery has been depicted in Fig. 7. The symmetryrelated triangles located on the right-hand part of the clusters have the same NICS(0) values as that of the left-hand part. As can be seen from Fig. 7, at the center of R1, the NICS(0) values for the planar Li-, Na-, and K-doped clusters are respectively +41.11 ppm, +19.60 ppm, and + 13.65 ppm indicating a strong anti-aromatic at the core of the planar clusters. For planar-doped clusters, the rings near alkali atoms (R2) have substantial anti-aromatic nature (for Li doping +39.84 ppm, for Na doping +25.90 ppm, and for K doping +18.41 ppm). On the other hand, in the case of quasi-planar clusters, the NICS(0) values at the center of ring R1 are respectively −25.45 ppm, −25.15 ppm, and − 25.48 ppm for the Li-, Na-, and K-doped clusters. Rings at the upper left (R5, R6, R7, R8) and upper right corners (R5*, R6*, R7*, R8*) of the pure planar and quasi-planar Al 13 + clusters are having quite a high negative NICS(0) values at the center of these rings. Among these, ring R6 has the highest negative NICS(0) value. For planar Al 13 + , this value is −18.03 ppm, and for the quasi-planar, it is −18.02 ppm. For the doped planar clusters, the highest negative NICS(0) occurs also at the center of ring R6 for Li-and Na-doped clusters (−32.82 ppm and − 20.24 ppm, respectively) and R5 for K-doped cluster (−25.29 ppm). For quasi-planar it is found at R6, for Lidoped cluster, this value is −28.91 ppm, for the Na-doped cluster −29.43 ppm, and for the K-doped cluster, the value is −10.74 ppm. In summary, the effect of alkali atom doping is to reduce the aromaticity compared to the parent cluster. Fig S2 depicts the NICS(0) values computed at the centroid of each of these triangles of the alkali-doped clusters at position 1. As each structure has bilateral symmetry, the symmetry-related triangles located on the right-hand part of the clusters have the same NICS(0) values as that of the left-hand part. As can be seen from  anti-aromatic at the core of the planar clusters. On the other hand, in the case of quasi-planar clusters, the NICS(0) values at the center of ring R1 are respectively 2.81 ppm, −1.44 ppm, and 2.22 ppm for the Li-, Na-, and K-doped clusters. This data reveals that doping of alkali metal induces anti-aromatic character of the central ring which relaxes to corresponding quasi-planar cluster by shedding anti-aromaticity. Rings at the upper left (R5, R6, R7, R8) and upper right corners (R5*, R6*, R7*, R8*) of the pure planar and quasi-planar Al 13 + clusters are having quite a high negative NICS(0) values at the center of these rings. Among these, ring R6 has the highest negative NICS(0) value. For planar Al 13 + this value is −18.03 ppm and for the quasiplanar, it is −18.02 ppm. For the doped quasi-planar clusters on the other hand, the highest negative NICS(0) occurs at the center of ring R7. For the Li-doped cluster, this value is −11.50 ppm, for the Na-doped cluster −9.88 ppm, and for the K-doped cluster, the value is −10.74 ppm. So even in the doped clusters, the top portion of the cluster retains substantial aromaticity. In summary, the effect of alkali atom doping is to reduce the aromaticity compared to the parent cluster.

Electron localization function analysis
Electron localization function (ELF) is a dimensionless quantity, and its value varies between zero and one [30]. The closer the value of ELF is to one, the lower is the probability of an electron of a particular spin to be present near another electron of the same spin at an arbitrary position r. A lower value of ELF indicates a higher level of electron localization, and a higher value indicates electron delocalization. Analysis of electron localization function provides clues to the presence or absence of aromaticity in a chemical system. Continuity of the ELF iso-surface at least at an iso-value of 0.70 is assumed to be the acceptability criterion for the existence of aromaticity in a chemical system. As one increases the iso-value from 0.70 toward 1.00, at a certain iso-value, the continuity of ELF isosurface appears to break, and these are known as the bifurcation points. The higher is the iso-value at which the bifurcation occurs in a chemical system, the higher is the electron delocalization and also the aromatic nature of the system.
The results of ELF analysis for the alkali-doped quasiplanar clusters (at position 4) have been depicted in Fig. 8. At an iso-value of 0.70, the electron delocalization is more prominent in the case of K-doped cluster compared to the Li-and Na-doped clusters (Fig. 8). It can be seen that at this iso-value, the parent cluster shows two bifurcations at the middle of the cluster on the periphery, but the doped clusters show an additional bifurcation at the top edge of the cluster. In this sense, the doped clusters are less aromatic compared to the parent cluster. At an iso-value of 0.75, in the case of the Li-, Na-, and K-doped clusters, these bifurcations are complete, and three delocalized regions at the lower end of the periphery, upper left, and upper right corner of the clusters are seen. The central delocalization is very small, and it is also separated from the peripheral delocalization. At 0.80 isovalue, bifurcation at the core region of the Na-doped cluster is completely removed which is same for other two clusters. Peripheral bifurcations are almost the same for the doped clusters. At an iso-value of 0.85, three distinct peripheral islands become thinner for the Li-, Na-, and K-doped clusters. At an iso-value of 0.90, no continuity of the iso-surfaces is left over the periphery for any of these clusters. This study indicates that alkali atoms reduce aromaticity of the cluster which also correlates with the NICS results.
