A set of three planer as well as quasi-planar Al13+ clusters with interesting metallo-aromatic properties have been recently reported by our group. 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. 1(a)). Also, these clusters have a unique commonality – all of these possess a bilateral symmetry with respect to a symmetry line that passes through the middle of the cluster bisecting the central triangular core with one of the Al atoms situated on this symmetry line. Besides bonding to two other atoms at the core, this particular Al atom also establishes bonding with three other Al atoms on the periphery of the cluster which is also crucial for the stability of the cluster. The present study aims to understand the effect of doping alkali atoms Li, Na and K right at the position of this crucial point of stability replacing the central Al(1) atom. 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 Al13+ 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 quasi-planar puckered structures.
Optimized geometries of alkali atom (Li, Na and K) doped Al13+ clusters have been depicted in Fig. 1. It is to be noted that, previously reported planar and quasi-planar Al13+ clusters possess a bilateral symmetry (Fig. 1a). The doping of alkali atoms at the position of Al(1) does not destroy this bilateral symmetry; rather, the alkali atoms occupy their positions on this symmetry line. In 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 1(b), Fig 1(c), Fig 1(d)).
In case of Li doping, lower part of the cluster is affected most, the upper portion remains nearly undistorted. Two rhombic grids at the middle of the planar Al13+ clusters are diagonally joined by the effect of the Li atom at position 1 which establish two shorter bonds Li(1)-Al(6) = 2.929 Å and Li(1)-Al(12) = 2.929 Å as compared to 2.736 Å between Al(1)-Al(3) and Al(1)-Al(2) in the undoped planar Al13+ cluster. Atoms Al(13) and Al(5) go away from the position of atom 1 which give rise to two approximate rectangular grids at the lower half of the cluster. The Li(1) – Al(4) distance is 2.665 Å which is smaller compared to Al(1) -Al(4) distance (2.714 Å).
On the other hand, the central triangle is also reformed maintaining its symmetry with Li(1)-Al(2) = 2.643 Å and Li(1)-Al(3) =2.643 Å as compared to 2.736 Å between Al(1)-Al(3) and Al(1)-Al(2) in the undoped planar Al13+ cluster. Even this effect of doping of lighter atom at position 1 also reduces bond distance among Al(2)-Al(3) {2.567 Å from 2.736 Å}. A pair of square at the bottom surface of the cluster has been formed due to doping. But geometry of top region of the cluster remains same. Maximum horizontal and vertical dimension ratio in this case is 7.930 Å: 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 1(b). It is interesting to note that, now the Li atom has swapped its position with Al(4) which was at the periphery of the pure Al13+ clusters. This effect is a generic feature and is observed in case of Na and K doping as well (Fig 1(c) and Fig 1(d)). Alkali atoms prefer to occupy the peripheral position compared to a bulk one. A comparison of the Li doped true minimum structure with the corresponding quasi-planar Al13+ 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 quasi-planar Al13+cluster. In this puckered configuration the cluster assumes a flying bird like shape with two symmetry related edges (formed by Al(5), Al(6), Al(7) and their symmetry related Al(13), Al(12) and Al(11)) analogous to two wings, Li(1) which is placed slightly downwards of the mean plane forms the tail and three aluminium aotms (Al(8), Al(9) and Al(10)) 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 have been provided in table 1and table 2 respectively.
In case of Na doped Al13+ cluster, doping of Na atom at position 1 enlarges the bond distance among Na(1)-Al(2)/Al(3) { 2.953 Å from 2.736 Å }.This effect of doping also enhances the bond distance among Al(2)-Al(3) {2.857 Å from 2.736 Å}. Due to presence of Na atom at position 1, Al(4) is displaced more downward and knocked out from the bond connected by Na(1), Al(5) and Al(13). The bilateral symmetry along y-axis remains intact even in the presence of Na. 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, Na(1) and Al(4) swap their locations along the symmetry line. Also Na(1) atom is located 2.46Å downward of the mean plane passing through the central Al3 triangular core. Aluminium atoms Al(5), Al(6) and Al(7) on the left edge, as well as their symmetry related counterparts Al(13), Al(12) and Al(11) moves 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 aluminium atoms Al(8), Al(9) and Al(10) forming the head portion of the cluster. Al(9) is placed slightly upward (0.43 Å) of the mean plane passing through the central triangular core.
In case of K doping also, both the planar and the quasi-planar clusters have the analogous topologies like those of the Na doped cluster. In case of the planar cluster K(1)-Al(4) distance is relatively longer compared to Li and Na doped clusters. Bond distances K(1)-Al(2)/Al(3) (3.116 Å ) is much longer than the corresponding distance of parent Al13+ cluster (2.736 Å). This effect of doping slightly increases the bond distance among Al(2)-Al(3) {2.927 Å from 2.736 Å}also. Maximum horizontal and vertical dimension of the cluster in this case is 8.159 Å: 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 Na doped 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 K doped clusters posses 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 downwards 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, y-axis passing thorough 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 figure 2(b) it can be seen that the distance of the alkali atoms from the origin (position of Al4) increases in accordance with the increasing atomic number of the alkali atoms. K is displaced downward highest (2.62Å) from the mean plane, Na has an intermediate downward displacement (2.46Å) and Li has the least (2.35Å) 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 figure 2, the central triangular core for all three clusters is almost identical. From figure 2(b) it is also evident that the upper part of the clusters (consisting of peripheral Al6, Al7, Al8, Al9, Al10, Al11and Al12) deviate 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 Li-doped 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 2a). For all three clusters, the upward deviation for Al7 and symmetry related Al11 are practically the same.
