Predicting the Photoelectron Spectra of Quasi Octahedral Al₆Mo^‐ Cluster

Abstract

We have recently developed a computational methodology to separate the effects of size, composition, symmetry and fluxionality in explaining the experimental photoelectron spectra of mixed‐metal clusters. This methodology was successfully applied first in explaining the observed differences between the spectra of Al₁₃ ^‐ and Al₁₂Ni^‐ and more recently to explain the measured spectra of Al_nMo^‐, n=3–5,7 clusters. The combination of our approach and new synthesis techniques can be used to prepare cluster‐based materials with tunable properties. In this work we use the methodology to predict the spectrum of Al₆Mo^‐. This system was chosen because its neutral counterpart is a perfect octahedron and it is distorted to a D_3d symmetry and was not observed in the recent experiments. This high symmetry cluster bridges the less symmetric Al₅Mo^‐ and Al₇Mo^‐structures.The measured spectra of Al₅Mo^‐ has well defined peaks, while that of Al₇Mo^‐does not. This can be explained by the fluxionality of Al₇Mo^‐, as at least 6 different structures lie within the range that can be reached by thermal effects. We predict that Al₆Mo^‐ has well defined peaks, but some broadening is expected as there are two low‐lying isomers, one of D_3d and the second of D_3h symmetry that are only 0.052 eV apart.

A new computational methodology has been developed and applied to explain the experimental photoelectron spectra of mixed‐metal clusters. The combination of the reported approach and new synthesis techniques can be used to prepare cluster‐based materials with tunable properties. In this work the spectrum of Al₆Mo^‐ has been predicted.

1. Introduction

The unique properties of small atomic clusters that are very different from those of the bulk of the same element make these systems a one of a kind laboratory to design new materials with very specific characteristics. Cluster of metallic elements often do not display metallic properties until they reach a certain critical size.1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 This size dependence of the metallicity of a cluster has been well explored and a good account of the factors that affect metallicity in pure clusters can be found in Refs. 1–13 and references therein. The technological potential is substantially increased when these clusters contain more than one element. Adding a single metallic impurity to a pure metal cluster can have important effects such as increasing/decreasing their reactivity or enhancing/ suppressing their magnetism. An excellent example of how dramatic these effects can be found in our recent work14 on the explanation the evolution of the photoelectron spectra (PES) from a 12 atom pure aluminum cluster to the 13 atom Al₁₃ ^‐ and Al₁₂Ni ^‐ clusters. The addition of an Al or Ni atom leads to substantially different spectra and we were able to separate the different effects of size, structure, symmetry, and composition. The spectrum of Al₁₂ ^‐ has three clear peaks at 2.8, 3.2, and 3.75 eV. The addition of an Al atom leads to a very symmetric Al₁₃ ^‐ cluster with one peak at 3.8 eV and a shoulder at around 4.1 eV. This dramatic change in spectrum is due to the conversion of the Al₁₂ ^‐ from a less symmetric Cs structure into a perfect icosahedron 13 atom cluster. This can be explained as a symmetry effect that leads to more degenerate energy levels. The spectrum of Al₁₂Ni^‐ has three broad peaks at 3.2, 3.75 and at 4.4 eV. Our computations showed that Al₁₂Ni^‐ is also a perfect icosahedron, but the explanation of such a different spectrum was due to the fact that the Ni atom brings 10 extra valence electrons and the interaction of these valence orbitals with those of Al₁₂ ^‐ explain the difference in spectrum. Another good example of the importance of bimetallic clusters can be found on the recent work of Khetrapal et al.15 in studying the structural evolution of mixed gold‐aluminum clusters using PES and density functional theory (DFT) computations. The proper identification of the structural and electronic properties of mixed‐metal clusters are therefore of great interest and shall be further explored. Another example is our work on mixed anionic aluminum‐molybdenum clusters16 where we applied the analysis developed in ref. [14] to explain the measured spectrum of Al_nMo^‐, n=3–5,7 and to separate the effects of size, symmetry, composition to explain the changes in spectrum of Al₄ ^‐, Al₅ ^‐, and Al₄Mo^‐.

In this work we predict the photoelectric spectrum of Al₆Mo^‐ and provide an explanation why this cluster was not observed in the experiment reported on ref. [16]. We present the lowest energy structure of the neutral and anionic Al_nMo clusters with n=1–7, their binding and vertical detachment energies, and use this analysis to explain the reason why the anionic Al₆Mo^‐ cluster was not observed in the experiment. In the next section, we present the methods used in this work. The results are presented in the following section and the last section is dedicated to concluding remarks.

