Analysis of MAl 12 clusters, M = B, C, Si, and P

Our investigation starts with the structural analysis of bare Al 13 0/− and doped MAl 12 (M = B, C, Si, and P) clusters. Figure 1 shows the optimized ground state structures of the clusters along with selected Al–Al bond lengths. All the geometries were optimized without any symmetry constraint. We have considered only endohedral doped Al icosahedral clusters since previous theoretical studies have reported that the endohedral doping is energetically more favorable than the exohedral doping30,31. The Al 13 and BAl 12 both have 39 valence electrons with electronic configuration of 1S21P61D102S21F142 P5. Since the icosahedral clusters have a degenerate 2P state that is partially filled, the clusters undergo a Jahn–Teller distortion from the symmetric shape as seen from a variation in the bond lengths. For example, the Al s –Al s bond lengths in Al 13 vary from 2.76 to 2.96 Å while it varies from 2.65 to 2.73 Å in BAl 12 . Here subscript s stands for the Al atoms on the surface. For BAl 12 , one expects a contraction in Al s –Al s distances as well as in the average bond length from the central site to Al s sites due to the smaller radius of a B atom. The average bond length from central site to Al s sites in Al 13 indeed decreases from 2.69 to 2.56 Å in BAl 12 . To achieve closed electronic shell of 40 e−(1S21P61D102S21F142P6), the central Al site was replaced with a C or a Si atom both of which contribute 4 valence e−’s. The closed electronic shell stabilizes the symmetrical icosahedral structure of CAl 12 and SiAl 12 as revealed by their Al s -Al s bond lengths (2.68 and 2.79 Å) shown in Fig. 1. The bond lengths in CAl 12 and SiAl 12 cages are slightly smaller than in iso-electronic Al 13 − due to the charged state. In order to create an analog of an alkali atom, the central Al atom was then replaced by a P atom that results in a valence pool of 41 e−’s. Since the extra electron is in a degenerate state of the symmetric cluster, a Jahn–Teller distortion with different surface bonds (Al s –Al s = 2.73–2.80 Å) is observed.

Fig. 1 Ground state structures of Al 13 0/− and MAl 12 (M = B, C, Si, and P) clusters. The Al–Al bond lengths are also shown and given in Å Full size image

Here, we are primarily interested in assessing the effect of shell filling on the electronic properties. Therefore, the adiabatic ionization energies (AIEs) of Al 13 and MAl 12 (M = B, C, Si, and P) were calculated by taking the energy difference between the ground state of the neutral and cationic species. The AIE values are plotted in Fig. 2 and given in Supplementary Table 1. It is interesting that the clusters with same valence electron count (despite a different composition) have comparable AIEs. The CAl 12 and SiAl 12 due to the electronic shell closure are marked by their high AIE of 6.63 and 6.73 eV respectively while Al 13 has a AIE of 6.13 eV slightly less than that of BAl 12 (6.64 eV) as Al 13 + is stabilized in the oblate structure than the icosahedral structure. Note that AIEs show only a small increment as one passes from 39 e− (Al 13 and BAl 12 ) to 40 e− systems (CAl 12 and SiAl 12 ) because of the same 2 P outer valence electronic shell, then a reduction of 1.5 eV in the AIE is observed as one approaches to 41 e− system (PAl 12 ). This sharp drop in the AIE represents the shell effect similar to atoms. The effect is, however, sizable only for one electron past the closed electronic shell.

Fig. 2 Electronic properties of ligand-free Al and doped Al clusters. Adiabatic ionization energies of bare Al 13 , MAl 12 (M = B, C, Si, and P) clusters. All the values are given in eV Full size image