Table 1: Geometrical parameter of the quasi-planar Li, Na and K doping Al13+ clusters
|
Li doping
|
Na doping
|
K doping
|
|
Bond distances (Å)
|
Bonds
|
Inner triangular core
|
Inner triangular core
|
Inner triangular core
|
4-2
|
2.653
|
2.657
|
2.666
|
4-3
|
2.653
|
2.657
|
2.666
|
2-3
|
2.670
|
2.763
|
2.749
|
|
Core-periphery
|
Core-periphery
|
Core-periphery
|
2-7
|
2.865
|
2.866
|
2.897
|
2-8
|
2.937
|
2.907
|
2.903
|
2-6
|
2.712
|
2.730
|
2.725
|
2-9
|
2.718
|
2.717
|
2.714
|
3-10
|
2.937
|
2.906
|
2.902
|
3-11
|
2.865
|
2.886
|
2.897
|
3-9
|
2.718
|
2.717
|
2.714
|
3-12
|
2.712
|
2.730
|
2.726
|
4-5
|
2.604
|
2.611
|
2.594
|
4-13
|
2.604
|
2.611
|
2.594
|
4-1
|
2.683
|
3.015
|
3.495
|
|
Intra periphery
|
Intra periphery
|
Intra periphery
|
1-5
|
2.900
|
3.310
|
3.793
|
13-1
|
2.900
|
3.310
|
3.793
|
5-6
|
2.495
|
2.502
|
2.508
|
13-12
|
2.495
|
2.502
|
2.508
|
6-7
|
2.615
|
2.605
|
2.601
|
12-11
|
2.615
|
2.605
|
2.601
|
7-8
|
2.502
|
2.524
|
2.523
|
11-10
|
2.524
|
2.524
|
2.523
|
8-9
|
2.622
|
2.622
|
2.621
|
10-9
|
2.622
|
2.622
|
2.621
|
|
Core bond angles(˚)
|
|
2-4-3
|
58.12
|
62.68
|
62.07
|
4-2-3
|
60.94
|
58.66
|
58.96
|
2-3-4
|
60.94
|
58.66
|
58.96
|
Table 2: Dihedral angles of quasi-planar Li, Na and K doping Al13+ clusters, for planar clusters corresponding dihedral angles are 180° each.
Dihedral angle between
|
Value of dihedral angle
|
Li doping
|
Na doping
|
K doping
|
R1-R8
|
48.13°
|
42.04°
|
36.79°
|
R1-R3
|
26.99°
|
21.56°
|
17.35°
|
R2-R2*
|
16.97°
|
15.94°
|
14.44°
|
R2-R3
|
46.55°
|
42.95°
|
39.32°
|
R3-R4
|
74.71°
|
73.91°
|
71.13°
|
R4-R5
|
7.69°
|
12.46
|
15.05°
|
R5-R6
|
30.19°
|
29.73°
|
29.21°
|
R6-R7
|
92.28°
|
92.75°
|
92.42°
|
R7-R8
|
34.02°
|
32.76°
|
32.42°
|
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 which is the (92.28°, 92.75° and 92.42° for Li, Na and K doped clusters) highest and 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.
Table 3: Dipole moments of clusters
Cluster
|
Planar/
Quasiplanar
|
Dipole Moments in Debye
|
µx
|
µy
|
µz
|
|µ|
|
Pure Al
|
Planar
|
-0.0000018
|
-0.3812093
|
0.000000
|
0.38
|
True minima
|
0.0000584
|
-0.4487331
|
0.0974657
|
0.45
|
Li doped
|
Planar
|
0.0002488
|
-1.807476
|
0.000000
|
1.81
|
True minima
|
0.0024805
|
-1.3447913
|
-0.9533147
|
1.64
|
Na doped
|
Planar
|
0.0003463
|
-2.4938611
|
0.000000
|
2.49
|
|
True minima
|
0.0037028
|
-1.9788788
|
-1.3849868
|
2.40
|
K doped
|
Planar
|
0.0004881
|
-1.6697678
|
0.000000
|
1.67
|
|
True minima
|
0.0054952
|
-3.0122418
|
-2.1733071
|
3.70
|
ESP surface of alkali doped Al13+ cluster has been depicted in Fig. 3. Dipole moment [25] of these clusters has been provided in table 3. In the Li doped cluster, Li(1) is the most electron rich region (red) throughout the whole cluster, whereas electron deficit regions (indicated by blue color) is spread over the periphery of the cluster. The net dipole moment of the cluster is aligned along symmetry axis (y-axis) of the cluster (-1.81 Debye). The x-component of the dipole moment has a negligible value. For Li doped qusi-planar structure, there is 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 case of Na doped planar cluster, Na(1) is the most electron rich region (red) within the whole cluster, whereas 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 negative y-axis (along symmetry line) of the cluster (-2.49 Debye). The x and z component of dipole moments have negligible values. For Na doped quasi-planar cluster the z-component of dipole moment and the total dipole moment values are respectively 1.38 Deby and 2.40 Debye.