2. Computational Methods

All the computations are performed within density functional theory using Gaussian 03. We used the Becke exchange17 and Perdew86 correlation18 functionals (BP86), and the Stuttgart (SDDALL) suite of pseudopotentials with the corresponding basis set as implemented in Gaussian 03.19 The selection of the BP86 exchange‐correlation functional and pseudopotentials is based on extensive tests that included a variety of alternative choices and are presented in detail in Ref. [16]. Stable structures were obtained by performing unconstrained gradient‐based minimization. Normal mode analysis was performed to distinguish between stable structures and transition state candidates. To obtain the photoelectron spectra we used a correction scheme to convert Kohn‐Sham (KS) single‐electron eigenvalues into electron binding energies.20 In this scheme the electron binding energy is obtained as

$${\displaystyle B{E}_i\left(N\right)=-{ϵ}_i\left(N\right)+{\Delta }_i\left(N\right)}$$ (1)

where,$B{E}_i\left(N\right)$ is the binding energy corresponding to the i ^th Kohn‐Sham energy level ${ϵ}_i\left(N\right)$ of the N‐electron system, and ${\Delta }_i\left(N\right)$ is the correction. The correction term is defined as a linear interpolation between correction terms of the i ^th energy level of the N‐1 electron system and the i+1^th term of the N electron system as indicated below:

$${\displaystyle {\Delta }_i\left(N\right)={\Delta }_i(N-1)+\left[{\Delta }_{i+1}\left(N\right)-{\Delta }_i(N-1)\right]{\alpha }_i\left(N\right)}$$ (2)

Where

$${\displaystyle {\alpha }_i\left(N\right)=\frac{{ϵ}_i\left(N\right)-{ϵ}_i(N-1)}{{ϵ}_{i+1}\left(N\right)-{ϵ}_i(N-1)}}$$ (3)

In order to determine all the corrections, one must compute the corrections to the highest occupied molecular orbital (HOMO) of the 1, 2, …, N electron system and recursively compute the corrections to the inner electrons. A full description of this method can be found in ref. [20]. As discussed in earlier work,7, 9, 10, 11, 12, 13, 14, 20 this scheme is robust, accurate, and can be applied to any DFT exchange‐correlation functional. The full scheme has been successfully applied to clusters and molecules.7, 9, 10, 11, 12, 13, 14

We have shown in ref. [16] that this methodology reproduces well the PES of Al_nMo^‐, n=3‐5,7. In this work we focus in predicting the PES of Al₆Mo^‐.

3. Results and Discussion

3.1. Structural Properties

In this section we report the lowest energy structures of neutral (Figure 1) and anionic (Figure 2) Al_nMo clusters, n=1–7. In many cases, the lowest energy isomer of the neutral and anionic clusters have the same packing. The exceptions are Al₂Mo, Al₆Mo, and Al₇Mo. In the neutral Al₂Mo the molybdenum atom is bonded to both Al in a C_2v structure, while in the anionic form the Mo is bonded to a single Al in a C_∞v arrangement. We should note, however, that a C_2v structure similar to the neutral lowest energy isomer is found only 0.013 eV higher in energy, it is therefore expected that both structures would contribute to the photoelectron spectrum. The neutral Al₆Mo, the main objective of this study, is a perfect octahedron in a closed shell configuration. This hints to a magic number system with enhanced stability. The anionic Al₆Mo^‐ is distorted from the O_h symmetry into a lower energy D_3d symmetry cluster. Given the possibility of a magic number cluster, one should expect that the electron affinity or the vertical detachment energy of this system to be lower as compared to their neighboring Al₅Mo and Al₇Mo clusters. We will discuss this subject in the next subsection. The neutral Al₇Mo cluster is a C_2v structure obtained by adding an Al atom to the Al₆Mo O_h structure, while the anion seems to be derived by the addition of 2 Al atoms to the Al₅Mo C_4v structure. This will probably have effects on the stability of the clusters. It is interesting to note that in both the neutral and charged forms the clusters start with a high spin state that is reminiscent from the electronic structure of the Mo atom that has a 4d⁵5 s¹ ground state. As the clusters grow in size Mo bonds to more Al atoms leading to lower spin states. In the neutral case, we first observe a zero spin ground state at Al₆Mo, while in the anions this happens for Al₅Mo^‐.

Figure 1.

Lowest energy isomer of neutral Al_nMo clusters, n=1–7. We present the bond lengths for the non‐equivalent bonds. The full structure of the Al₇Mo cluster can be found in the supplementary materials.

Figure 2.

Lowest energy isomer of anionic Al_nMo^‐ clusters, n=1–7. We present the bond lengths for the non‐equivalent bonds.