The study of the electron localization function (ELF) and its bifurcation points for the quasi-planarAl 13 + clusters has been compared with the alkali-doped clusters at position 1 in Fig. S3. The total electron localization functions of the quasi-planarAl 13 + cluster show that at an iso-value of 0.70, the ELF surface consists of two distinct islands spread over the periphery of the cluster. There is also a visible delocalization over the triangular core of the cluster. In the case of alkali-doped clusters, the continuity of iso-surface is spread over the aluminum atoms, and the alkali atoms are separately enclosed by a distinct spherical iso-surface. The electron delocalization, in this case, has a total continuity over the whole periphery traced through the Al atoms excluding the alkali atoms at the lower tip of the cluster. It is to be noted that there is also an electron delocalization over the triangular core of the doped clusters which is in "Y" shape, and this connects the core region to the peripheral delocalized iso-surface. In the case of the Li-doped cluster at an iso-value of 0.70, this core delocalization ("Y") is slightly more elongated compared to the Na-and K-doped clusters. At an iso-value of 0.75, the parent Al 13 + cluster has three distinct islands over the periphery, and the delocalization over the core of the cluster is detached from the periphery. At this iso-value, in the case of the Li-doped cluster, there is a bifurcation at the lower end of the periphery, and the central delocalization is also separated from the peripheral delocalization. In the case of Na-and K-doped clusters though the peripheral delocalization is maintained even at this iso-value, the core delocalization just gets detached from the peripheral delocalization. In the case of the K-doped cluster, the peripheral delocalization is more dominant compared to the Nadoped cluster. At an iso-value of 0.80, the parent Al 13 + cluster still retains the three distinct delocalized regions at the upper left, upper right, and the lower tip of the cluster with a reduced spread of the iso-surface. But at 0.80 iso-value for the Lidoped cluster, there is complete detachment of the isosurface through peripheral bifurcations at the top left and top right corner of the cluster, which appears to be setting in for Na-and K-doped clusters. At an iso-value of 0.85, there are six distinct separated iso-surfaces over the periphery for the Li-doped cluster, but four distinct iso-surfaces in the case of Na-and K-doped clusters. At an iso-value of 0.90, there is no continuity of the iso-surfaces left over the periphery for any of the clusters. This study indicates that alkali atoms do not cooperate with Al atoms in electron delocalization. Aluminum atoms over the periphery and the triangular core have distinct delocalization. The peripheral delocalization appears to be stronger compared to that at the core. In the presence of alkali atoms, the peripheral delocalization among the nine aluminum atoms becomes stronger compared to the ten aluminum atoms of the parent Al 13 + cluster. The alkali atoms though are not directly part of these delocalized iso-surfaces surely influence the cooperativity among the aluminum atoms themselves, and the strength of influence increased in the sequence Li, Na, and K. Alkali atoms thus act as foreign attackers which catalyze the cooperativity among the aluminum atoms themselves.

Conclusions
In summary, we have explored in detail the effect of doping alkali atoms Li, Na, and K at position 1 and position 4 of both planar and quasi-planar minimum energy Al 13 + clusters. Doping at position 4 leads to the lowest energy doped isomers which have a bowl shape, and the alkali atoms are located on the concave side on top of the central triangular core. There are quite a few interesting findings regarding alkali-doped clusters. First of all, even in the presence of doped alkali atoms, the clusters retain bilateral symmetry. So, the bilateral symmetry is a robust feature of the Al 13 + and its alkali-doped counterparts. The second interesting observation is that the polarity of the clusters increases substantially (nearly ten times) compared to the pure Al 13 + cluster when alkali atoms of a higher atomic number are doped. In all cases, the dipole moment is directed along the symmetry axis of the cluster. The third interesting observation is that the alkali atoms prefer the peripheral positions instead of the central position which facilitates energy minimization. So, aluminum atoms try to remain together through homo-philicity, and dopant atoms are favored outside the cluster in such a way that the cluster tends to maintain the inherent bilateral symmetry. The HOMO-LUMO energy gap tends to reduce in the presence of alkali atoms, which all fall in the semiconducting region. NICS(0)results show that alkali doping tends to reduce the aromatic character of the cluster compared to the undoped parent cluster. ELF study indicates that electron delocalization and cooperativity among the aluminum atoms are reduced in the presence of alkali atoms in the sequence Li, Na, and K. Finally, metal nano-clusters, which have found many potential technological applications, are attracting the attention of the scientific community due to their tunability both by controlling shape and size. The present study has revealed that the polarity of the HOMO-LUMO energy gap of planar and quasi-planar Al 13 + clusters are tunable through doping alkali atoms which should find an application of this cluster in the field of nano-electronics.