Analysis of ligated clusters

At this point, we wanted to investigate if it is possible to go beyond the shell effect namely, is it possible to create alkali-like species without changing the valence count? More importantly, can one form super donors that can donate multiple electrons without substantial increase in the successive ionization energy? We will now show that this can be accomplished by attaching ligands that form charge transfer complexes. An EP ligand with donor characteristics looked promising. To explore this exciting possibility, we first examined the ground state structures of the Al 13 (EP) n and MAl 12 (EP) n (n = 1–3) clusters. Various positions of the ligands were tried to find the ground state structures. Figure 3 shows the ground state structures of the ligated clusters. While the 1st EP ligand binds to top Al site of the metallic core, 2nd EP ligand always prefers the meta position rather than an ortho or para position in the ground state. We find that the para position is destabilized by the ligand inducing an electron donor site on the opposite side of the clusters with closed electronic shells such as CAl 12 and SiAl 12 13. For the case of open shell Al 13 , and BAl 12 , the para position is only slightly less stable because the induced active site is half-filled. The ortho position is close in energy to the meta position in all cases, but is destabilized due to steric interactions. The ortho, meta, and para positions relative to 1st ligand are shown in Supplementary Fig. 1. In Al 13 (EP) 3 , SiAl 12 (EP) 3 , and PAl 12 (EP) 3 , the 3rd ligand stabilized in an ortho position, while it is the meta position for BAl 12 (EP) 3 and CAl 12 (EP) 3 . Total energies of the optimized structures with various positioning of the ligands are given in Supplementary Figs. 1–3. As expected, the successive attachment of ligands induces the distortion in the symmetric CAl 12 and SiA1 12 clusters, for instance, Al s –Al s bond length varies from 2.68 to 2.80 Å in CAl 12 (EP) n (n = 1–3). Similar variation in Al s –Al s bond length is observed for other ligated MAl 12 clusters. Interestingly, the average bond length from the central site to Al s site is nearly unchanged during ligation indicating that the bonding characteristics within the clusters were largely unperturbed. Knowing the donor characteristic of an EP ligand, we determined the gross charge on the metallic core in the ground states via Mulliken population analysis. We have given the calculated values in Supplementary Table 2. Figure 4a shows the charge accumulated ΔQ n−(n−1) (relative to corresponding precursors) on the metallic core during successive ligation. The BAl 12 and Al 13 core gain 0.40 and 0.39 e−respectively from the 1st EP ligand while it is 0.38 and 0.36 e−for CAl 12 and SiAl 12 , respectively. On the other hand, charge transfer from 1st ligand to PAl 12 is found to be 0.35 e−. One can see that ΔQ n−(n−1) does not decrease with increasing number of ligands. In fact, 3rd EP ligand donates more charges than the 2nd EP ligand as shown in Fig. 4a. However, nearly equal amount of charge on the metallic core with a given number of ligand implies the non-sensitivity of charge transfer to the electronic character of the bare clusters. Since EP ligands donate the charge to core, it will be interesting to see how strongly the ligands are bound to the cluster. We therefore calculated the successive ligand-binding energy using Eq (1).

$${\mathrm{BE = E}}\left( {{\mathrm{MAl}}_{{\mathrm{12}}}\left( {{\mathrm{EP}}} \right)_{{{n - 1}}}} \right) + {\mathrm{E}}\left( {{\mathrm{EP}}} \right) - {\mathrm{E}}\left( {{\mathrm{MAl}}_{{\mathrm{12}}}\left( {{\mathrm{EP}}} \right)_{{n}}} \right){\mathrm{,}}$$ (1)

where n = 1–3 and M = Al, B, C, Si and P. Here E presents the total energy of the system. Figure 4b shows the variation in the calculated BE, while the numerical values are given in Supplementary Table 3. The BE is found to decrease with increasing number of ligands due to charge accumulation on the precursors, though the 1st EP ligand binds more strongly to Al 13 and BAl 12 than others. This is because of their electron deficiency to complete the electronic shell. The BE of 2nd EP ligand turns out to be around 0.7 eV irrespective of the clusters consistent with the amount of the gross charge on the metallic core. Similar results are obtained with 3rd EP ligand.

Although the BE of ligands turns out to be small, we find that the ligation dramatically influences the electronic properties. To demonstrate this, the variation in the AIEs of ligated Al clusters are shown in Fig. 5a. The AIEs in all the cases continuously decline with the successive addition of EP ligand, for instance, 1st EP ligands drop the AIE of CAl 12 by 1.06 eV while it is 2.47 eV with 3 EP ligands. Similarly, Al 13 (EP) 3 turns out to have AIE of 3.51 eV smaller than that of Al 13 . All the values of AIEs are given in Supplementary Table 1. The identical trend in the AIEs indicate the emergence of alkali-like character, though the underlying cause of this captivating phenomena is not clear. What is even more intriguing is that not only the decrease in the AIEs systematically increases with the number of ligands but also that the magnitude turns out to be almost identical irrespective of the initial clusters. At first, one might guess that even though ligands do not attached to clusters very strongly, yet ligands alter the effective valence electron count. However, this hypothesis turns out to be incorrect. According to this hypothesis, the AIE of Al 13 should increase since the charge donation of around 0.90e− in Al 13 (EP) 3 would make it closer to have a filled shell. However, AIE of Al 13 gets reduced to 3.51 eV from 6.13 eV as shown in Fig. 5a. This interesting scenario is even more puzzling if one looks at the multiple ionization energies of the CAl 12 and Al 13 clusters. Figure 5b compares the 1st and 2nd AIE of the CAl 12 and CAl 12 (EP) 3 clusters. The 2nd AIE of CAl 12 and CAl 12 (EP) 3 are found to be 9.97 and 6.84 eV, respectively. Note that the 2nd AIE is reduced by 3.13 eV more than (2.62 eV) the 1st AIE. Moreover, the 2nd AIE of CAl 12 (EP) 3 is less than the 1st ionization energy of most non-alkali atoms. On the other hand, 2nd AIE of Al 13 (EP) 3 is found to be 7.21 eV compared to the corresponding value of 9.60 eV for an Al 13. All these results imply that decrease in the AIE is probably not associated with the filling of the electronic shell.