In Figure 3 we present the binding energy per atom of the neutral and anionic clusters that were calculated according to:

$${\displaystyle BE\left({\mathrm{Al}}_n\mathrm{Mo}\right)=\left[nE\left(\mathrm{Al}\right)+E\left(\mathrm{Mo}\right)-E\left({\mathrm{Al}}_n\mathrm{Mo}\right)\right]/(n+1)}$$ (4)

$${\displaystyle BE\left({\mathrm{Al}}_n{\mathrm{Mo}}^{-}\right)=\left[nE\left(\mathrm{Al}\right)+E\left({\mathrm{Mo}}^{-}\right)-E\left({\mathrm{Al}}_n{\mathrm{Mo}}^{-}\right)\right]/(n+1)}$$ (5)

Figure 3.

Binding energy per atom of neutral (red) and anionic (anion) Al_nMo clusters, n=1‐7, computed using Eqs. (4) and (5).

where $E\left(\mathrm{Al}\right)$ , $E\left(\mathrm{Mo}\right)$ and $E\left({\mathrm{Mo}}^{-}\right)$ are the total energies of Al atom, Mo atom and of the Mo anion. Eqs. (4) and (5) refer to the binding energy of the neutral and anionic clusters, respectively. We chose the breakdown in energy in Eq. (5) because the electron affinity of Mo is higher than that of Al. The binding energy per atom for both neutral and negatively charged species seem to increase quickly from AlMo to Al₄Mo and then start to level off for the larger sizes. But, one can note that the graph seems to display a local maximum at the neutral Al₆Mo that is not seen on the anionic counterpart. This indicates that the Al₆Mo⁻ is relatively less stable than Al₆Mo when compared to the Al₅Mo and Al₇Mo counterparts. This can be viewed as a hint of why Al₆Mo^‐ is not seen in the experiment. It will indicate that the vertical detachment energy of Al₆Mo^‐ should be substantially lower than the ones observed for Al₅Mo^‐ and Al₇Mo^‐, further corroborating the idea of a magic cluster.

To more appropriately quantify the relative stability of the clusters we use the 2nd energy difference defined as:

$${\displaystyle {\Delta }^{2}E\left({\mathrm{Al}}_n\mathrm{Mo}\right)=\left[E\left({\mathrm{Al}}_{n+1}\mathrm{Mo}\right)-2E\left({\mathrm{Al}}_n\mathrm{Mo}\right)+E\left({\mathrm{Al}}_{n-1}\mathrm{Mo}\right)\right]}$$ (6)

The results of the second difference are shown in Figure 4. As one can see the peaks are at n=3 and 6. More importantly the neutral Al₆Mo displays a more pronounced peak than Al₆Mo^‐, indicating that the neutral is more stable than the negatively charged form. Another indication on the difficulty of observing the Al₆Mo^‐ cluster.

Figure 4.

Second energy difference (Eq. (6)) of neutral (red) and anionic (blue) Al_nMo clusters, n=1‐7.

3.2. Vertical Attachment and Detachment Energies

The photoelectron spectra peaks are manifestations of vertical processes, where the extracted electron transitions from the ground state of the anionic cluster into the frozen neutral counterpart. Thus, the need to compute the vertical detachment energies of the anionic clusters to compare with the experiment. In this work we also present the energy needed to add an electron to the frozen neutral cluster. We call it the vertical attachment energy. In Table 1 we present the vertical attachment and detachment energies for the neutral and anionic Al_nMo clusters, n=1–7. For the cases studies in reference [16] we also present the measured values of the 1st detachment energy and the adiabatic electron affinity. Comparing the computed values with the experiment one can see that there is very good agreement. In ref. [16] we estimated that the accuracy of our DFT calculations were within 0.1 eV, estimate confirmed by the numbers in Table 1. The vertical attachment energies to the neutral clusters for all sizes but Al₇Mo were slightly lower than the detachment energies of the corresponding anion. This is because the geometric and electronic structures of these clusters are very different. In addition, one can observe that the vertical electron detachment energy of Al₆Mo^‐ is substantially lower than those of Al₅Mo^‐ and Al₇Mo^‐. It is possible that this cluster converts into the neutral before the time‐of‐flight portion of the experiment, making its signal weaker and harder to observe.

Table 1.

DFT computed vertical attachment (VAE) and detachment energies (VDE) of neutral and anionic Al_nMo lusters. Also presented are the measured vertical detachment energy and adiabatic electron affinity (EA) of Al_nMo⁻ (ref. [16])

	Computed		Experiment
n	VAE(eV)	VDE(eV)	EA	VDE
1	1.016	1.255	–	–
2	1.523	1.691	–	–
3	1.941	2.229	2.05	2.25
4	1.971	2.131	2.15	2.20
5	2.035	2.163	2.20	2.30
6	1.735	1.872	–	–
7	1.929	2.644	2.50	2.65

3.3. Photoelectron Spectrum of Al₆Mo^‐

In this section we will make a prediction of the photoelectron spectrum of Al₆Mo^‐. In order to place this spectrum in perspective, we reproduce here the measured spectra of Al₅Mo^‐ and Al₇Mo^‐ from our recently published work.16 In Figure 5 we present the spectra of Al₅Mo^‐ and Al₇Mo^‐. As discussed in ref.16 the first isomer of Al₅Mo^‐ does reproduce qualitatively as well as quantitatively the peaks of the measured spectrum, the largest discrepancy is 0.1 eV. The lines corresponding to the second isomer, lying 0.283 eV higher in energy, also fall under the measured spectrum, but the features are different. This is a great indication that for this case we only need to invoke the lowest energy isomer to explain the measured spectrum.

