Ionization Potentials. Some Variations, Implications and Applications


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This analogy between metallic clusters and atoms has led to the concept that stable clusters with a well-defined valence can be classified as superatoms forming a 3rd-dimension of the periodic table. Over the past two decades, numerous superatoms resembling the alkali, halogen, inert, and magnetic atoms have been proposed 7 , 8 , 9 , 10 , For example, an Al 13 with 39 valence electrons occupying 1S 2 1P 6 1D 10 2S 2 1F 14 2P 5 shells requires one electron to fill the last shell.

Our previous study showed that it has a very high electronic affinity of 3. The identification of stable clusters with a well-defined valence has led to another promising direction in nanoscience namely synthesizing nano-scale materials with superatoms as building blocks While such solids have been synthesized, in many cases, the reactive nature of metallic clusters has prevented stability of such solids as the clusters coalesce when put together.

One way to circumvent this problem is to use ligands around the metallic cores that avoid a direct interaction between the building blocks 13 , In addition to passivating surfaces, the ligands can also alter the valence electronic count of the cluster offering a viable path to stabilize clusters.

These two aspects have been highly effective in the stability of numerous cluster assemblies synthesized over the past few years 15 , For example, numerous assemblies based on pure gold or mixed clusters ligated with thiols such as Au SR 44 17 , 18 , 19 have been synthesized. The stability these ligated clusters is generally rationalized within the superatomic framework. For example, in Au SR 44 , the outer 44 gold atoms are linked to thiols making covalent bonds, while the 58 atoms within the core provide of 58 electrons which leads to a closed electronic shell.

In this paper, we propose an alternative strategy to design the superatomic clusters that can be transformed into donors or acceptors of multiple electrons independent of whether the cluster has an open or closed electronic shells. We accomplish the above transformation by attaching the suitable ligands to the metallic cores that form charge transfer complexes. Unlike thiol ligands, these ligands leave the effective valence count of the metallic core intact, though the exchange of local charge does take place between the ligands and metallic core.

An EP ligand is a monomer unit of Poly N-vinylpyrrolidone that has been shown to stabilize gold clusters and an exchange charge with metal core in the reported experimental and theoretical studies by Tsunoyama et al. The Al based clusters are chosen because of their metallic nature and the applicability of the confined nearly free electron gas model to describe their electronic structure. We show that the local charge donated to the metallic core primarily lifts the electronic spectrum to lower the ionization energy.

This process is analogous to the shift in the work function of a surface based on a dipole moment, although additional effect are found to enhance the lowering of the ionization potential beyond that of a simple electrostatics argument 25 , 26 , 27 , 28 , Another crucial result of our study is that successive ligation not only lowers the ionization energy but also that the amount of lowering of the ionization energy is comparable irrespective of the filling of the valence shell.

The observed ligation effect is even more spectacular for the clusters with highest occupied molecular orbital HOMO that contains multiple electrons. Furthermore, this effect allows for the formation of effective multiple electron donors as the reduction in the 2nd ionization energy of the bare species can be even more than that of in the 1st ionization energy. 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 doping 30 , 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. 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. 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.

Here, we are primarily interested in assessing the effect of shell filling on the electronic properties.

Ionization Energy

The AIE values are plotted in Fig. It is interesting that the clusters with same valence electron count despite a different composition have comparable AIEs. 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. Electronic properties of ligand-free Al and doped Al clusters.

All the values are given in eV. 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. Various positions of the ligands were tried to find the ground state structures.

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 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. Total energies of the optimized structures with various positioning of the ligands are given in Supplementary Figs. 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. 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. The BAl 12 and Al 13 core gain 0. On the other hand, charge transfer from 1st ligand to PAl 12 is found to be 0. 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. Here E presents the total energy of the system. 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.

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. 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. However, AIE of Al 13 gets reduced to 3. This interesting scenario is even more puzzling if one looks at the multiple ionization energies of the CAl 12 and Al 13 clusters. Note that the 2nd AIE is reduced by 3. All these results imply that decrease in the AIE is probably not associated with the filling of the electronic shell.

Excitation and Ionization Potential

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. The effect of ligands on Al and doped Al clusters. Electronic properties of ligated Al clusters. We noticed two major effects in the electronic spectrum.


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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. 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.


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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 Therefore, frontier MOs do not participate in the charge transfer to CAl 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. 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. While this observation for a closed shell system is quite intriguing, we found similar effect for an open shell systems.

first ionisation energy

Both the majority and minority spin states near the HOMO undergo a rise in the energy that increases with the number of ligands. Our result is also consistent with the results reported by Watanabe et al. All these results strongly confirm the effective valence count in CAl 12 and Al 13 unchanged after ligation.

The occupied and unoccupied states are represented by solid and dashed lines. The levels are also marked with their angular character. States marked with star symbol present the anti-bonding states. The up and down arrows indicate the majority and minority spin channels. 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. 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. To analyze the effect of such local charges transfer on the electronic structure, the excess charge of 0. 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 surface 25 , 26 , 27 , 28 , For reference, we have included the change in the work function caused by the binding of EP ligands to an Al and Al surface in Supplementary Fig.

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. We note that both of these effects are mostly independent of the electronic structure of the cluster core.

Ionization Energies

We now show how the shell and ligand effect can be combined to create a motif with exceptionally low ionization energy. The AIE further decreases by a large value of 3. 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.

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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. The Slater-type orbitals STO located at the atomic sites are used to make the atomic wave functions.

A linear combination of these atomic orbitals are combined to form the cluster wave functions A TZ2P basis set and a large frozen electron core was used to ascertain completeness. Trial structures for ligated clusters are obtained by attaching the ligands to previously available structures of Al based clusters. The quasi-Newton method is used to obtain the local minimum for each structure without any symmetry restriction. Relativistic effects are incorporated in this study by using the scalar-relativistic zero-order regular approximation ZORA 35 , Thus, different complexes such as 1 -O and 1 -CH 2 can have very similar reaction energies for H 2 addition arising from opposing hydride and proton affinity effects.

Additional calculations on methane C—H bond addition to 1 -X afford reaction and activation energy trends that correlate with the reaction energies of H 2 addition leading to the Y-product. Additional tables with electronic energies and Cartesian coordinates. View Author Information. Cite this: Inorg. Article Views Altmetric -. Citations 7. Supporting Information. Cited By. This article is cited by 7 publications. Boushra S. Goldman, Faraj Hasanayn. Inorganic Chemistry , 57 13 , DOI: Seco, Antonio J.

Theoretical and Experimental Studies. Inorganic Chemistry , 57 9 , Nicholas Lease, Elizabeth M. Organometallics , 37 3 , Reuben B. Leveson-Gower, Paul B. Webb, David B. Cordes, Alexandra M. Slawin, David M. Smith, Robert P. Tooze, and Jianke Liu. Organometallics , 37 1 , Ekaterina M.

Titova, Elena S. Osipova, Alexander A.

Ionization Potentials. Some Variations, Implications and Applications Ionization Potentials. Some Variations, Implications and Applications
Ionization Potentials. Some Variations, Implications and Applications Ionization Potentials. Some Variations, Implications and Applications
Ionization Potentials. Some Variations, Implications and Applications Ionization Potentials. Some Variations, Implications and Applications
Ionization Potentials. Some Variations, Implications and Applications Ionization Potentials. Some Variations, Implications and Applications
Ionization Potentials. Some Variations, Implications and Applications Ionization Potentials. Some Variations, Implications and Applications

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