Fig. 3 Ground state structures of neutral Al 13 (EP) n and MAl 12 (EP) n (M = B, C, Si, and P) clusters where n = 1–3. The Al–Al bond lengths are also shown and given in Å. The average bond lengths of interior central atom to surface Al atoms are given in magenta text, while the Al–O bond lengths are given in light blue text Full size image

Fig. 4 The effect of ligands on Al and doped Al clusters. a Accumulated charge and b Ligand-binding energies in Al 13 (EP) n and MAl 12 (EP) n (M = B, C, Si, and P) clusters where n = 1–3 Full size image

Fig. 5 Electronic properties of ligated Al clusters. a Adiabatic ionization energies of bare Al 13 (EP) n , MAl 12 (EP) n (M = B, C, Si, and P; n = 0–3) and b First and second adiabatic ionization energies of bare CAl 12 , CAl 12 (EP) 3 , Al 13 , and Al 13 (EP) 3 clusters. All the values are given in eV Full size image

Analysis of electronic structure

To gain better insight into the nature of decrease, we examined the one-electron energy levels of CAl 12 (EP) n (n = 0–3) clusters. Figure 6 shows the one-electron levels of CAl 12 (EP) n (n = 0–3) where all the clusters have singlet ground states. We noticed two major effects in the electronic spectrum. First, degeneracy in the superatomic states of CAl 12 is lifted due to geometric distortion induced by the ligation. Second, the addition of ligands continuously lifts the superatomic states towards higher energy as shown by the absolute energy of the HOMO. For example, the HOMO of CAl 12 (EP) 3 turns out to be 2.10 eV higher than that of CAl 12 . Since the ionization of any electronic system occurs from the HOMO, drop in the calculated AIE of CAl 12 (EP) 3 is consistent with the rise of the electronic spectrum. Note that the HOMO-LUMO gap in all the cases does not undergo any appreciable change with ligation indicating that the shell structure and the associated electron count are largely unperturbed. To further confirm this, we performed a fragment analysis by taking CAl 12 and EP as two separate fragments of an optimized CAl 12 (EP) cluster and the results are shown in Fig. 7. Such an analysis can show how superatomic states of CAl 12 interact with a EP ligand. We identified the superatomic states via states delocalized over the CAl 12 . One can see that none of the frontier 1F or 2P superatomic MOs near HOMO interact with the lone pair of oxygen (of EP ligand) apart from shifting to higher energy. Therefore, frontier MOs do not participate in the charge transfer to CAl 12 . On the other hand, the interaction of the 1S and one of 1D (D yz ) superatomic MOs with the lone pair of oxygen forms the fully occupied bonding and anti-bonding states as shown in Fig. 7. Therefore, interaction between deeper superatomic states and ligands facilitate the charge rearrangement via Al–O bonding. In addition, we can identify all the superatomic MOs (Supplementary Fig. 4) that form the electronic shell closure of CAl 12 in CAl 12 (EP). While this observation for a closed shell system is quite intriguing, we found similar effect for an open shell systems. Here, one-electron energy levels of Al 13 (EP) n (n = 0–3) with open shell electronic configuration were examined. Figure 8 shows the electronic structures of Al 13 (EP) n demonstrating an evolution analogous to that in CAl 12 (EP) n . Both the majority and minority spin states near the HOMO undergo a rise in the energy that increases with the number of ligands. Note that one of minority 2P states in Al 13 (EP) n (n = 0–3) always remains unoccupied even in case of Al 13 (EP) 3 although a charge transfer of 0.9 e− takes place from three ligands. Our result is also consistent with the results reported by Watanabe et al. as they confirm the 1F angular character of last unoccupied state32. All these results strongly confirm the effective valence count in CAl 12 and Al 13 unchanged after ligation.

