Structure, stability, absorption spectra and aromaticity of the singly and doubly silicon doped aluminum clusters AlnSim0/+ with n = 3–16 and m = 1, 2

Structures of the binary AlnSim clusters in both neutral and cationic states were investigated using DFT and TD-DFT (B3LYP/6-311+G(d)) and (U)CCSD(T)/cc-pvTZ calculations. Silicon-doped aluminum clusters are characterized by low spin ground states. For small sizes, the Si dopant prefers to be located at vertices having many edges. For larger sizes, the Si atom prefers to be endohedrally doped inside an Aln cage. Relative stability, adiabatic ionization energy and dissociation energies of each cluster size were evaluated. A characteristic of most Si doped Al clusters is the energetic degeneracy of two lowest-lying isomers. Calculated results confirm the high stability of the sizes Al4Si2, Al12Si and Al11Si2+ as “magic” clusters, that exhibit 20 or 40 shell electrons and are thermodynamically more stable as compared to their neighbors. Electronic absorption spectra of isoelectronic magic clusters Al13−, Al12Si, and Al11Si2+ that have two pronounced bands corresponding to blue and violet lights, have been rationalized by using the electron shell model. The magnetically included ring current density (MICD) analyses suggest that they are also aromatic structures as a result of the “magic” 40 shell electrons.


A brief description of Jellium model
The jellium model has successfully been developed for the theoretical modelling of clusters for decades [1,2,3].The jellium model considers a cluster of atoms as a superatom, where the cores of constituent atoms form a constant positive background, the so called "jellium density", and only valence electrons are treated explicitly.Under the model, the shell molecular orbitals of the clusters are denoted as 1S, 1P, 1D, 2S, 2P, 1F, … (usually the notation 1s, 1p, 1d, 2s, 2p, 1f, … have also been used), rather than as the atomic orbitals 1s, 2s, 2p, 3s, 3p, 3d, … of hydrogen-like atoms. [4]

A brief description of magic clusters
Magic clusters are clusters having all the energy levels are filled, or clusters having a certain number of atoms that are more stable than others.For instance, magic clusters are characterized by large ionization potentials that drop abruptly as one increase/decrease the cluster sizes by the addition/removal of an atom [5].
Substitution of one of Al atoms on the surface of an icosahedron by the second Si atom not only induces a stronger attraction with electron along the Si-Si axis, but also lowering the symmetry of the Al 11 Si 2 + cluster as compared to the two other clusters.This constitutes a reason for not only the splitting of the 1F levels, but also for the 1P, 1D and 2P levels.Concretely, the P shell orbitals (1P and 2P) break into two different sub-levels, namely, the P shell along the Si-Si line is located at lower energy, and the two other P shell orbitals at higher position levels.
If we now set the Si-Si axis to be the z-axis, then we could see that the 1D shell orbitals split into three levels, namely the 1D whose shape is similar to the 3d z 2 atomic orbital located even lower in energy than the 2S.The two other 1D levels whose shapes are similar to those of the 3d(xz) and 3d(yz) orbitals come next, and then the two other 1D whose shapes can be compared to those of the 3d (x 2 -y 2 ) and 3d xy AOs.This is represented in Figure 5c of the MO diagram of the Al 11 Si 2 + cluster.
The splitting of 1F shell orbitals could be described as follows: those that are composed mainly of s(Al) AOs and those having lobes along the Si-Si axis, are energetically located below, and those having lobes farther away from the axes are located above.

Figure S1 . 12 Figure S2 .
Figure S1.Shapes, electronic states and relative energies (∆E, eV) of the lower-lying isomers Al n Si with n = 3 -16 at the neutral and cationic states.∆E values are obtained from (U)CCSD(T)/cc-pVTZ + ZPE computations.

8.Figure S5 .Figure S5 .
Figure S5.Profiles of current density for Al 13 -and Al 12 Si at the planes located above and below the center atoms by a) ± 2 Bohr; b) ± 4 Bohr; and c) ± 6 Bohr.Red to blue arrows represents weak to strong current density with the range: 0 to 0.0006 a.u.

Table S1 .
Absorption energy (eV), absorption wave length (nm), oscillator strength and major contributions corresponding to the absorption peaks A and B of the most stable isomers displayed in Figure6.

B Figure S4. MO diagram of Al 11 Si 2 + cationic cluster, isomer C.11.2.B 4. Occupation numbers and energies of the shell MOs of the investigated clustersTable S2 .
Occupation numbers and energies of shell MOs of the Al 13 -anionic cluster (

Table S3 .
Occupation numbers and energies of shell MOs of the Al 12 Si neutral cluster: isomer

Table S4 .
Occupation numbers and energies of shell MOs of the Al 11 Si 2 + cationic cluster -isomer