For the K doped cluster, the most electron concentration occur around the K(1) atom the centre of the cluster. Upper left (comprising of Al(7) and Al(8) ) and upper right (comprising of Al(10) and Al(11)) corners of the cluster are the electron deficit regions. Rest of the other region of the cluster has intermediate electron density. Net dipole moment of the cluster is aligned along the symmetry line of the cluster (y-axis) and has a value -1.67 Debye. For the corresponding quasi-planar cluster the z-component of dipole moment and the net dipole moment values are respectively 2.71Deby and 3.70 Debye respectively.
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 Debye to 2.40 Debye to 3.70 Debye. This trend in the systematic increase in the dipolemoment vlaues can be understood from the fact theat he 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 atom of various sizes keeping the direction of the dipole fixed. Also it is to be noted that whereas in the pure Al13+ cluster the net dipole moment value is quite small (0.45 Deby), 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 [26]. Delocalized electronic orbitals are directly related to the aromatic/anti-aromatic character of a system. Energy difference between 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 in nature. Fig 4 depicts the HOMO-LUMO orbitals and the HOMO-LUMO gap for all the clusters.
For pure Al13+ cluster, HOMO has substantially delocalization due to π-electrons and LUMO has significantly delocalization due to purely σ-electrons for planar structure and for quasi-planar structure it is π character. HOMO-LUMO gap for the planar cluster is 1.583 eV and for the quasi-planar cluster, it is 1.373 eV. For Li doped cluster, 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 0.536 eV and 1.251 eV respectively for planar and quasi-planar structures. For Na doped Al13+ cluster, 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 0.386 eV and 1.231 eV respectively for planar and quasi-planar structures. For K doped Al13+ cluster, HOMO has substantially delocalization due to π-electrons and LUMO has significantly delocalization due to purely σ-electrons. For quasi-planar structure both are σ characters. In this case, the HOMO-LUMO gap is 0.83 eV and 1.331 eV respectively for planar and quasi-planar structures.
From the HOMO-LUMO gap values it is clear that for pure quasi-planar Al13+ cluster the gap is higher (1.373 eV) compared to the alkali doped clusters, among which Na doping leads to the highest reduction in the energy gap value (to 1.231 eV). So, the doping of alkali atom at the core, tend to reduce the energy gap of the cluster. It is interesting to note that energy gap values are in the semiconducting region which is tunable through the doping by alkali atoms.
Nucleus Independent Chemical Shift (NICS) analysis:
Nucleus independent chemical shift (NICS) is the widely used magnetic criterion of aromaticity [27]. 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 = 0Å height at the centroid of a ring.
As shown in Fig 5, each cluster consists of fourteen triangular sub-regions. NICS(0) values have been computed at the centroid of each of these triangles. 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 Fig 5, at the centre of the planar and quasi-planar pure Al13+ clusters the NICS(0) values are respectively -5.82 ppm and -4.40 ppm. Corresponding NICS(0) values for the planar Li, Na and K doped clusters are respectively +18.57ppm, +25.73ppm and +38.97ppm indicating a strong 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 centre of ring R1 are respectively 2.81ppm, -1.44ppm and 2.22ppm 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 Al13+ clusters are having quite a high negative NICS(0) values at the centre of these rings. Among these, ring R6 has the highest negative NICS(0) value. For planar Al13+ this value is -18.03ppm and for the quasi-planar, it is -18.02 ppm. For the doped quasi-planar clusters on the other hand the highest negative NICS(0) occur at the centre of ring R7. For the Li doped cluster, this value is -11.50ppm, for the Na doped cluster -9.88ppm and for the K doped cluster, the value is -10.74ppm. 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 with respect to the parent cluster.
Electron Localization Function (ELF) analysis:
Electron localization function (ELF) is a dimensionless quantity and its value varies between zero and one [28]. 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 towards 1.00, at a certain iso-value the continuity of ELF iso-surface 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 study of the electron localization function (ELF) and its bifurcation points for the quasiplanar Al13+ clusters have been compared with the alkali doped clusters in Fig. 6. The total electron localization function of the quasi-planar Al13+ cluster shows 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 aluminium 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 Al13+ 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 Na doped cluster. At an iso-value of 0.80, the parent Al13+ 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 Li doped cluster, there is complete detachment of the iso-surface 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. Aluminium 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 aluminium atoms become stronger compared to the ten aluminium atoms of the parent Al13+ cluster. The alkali atoms though are not directly part of this delocalized iso-surfaces, surely influence the cooperativity among the aluminum atoms themselves, the strength of influence increasing in the sequence Li, Na and K. Alkali atoms thus act as foreign attackers which and catalyzes the cooperativity among the aluminium atoms themselves.