Fig. 6 One-electron energy levels of CAl 12 (EP) n (n = 0–3) clusters. The occupied and unoccupied states are represented by solid and dashed lines. The levels are also marked with their angular character Full size image

Fig. 7 Fragment analysis of CAl 12 (EP) with CAl 12 and EP fragments. The occupied and unoccupied states are represented by solid and dashed lines. States marked with star symbol present the anti-bonding states Full size image

Fig. 8 One-electron energy levels of Al 13 (EP) n (n = 0–3) clusters. The occupied and unoccupied states are represented by solid and dashed lines. The up and down arrows indicate the majority and minority spin channels Full size image

Analysis of charge transfer

The above discussion brings out two important results. First, the AIE drops with successive ligation and second, this evolution is not due to change in valence count of the cluster. Hence, the microscopic origin of raising the spectrum has to be looked elsewhere. To answer this, we carried out a natural bonding orbital (NBO) analysis for CAl 12 (EP) 3 to find out the local atomic charges. We found that there is a local rearrangement of charge reminiscent of the charge transfer complexes. Particularly, the Al sites near to oxygen gain more charge relative to others because of polarized Al–O bonds. The overall charge on CAl 12 core turns out to be −0.39 e−though much smaller than the value predicted by a Mulliken population analysis. To analyze the effect of such local charges transfer on the electronic structure, the excess charge of 0.39 e− is divided into three equal fictitious point charges of −0.13 e− and located 0.5 Å away from the Al sites of CAl 12 where ligands were attached. The HOMO of CAl 12 in the presence of point charges shifts to higher energy by 1.61 eV relative to that of bare CAl 12 . This shift in the HOMO is only ~0.5 eV smaller than that of in the ligated cluster (2.1 eV). Therefore, a dominating effect of ligands is to create a crystal field like effect that raises the electronic spectrum while making the charge transfer complexes. Part of this effect is analogous to the change in work function caused by a dipole moment on a surface25,26,27,28,32. For reference, we have included the change in the work function caused by the binding of EP ligands to an Al(111) and Al (100) surface in Supplementary Fig. 5. A second related effect is that the binding energy of the ligand to the charged cluster is likely to be larger than to a neutral cluster. To separate these effects, we may use the absolute position of the HOMO in the neutral cluster to indicate the initial state electrostatic lowering of the energy levels, and the change in the adiabatic ionization energy to include both electrostatic effects, the binding enhancement of the ligand, and any other final state stabilization of the cation that may be caused by the ligands. The change in the absolute position of the HOMO of the neutral cluster is analogous to the relative position of the vacuum energy and Fermi energy in a surface. In our method, the vacuum level is 0 eV by definition, so the absolute position of the HOMO includes this electrostatic effect. For example, the addition of EP to Al 13 lowers the HOMO by 0.70 eV, while the AIE is lowered by 1.05 eV. This suggests that about 70% of the effect is due to the effective dipole moment lowering the ionization energy, with 30% being due to an enhancement in the bonding and other final state effects. Averaging over all of the clusters studied here, about 79% of effect is due to electrostatic effect, and 21% is due to the binding enhancement. We note that both of these effects are mostly independent of the electronic structure of the cluster core.

Effect of ligands on PAl 12

We now show how the shell and ligand effect can be combined to create a motif with exceptionally low ionization energy. As we mentioned earlier, PAl 12 has one electron over the filled shell of 40 e− within jellium model resembling the situation in alkali atoms. As the electron count goes from 40 e− (CAl 12 ) to 41 e−(PAl 12 ), the ionization energy drops by 1.53 eV due to shell effect shown in Fig. 2. The AIE further decreases by a large value of 3.1 eV with the addition of 3 EP ligands (ligand effect) creating an alkali-like superatom with AIE of 3.25 eV even less than that of any alkali atom.

Discussion of ligand effects

In summary, the present studies offer an alternate strategy to control the ionization characteristics of metallic cores that differs from the conventional approach in which filling of electronic shells leads to lower ionization energy. As we show, the ionization energy of metallic cores can be reduced by attaching ligands that form charge transfer complexes. The local charge transfers act to raise the electronic spectrum in a crystal field like effect that progressively lowers the ionization energy as additional ligands are added. Part of this mechanism is due to a cluster version of the change in work function of a surface due to adding a dipole moment, while the remaining effect is due to binding enhancement in the cation and the stabilization of the charged state of the cluster by the ligands. The ligand effect has several new features. First, the ionization energy can be controlled by changing the number of ligands as the shift in the electronic spectra is due to the coulomb well formed by the local charge exchange. Second, the ligand effect is independent of the occupation of the electronic shell of the cluster and hence allows a pathway to create donor species that can donate multiple electrons. Finally the ligand effect can be combined with shell effect to create multiple donor species with very low ionization energies that can have applications including newly discovered superatom doped semiconductors. We would like to add that the while current work focused only on reducing the AIE by adding donor ligands, an opposite effect, namely an increase in the electron affinity using acceptor ligands is under investigation and will be reported later. We hope that the present findings would stimulate further interest in using ligands for control of oxidation state in clusters.