Figure 5.

a) Measured photoelectron spectrum of Al₅Mo^‐ . b) Measured photoelectron spectrum of Al₇Mo^‐ . Data from our earlier work of ref [16].

In Figure 5b) we present the measured spectra of Al₇Mo^‐. The features in the experimental spectrum in this case are less defined than the case of Al₅Mo^‐. Although one could argue three or four different peaks, the overlap between them result in a broader peak centered around 3 eV with a width of roughly 1 eV. One should expect that this could be a result of many different isomers contributing to the final spectrum. In fact, as discussed in reference16 the first six isomers of Al₇Mo^‐ are separated by about 0.184 eV which is substantially lower than the corresponding thermal energy at room temperature of 0.465 eV. If we invoked just the first isomer, the spectrum should have 3 well defined peaks. However, as we include all the isomers, the overlap of all the peaks would be enough to spread the features and have a less well defined spectrum that is observed in the experiment.

The question that we want to ask is whether the Al₆Mo^‐ spectrum has well defined peaks like Al₅Mo^‐ or more spread like Al₇Mo^‐. Given that the Al₆Mo^‐ lowest energy isomer is highly symmetrical we expect it to have well defined peaks, but in order to answer it more definitely we must look for other low‐lying isomers as seen in Figure 6. A very thorough search yielded only two structures within the computed thermal energy at room temperature. They are a D_3d structure that is slightly distorted from the perfect octahedron and a D_3h structure that corresponds to a 60° rotation of one of the Al₃ trimers around the original C₃ axis of the D_3d structure. This second structure is only 0.052 eV higher in energy, and is therefore expected to contribute to the PES spectrum. In Figure 7 we represent the line spectrum (vertical lines) representing individual electron binding energies and a simulated spectrum (red line) resulting from a 0.1 eV broadening of the computed lines. If measurements are made in Al₆Mo^‐ the spectrum will clearly have a sharp peak centered about 1.9 eV and then a second broad peak around 2.6 eV and a smaller peak at around 3.2 eV. This peak is a result of lines from the second isomer. These lines are also present in the D_3d isomer, buy they lie beyond the energy range of the experiment described in ref. [16].

Figure 6.

Low energy isomers of Al₆Mo^‐.

Figure 7.

DFT computed electron binding energy spectrum of Al₆Mo^‐. The solid lines correspond to the D_3d lowest energy isomer and the dashed lines correspond to the D_3h 2^nd isomer. The red continuous line corresponds to a 0.1 eV Gaussian broadening of the computed (vertical lines) of the two low energy isomers.

4. Conclusions

We presented structural and electronic properties of neutral and anionic Al_nMo (n=1‐7) mixed clusters. The binding energy per atom and the 2^nd energy difference points to an enhanced neutral Al₆Mo cluster, while the anionic counterpart seems to have similar energetic properties as the Al₅Mo^‐ and Al₇Mo^‐. Therefore, Al₆Mo^‐ has a relatively low vertical detachment energy that does not follow the increasing trend as a function of cluster size. This is an indication that the neutral Al₆Mo cluster can be viewed as closing the magic number of valence electrons resulting on a very symmetric O_h structure. The lowest energy structure of the anionic counterpart is a distortion from O_h to the lower D_3d group. We also found a D_3h structure that is a trigonal prism with a Mo atom in the center. This structure is 0.052 eV less stable than the first isomer. Because of the relatively low vertical detachment energy, the signal in the time‐of‐flight spectrum might be too low and this could explain the difficulty of getting a well‐defined photoelectron spectrum for this system. Nevertheless, we believe that having an idea of the predicted spectrum might help identifying this spectrum in a future experiment. Our simulated spectrum (Figure 7) results from a 0.1 eV broadening of the computed lines for the two low energy forms of Al₆Mo^‐ we found in this study. The main features identified in this work are one peak centered at 1.9 eV a second broader peak around 2.6 eV and a smaller peak at 3.2 eV.

Supplementary Information

See supplementary material for the full structure of the lowest energy isomer of Al₇Mo.

Conflict of interest

The authors declare no conflict of interest.

Supporting information

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Supplementary

P. H. Acioli, ChemistryOpen 2020, 9, 545.